Basic Physics Online Free

Basic Physics best simple learning Tips and Trick is here.If you want to Know, what is Physics ? Then you are at right place. Because i am going to explain here from very basic concept to depth concept about Physics.  And you  are going to enjoy this post, Physics as fun. So lets start our topic. What is Physics ? Well Physics is a science subject, in which you study about nature.

Hence let me explain from very basic point. why Physics is science ?  Well Physics provide the answer of all Physics questions, For example how, why, when for any natural event happening. And in other words, this is called practical subject. Because Physics explain the practical reasoning behind any natural event. So Physics is called science subject. Therefore learn physics true concept here.


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Well Physics is study of nature. But why do you want to study about nature ? Common here nature is complete universe. So you are able to see the nature, Which is around you. Hence by using this natural resources, you want to make your daily  life simple and easy.

Because you are living in this world or universe, So you can make life better by doing development here. Therefore One point is very important to note. Whatever do you study in Physics, most of the quantity is invisible.

And this is one of the reason, Why Physics is not easy subject. So whenever your eyes is fail to see, Then you should apply your brain to see the things. Because eyes can see a particular size of object, but your Brain can see, Which is invisible to eyes. So basic Physics is here for your help.

Hence for example Force, Electric field, Magnetic field, Charge, Current, Wave, Sound, Energy. Here all these quantities are invisible. And due to invisibility of these quantities, Our development is very slow.


Why do you study of nature in Physics ?


So here is a catch to understand, and that is Physics deals with Study of nature. Therefore Physics lead the road map for study of  complete universe. But we are living on the Earth, and are doing development on the Earth only. So that we can make our life style better on the Earth planet.

Human has not done anything special for other planets till date. Therefore a lot of development is due. So for example, now all over the world scientist are working on MARS planet migration project. Scientist are trying to human plantation on MARS.

But according to scientist, it will take more 5 to 7 years, then human plantation is possible. But there is challenges. Because huge amount of dollar is required, for migration from Earth to MARS planet, for a single person.

And this is not possible for a normal human to spend that much of amount. So still it is a challenges for scientist. Well perhaps you heard the name Elon Mask. Do you know Who is Elon Mask ? allow me to explain in short. He is challenging man of the Earth.  And Owner of SPACEX company. This company is taking registration for MARS planet travel. So for more details, you must read Elon Musk Biography and take inspiration.


Physics Tuition online Free ?


Well Physics is Study of natural laws. Then what is natural laws ? natural law is based upon the nature event and facts. And this is govern by the nature. Which is never change by nature. Suppose for example gravitational law. This is a natural law.

Because every object is always, attracted towards the center of the Earth. Hence whenever you drop any ball, it is always fall on the Earth. And this is happening, since Earth is made. Then later on this is proof by Newton.

Therefore this is called Newton’s law of gravitation. And till date this natural law is working, same as when Earth is made. Human law is change, but nature never change its law. Hence this is called natural law.


What are the basics physics Concept ?


Well basic Physics, this universe is made by two things, Matter and Energy. And Physics is study of nature. So Physics basics is also matter and energy. And you must know, this matter and energy is constant. Here i want to say whole universe mass and energy is constant and it is fixed.

Therefore it can’t be created and destroyed. But it can transform only, from one form to other form. So how its form is going to change ? This is only possible by motion.

Hence Physics basics is matter and its motion through space and time. And whenever there is motion, this is cause of force. Therefore final basics is matter, energy and force.


What are the five main branches of physics ?


Mainly Physics is divided into two branches. Which is given below.

  • Classical Physics >> This is that branch of Physics, in which we study about astronomical objects motion, in other words it describe heavy objects motion. such as our planets, stars and Galaxy. Now classical Physics plays very important role in our life.

Because it help to predict the final state and motion of body, with the help of initial state and condition of body. So for example suppose, if you know the initial motion of the body, then you can easily find out, how it will move in future.

Hence this is the power of classical Physics. And this is also called Newtonian Physics. Because it is based upon Newton’s Physical concept and mathematical model. But it has limitation, and that is velocity of object should not approach the speed of light. Then its provide the accurate value of prediction.

  • Quantum Physics >> This is that branch of Physics, in which object mass and size is very very small. Such as diameter of an atom. So quantum physics work on subatomic level. This is very interesting, allow me to explain.

Amazing World of Quantum Science


Well meaning of Quantum word is very small particles, such as atoms, electrons and photons. So lets connect with this world. Hence first what is Quantum Foam ? well how do you differentiate past, present and future ? It is easy for you, the time which is pass away is called past.

And the time currently running is present. The time which will come is future. But in quantum world space time fabric is not simple. By Physics Best Simple Learning Tips.

Because in quantum past, present and future, all are overlapping with each other. So this is called Quantum Foam. This is different to your normal past, present and future time. Because in quantum space time, future event effect past event.

Are you not digesting this sentence ?  Don’t worry this is start of story. Lot of amazing points are waiting about quantum for you. So lets what is Quantum Tunneling ?  Suppose if you want to cross a high mountain. Then what do you needed to cross that mountain.

obviously you required energy to cross that mountain. There are two ways, either by climbing yourself or by using any external agency like vehicle. But in both the cases, energy must be required to cross that mountain. Because this energy is your barrier.


What is Quantum  Tunneling


And what do you think about Quantum Tunneling ? It is very interesting. In Quantum world particle does’t required energy to cross the barrier. So how does it happen ? It is found by experiment particles disappear at one barrier end, and appears on the other barrier end.

just like it is passes through a Tunnel. What is Uncertainty and Probability in quantum ? Well in quantum world no any event is fixed. There is only probability to predict. So according to condition,  some event probability is more and some is less. It totally depends upon the condition and is not fixed.

Hence you can’t find the accurate location of quantum particles. So you can only predict, the changes of probability to be there. Therefore one particle can be at different location at same time. By Physics Best Simple Learning Tips.

And in other words, one particle can use more than one way, to go at other location at same time. So this is called Uncertainty and Probability of quantum particles.


What is dual nature of Particle in quantum ?


Well you have seen the water wave near the sea mountain collision. Here what i want to say, mountain is a big solid particle and water is a wave. But how you will feel, if mountain particle work as wave, and water work as solid particle. So this happens in quantum world every time.

Hence every quantum particle works as wave and particles. And this is called dual nature. Therefore its mean that electron is particle and wave both. Now what is Quantum Entanglement ? This is very contradict, it may be undigested to you. But this is fact of quantum Physics.  By Physics Best Simple Learning Tips.

So allow me to explain this. Quantum Entangle particle is that particle, in which they are connected to each other, by any means, but whenever one Entangle particle is disturb, Then other Entangle particle is effected immediately. Without any delay, So how it happens God knows well.


Why electron has dual nature Quantum ?


Therefore to understand this, suppose one Entangle particle is at Earth. And other Entangle particle is at Mars planet. Then If you disturb Entangle particle at Earth. Immediately Entangle particle at MARS planet is disturb. Do you know ? light take average time 12.5 minute to reach Mars from the Earth.

But this Entangle particle at Mars get disturb immediately without taking any time. So how this is happen. It seems like unbelievable, but it is true. Now it may be you are thinking. All this quantum Physics point are correct. Hence for your information quantum physics is right and correct.

Because quantum theory is very effective, in Physics history till date. Therefore quantum Physics is so accurate, using this theory, electronics devices and circuit are design . For example Transistor, logic gates, ICs.

If quantum physics does’t correct. Then no any electronics devices is developed like Mobile, TV, Computer, GPS and internet. So you can think, how powerful is quantum Physics.


What is Five Subdivision of Physics ?


Physics is science and study of nature. So its main five subdivision is important to understand Physics, And this is given below. By Physics Best Simple Learning Tips.

  • Motion >> Well motion is everywhere in universe. So you can’t find any place or space, where motion is not happening.  Whether it is smallest particle or any big mass all are doing motion continuously. Now allow me to explain little bit.

If Motion will stop, then time is stop and universe is gone. You know Earth is moving about its axis, no any doubt. But Suppose if Earth stop its motion, then what will happen ? Can you amazing, what is going to happen ?

Well Whatever the things are available on the surface of the Earth, will separate away. Here i want to say Your house, Building, trees all will run away from the Earth. But don’t worry it is not going to happen right now.

It will happen with Earth but after very long time. If you want to Know, why it is happen after stop of Earth motion. Then you should refer my previous post Circular motion all post. Here i can’t write because this post will be very long.

So lets come to our motion topic. Even you are reading and thinking there is also motion in your brain, Neurons are moving in electrical pulse. Hence you are thinking and understanding. Now don’t confuse there are many types of motion, refer previous post. Here i am talking only about motion.


What is simple definition of Motion in Science ?


So your blood and heart are also doing motion. If you are sitting in room, And you see the wall and feel there is no motion. But think wall material is having electron, which is moving inside the wall. So there is also motion. Hence solar system, planets, stars and Galaxy all are moving.

So you can’t find any place, there is no motion. Therefore you can think importance of motion. And hence it is very important to understand concept of motion. Therefore when one body or particle move from one location, to other location under universal laws, It require space and time.

And this is called motion. But can you tell me, why do we need to study motion ? Well If you want to send one body or particle, from one point to other point in space. And what do universe impose law to move any particle from one point to other point.

Then you can easily predict the feature. Hence after knowing the universal law, it is easy for you, to find out at what speed, you will send the particle to reach destination. And when it is going to reach at destination. So motion is done easily from one location, to other location.


What is Gravity according to Science ?


Well you can think gravity is that things, Which attract any object that has mass. So gravity is everywhere and its best example is you. How you are attracted towards the Earth, and stable on the surface of the Earth.

And solar system is also example of gravity, How planets are balance and revolving around the Sun. Therefore for more details about gravity, you refer my previous gravity post.

  • Space >> Well space and time are related to each other. Neither time nor space are absolute. So all are relative. As you approaches towards light speed time is going to slow down. Hence time is not absolute in the Universe.

It depends upon the planet gravity. For example suppose you are living on Jupiter planet, Hence gravity of Jupiter is more than Earth. So here time will pass slow, and his life will be more, than people living on the Earth.

Therefore whatever is around you, this is space. Now to represent the location of object in space you need three dimension. And this is generally represented by xyz axis. Which is (length, breath, height). Now if you add one more dimension time.


How Gravity is changes with mass ?


Then it is space time four dimension. Hence scientist Einstein told that space and time exist together. So how can you verify this statement is true. Now take an example, Suppose you have a unknown friend through chat, and you want to meet with her.

Then how you will meet ? Here you have to specify location as well as date and time. Then only possible to meet her. If you only specify location then you can’t meet.

And in other case if you told her only time, then you are not going to meet her. Therefore time and space exist together.

Now if you want to learn more Physics Easy Tips. Then you must refer my previous post. This link is given below. Physics Best Simple Learning Tips

I hope you enjoy learning Basic Physics Online Free. If this article is helpful for you, then like share and comment. Otherwise dislike. And having any doubt ask me always here for your support. Thanks for sharing this article.

Mechanical Properties Of Solids (Physics 11th class Amazing Concept)

Mechanical Properties Of Solids best and easy definition is here. If you want to know Mechanical Properties Of Solids hidden concept. Then enjoy your expectation. Because i am explaining here, Mechanical properties of solid very simple, with easy tips.

So you can remember concept easily and never forget. And full enjoy learning Mechanical properties of solid ever before. Therefore lets start. What is in mechanical properties of solids ?


What are the mechanical properties of solids ?


Well see the above pictures. These are some amazing building, bridges and crane. And many more you see everyday. So there all are solids. Which is made by solid substances. Hence in this post you are going to learn that things,

which need to know you for designing these solids.  Therefore you can think that, Whatever you are going to learn here, is very much physical and practical importance.

So this is very useful topic for engineering point of view. Hence all civil engineers must have depth knowledge of this topic.  Because civil engineers are responsible for designing this building and bridges.

So very first it is important to know. What is a Rigid body ? Well it is that body, which can’t be deform. In other words rigid body shape and size can’t change.  But if we talk practically. Then there is no any such type of body exist in the world, which is rigid. Hence every object shape and size can be change.


Real example for mechanical solid compression and deformation 


Now take some example for clarity. Suppose you have three metal, and these are rubber, spring and iron rod. If you are pulling with some forces at both end of rubber and spring. Then what is going to happen with rubber and spring.

So Obviously both rubber and spring shape will change. Now take iron rod and do the same. Then Can you tell me, what is happening in this case ? Well feel iron rod shape is not change.

But actually iron rod shape is change, very very small elongation, which is not visible to you. Therefore iron rod length is change in the same way, as rubber and spring length is change. But the only difference is iron rod elongation is very very small.

Similarly if any other metal rod like, Aluminium, copper glass, and you will pull at the both end with some forces, it is changed.  So in this topic, you are learning about the elongation, which is happening after stretch in depth.

Hence the first question arises that, why this elongation is done ?  Therefore to understand this chemistry concept. You can just think, rubber band is made with many molecules. Now what is molecules ? .

well it is smallest particle of a compound. Again this molecules are internally connected with small spring. And this is true for all the metal.  But the difference is only that, in case of rubber band.

These internal small spring between two molecules are lose.  And in case of iron rod that spring are tight spring. So iron rod elongation is very very small.


What are the elastic properties of solids ?


As seen from the above picture. Solids are made of molecules, and these molecules are connected with small spring in every objects. which are shown in picture.  Hence due to this properties solids are elastic in nature. Now let me ask a very simple question. So refer picture below.

Think and tell me, what is your answer ? Well in both the cases elongation will be same. But how and why ? See the difference in B case. And that is one end is fixed with wall. So think whenever you are pulling the other end, then rod will try to move ahead.

Hence the rod is pulling the wall ahead. Therefore according to Newton’s third law, Wall is pulling the rod with 100N force towards itself.  So effectively in both the cases, force is same. Hence the elongation is same in both the cases.

You are not seeing this force, but actually wall is pulling that end with 100N force towards itself. Now i am going to define some terms.  Which is very important, So you must know and remember that terms to understand this topic. So refer below picture.


What is stress and strain ?

Strain > is a unit less quantity. Because it is the ratio of length. It is also called longitudinal strain. There are three types of strain.  Which is given below.

  • Longitudinal strain
  • Shear strain
  • Volume strain

Stress > it is define as restoring force/area = Stress = F/A and its unit is N/m*m or pascal. Here force F is restoring force, Not external force.  Which are called tensile and compressive stress.

Tensile stress is that stress in which length of the rod is increase. Whereas compressive stress is opposite of tensile. Hence in this case force direction is opposite and compressive in nature. Three are three types of Stress.

  • Tensile Stress
  • Shear Stress
  • Volume Stress

Mechanical properties of solids class 11

Hook’s Law state about elasticity and plasticity of material. Now what is elasticity ? Well if you pull any object and released, and after release. if that object regain its original shape, then this is called elasticity.

So if any object which does’t gain its original shape, after pulling and release are called plastic material. Therefore Hook’s law also state that, Stress is directly proportional to strain, Within the elastic limit.

So which is more elastic rubber or steel ?  What is your answer. If your answer is rubber. Then your are wrong. Because steel is more elastic than rubber.  But how try to understand the point.

You feel that rubber regain its original shape, after removal of deforming force. Whereas steel does’t , So rubber is more elastic than steel. Of course you are right, but you must remember within the elastic limit.

Therefore within the elastic limit steel is more elastic than rubber. Because within elastic limit steel regain its shape faster than rubber. So steel is more elastic than rubber. I hope you got the point.

Inter molecular forces between two molecules, This is also called restoring force. Which is responsible for elasticity for any object. Refer above picture, small spring force in the picture.


What is elastic Behavior of solids  ?

Now you can ask, why is elasticity properties exist in any object ? As i told you inter molecular or restoring force is responsible for elasticity. So actually molecules of any object, want to live at a optimal distance.

This is called intramolecular distance, which is at minimum potential energy level. Because object is stable at minimum potential energy level.

Therefore as you apply deforming force on the object, Then molecules does’t want to displace from its intramolecular position, And apply a restoring force opposite to external deforming force.

Now you can solve numerical example with, help of formula derived for Stress, strain and Young’s modulus.

So if you want to learn more physics post. Then refer my previous post. This link is given below.

Mechanical Properties Of Solids (Physics 11th class Amazing Concept)

Mechanical Properties Of Solids best and easy definition is here. If you want to know Mechanical Properties Of Solids hidden concept. Then enjoy your expectation. Because i am explaining here, Mechanical properties of solid very simple, with easy tips.

So you can remember concept easily and never forget. And full enjoy learning Mechanical properties of solid ever before. Therefore lets start. What is in mechanical properties of solids ?


What are the mechanical properties of solids ?


Well see the above pictures. These are some amazing building, bridges and crane. And many more you see everyday. So there all are solids. Which is made by solid substances. Hence in this post you are going to learn that things,

which need to know you for designing these solids.  Therefore you can think that, Whatever you are going to learn here, is very much physical and practical importance.

So this is very useful topic for engineering point of view. Hence all civil engineers must have depth knowledge of this topic.  Because civil engineers are responsible for designing this building and bridges.

So very first it is important to know. What is a Rigid body ? Well it is that body, which can’t be deform. In other words rigid body shape and size can’t change.  But if we talk practically. Then there is no any such type of body exist in the world, which is rigid. Hence every object shape and size can be change.


Real example for mechanical solid compression and deformation 


Now take some example for clarity. Suppose you have three metal, and these are rubber, spring and iron rod. If you are pulling with some forces at both end of rubber and spring. Then what is going to happen with rubber and spring.

So Obviously both rubber and spring shape will change. Now take iron rod and do the same. Then Can you tell me, what is happening in this case ? Well feel iron rod shape is not change.

But actually iron rod shape is change, very very small elongation, which is not visible to you. Therefore iron rod length is change in the same way, as rubber and spring length is change. But the only difference is iron rod elongation is very very small.

Similarly if any other metal rod like, Aluminium, copper glass, and you will pull at the both end with some forces, it is changed.  So in this topic, you are learning about the elongation, which is happening after stretch in depth.

Hence the first question arises that, why this elongation is done ?  Therefore to understand this chemistry concept. You can just think, rubber band is made with many molecules. Now what is molecules ? .

well it is smallest particle of a compound. Again this molecules are internally connected with small spring. And this is true for all the metal.  But the difference is only that, in case of rubber band.

These internal small spring between two molecules are lose.  And in case of iron rod that spring are tight spring. So iron rod elongation is very very small.


What are the elastic properties of solids ?


As seen from the above picture. Solids are made of molecules, and these molecules are connected with small spring in every objects. which are shown in picture.  Hence due to this properties solids are elastic in nature. Now let me ask a very simple question. So refer picture below.

Think and tell me, what is your answer ? Well in both the cases elongation will be same. But how and why ? See the difference in B case. And that is one end is fixed with wall. So think whenever you are pulling the other end, then rod will try to move ahead.

Hence the rod is pulling the wall ahead. Therefore according to Newton’s third law, Wall is pulling the rod with 100N force towards itself.  So effectively in both the cases, force is same. Hence the elongation is same in both the cases.

You are not seeing this force, but actually wall is pulling that end with 100N force towards itself. Now i am going to define some terms.  Which is very important, So you must know and remember that terms to understand this topic. So refer below picture.


What is stress and strain ?

Strain > is a unit less quantity. Because it is the ratio of length. It is also called longitudinal strain. There are three types of strain.  Which is given below.

  • Longitudinal strain
  • Shear strain
  • Volume strain

Stress > it is define as restoring force/area = Stress = F/A and its unit is N/m*m or pascal. Here force F is restoring force, Not external force.  Which are called tensile and compressive stress.

Tensile stress is that stress in which length of the rod is increase. Whereas compressive stress is opposite of tensile. Hence in this case force direction is opposite and compressive in nature. Three are three types of Stress.

  • Tensile Stress
  • Shear Stress
  • Volume Stress

Mechanical properties of solids class 11

Hook’s Law state about elasticity and plasticity of material. Now what is elasticity ? Well if you pull any object and released, and after release. if that object regain its original shape, then this is called elasticity.

So if any object which does’t gain its original shape, after pulling and release are called plastic material. Therefore Hook’s law also state that, Stress is directly proportional to strain, Within the elastic limit.

So which is more elastic rubber or steel ?  What is your answer. If your answer is rubber. Then your are wrong. Because steel is more elastic than rubber.  But how try to understand the point.

You feel that rubber regain its original shape, after removal of deforming force. Whereas steel does’t , So rubber is more elastic than steel. Of course you are right, but you must remember within the elastic limit.

Therefore within the elastic limit steel is more elastic than rubber. Because within elastic limit steel regain its shape faster than rubber. So steel is more elastic than rubber. I hope you got the point.

Inter molecular forces between two molecules, This is also called restoring force. Which is responsible for elasticity for any object. Refer above picture, small spring force in the picture.


What is elastic Behavior of solids  ?

Now you can ask, why is elasticity properties exist in any object ? As i told you inter molecular or restoring force is responsible for elasticity. So actually molecules of any object, want to live at a optimal distance.

This is called intramolecular distance, which is at minimum potential energy level. Because object is stable at minimum potential energy level.

Therefore as you apply deforming force on the object, Then molecules does’t want to displace from its intramolecular position, And apply a restoring force opposite to external deforming force.

Now you can solve numerical example with, help of formula derived for Stress, strain and Young’s modulus.

So if you want to learn more physics post. Then refer my previous post. This link is given below.


This post is helpful for you, Then like ,comment and share  in social media. If you have any doubt, ask me i am here for your help. Thanks for sharing, hope you have enjoyed learning Mechanical Properties Of Solids.


 

Physics Best Simple Learning Tips | Amazing World of Quantum Physics

Physics best simple learning Tips is here.If you want to Know, what is Physics ? Then you are at right place. Because i am going to explain here from very basic concept to depth concept about Physics.  And you  are going to enjoy this post, Physics as fun. So lets start our topic. What is Physics ? Well Physics is a science subject, in which you study about nature.

Hence let me explain from very basic point. why Physics is science ?  Well Physics provide the answer of all questions, For example how, why, when for any natural event happening. And in other words, this is called practical subject. Because Physics explain the practical reasoning behind any natural event. So Physics is called science subject.


What is Physics Best Simple Learning Tips ?


Well Physics is study of nature. But why do you want to study about nature ? Common here nature is complete universe. So you are able to see the nature, Which is around you. Hence by using this natural resources, you want to make your daily  life simple and easy.

Because you are living in this world or universe, So you can make life better by doing development here. Therefore One point is very important to note. Whatever do you study in Physics, most of the quantity is invisible.

And this is one of the reason, Why Physics is not easy subject. So whenever your eyes is fail to see, Then you should apply your brain to see the things. Because eyes can see a particular size of object, but your Brain can see, Which is invisible to eyes.

Hence for example Force, Electric field, Magnetic field, Charge, Current, Wave, Sound, Energy. Here all these quantities are invisible. And due to invisibility of these quantities, Our development is very slow.


Why do you study of nature in Physics ?


So here is a catch to understand, and that is Physics deals with Study of nature. Therefore Physics lead the road map for study of  complete universe. But we are living on the Earth, and are doing development on the Earth only. So that we can make our life style better on the Earth planet.

Human has not done anything special for other planets till date. Therefore a lot of development is due. So for example, now all over the world scientist are working on MARS planet migration project. Scientist are trying to human plantation on MARS.

But according to scientist, it will take more 5 to 7 years, then human plantation is possible. But there is challenges. Because huge amount of dollar is required, for migration from Earth to MARS planet, for a single person.

And this is not possible for a normal human to spend that much of amount. So still it is a challenges for scientist. Well perhaps you heard the name Elon Mask. Do you know Who is Elon Mask ? allow me to explain in short. He is challenging man of the Earth.  And Owner of SPACEX company. This company is taking registration for MARS planet travel. So for more details, you must read Elon Musk Biography and take inspiration.


What is the study of physics ?


Well Physics is Study of natural laws. Then what is natural laws ? natural law is based upon the nature event and facts. And this is govern by the nature. Which is never change by nature. Suppose for example gravitational law. This is a natural law.

Because every object is always, attracted towards the center of the Earth. Hence whenever you drop any ball, it is always fall on the Earth. And this is happening, since Earth is made. Then later on this is proof by Newton.

Therefore this is called Newton’s law of gravitation. And till date this natural law is working, same as when Earth is made. Human law is change, but nature never change its law. Hence this is called natural law.


What are the basics of physics ?


Well this universe is made by two things, Matter and Energy. And Physics is study of nature. So Physics basics is also matter and energy. And you must know, this matter and energy is constant. Here i want to say whole universe mass and energy is constant and it is fixed.

Therefore it can’t be created and destroyed. But it can transform only, from one form to other form. So how its form is going to change ? This is only possible by motion.

Hence Physics basics is matter and its motion through space and time. And whenever there is motion, this is cause of force. Therefore final basics is matter, energy and force.


What are the five main branches of physics ?


Mainly Physics is divided into two branches. Which is given below.

  • Classical Physics >> This is that branch of Physics, in which we study about astronomical objects motion, in other words it describe heavy objects motion. such as our planets, stars and Galaxy. Now classical Physics plays very important role in our life.

Because it help to predict the final state and motion of body, with the help of initial state and condition of body. So for example suppose, if you know the initial motion of the body, then you can easily find out, how it will move in future.

Hence this is the power of classical Physics. And this is also called Newtonian Physics. Because it is based upon Newton’s Physical concept and mathematical model. But it has limitation, and that is velocity of object should not approach the speed of light. Then its provide the accurate value of prediction.

  • Quantum Physics >> This is that branch of Physics, in which object mass and size is very very small. Such as diameter of an atom. So quantum physics work on subatomic level. This is very interesting, allow me to explain.

Amazing World of Quantum Physics

Well meaning of Quantum word is very small particles, such as atoms, electrons and photons. So lets connect with this world. Hence first what is Quantum Foam ? well how do you differentiate past, present and future ? It is easy for you, the time which is pass away is called past.

And the time currently running is present. The time which will come is future. But in quantum world space time fabric is not simple. By Physics Best Simple Learning Tips.

Because in quantum past, present and future, all are overlapping with each other. So this is called Quantum Foam. This is different to your normal past, present and future time. Because in quantum space time, future event effect past event.

Are you not digesting this sentence ?  Don’t worry this is start of story. Lot of amazing points are waiting about quantum for you. So lets what is Quantum Tunneling ?  Suppose if you want to cross a high mountain. Then what do you needed to cross that mountain.

obviously you required energy to cross that mountain. There are two ways, either by climbing yourself or by using any external agency like vehicle. But in both the cases, energy must be required to cross that mountain. Because this energy is your barrier.


What is Quantum  Tunneling

And what do you think about Quantum Tunneling ? It is very interesting. In Quantum world particle does’t required energy to cross the barrier. So how does it happen ? It is found by experiment particles disappear at one barrier end, and appears on the other barrier end.

just like it is passes through a Tunnel. What is Uncertainty and Probability in quantum ? Well in quantum world no any event is fixed. There is only probability to predict. So according to condition,  some event probability is more and some is less. It totally depends upon the condition and is not fixed.

Hence you can’t find the accurate location of quantum particles. So you can only predict, the changes of probability to be there. Therefore one particle can be at different location at same time. By Physics Best Simple Learning Tips.

And in other words, one particle can use more than one way, to go at other location at same time. So this is called Uncertainty and Probability of quantum particles.


What is dual nature of Particle in quantum Physics ?

Well you have seen the water wave near the sea mountain collision. Here what i want to say, mountain is a big solid particle and water is a wave. But how you will feel, if mountain particle work as wave, and water work as solid particle. So this happens in quantum world every time.

Hence every quantum particle works as wave and particles. And this is called dual nature. Therefore its mean that electron is particle and wave both. Now what is Quantum Entanglement ? This is very contradict, it may be undigested to you. But this is fact of quantum Physics.  By Physics Best Simple Learning Tips.

So allow me to explain this. Quantum Entangle particle is that particle, in which they are connected to each other, by any means, but whenever one Entangle particle is disturb, Then other Entangle particle is effected immediately. Without any delay, So how it happens God knows well.


Why electron has dual nature Quantum Physics  ?

Therefore to understand this, suppose one Entangle particle is at Earth. And other Entangle particle is at Mars planet. Then If you disturb Entangle particle at Earth. Immediately Entangle particle at MARS planet is disturb. Do you know ? light take average time 12.5 minute to reach Mars from the Earth.

But this Entangle particle at Mars get disturb immediately without taking any time. So how this is happen. It seems like unbelievable, but it is true. Now it may be you are thinking. All this quantum Physics point are correct. Hence for your information quantum physics is right and correct.

Because quantum theory is very effective, in Physics history till date. Therefore quantum Physics is so accurate, using this theory, electronics devices and circuit are design . For example Transistor, logic gates, ICs.

If quantum physics does’t correct. Then no any electronics devices is developed like Mobile, TV, Computer, GPS and internet. So you can think, how powerful is quantum Physics.


What is Five Subdivision of Physics ?

Physics is science and study of nature. So its main five subdivision is important to understand Physics, And this is given below. By Physics Best Simple Learning Tips.

  • Motion >> Well motion is everywhere in universe. So you can’t find any place or space, where motion is not happening.  Whether it is smallest particle or any big mass all are doing motion continuously. Now allow me to explain little bit.

If Motion will stop, then time is stop and universe is gone. You know Earth is moving about its axis, no any doubt. But Suppose if Earth stop its motion, then what will happen ? Can you amazing, what is going to happen ?

Well Whatever the things are available on the surface of the Earth, will separate away. Here i want to say Your house, Building, trees all will run away from the Earth. But don’t worry it is not going to happen right now.

It will happen with Earth but after very long time. If you want to Know, why it is happen after stop of Earth motion. Then you should refer my previous post Circular motion all post. Here i can’t write because this post will be very long.

So lets come to our motion topic. Even you are reading and thinking there is also motion in your brain, Neurons are moving in electrical pulse. Hence you are thinking and understanding. Now don’t confuse there are many types of motion, refer previous post. Here i am talking only about motion.


What is simple definition of Motion in Physics ?

So your blood and heart are also doing motion. If you are sitting in room, And you see the wall and feel there is no motion. But think wall material is having electron, which is moving inside the wall. So there is also motion. Hence solar system, planets, stars and Galaxy all are moving.

So you can’t find any place, there is no motion. Therefore you can think importance of motion. And hence it is very important to understand concept of motion. Therefore when one body or particle move from one location, to other location under universal laws, It require space and time.

And this is called motion. But can you tell me, why do we need to study motion ? Well If you want to send one body or particle, from one point to other point in space. And what do universe impose law to move any particle from one point to other point.

Then you can easily predict the feature. Hence after knowing the universal law, it is easy for you, to find out at what speed, you will send the particle to reach destination. And when it is going to reach at destination. So motion is done easily from one location, to other location.


What is Gravity according to Physics ?

Well you can think gravity is that things, Which attract any object that has mass. So gravity is everywhere and its best example is you. How you are attracted towards the Earth, and stable on the surface of the Earth.

And solar system is also example of gravity, How planets are balance and revolving around the Sun. Therefore for more details about gravity, you refer my previous gravity post.

  • Space >> Well space and time are related to each other. Neither time nor space are absolute. So all are relative. As you approaches towards light speed time is going to slow down. Hence time is not absolute in the Universe.

It depends upon the planet gravity. For example suppose you are living on Jupiter planet, Hence gravity of Jupiter is more than Earth. So here time will pass slow, and his life will be more, than people living on the Earth.

Therefore whatever is around you, this is space. Now to represent the location of object in space you need three dimension. And this is generally represented by xyz axis. Which is (length, breath, height). Now if you add one more dimension time.


How Gravity is changes with mass ?

Then it is space time four dimension. Hence scientist Einstein told that space and time exist together. So how can you verify this statement is true. Now take an example, Suppose you have a unknown friend through chat, and you want to meet with her.

Then how you will meet ? Here you have to specify location as well as date and time. Then only possible to meet her. If you only specify location then you can’t meet.

And in other case if you told her only time, then you are not going to meet her. Therefore time and space exist together.

Now if you want to learn more Physics Easy Tips. Then you must refer my previous post. This link is given below. Physics Best Simple Learning Tips


If you feel this post is valuable for you, then like and share in social media. Because your feedback is very important for me. I hope you enjoy learning  Physics Best Simple Learning Tips | Amazing World of Quantum Physics . If any doubt ask me, i am always here for your help. Thanks for like and share.


 

Work Energy And Power Physics Best Concept Free

Work Energy And Power Concept is an important topic in Physics. Because this chapter deals with new concept. Through which some mechanics difficult problem is easy to solve. So learn here easy mechanics concept. Because you have studies in mechanics, these equations v = dx/dt, a = dv/dt and F= ma so far. And these equation are very powerful to solve any mechanics problems. But it is important to note.

Some mechanics problem is difficult to solve using above equations. Because it is complicated and become long derivation. And using work energy and power new concept it is easy to solve the problems. Therefore work energy and power concept is very important to understand.


Work power and Energy definition


Hence I  like to tell you the one fact about this topic. Do You know scientist Newton ? Well i hope you know. He was a great scientist. He had discovered many laws in Physics and invented calculus. What do you think ? Which equations Newton use to solve mechanics problems ?.

Well he was using equations v = dx/dt, a = dv/dt and F= ma, to solve each  mechanics problem. Because that time new equation was not derived. Therefore later on after Newton, other scientist derived a new equation. By using these v = dx/dt, a = dv/dt and F= ma equations.

Hence the new equation is very powerful equation, to solve mechanics problem. And that equation you learn in this chapter. So this is very good chapter for you. Because after study this new equation concept. You will be able to solve, some difficult problem in one line easily. So now lets start.


Why work done is dot product of force and displacement ?


Well first i like to explain work definition. “Work is done, When force is applied and displacement takes place”. This is the simple definition of work. Hence important point is, how force is applied on the body. So there are two method to apply force on any body. Which is explained below.

Contact force (Which is directly apply on body by touching the body. like you are pushing or pulling body touching it by your hand). And this is called contact force.

Field force (It is non touching force, which is applied by the fields. For example gravitational, electrostatic, and magnetic field ). So this type of force is called field force.

So any method can apply force on body. Now next important point is, its point of application. In other words, at what point force is applied. Hence from that point, you need to calculate displacement. Therefore mathematical work done formula is W = F.S = Fscosθ.

Work done by different forces

Which is called dot product of force and displacement.  And θ is angle between force and displacement. Hence work is a scalar quantity. And work is a form of energy.

When work is done by an object, then it losses energy. And when work is done on an object, then it gains energy. Therefore work is transformation of energy. So work unit is joule. Which is same unit of energy. Now i hope, you know energy is conserved. And it can neither be created nor be destroy. So what, it can only be transfer one form to other form.

Hence energy transformation does’t depend upon the frame of reference. If you change the frame of reference. But actual energy transfer, can be observed from any frame of reference. And energy is also a scalar quantity. So this is reason, why work is dot product of force and displacement.


Why work done is not cross product ?


If work is cross product of force and displacement. Then work will be a vector quantity. And energy transfer is observed different from different frame of reference. Which is contradiction of energy transfer and work done. So work done is not cross product of force and displacement.

How many Type of forces ?
There are two types of forces. And these two type of forces, are very important concept about force. Hence you must know the difference between these two forces. So that you can better understand work done concept. Therefore see the below two types of forces and their difference.

What is conservative force ?

The work done by such force, Which does’t depend upon the path, but only depend upon the initial and final point, Such forces are called conservative forces. So for example gravitational force, spring force and electrostatic force are conservative forces. Because work done by these forces does’t depend upon the path.  Therefore see the gravitational force picture.

Work done example conservative and non conservative force

Suppose a mass m is bring through path A to C, Then how much work done by gravitational force. Work done Wac = Fscos(90+θ) = -mglsin(θ). Now again calculate work done by gravitational force by path AB to BC. So in this case work done during AB path is zero. Because mg force and displacement
are perpendicular.

And work done during path BC is -mglsin(θ). So in this case force and displacement are anti-parallel. Hence work done is negative. Therefore work done by gravitation force is equal in both the path A to C and AB to BC. So it is clear that, gravitational force work done is not depending upon path.
Hence it is called Conservative force.


What is work done by conservative force ?


So one important conclusion. Work done by conservative force in a closed path is always zero. But can you think why ? well it is because of, initial and final position is same in closed path. And you know Conservative force depend upon initial and final point. So work done is always zero in closed path by conservative force.

Now i want to ask a question. If displacement is zero, What is work done ? Do you know ? Well you study in Physics if anywhere displacement is zero. Then work done is always zero.

But this is not always true. So you must know this is only true, in case of conservative force. And it is not true in case of non conservative force.

What is work done by non conservative force ?

A force which is not conservative is non conservative force. So a non conservative force does’t depend upon initial and final point. But its depend upon the path taken. See the picture of non conservative friction force.

Hence a block of mass m is moving from A to B. Then work done by friction force is (-frs). Here negative sign is because of friction force and displacement are in opposite direction. Now again block is moving from B to C, which is same distance in close path. Hence work done by friction force is (-frs).

So total work done is (-2frs) by friction force . Therefore in close path non conservative force work done is not zero. Whereas its initial and final point is same. And block displacement is zero. But work done is not zero by friction .

Therefore this is confirm that, if displacement is zero. But it is not necessary work done is zero. Because friction force is non conservative force. Now i hope that, your concept is clear for conservative and non conservative force .


How do you find given force is conservative or non conservative ?

Suppose a force F = xi^ +yj^ is given, Then can you tell me this force is conservative or non conservative. So to check this force, you need to apply some method. Which is given below.

First you write the force in this form F = Fxi^ + Fyj^ +Fzk^ . Then check the partial differentiation like this.

  1. ∂Fx/∂y = ∂Fy/∂x
  2. ∂Fx/∂z = ∂Fz/∂x
  3. ∂Fy/∂z = ∂Fz/∂y

If above all three condition is satisfied. Then given force is a conservative force. And if above any one condition is not satisfy. Then it is a non conservative force . I hope you know the partial differentiation . If you take Fx component then other Fy and Fz is treated as constant.

Hence lets check F = xi^ + yj^  . Now compare with above equation Fx = x , Fy = y and Fz = 0

∂Fx/∂y  = ∂x/∂y  = 0 ( Because x will look like constant with respect to y).

∂Fy/∂x = ∂y/∂x = 0 ( Here y will look like constant with respect to x ).

So similarly  you can check .

∂Fx/∂z = ∂Fz/∂x = 0 and  ∂Fy/∂z = ∂Fz/∂y = 0 . Therefore all three equation is satisfying . Hence given force

F  = xi^ + yj^  is a conservative force.

Q A force F = 5i^ + 8yj^ acts on a body and follows the path coordinate O(0,0), A(0,a), B(a,a) and C(a,0). Then calculate the net work done .

This question is for you . Solve yourself what do you think to take first step. Hints first you should check this is a closed path. So check about force conservative or non conservative and proceed further.


Work Energy theorem 


Work Energy theorem is states that, “Work done by all the forces on a body, is equal to change in kinetic energy of the body”.  This is simple definition of work energy theorem. Hence in this theorem all the forces are included .  Whether it is internal, external, conservative or non conservative forces. But you are required to include all the forces.

Therefore if work done is positive, Then kinetic energy of the body is increases. Suppose any body is moving slowly. And then you apply a force on the body in the moving direction. After that velocity of body is increases. Therefore kinetic energy is also increases.

And If work done is negative. Then kinetic energy is decreases.  Because you are applying force in opposite direction of motion, So velocity of body is decreases and therefore kinetic energy is decreases.

Hence in mathematical form.  work energy theorem is written like this.

(Wc + Wnc + We + Wi + ……..)  =    ΔKE  or  ( Work done by all forces )  =  (KEf – KEi ) . Now it is  also written the equation in differential form .

(dW by all forces )  = d(KE)  ( for very small work done and change in kinetic energy ). So this is new equation ,through which you are able to calculate work done.

Hence now you have two formula for work done calculation. Which is given below.

F = Fscosθ  and  ( Work by all forces ) = ΔKE.


How to Solve Work Energy And Power Questions

See the above question. Here force is not given. But you are ask to find the work done. So how you calculate work done ? Well you are having second equation for work energy theorem . So apply this formula and easily find out work done.

Hence Work (w)  = ( Change in kinetic energy )   or  W  = ΔKE .

Therefore  W =  (KEf – KEi )  so here  Initial velocity is vi = 10m/s and final velocity is vf = 0m/s. Now use the equation  W  = 1/2mvf² – 1/2mvi²  = 0 – 1/2 (5×10²) = 0- 500/2 = -250J .

So work done W = -250J  ( here work done is negative because velocity is decreasing ) . Hence you  see how powerful is work energy theorem. And numerical problem is easily solved by this equation.


Relation between Work Energy And Power formulas  

Work energy and power formula is very important. So here is relation between work and energy formula. Which is given by W  = ΔKE .

What is power ?

Power is rate of doing work. Hence in other words, how fast work is done that is called power of the system . So mathematically, it is define as power P = Δw/Δt  or  dw/dt  or W  = Pt .

  1. Δw/Δt ( Average power)
  2. dw/dt ( Small variable power)
  3. W  = Pt ( Constant power )

Therefore relation between work energy and power is W = pt = ΔKE .

If you want to learn more about work energy and Telecom technology. So you  refer my previous post.  link is given below.

  1. What is Work ?
  2. What is Energy conservation laws ?
  3. What is important concept for force ?
  4. Gravitational Field and Intensity best concept
  5. What is 5G Technology ?
  6. What is Electromagnetic Wave ?
  7. What is difference between Analog And Digital Signal ?

I will continue with more hidden concept of Physics topic. You feedback is important . If you have any doubt can ask through mail .And hope that you enjoyed learning Work Energy And Power. Thanks for like and share in social media. 


 

 

What is Energy meaning ? | And What is Law of Conservation of Energy ?

What is Energy , If you want to know simple meaning. Then first you need to understand, law of conservation of energy. Because it has many form. But this is divided into two types of energy .which is kinetic energy and potential energy.


What is Law of Conservation of Energy ?


 

 

Can you tell, which body has energy. Let me explain, A agent which can apply force has energy. If that agent has capacity to apply force, then you can say that agent has energy.Because applying force and making displacement is doing work. So anything which can do the work has energy.
Hence it is not necessary agent do the work all the moment. But it possess energy. So take an example to understand it. Suppose a bottle has petrol. Here petrol is simply into the bottle but not doing any work. So it does not mean petrol has not energy. If the same petrol is fill into the motorcycle, Then motorcycle engine is start and apply a force on motorcycle piston.

And due to this petrol a force is applied on motorcycle. Therefore motorcycle moves and do the work. But it is important if you don’t fill the petrol into the motorcycle. Then motorcycle will not move. Hence it does’t do any work. So it is clear that,which has capacity to do work motorcycle or petrol. Obviously your answer is petrol.


Understand simple concept what is energy ?


So from above explanation. I hope you have got the concept what is energy. And you can say “Energy is capacity to do work”. Therefor motorcycle does’t has energy. Petrol has energy because it has capacity to do work.

Hence motorcycle is a device. Which take energy from petrol and converted into other form like heat. And the process of energy conversion is work done. So energy does the work. If a body or anything, which has no energy. Then it can’t do any work.


Different Types of Energy


 

Energy is invisible and has many forms like light hear, sound, wave. But which has mainly two category kinetic and potential.Hence it can transform one category to other category. And it can also change one form to other form as well. But important point to remember, energy can’t be created or destroyed. This property of energy is called, law of conservation of energy.


What is kinetic energy ?

 

Kinetic energy is a form of energy, when a object or particle is in motion. Hence Can you tell me, where does this kinetic energy comes from. Well this comes from the potential energy that an object or particle has. So kinetic energy is the capacity to do work.

Hence from the above picture . What do you think about kinetic energy ? Does it depends upon frame of reference ? Yes kinetic energy depends upon frame of reference. Let me explain.

You know formula of kinetic energy is mV²/2. Now from the above picture. If train is moving with velocity V, then kinetic energy of train is mV²/2. Where m is mass including with person A and B. Therefor what is kinetic energy of A and B with respect to trail ?

Obviously it is zero. Because with respect to train both person A and B are sitting. They are not moving or not changing their position. But with respect to person C sitting on the ground. Both A and B are moving with same speed of train.

Hence their kinetic energy is MaV²/2 and MbV²/2. So it is clear. When you change the reference frame. Same person kinetic energy is different. Therefore kinetic energy depends upon frame of reference.


What is potential energy ?

Potential energy is the energy, which is stored energy due to its position. So initial and final position is consider for potential energy. Therefore potential energy can be negative, positive or zero. Do you know ? where does this energy comes from ? Well this energy comes from work done on object.

Why potential energy is called stored energy ? Well this is Because of it is used in future. If you do some work and if kinetic energy is not change. Then what do you think, where does this work gone. Does this stored in potential energy. BIG no let me explain this. Suppose you are pushing a block on floor surface here and there. And finally block is stopped, then block kinetic energy is now zero.

I hope you are agree ? Because block final velocity is zero. Also block potential energy is not changed. Because potential energy is define for very special force. It is not define for all forces. Hence do you know conservative force ? let me explain.

Therefore for conservative force, work done does not depend on path taken. Such types of force is called conservative force. And potential energy has only meaning for conservative forces. So friction is not a conservative force . Hence work done by friction force is not stored in potential energy.

Therefore friction force work done is dissipated, in the form of heat and sound energy.


What is Mechanical Energy ?


 

Mechanical energy is define as sum of kinetic and potential energy. Which is  used to do work.  Hence in other words, it is energy in an object due to its motion or position or both. When the work is done upon the object. Therefore that object gains energy. The energy received by the object, due to work done is called Mechanical Energy.

Mechanical energy can be either kinetic energy (Energy of motion) or potential energy (Stored energy of position). From the above picture moving mass M possesses Mechanical energy due to its motion (Kinetic energy). Therefore a moving ball possesses mechanical energy, due to both its high speed (kinetic energy) and its vertical position above the ground (gravitational potential energy).

For more information about What is Energy concept, you can refer my previous post given link below.

  1. Work Physics Concept
  2. Gravitational Potential Energy
  3. Hidden Concept  Force

I will continue in next post with more hidden concept of Physics. And i hope you have enjoyed learning What is Energy ?. So you are most welcome for your feedback, comment and share. Learn more new Tips and grow. Thanks for sharing.


 

Work Physics | How easy to understand | What is work ?

Work Physics -Best definition. If you want to know, What is work ? and actual work meaning. So you are at right place for work definition physics. Because learn here, what is work done. And relation between work and energy.


Understand  work meaning in Physics


Work meaning- ” To do anything which involves mental or physical effort “.  But in Physics work is different, With normal definition of work. Because in Physics mental work is not considered work .Here i want to clear you, in day to day life, which you understand meaning of work is different in Physics.

Hence suppose if you are reading hard for your examination. So you are doing mental work, but in Physics meaning you are not doing any work. To understand Physics work, force and displacement are consider. See the above picture, how man is doing work ?whereas lady is not doing any work.


 Force and displacement meaning according to Physics 


                                                                           → →

According to Physics definition of work = F⋅ S  or FScosθ, taking dot product of force and displacement. Where θ is angle between force and displacement vector. This is simple way to define work in Physics.

Some important points for work

 

Hence from the above figure. you have notice that, when force and displacement are parallel, then work is positive. And If force and displacement are anti-parallel, then work is negative. Another important point work is scalar quantity. Some people confused due to, sometime work is positive or sometime negative.

Because they thought that if work is positive, So its direction is toward right. And if it is negative then direction is towards left. But this is not correct at all. Because work is a scalar quantity, you can’t associate any direction with it. Work is calculate with the help of force and displacement.

Therefore force is a vector quantity, and displacement is also a vector quantity. But work is dot product of force and displacement, So it is a scalar quantity. Hence sign of work indicate, the direction of force and displacement. If work sign is positive then force and displacement direction are same.

And if it is negative, then force and displacement direction are opposite. This is true meaning of work sign.


 If force and displacement are perpendicular 


What is work ? You know work done formula is define as work  = Fscosθ, where θ is angle between force and displacement. So cos90° value is always zero. Hence work done in this case will be always zero. Therefore you can just refer the above first picture. why work done by lady is zero ?

Well this is simple, because force applied by lady in upward direction on the sack. Whereas she is moving  forward, so sack displacement is in the direction forward. Which is perpendicular to the applied force. Hence force and displacement are perpendicular in this case.

Therefore  work done by lady is zero. Hence lady is carrying sack from one place to other place, but she is not doing any work according to Physics definition.

But according to day to day life lady is doing hard work . I hope you have got the point.


 Force is applying but work done is zero how ?

See the above picture. A block is placed in the corner of the wall. And a man is pushing the block with 30N force. What will be work done by this man ? Well work done by man  Wman = Fscosθ. Now look here man is applying force but block does not displace.

Hence if displacement is zero, then work done by man will be obviously zero. Because work is directly proportional to displacement. So it is a important point . If displacement is zero, then work is zero. Even if force is applying or acting on the body. In normal language, this man is doing work.

But in Physics language, this man is not doing any work. Because displacement of block is zero.


If force and displacement are at some angle


A block of mass m is sliding on an incline plan as shown. What will be work done by mg force acting on the block. Hence work done will be W = Fscosθ. So put the value θ = 37° and m= 5kg , you will get W = mgscosθ = 5×10×5×cos37° = 250×cos37° = 250×4/5  = 50×4 = 200J.

Here i want to explain you this visualization in other way. Hence see the value F(scosθ), take (scosθ) together. So in this case (scosθ) is representing vertical height, that is 4m. Therefore put again the value of force mg and 4m, you will get the same work value.

So the formula of work done. You can write as W = F(scosθ)  = F(displacement along the force). Hence it is important point, If force vector and displacement vector are at some angle. Then work done can be written as W = F×(Displacement along the force).

Therefore in some situation it is difficult to find, displacement along the object movement. So in that case you can directly apply the concept of (Displacement along the force). And your problem will solve easily, Which is convenient to solve numerical problems. So remember this concept.


Important point regarding force and displacement 


When you define work done, dot product of force vector and displacement vector. Then s is displacement of point, where force acts. So you have to see, exactly the displacement of that point where force is acting.

From the above picture as shown. Man is pulling rope with a force of 100N. Hence block of mass 2kg is moving upward 2m as shown. Then you have to calculate work done by man. So can you tell, what will be work done by man ? Well  according to work done formula.

Work = Fscosθ, here F = 100N pulling downward and 2kg block is moving upward 2m. Hence angle between displacement and force is 180°. Therefore Work = 100× 2×cos(180°) = -200J.

So If you are calculating work done in this way, then it is WRONG. Now think why this is wrong ?

OK i already explained that you have to see, the force applied point and displacement exactly at that point. Hence force is acting on rope in downward direction. And rope is also moving in downward direction from force applied point. So work done by man W = Fscos0° = 100×2×1 = 200J.

If it is asked to you, what is work done by man on the block ? So it is clear that man is not doing work on the block. it is zero. Because man is not applying any force on the block directly. Man is only applying force on the rope. Then who is doing work on the block ?

This is rope tension force, which is doing work on the block.


Work and Energy 


The concept of work and energy is related to each other. Because force can do work on an object and cause a change in energy. And energy is ability to do work. Hence in simple, when you do work on an object, then its energy is changed. Therefore when energy is change then work is done.

Work done by friction force .  Do you know ? How do you walk on the ground ? Well due to friction force. You must know, without friction force you can’t walk on the ground.

But it is really interesting, friction force and displacement are in the same direction .Whereas work done by friction force is always zero. Because your one foot is always in contact with ground . And friction force act on that foot only.

Which is at rest . And your other foot is moving. Hence friction force work done is zero.

If you want more information about force and displacement. You can refer my previous post link below.

Force Concept 

Displacement concept

Friction Force concept


I will continue with other topic of Physics hidden concept . Always target to provide you my best effort.  So i hope  you have enjoyed learning about work Physics.  your feedback is important for me comment, likes and share. Thanks for sharing. Learn and grow.


 

Geostationary Satellite | best concept satellite communication

Geostationary Satellite height is fixed 35800 km above the Earth surface, So that its rotation time period is fixed 24 hours. Located exactly radially above the equator, same axis of rotation that of Earth, So best concept satellite communication. It is moving same as with Earth, hence easy to send and receive signals using satellite internet
satellite camera catches Earth images called satellite images


What is Geostationary Satellite ?


How the name is given Geostationary satellite ? Well Earth is rotating all the times 24 hours. As shown in satellite picture, The time period of rotation for satellite is also 24 hours. By adjusting the height of satellite. You know that height and time period is related to each other. Suppose that satellite is above your head in the space.

Now as Earth is moving . you are also moving, and satellite is also moving. The time period of rotation is same. Hence whenever you will see the satellite. You will find satellite is over your head. You are on the Earth. So with respect to Earth. Satellite will look like stationary. Hence it is called Geostationary satellite.


What is advantage of  satellite communication ?


If you want to communicate with Geostationary satellite. You will fixes an antenna on the Earth. which is directed towards Geostationary satellite. Then you no need to change. The direction of antenna on the Earth. Antenna will be always directed, towards the Geostationary satellite.

Because both are rotating with same time period. This makes best concept satellite communication. You can send and receive signals, Every second from Geostationary satellite, Which make easy satellite communication. Really cool to use GPS, to track your location on the Earth.

Some more advantages. you are using satellite internet, TV satellite. Hence easy Geostationary satellite communication. If you want to know, more about satellite motion, You can Refer previous post elliptical orbit solar system.

 

 


Where should located  satellite ?


To make best satellite communication. As well as efficient satellite communication. Geostationary satellite must be located above the equator, So that its center of rotation, As well as its axis of rotation, everything matches with the Earth. Then it will appears, As a part of the system. And it will remain stationary. 

 You should remember that, axis of rotation is same, for Earth and satellite. which is called equatorial plane. 


What is Application of  Geostationary satellite ?   


Geostationary satellite is use, for signal communication. Just see above picture, how satellite communicate from the Earth . You  generally use this for, TV satellite signal  and GPS location track . It is also use,  for all types data exchange services.  So internet communication is done easily.

It is also use for Earth images.  Which is called satellite images . It has a camera. Which scan the Earth images all the time. Satellite send Earth images, whenever you want Earth images. 


General types of Satellite

Satellite is categorize on two basis. First on the basis of altitude, and second on the basis of time period rotation. Do you know satellite rotation time period is directly proportional to distance ? This distance is from, the surface of the Earth to satellite location in the space.

Means if satellite is far distance from Earth, then its time period of rotation will be more. If distance is less, then time period of rotation will be less. This is also explained by Kepler’s third law. Now satellite speed formula is √GM/r.

Where G is universal gravitational constant, M is mass of the Earth. And r is distance from the surface of the Earth. In previous post, well explained this formula. You can refer satellite orbital velocity.

This formula √GM/r  indicate ,if satellite will be far distance from the Earth, then speed of satellite will be less. And if distance will be less, then speed of satellite will be more. I am talking about here tangential speed.


Three different Satellite name moving in space


There are three types of satellite. Which is generally used for different purposes.  And each satellite has unique feature.  This is given below with their orbit of rotation.

  • LEO  ( Lower Earth orbit, its range is 200km ∼ 2000km. Rotation time period is 1.5 ∼ 2 hours )
  • MEO ( Middle Earth orbit, its range is 2000km ∼ 35000km. Rotation time period is about 12 hours )    
  • GEO  ( Geostationary orbit, its range ∼ 36000km. Rotation time period is 24 hours ) 

 If you want to learn more about Telecommunication and Technology. Then refer my previous post . This link is given below.

 

Kepler’s laws | elliptical orbit astronomy solar system

Kepler’s laws for solar system.  Explain astronomy really very interesting.  Because  You will learn. About Earth motion elliptical orbit. planetary motion in this topic.

Solar System

How does planets,  motion around the Sun ? Why planet motion,  around the Sun ? Why every planet motion,  in different elliptical path ? What do you think,  about the Sun Motion.  All hidden concepts,  for planets motion, I will discuss in this topic. In simple way , So lets start .


Kepler’s law great astronomer mathematician 


 

Kepler Astronomer German

Kepler a German mathematician.  He was assistant astronomer Tycho Brahe.  Kepler lived in an era.  when there was no clear distinction,  about Astronomy and Astrology . But there was a strong,  division between astronomy (mathematics) and Physics (Natural philosophy).

Kepler also incorporated religious arguments.  And reasoning into his work,  Motivated by the religious conviction, and belief that God has created the world.  According to an intelligible plan,  that is accessible,  through the natural light of reason.


 Planet Motion Astronomy details 


When Kepler described his new astronomy.  About celestial Physics. Then Kepler first major astronomical work.  Demonstrating the periodic conjunction of Saturn and Jupiter planets.  He realized that regular polygons,  bound one inscribed and one circumscribed,  circle at definite ratios.

He provided information, about the universe  on the basis of geometry . Kepler found that,  the spheres of planet is placed,  an intervals according to the relative sizes of each planet’s .  Assuming the planets is moving around the Sun.

Kepler was thinking . he had revealed,  God’s geometrical plan for the universe. Kepler provided,  three beautiful law’s,  for planets motion . One the observation done.  i will discuss these laws in this post . It was ancient believe,  that Earth is centre of the Universe,  and all other planets,  including the Sun . Moves around the Earth.

But later ,  Galileo declared that Sun is the Center,  of the universe.  And all other planets,  including the Earth moves around the Sun.


Why all Planets moves around the Sun ?


The mass of the Sun,  is very very large,  in the solar system.  in other words,  you can say,  Sun has 99% of  solar mass system.  And  rest 1%,  of mass is for other planets. 

Due to Sun heavy mass .  its gravitational force,  attraction is very very large.  So all other planets, are moving around the Sun.  All planets are bounded. with negative energy to Sun.  Now you can ask,  due to large gravitational force attraction,  of the Sun,  all planets should attracted towards the Sun.  And collapse with the Sun . But this does not happen .


Centripetal force is responsible for planets rotation

Well this does not happen. Due to centripetal force,  balanced by gravitational force attraction. Just like,  moon does not fall on the Earth.  Actually moon falls, towards the Earth.  But due to centripetal force attraction.  And Earth motion, Moon goes into circular motion.  Around the Earth.  for hidden concept of satellite orbital.  You can refer,  previous post satellite orbital velocity


Why all planets move in different elliptical path ?


The reason for elliptical path,  depends  mainly on three factors.  Mass, velocity and distance.  Then Gravitational influence is determine.  take an example,  for the Sun and the Earth.  since mass of the Sun , is very very large.  than mass of the Earth.

So the common centre of mass . for these two bodies,  is called barycentre.  Which will be near,  to the heavy mass. And both body,  will move  around this barycenter, as a centre point.


Elliptical orbit is due to barycenter

Earth and Sun moving velocity is different.  So sometime,  gravitational influence,  between these two bodies , will be more . due to different velocity,  then Earth will go closer,  to the barycentre.  That is near the Sun.

Sometime gravitational influence,  will be less,  then Earth will far,  from the barycentre.  So here barycentre,  is the distance for these two bodies.  which is changing,  according to time changes,  and hence every planets,  moves in an elliptical path.

If both object,  mass and velocity , become same.  then it will move in a circle . rather than elliptical path.

Every planets have different path . Due to different barycenter,  for all planets .  in the solar system,  and every planet will move around,  its own barycentre.  Hence every planets , have different elliptical path.  In the solar system.


What does the Sun revolve around ?


This is Very interesting,  in Solar system.  All planets move around the Sun.  But do you know.  what does the Sun revolve,  around ?  Well you will know,  this question answer.  in this topic.  see the below picture.

 

super massive black hole

First you should know, where is the Sun stable,  in this universe.  see the above picture,  moving Galaxy,  is spread in one lakh light year distance .

And Sun is,  about 30 thousand light year , from the super massive black hole.  centre in the Galaxy.  as shown in the picture,  at this location.  the Sun is stable.


Super massive hole of Solar system

Super massive black hole,  is biggest black hole.  it is in every Galaxy.  its mass is very very huge . million times of the Solar system.  All the element present,  in the Galaxy,  including Sun,  stars moves , around the super massive black hole.

And one day , every element of the Galaxy,  will be consumed.  by this super massive black hole.  and will be compress,  all element in this hole . But it will take,  billion of years.

Hence the Sun is moving,  around the super massive black hole,. it is important to know,  that not only the Sun,  but whole solar system . moves around the super massive black hole.

The Sun rotate,  about its own axis , time taken 25 days, relative to Earth.  means one day at Sun,  will be equal to 25 days of the Earth.


Kepler’s Laws of planetary motion


Kepler was the first scientist, who does foundation for gravitational force , action between two massive bodies, on the basis of mathematical data observation,  for planets position and motion in the universe. data collected from Tycho Brahe observation done.

Actually Kepler was not able to explain,  the cause of planetary motion, means why planets do motion in such a way, he was having the mathematical data proof,  but unable to explain the cause.

So later this law’s of gravitation  published by Newton . with cause and proof. But you should remember, gravitational force foundation given by Kepler. Hence you will learn all three Kepler’s laws .

 Kepler’s first law

First law of Kepler’s explain, about law of orbits. Which state that any planets or stars moves,  in which path, Kepler told that it moves in a closed path,  then closed path may be circle, ellipse, square . close path is such that, which starting from one initial point,  and finally reached at initial point, that is closed path.

Hence Kepler told that, planets moves around the Sun, in a closed path .and that shape is ellipse, not a circle so the path is elliptical orbit.

 

Orbit law

See the above picture of ellipse, you know ellipse has two foci as shown in picture, A simple property of ellipse is the sum of the distance r1 and r2 from any point on ellipse is always remain a constant value.

Which is (r1+r2) = constant now where will be the Sun ? Kepler told Sun may be either of foci 1 and foci 2 not at ellipse centre and planets are moving around this as shown in elliptical path.


Kepler’s first law statement : All planets moves in elliptical orbit, with Sun at one foci of ellipse .


Kepler’s second law

Kepler’s second law is about, law of Area,  see the below picture.  planet is moving in elliptical path here r1 ,r2 and r3 are called position vector. The area covered in one second is called areal velocity v1, v2 and v3 are areal velocity.  

                                                                              

Kepler’s law told that, area covered in one second,  at any point of path is equal. So three area shown in figure in one second are equal.


Kepler’s Second law statement : Areal velocity of planet, around the Sun remains constant.


Areal velocity = Area swept by position vector in one second = 1/2*v1*r1  ( for small angle r1 is taken as height ) here base of triangle is taken in one second so using formula s = vt = V1*1 = v1 . According to this law if the areal velocity is same in one second then you can write.

1/2*v1*r1 = 1/2*v2*r2 = 1/2*v3*r3  = constant 


Areal velocity concept

v1*r1 = v2*r2  or v1/v2  = r2/r1 or  V is inversely proportional to r , Hence it gives a conclusion that if radius will be small then velocity will be large and if radius is large then velocity of planet will be slow. this is very important conclusion.

Now you can tell which velocity is fast in v1 and v2, Well i hope your answer will be v1 because radius is small r1 than radius r2. Hence you can think when planets moves around the Sun then which time velocity is fast ?

well when planet is nearest to the Sun it moves fast and when far away from the Sun the moves slow.

Kepler’s third law    

Kepler’s third law is law of time, now till you were studying about only one planet, but many planets moves around, the Sun in different orbit, and all have different orbit time. So Kepler established a relation between orbital time and distance from the Sun. 


Kepler’s third law statement :  For different planets in motion, square of time is proportionate cube of distance . 


T²/r³  = constant, where T is orbital time, of planet and r is distance from the Sun. It is a very important number.

Kepler’s Constant 

All the planets, which are moving around the Sun . if you will calculate T²/r³ it will give you a same value.  

T²/r³ = 2.95×10⁻³⁴ y²m⁻³  so from this value, you can calculate, any planet orbital time period .if distance is given or if distance is given , then you can calculate orbital time period of that planet.


I will continue in next post, with more hidden concepts of Physics topic. I hope that ,you have enjoyed learning Kepler’s laws. I want your feedback, comments, and share on social media . Learn more and grow, Thanks for sharing.


 

 

 

learn Physics Free best concept

Learn Physics Free Best Concept If you want to learn Physics free and Technology. Then you are at right place. Because i am providing here free learning Physics and Telecom technology. With best simple and easy concept. So that you can enjoying learning Physic and Technology. And become mastering physics answers very well yourself.


 Learn Physics and Telecommunication Free technology  best concept


The Education Big Message of this Website must read !!!


The Education system is not good, The concept of education is not good, The education importance is not good.You will ask why? Then I will ask a question. How many Peoples get up in the morning as a intention that today I will learn something new. Can you answer the question? Well I can answer as per survey record only 6% people have intention every day to learn something new. Now important point, why such a less percentage of people? The answer is most of the people have no purpose of life and education importance.
All behind this is true meaning of education system is not good, Lets to elaborate this, The teaching style of teachers are not good and that is reason students are not participate in the class actively. Students are not getting interest in whatever they are learning.

Mastering Physics Solutions True Education

Education Importance

Teachers inter in the class room and just write down the menu of syllabus, you have to study in this subject xyz  and will be cover one by one without giving any practical application and uses of any topic of the syllabus menu. Just think this is right way of teaching. . Not at all teachers have to think like mastering Physic solutions.

But this is due to Incompetent faculty in colleges, Actually colleges are now became business for more profit they hire low salary base faculty, This is education system. This is true meaning of education, This is the concept of education . Believe me that is the main reason students don’t participate in the class actively. Because they don’t know the importance of education they are studying right now.

So what student can do, If any student really want to learn true knowledge. Then mastering physics online. There are so many good materials and teachers are teaching free through Video as well as website. Like this website provide you simple word learning Physics by easy Tips and Trick totally free of cost.  If student have any doubt, then can ask to teacher as well, and can also take help of  mastering physics help forum any time online. This is the main advantage of this Internet era.
Well Student level of preparation and level of aspiration ground and sky gap. Today education is for degree not for knowledge .Well filled mind not well formed mind and this well filled mind will give you nothing.Incompetent faculty teaching with conversational theoretical classroom based approach. 
Students don’t know why they are studying this topic and what they are studying in this topic, What is the practical uses of that topic in life. You can ask this question but most of the student don’t know what they are studying and why they are studying.
Where they can use this knowledge in their daily life .This is main reason of confusion in study and life.  
Their goal is not clear, what to do and what they can do better.
Instead of giving the education syllabus menu, Teachers should emphasizes the practical uses and applications of the topic before teaching that topic. So that teachers can attract the attention of Students in the class room .
Due to this type of education system students are just memorizing the things or topic not understanding the things or topic fully. So Confusion continue in study and life forever.
To make education learning practical approach and application based. And its implementation in real life it will require more effort from each of us to change the present education system.
So I am doing my effort in the field of Physics and Telecommunication technology.  please come and join this effort to make it successful .So that when everybody get up in the morning as an intention to learn something new and that percentage will increase from 6% , then successful person percentage will increase automatically in the world. And it is better for the humanity help. 
If you can not do this but at least you can support if someone is doing good work. Don’t forget this is also a type of help.

I don’t know, what do you mean by success ? but my opinion Success is freedom, your own choice for your life. Do what love to do, it will give you definitely success in your life without any doubt. 


Share Knowledge of science Physics and technology Telecommunication to Society those who want to learn concept of Physics and Telecommunication in easiest way free of cost you will never forget as simple and practical .If you hate Physics and technology there may be some reason to hate and it is as simple you have not studies the way your brain want to accept.

you have learnt from wrong teacher. after a long experience here i will teach you the way you never study before and never thought Physics is as simple. it will be Physics magic, each and every topic will be covered with key concept in depth analysis based upon the facts and experience close visualization for topic you will study.

 Everyday you will learn new concept and be the master of that topic after reading content and follow my tips. it is my commitment you will love Physics. Only you need to read every topic content.
see science is organised language. Jut for example we learn first letter A,B,C…Z counting 1,2,3….9 after understanding this we can make any word and number easily .
So in same manner every topic is link with each other. Every topic content will be very valuable and conceptual you will not get in any book it is based upon my long experience of study, which i want to provide you.    
Well are you ready to get that valuable hidden concept ?.         
Before going to start physics Magic !
You must learn, what are the ways through which you learn anything from society. whatever you have learned from childhood to till now is based upon only Four facts.  
 
1  Reading 
2  Writing
 Speaking
4 Listening.
 
Education lead the society towards development 5 year back internet was costly, data speed was on 2G, 3G technologies and was not available easily. But now 4G technology available at low coast and free data.
One important general question ask by students difference between online  learning and class lecture learning,  and which one is best. According to my view online learning is best but why ???
 
Benefit of online learning.
 
1 your travel time is save no tidiness feeling be energetic at your own place to learn.
2 you can learn as per your schedule whenever you want to learn and how much time you want to learn.
3 you can repeat again and again the topic you want to learn where concept is not clear but in live class it can’t be repeat as per your wish.
4 Free of Cost without paying any fee. 
 
Important Point for learning
 
How our Brain work  Before going to study, it is very important to understand brain process.
 
Learn Physics Free best concept
Actually your Brain understand and process image only no any text like A,B,C and any word.
Take an example, when you remember you friend Mohan it will show you your friend face, body image only no any meaning of Mohan for brain. Take an another example, when you recall those friends or relative whoever not met before, it will not process image. its mean that person has some name but not understanding text want image but not seen your friend before, so brain is now confused. 
Similar fashion in study brain want to visualize very closely whatever you study . You need to visualize topic, So that you will never forget and brain will memorize the topic forever .
This make seance for better study. 
Now after this discussion most important point is why you Study ???
This is really very important point to understand the purpose of your learning or study. Think yourself and ask the answer from your brain. Well i hope somebody will say for earning money and some for degree and knowledge.
But i will say, your study purpose is to solve the problem of mankind in society. where you live make better human life.Face challenges to make life easy.
Hence learn here Physics, Telecom and Technology  free in challenging way.
Think every development like mobile, washing machine, AC made all these make human life easy, So study purpose is to research some new ideas contribute  for development in society for mankind, from which society can take advantage of your research and contribution. This is main purpose of your study and learning.  I hope the point is now clear for mastering physics answers.  

As well as this make seance  for true learning. 

Now today our question is very basic but important and hard . Are you ready to face the question ? Well 

What is Physics ???.

Before going to definition of Physics. it is important to understand what you will learn in this subject so that your concept  will clear and will be interesting and fun for you. just like when you make a picnic plan then you prepare for that plan like,
How you will go and where you will stay, what is the spot places. Everything you plan before visit picnic place.  Then why not you do in the same way, you have to prepare to understand Physics.

Hence my motive is to provide you Physics, Telecom and latest technology  free true knowledge. So that you are able to know the technology latest development as well as applications.

 

mastering physics answers  


Physics is science deals with “study of nature” around us not only Earth but whole universe. how interesting is this ? wait for a second many of us taken this subject and scored good marks many of them has read Physics but most of them has not learned Physics. 
If you have true knowledge of Physics, Telecom and technology, Then you can easily make your own products. This is advantage of  true learning.

Definition point of view Physics is a Greek language meaning Law’s of nature.Where we use Physics the phenomenon which we can’t see but we observe that happens and is advantage for our learning and development. Take an example all of us know Newton’s Law of gravity anything we through upward it come down towards the Earth .
You have only  seen the ball is coming down but never seen gravity. Even Newton has not seen gravity here we use Physics . Take an another example you have experiment in School classes taking a comb and pieces of  paper comb our dry hair and brought comb near to pieces of paper what happens pieces of paper attracted towards comb and attached with comb. you can see pieces of paper yes, you can see comb yes but you can’t see force of attraction here we use physics. 
Now i hope some concept may be cleared and visualize in your brain. thanks for reading . I hope you have enjoyed learning Physics. I will continue this post with more concept in next post. I want your comment, likes and share, thanks for sharing.
Now for basic Physics concept . You can refer this book . This is a good book . Here some example are illustrated very well, This can build your concept.
If you want to Learn top Physics and technology post. then see my previous post this link is given below.

Physics (Volume – I)

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I hope you are enjoying learning Physics And Telecom. So your feedback is very important for me. Thanks for comments, like and share Physics And Telecom. If you are having any doubt, feel free to ask any question. Always here for your support.


What is Science gift of nature

Today you are going to learn exact meaning  of what is science ?

So you should know Science is everywhere. Science is not a book.

Science is present in every moment of your life. 

Here you’ll learn best concept of science, so that you’ll never forget what is science.

So are you ready to learn, What is science meaning for you ?

Let’s dive right in.

Do you ever think much beautiful is our physical world ?

Yes or No

I’m going to explain here hidden concept of physical world  right now keep reading.

If you recall this is first chapter of class XI Physics, Study of Physical world is actually starting of Physics.

Because you know study of nature is Physics. Well and Physics is science.

But before going in depth, I want to answer some FAQ Question about science. 

So you see the FAQ question and answer.

[faq title=”Frequently Asked Questions (FAQ)” open1st=”0″ openAll=”0″][faq_item title=”What is the easy definition of science?” number=”1″]Science is a branch of practical knowledge, Which has a theoretical and mathematical proof through experiment. And dealing with facts about any event occure in the nature or physical world govern by a natural law. This is actual science.[/faq_item][/faq]

What is Science?

Well it is very important to understand physical world to understand science better.
Because a famous  saying, perhaps you know “well began is half Done”.
So its meaning is if you start well that indicate 50% of your work is done.
Therefore if you want to really learn Physics, You must first understand physical world.
This is REALLY very interesting topic,You will really enjoy to learn this topic .
This is small topic but very important for concept  and basic understanding about science.
In other words I can say. This  is pillar of Physics, So lets start.
what is in this beautiful physical world for you to learn  about science? 
Physical World meaning world of Physics ( Physics Ki Duniya )   
Very first i will Welcome you to Physics World.

 

Understand our physical world 
Well i ensure you today you will get the key of Physics treasury, just open your eyes and brain to take it.
How interesting is this and what you will learn here, I can simply say you’ll learn more than your expectation.

As I have already discussed in Physics definition it is branch of science now the question arises what is science ???

So first you should understand about “science” for this you have to go in ancient time.
Do you know ? when the world was made in the ancient time, people started to see the natural phenomenon very closely and started to think over natural phenomenon.
like everyday sun set in the east every morning and sink in the west every evening.

Due to this natural phenomenon happening that time peoples concluded that the Sun is moving around the Earth.
The person who was thinking like this was called Philosopher that time and this knowledge was called philosophy and those time different person were thinking about different things .

Peoples had freedom to think about their interest after this the knowledge became very vast and big.
So it was really very difficult to study. Then people started classification of knowledge and this was the time when people made a boundary and divided in Science or Arts,
Now this is coming from Ancient time to till date the boundary of science and arts. This boundary comes when you just pass 10th class.

What is scientific method psychology

So you called to choose your interest Arts or Science for further study. 

If you want to know learn Physics best concept, check this link

now I will focus on difference between Arts and Science.Arts is a skill like develop speaking, develop drawing skill like this, but wait now I will discuss science. 

In Ancient time Someone seen natural phenomenon happened then he observed that natural phenomenon through his eyes,

And written down in note book and then experiment that natural phenomenon in the lab and given his thought and ideas and also made some rule and Laws.

After that another generation came study this rules and laws and think ahead of this carry out further enhancement written down his observation experiment and ideas.

now third generation came and further carry out improvement in 2nd generation rules and laws.

here what we see first generation made some rules and laws 2nd generation started from first generation left point third generation

started 2nd generation left point wait 2nd generation will not start from initial zero point otherwise development will stop, and take long time actually,

what we see here in the Science every phenomenon is observed, written, experiment give ideas made rules and Laws .what we see here this is in the organised manner. So “Science is Organised knowledge”.

 

Well which knowledge, I am talking here, don’t be confuse this is about “Nature” so Science is study about nature.
you study how rain fall, sometime wind blow from east to west sometimes west to east, study about days and night this is all about Nature.
so what is base of Science it is simple Nature. wait what is around us nature so in Science nothing is study outside nature this is key of Physics.

What is scientific method definition Organised knowledge ?

Whatever phenomenon happening in nature, we have made a scientific study method to observed if the phenomenon fit in scientific study method.
then it is ok otherwise it is just illusion. There are some point in scientific study method and very important to understand one by one each point is important.
Scientific method definition to study Nature.
Remember we always study nature in scientific method not a person otherwise it will be psychology.steps for scientific method
1 Observation : 
First we observed  natural phenomenon around us like in rainy season water falls from sky to earth, sometime winter comes and sometime summer in a year,
river water flows from west to east when we through a ball upward it come down to earth always not goes up all these phenomenon simply observed.
2 Controlled Experiment :
Here we copy the natural phenomenon in our lab in a controlled manner just we take example of rain we observed that before rain earth is heated
then rain falls so same thing is repeat in lab first we heat water take a pot above the heated water we see some water molecules cloud on cold pot and made water drop just like rain.
take an another example of water flow in case of river we go in our lab take a tube we want water flow from left to right then we put left side high.
we see water is flowing from left to right we change our direction direction east, west, north, south in controlled manner but always water flows from left to right.
you should know that knowledge comes from experiment and brain not from book. Science always start from Lab then it is written in book.

What is the scientific method steps

take an example of ball through upward always come down to earth.
Newton first observed this then experiment in Lab taking two heavy masses hang in the air seen that both masses come closer to each other
then he told each mass body attracted each other then he written the laws in book Gravitation.  
3 Reasoning (Qualitative/Quantitative) :
This is important point where we think logically the reason for natural phenomenon happening first qualitative means focus on characteristic.
take an example when we through ball it always come down this is it quality whether the ball mass is small or big it always come down.
Newton after experiment was thinking why ball comes down towards earth of course there is something in the Earth
and finally concluded earth having heavy mass due to this earth attract the ball then question arises that Sun and other planet having heavy masses .
why not sun attracted ball wait Sun also attract ball but due to sun large distance its force is very small compare to force of Earth .
everybody having masses attract each other Sun attract Earth due to which Earth rotate about Sun, Earth attract Moon due to which moon rotate around earth.
now the question is why moon not fall on earth ? in universe every planet, star, galaxy attract each other and moving in universe.
why moon rotate around earth because earth has more gravitation attraction on moon than other planet so it is bounded to earth similarly Sun has more affect on earth so earth rotate about sun.
Quantitative is change in parameter how output result change putting different parameter and analysis of output result how much changes happens.
4 Mathematical Modelling:
This is simply making of formula and should be correct for each condition apply lets an example we know Gravitational formula.
F= Gm1*m2/R^2 if you want the upward through ball attracted by moon it is possible increase the distance from earth and near to moon simple moon will attract ball without fall down to the earth.

What is scientific method conclusion ?

what we see here this formula is correct for earth and moon both  gravitation phenomenon.
take another example motion we will study in motion topic latter v = (u+at ) here v is final speed u is initial speed a is acceleration .
if a car is moving with acceleration and want final speed at an instant we can calculate easily with this formula so this is simply formula using mathematics tools.
without this our scientific study incomplete. many scientist research rules and Laws but due to lack of mathematical modelling .
their research was not added in Laws and not publish. next generation given mathematical modelling and latter laws published. what we do with mathematical modelling.
5 Prediction:
using mathematical modelling we start prediction take an example we want to send an aircraft on moon
then what will do just send it will reach no wait here mathematical modelling will be use we know from gravitation moon will attract aircraft only it will be near to moon means earth gravity force.
will be less than moon where this point will be calculated F = Gm1*m2/R^2  it will give distance from earth now use formula v =u+at to calculate time .
when it will reach that distance now stop the aircraft engine moon will attract aircraft on its surface.what we are doing prediction on the basis of mathematical modelling.
now our aircraft is going for mission on moon what next will happen wait and see.
6 Verification/falsification:
there will be two condition either aircraft will land on moon or earth will pull down aircraft.
if aircraft will reach on moon then our mathematical modelling is correct this fit for scientific study. if aircraft will pull down by earth then our mathematical modelling is not correct.
now we will have to correct is again till it become correct it happens with scientist after 50 times correction they reach at correct mathematical modelling.
Newton was made a mathematical modelling for sound and calculated value for sound speed which give speed of sound 280 m/s .
which was incorrect actual value of sound is 320 m/s latter we will study it takes many years to make correct formula mathematical modelling .
but we just read in 5 minute we no need to expand year on it this is Science now 6 steps Scientific study is completed and it is important what is scientific study ?? 
So what so far we have seen Scientific study is totally different from illusion so it is called science any natural phenomenon pass in scientific study then it is ok otherwise we not accept it in science and it is illusion.

Define technology Important point for science Development 

                  Physical World 

 

 Science is dynamic nothing is final in science and it is good for human or mankind.
anyone should not rigid on his rules and Laws it may be correct or may not be correct due to this rigidity in Ancient time world has lost a good scientist.
In Ancient time human Church believes was that our Earth is great than other planet even Sun rotate about our Earth and was rigid on their faith that time a young scientist Galileo vision.
He was very fast he told that no Earth rotate about Sun after his announcement stir among church people and was called him heretic and was finally Galileo was under house arrest until his death .
some time passes and latter on it was proved that Earth rotate around Sun but it was late world was lost good Scientist.
so nothing is final in Science we should welcome others new ideas now we have scientific method if it can proof through scientific method then accept it  never rigid on your study and faith.
 
Above picture shown you the light nature what is light and how it travels from Sun to Earth very first Newton explained about light  travels in straight line like arrow from Sun.
latter on Heisenberg experiment and told no light travels like water flows now which one is wrong both of them has done experiment and scientific study latter on it was proved that light has both nature no one is wrong.
  

             #Conclusion:

I hope you enjoyed learning what is science. If this post is helpful for you share , like and comment. As well as having any doubt, ask me i’m always here for your support. Thanks for sharing. 

How to study physics right direction

How to study physics right direction 

We will see here the right method of physics study so that it will be easy for our study physics very interesting
                                                  
How to Study physics
There are two important thrust areas through which our study became easy. Meaning of thrust is focus on that areas to make physics study easy.lets see these two important point.
1 Unification 
2 Reduction
 
Unification: 
Now what is meaning of Unification here lets start unification word is made from unique means one. whatever the quantity we study it should be unique measurement whole over the world and every people of world should use this measurement from any part of the world.take an example for length. One person from rural area come to the cloth shop and told shopkeeper give me five hand Sari another person come and told shopkeeper give me 3 meter Sari third person come and told shopkeeper give me 2 gauge Sari fourth person come and told shopkeeper give me 4 feet Sari. Now think how many measurement shopkeeper will kept and how difficult to manage. take an other example Energy a 5kg mass is lifted 10m height from ground here work is converted into energy of approx 500 joule. we eat food and 2400 calorie every day. we use electricity in our home bill generated by electric department is kwh so we have to study all unit by different department but Physics thrust to use only one measurement for a unique quantity whether is comes from chemical, mechanical or electrical energy unit should be only one so how it will be easy and simple for study Physics we will need to study only one unit rather than four and more. different phenomenon of nature must be explain in single or minimum laws take an example apple fall on the earth we made a law. Earth rotate around Sun we made another law moon rotate around earth we made another law in this manner how complicated will be Physics to study so Physics thrust on different type of phenomenon must be explained by a single law this is called unification here law of gravitation will explain all three phenomenon then how it will become easy now i hope unification method is clear. 


 
Reductionism :   
 
 A Complex process to study which can’t be understand easily then we use Reduction process which state that break the process in small sub process to understand easily.
take an example Coal to generate electricity it is a complex process  now will go step by step.
Coal is combustion will give heat energy.this heat energy is use to boil water and make steam now this steam is use to hit turbine blade now turbine is connected with shaft to generator which produces electricity.
In this world only two forces are prominent gravitational force and electrical force then what about other forces friction force, bouncy force, elastic force these all forces can be explained by prominent force. Einstein desire was to make only one force through which every phenomenon and law can be explained think if it happen how easy will be physics only one law and force will need to Study  how simple will Physics by Unification ? 
 
Scope of Physics :
How big and how small we study in Physics. big is our universe we study this big of mass 10^25m and smallest is atom electron 10^-14m the object we can see through naked eye is called Macroscopic and the object which can’t be seen through naked eye is called Microscopic so in Physics we study as large as universe and as small as electron this is scope of Physics.what is macroscopic the object which is seen though naked eye is called macroscopic example earth, moon, sun, moving car, ball falling under gravity and many more which we see in our nature these all study come under macroscopic. now microscopic is that object which we can’t see through eye but we study and analysis through its characteristics and behavior and made laws for this on the basis of their effect and proof this laws like atom,electron,force, charge. electric field, magnetic field and many more we will study latter.this is complete scope of Physics all object we study.         
excitement of Physics:
The excitement of Physics is all electronics devices which make our life easy entertainment like mobile, computer, tv,  Aeroplane.
now without this no life. new generation is coming with robot in place of mobile they will have Robot in their hand.When the first computer was made its memories was 1Mb storage data and size was as large as our table size compare with today’s era size is compact and memories increases how it became possible due to excitement of Physics development in semiconductor material integrated chips.Physics excitement give us new technology development and enhancement for better and easy life.
 
Physics Relation with other science subject:
 
Real science is Physics other subject chemistry, biology is derived science physics laws is apply in chemistry to make any reaction on the basis of energy and force in atomic structure chain reaction physics decide which reaction will take place on the basis of energy and force so without physics chemistry development is not possible.
Biology development is also not possible without physics whatever study in biology with the help of microscope physics has made microscope through which study of tissue and cells, laser operation, ultrasound, xray, CT scan, MRI all this is given by Physics for the development of biology without Physics biology is lame. what is mathematics it is not science it is powerful tool for every science which help Physics, chemistry, biology. if you really want to study science your choice should be Physics.Even in our human body physics is apply whole human body is working on current principle
nervous system in our brain is like wire when we see an object through eye a current is generated on eye which goes to our brain through nervous system and inform the object.this current value is very small but work same like electricity so how interesting is real science Physics to find out the age of any old object we use carbon dating and radio activity which is also physics.             
Thanks for reading How to Study Physics.
          

What is a simple definition of force | Know Important concept for Force

 Force best definition is here ?  If you want to know, What is a simple definition of force ? then you are at right place. Because i am going to disclose, the hidden concept about force in this topic.  So it may be possible, you are not learn this concept before.
Hence read complete post to know the hidden concept about force. Therefore i ensure  that, you are going to enjoy this topic, because you will get hidden concept about force. So let me start, What are you going to learn new here ?

What is a simple definition of force ?


Well do you know ?  what do you maximum study in Physics ? common This is force. So if you want to learn Physics. Then your concept about force must be clear. And hence i am here to give you that hidden concept about force in this post.

What is force short answer ?


So now let me explain, what is force in Physics world ? You have studies in previous classes some idea about force.  Just recall force is push or pull. And what is meaning of push and pull? Newton has written in his book about push and pull.
But Newton was worry about pull.  Because there is no any pull force.  For an example, when you open the door, then you apply force from front. And this is called push. In other case, when you apply force from back.
Then you say pull.  But wait in both the cases, actually you are pushing.  So just open your eyes. You will understand this, when you pull the door. What you are doing here, think over it, you put your hand, inside the handle of the door and pushing the handle of the door. 
Hence force only depend upon point of contact.  So here in door case point of contact is same. For push and pull. Because at same contact you push and pull the door. If you are having any doubt.  Then what can you pull,  just give me any example.
So you can’t give any action, in which there is purely pull.  But just wait  take an example. When you drop a ball, vertically and that ball come down to the Earth. Can you tell me, what is this pull or push ? common this is pull. i hope you got, what is force ?. 

What is an example of a pushing force ?


Because Earth is pulling, and this is an example of pull.  But scientist Einstein was worry, Why if there is no push, then how ball is falling to the Earth.  And then he made a space theory, Which explain that, in the Universe, there are two things. Hence he told, one is material and other is sky.
So when you take a ball in your hand. Then Earth pushes that ball, and sky also  pushes that ball. But since sky force is greater than, Earth force. Therefore ball come down to Earth. And this is according to modern physics.  Where it is difficult to understand for all.
But don’t worry. Here you need to study classical Physics.  Which is before 1900. And after 1950 modern physics is introduce.  So in 11th class,  you need to study Classical Physics only.  But In 12th class, you will study about modern physics.
Therefore in Classical Physics concept, every object interact with each other in this world.  And this is called force.  So this may be push type or pull type. So when ball is falling under gravity is consider as pull force.  Because Earth is pulling ball.
So that space type theory was not available that time. Hence how many types of forces in classical physics.  Take few examples you study . There are many types of forces. Suppose when  flood came and due to this wall is broken. So this is type of water force.

What do you mean by force give examples ?


you study a man pushes the other man.  And fall on the ground, this is type of muscular force. Again car was running on the road, and  off the engine, then car is stopped.  This is due to friction force.  When you jump in the water, and come up from the water, this is bouncy force. And a iron ball is drop, just  it goes into the water, but when a light plate is just, kept on water it does not sink into water.  this is surface tension force , and many more example of forces.
now what is law in physics study Unification. which is well explained previous maximum phenomenon can be explained.  in a single law so no need to made many force only a single force will explain all these phenomenon. then it will be easy for our study.
scientist has view from starting there should be only a single force through which all the phenomenon can be explain. but all forces are different. how it will be possible to explain through a single force. so  scientist tried to categories sources of different forces. and minimizes force .
lets see a ball falls on the earth this is gravitational force, moon rotate around the earth. this is also gravitational force, earth rotate around sun, this gravitational force, sea water confined in sea does not come out on the road. this is gravitational force each phenomenon try to explain and solved as a single gravitational force. half of the phenomenon in nature was solved by gravitational force.

What are the 4 types of forces ?

now similarly half of the phenomenon was solved by electrical force. when two bodies come in contact then electron exchange between them, one become positively charge and other become negatively charge. wait which body will be negatively charge, it depend upon electron affinity now this two body will attract each other.
friction is electrical force this appears due to, exchange of electron.white washing is also type of electrical force, in this manner scientist analysis all type of forces, and finally come out the conclusion either, it will be a gravitation force or electrical force.  then it was declare that there is only two type of forces through which, all the forces phenomenon can be explain.
now it became easy only two forces, now it was only to search the way of force source, if electron exchange then it is electrical force. take an example viscosity force is also an example of electrical force. now finally scientist were happy having only two forces. but latter on when modern physics introduce.
scientist were study about atom now study of atom found that in an atom there is a nucleus proton, electron proton present in nucleus electron moves in outer orbit proton has positive charge electron has negative charge.

What are the four forces?

Rutherford model about atom explain that proton lives in nucleus. now problem create here all proton lives in nucleus, all proton having positive charge, then there should be a big repulsive force between proton plus charge, repeal each other since electrical force is stronger than gravitational force.
but through experiment it was seen, that many proton living with, each other without any repulsion. how it is possible. now scientist were worry not to explain this force, neither through gravitational nor through electrical force. finally not able to explain then scientist give this third force name “nuclear force”.   since this force is present inside  nucleus. science positive , positive charge was unable to repeal each other. its mean that nuclear force is stronger than electrical force.
after that atom bomb made and nuclear blast, now all scientist concentrated on nucleus study breaking the nucleus and try to find out the smallest particle in nucleus. through which atom is made molecules is made and this universe is made. searching for that smallest particle. some time scientist think atom is smallest particle.
some time molecule, some time nucleus, some time electron confusion was there where it will be last no ideas but continue in search of that smallest particle. Scientist has finally claim that we have found that smallest particle and given name “God particle”. because God has made this nature.

What are types of force?

Now after breaking nucleus all nuclear particle like alpha, beta, gama, meso, these particle also interact with each other but their force is weak in comparison of proton proton nuclear force so finally its name is weak nuclear force and proton proton force is strong nuclear force hence we have finally four forces for study in Physics.
that is in universe in macroscopic study gravitational force and electrical force and in nucleus weak nuclear and strong nuclear force. latter we will study in details about these four forces.basic review gravitational force cause is mass heavy mass having large gravitational force. electrical force cause is charge heavy charge having large electrical forces.
its range is up to infinity means existence in whole universe or both forces are called long range force. nuclear force range is 10^-7m only. nuclear forces are called short range forces.In nature or Physics we study these four forces.Now i hope that force concept will be visualizes. 

Energy Conservation Laws:

What is Conservation laws ? our philosophy is combined with conservation laws.
Energy Conservation Laws

This philosophy indicate us we are not God we are nothing how we are nothing ? its mean that we can’t lift any think by our force we can’t displace anything by our force. we can’t make anything we can break anything this is like Gita discourse. but it is true.this is discourse of Physics. God and Physics little bit difference because Physics is Study of Nature.
And God has made this Nature so we study Nature. which is made by God.Hence when scientist got ultimate particle its named as God Particle. In this manner Physics teaches us we can’t made we can just transfer it.  like whatever energy is available in coal it can be transfer to heat energy process is to combustion of coal.
And transfer it to heat energy and to steam to pressure on turbine bled rotate generator and make electricity but think without providing anything if told to generate your electricity can we produce electricity big no we need to take whether water,diesel, coal,or nuclear from anywhere we have to take energy then it is possible to generate electricity.

What is force in science?

here we can transform one energy to other energy like electrical to mechanical or chemical just transform. see given electrical energy to fan converted into mechanical motion to fan and fan wind energy in form of mechanical so without giving electrical energy we can’t get mechanical energy.
if you will claim i can use my hand for mechanical energy then my answer is you are giving your hand energy from your body which comes from taking food just remember when you was born you was not able to do this activity after taking energy from food you have right now energy in your body so we can only transform energy one form to other form.
it is simple energy is stored in nature we take from one place and put to other place but anytime God comes everyday and count the total energy lets 1000 energy but we have displaced one form to other form and one place to other place we can’t destroyed in night God comes and count how much it will be 1000 so this is called Conservation.
and called Conservation Laws here we are discussing about energy similar for mass one thing break and other thing made.you will question when coal is combustion its mass is destroyed wait carbon is converted into CO2 not destroyed just converted mass is same similarly we can’t make carbon so human should understand difference between God and men.

what is force system

even we can’t make a smallest particle in nature so nature is conserved always total mass or energy will be same anytime.one quantity in physics is also conserved its name is momentum latter we will study what is momentum in details but short view momentum is how fast a body is moving how difficult to stop it take an example.
four bodies are moving with different velocity and collide with each other after collusion each has moving with again different velocity but its momentum is conserved. what so far we have seen conservation three quantity mass, energy and momentum.
now how much charge nature has created we can’t create or destroyed we take charge from powerhouse glow our bulb and return it in form of light.when we rub two bodies one become positive charge and other become negative charge sum is zero.
so in universe same quantity of positive charge and negative charge exist in nature and its sum is always zero we just take charge from one body to put in other body and this is called Conservation of charges again charge is conserved.

Fundamental Rules of Physics:

 

Whatever the phenomenon happen in this world there must be a single cause.If any process takes place their must be a single cause what is that every object of this universe wants to continue in minimum energy level means want to spend minimum energy take an example we go to school if time for class start left is 5m school is far.
then how we will go time is minimum so run fast but time is 1hr then we like walk why because we want to spend minimum energy in walk minimum energy spend.we like to stand in bus rather than walk if we get seat .
then we not stand occupied seat so that minimum energy can spend if we long journey we like to sleep rather than seating or standing so that want to spend minimum energy we like action of minimum energy spend similarly every object of universe want to continue in minimum energy level

why we can’t create Force ?

its is fact that we cant create force then how we apply force the answer is we take force in loan how we take loan take an example when we apply force on a standing car then we stretch our body push the earth through feet backward and earth pushes us forward.
we get loan from earth and pushes the car. if you have doubt you can proof yourself just put banana rind you can’t push the car now because your contact is not with earth same your body and car but can’t push why because you are not taking loan from earth.
then you can’t give the force to car. force always create in pair here one force we pushing earth backward and earth given that force forward to our body as a loan.
Principle of Physics use to make technology:
Using Bernoulli’s theorem aeroplane technology was made.
Using electromagnetic induction electricity technology was made.
Thanks for reading Know Important concept for Force .
If you want to learn more about Physics topic . Then you can refer my previous post. This link is given below.

You can refer this book . This is best book for Physics. Theory as well as numerical are elaborated in best way. So your concept will clear .

Satellite orbital velocity

Satellite orbital velocity

Satellite is an object which is moving around the Earth. There are two types of satellite one is natural satellite made by nature (Moon) and other is artificial satellite which is made by men.
One important point i want to make it clear here from childhood you learn that every planets move around the Sun, Moon moves around the Earth, even any picture of solar system shows all planet moves around the Sun including Earth.
But you will shock, When i will tell you this is technically wrong all planet and Moon does not moves around the Sun and Earth.
 
Then you will ask me if all the planet does not moves around the Sun, which is that body around it all planet moves. And your next question will be if it is wrong then why teach like this wrong concept in book ?
 
Well actually books and pictures shows all planets moves around the Sun is correct, so that you can easily understand the solar system behavior without knowing the technical point.
Now here you will learn around which all planet moves and even Sun moves around which,  
and also why do you teaches that all planet moves around the Sun ? 
 
Planets and Stars moves around the common centre of mass, This common centre of mass is also known as barycenter to understand barycenter you must know centre of mass you can refer my previous post center of mass concept.
Centre of mass is that point at which whole mass of the body or system lies at that point, means body is  balanced, sometimes it can lies outside the body, some time between two masses and sometimes near the heavier mass depends upon the mass quantity and its shape and size, for more details refer above link.


                                                                     

        


                                                                                 
In space every two bodies there is a common centre of mass which is known as barycenter as shown in above picture mass M1 and M2 point C is called barycenter around which mass M1 and M2 will move, Similarly this is the point around which planets and starts also move.
 
For example if you consider the Sun and the Earth then mass of the Sun is about 333,000 times heavier than Earth, so barycenter of Sun and the Earth lies near the Sun centre hence the Earth as well as the Sun move around this barycenter.
So you see from the Earth perspective and feel that Earth is moving around the Sun because this point is near and inside the Sun.
 
When you consider Jupiter planet it is very bigger than Earth, you can think Jupiter mass is 318 times heavier than mass of the Earth. Now if you will consider the Sun and the Jupiter barycenter then this barycenter will lies outside near the Sun, Hence Jupiter and Sun moves around this barycenter and you see a different elliptical path.
 
If you talk about the Solar system including all objects and planets masses then it has own barycenter including all masses.All objects and planets moves around this barycenter, This point is not fixed it change its location depends upon at a particular time where is this all planets in the orbit according to that barycenter location depend.


 
Since Mass of the Sun is very very heavy in Solar system so most of the time barycenter lies inside the Sun. Hence all planets moves around this barycenter and you feel that all planets move around the Sun .Due to barycenter Sun also moves little bit around it.
Barycenter evey year change its location. So this barycenter concept apply for all planet and natural satellite.
 
Take an example of Earth and Moon, You know Earth is very heavy than Moon you can think Moon mass is 1.2% of Earth mass, So barycenter of these two bodies lies inside the Earth approx 4671 km from the Earth centre.
The Moon and the Earth both move around this barycenter. Moon moves around this barycenter but you feel Moon is moving around the Earth. Now i hope you have understand the concept of barycenter,       

Satellite orbital velocity

How Satellite move around the Earth, A satellite must have two things to move around the Earth first it must have kinetic energy and second centripetal force, if this is available for any object then that object can move around the Earth see the picture below.

                                                                 

                                                                 

        


 Orbital velocity is the velocity with which satellite moves in the orbit, Due to centripetal force satellite moves in a circular path.
suppose m is mass of the satellite then centripetal force Fc = mv²/(h+Re) , now this force is balanced by gravitational force, You know gravitational force Fg  = GMem/(h+Re)² 
now equate this two force Fc = Fg  
mv²/(h+Re)  =     GMem/(h+Re)²   ( V = Vo = orbital velocity )   
Vo²  =  GMe/(h+Re) or  Vo  = √GMe/(h+Re)
You also know that g = GMe/Re² so from here GMe  = gRe² now put this value in above equation Vo  = √GMe/(h+Re)  = √gRe²/(h+Re)  = Re√ g/(h+Re) 
This is equation of orbital velocity for satellite, now suppose one more satellite is moving above this orbit, then can you tell me which satellite velocity will higher .
 
Well as from the orbital velocity equation you can see velocity is depending upon inversely distance from centre of Earth , Hence closer to the Earth satellite velocity will be higher and far satellite will be less velocity.

Velocity of satellite closer to the Earth

from above equation Vo =  Re√ g/(h+Re)  near closer to the Earth (h+Re)→Re since h is very very small compare to Re so Vo =  Re√ g/(h+Re) = √gRe = √9.8x6400x1000 = √627.2×10⁵ = √62.72×10⁶ = 7.91×10³ m/s  7.91 km/s.
 
 
I will continue this post with more concepts, i hope you have enjoyed learning satellite orbital velocity, i want your feedback, comment, share  and likes, thanks for sharing, learn and grow.
 
Dated 27th Jan 2019
 

escape velocity

Escape  velocity

In the universe massive bodies have bounded all small bodies with bound energy, Now to escape small bodies from the surface of massive bodies gravitational field influence, You must required a minimum velocity to free small object from massive bodies surface, this minimum velocity is know as escape velocity.

What is escape velocity 

Escape velocity of a planet is that minimum velocity given to an object on that planet due to which it will just escape the planet and will never come back again on that planet.
 
When you through an object from the surface of the Earth, it goes up some height and then start fall back towards  the Earth surface, This happen due to gravitational field attraction by Earth around it.
Earth gravity acts vertically downward continuously and due to this object speed decrease continuously at per second  9.8 m/s and finally reaches at a height at which final speed becomes zero, but gravity acceleration acting downward and then object start coming back towards surface of the Earth similarly every second speed increase 9.8 m/s and finally reaches the Earth Surface. 

 

But when you will through the object with so much high velocity that it will reach very high where gravity pulling effect vanishes and then the object velocity becomes zero that that point object will stop in space and will never come back on the Earth surface that minimum through velocity is escape velocity.


See the below picture.

                                                                 

Escape Velocity

                                                                       

Path of escape velocity

When you through an object horizontally with some velocity that object fall on the Earth surface, but as you increase the greater velocity that object does not fall on the Earth surface but it rotates around the Earth surface in an elliptical path.
But this is not the escape velocity because object is in the gravitational field influence not crosses the gravitational field. 
 
Again you through the object with more velocity then object does not fall on the Earth but rotate in circular path, but this is not escape velocity, object is in the gravitational field influence, it has not crosses the gravitational field.
 
Again you increase more velocity and thrown object horizontally it will rotates in elliptical path around the Earth but does not fall on the Earth due to Earth rotation as the distance fall by object Earth displace the other location.
Hence object fall always the distance but never fall on the Earth surface.
 


Now you through the object with very high velocity such that the object crosses the gravitational field, So in this case the path of the object will be parabola and it will not rotates around the Earth surface it will reach at infinity. It has escaped or crosses the gravitational field now Earth gravitational field will not attract the object and this velocity is called escape velocity.
See the picture below.
                                                                     
Escape velocity curve
Where does Earth gravitational field becomes zero ? Well Earth gravitational field only and only zero at infinity, So to escape the gravitational field thrown object must reach infinity, now at infinity the object velocity will be zero, but at this point Earth will not attract the object.
Imagine before infinity if object velocity will be zero then again Earth will attract that object and will continue to fall and rotate around the Earth.
 
Now this is assumption that in space Earth is available only otherwise other planet will also attract that object. So to escape any object that means that object must reach at infinity.       

How escape velocity is calculated ? 

Escape velocity is calculated using energy conservation, Total initial mechanical   energy equal to total final mechanical energy. You can refer previous post for potential energy concept, I have discussed at infinity potential energy is zero because there is no gravitational field effect.   
 
KEi + PEi   = KEf  + PEf 
1/2mve² – GmMe/Re  =  0 + 0    (gravitational field at infinity is zero so potential energy is zero and at that point object velocity will also be zero, so its kinetic energy will be also zero)
 
So   1/2mve² – GmMe/Re = 0 
1/2mve²  = GmMe/Re  or  ve²  = 2GMe/Re   Vₑ  =√2GMe/Re here G is universal constant Me is mass of the Earth and Re is radius of the Earth so escape velocity depend upon only planet so for different planets its value will be different, it does not depend upon any other things even projected mass.
 
You know g = GMe/Re² so GMe  = gRe² put this value in the above equation Vₑ  =√2GMe/Re  =  Vₑ   = √2gRe   now put the value g 9.8m/s² and Re = 6400 km  you will get  Vₑ = 11.2 km/s .


Vₑ   = 11.2 km/s this is escape velocity . If any mass given this velocity at surface of the Earth it will not come back again on the surface of the Earth.

Escape velocity question

                                                               
See the above picture an object of mass m thrown from height h = Re, then find the escape velocity .
 
You know that to calculate escape velocity for any planet, you must use mechanical energy conservation concept, and for escape velocity just remember that object must reach infinity.
So use these two concept, you can find velocity.
 
Hence mechanical energy conservation  Ui  = Uf  or  (KEi + PEi )  =  ( KEf + PEf )  
1/2mV²e  + (-GMem)/2Re  = 0 + 0 
 1/2mV²e  =     GMem)/2Re  or  V²e = GMe/Re  V’e  = √GMe/Re , you know that Ve = √2GMe/Re hence V’e  = Ve/√2 = 11.2/1.414 = 7.92 km/s
Hence escape velocity v’e  = 7.92 km/s.

Q What will be Escape velocity find in the figure given ?
                                                                     

  
As from figure mass m is to escape from the surface of the Earth, and away from the Sun along the line joining Earth and Sun.

Where Mass of Sun is given Ms = 3×10⁵Me and r is distance between Earth centre and Sun centre and given r = 2.5×10⁴Re , Where Me is mass of Earth and Re is radius of Earth.
it is also given that normal escape velocity from the surface of Earth is Ve = 11.2 km/s .

Now suppose that escape velocity is Ve’, now you know that only in case of Earth escape velocity of any mass is 11.2km/s, but here Sun is also available so you have to consider Earth and Sun together as system and apply conservation of mechanical energy.

Hence Ui  = Uf 
(PEi + KEi )  = ( PEf + KEf )
-GMem/Re -GMsm/(Re+r) +1/2mV’²e = 0 + 0  ( final kinetic and potential energy is zero at ∞)

-GMe/Re – GMs/r + 1/2V’²e  = 0  ( here Re is very very small than r so (Re+r)→r )
 1/2V’²e  =  GMe/Re + Gx 3×10⁵Me/2.5×10⁴Re  ( Put value of Ms and r from above )
  1/2V’²e = GMe/Re +   12GMe/Re  = 13GMe/Re 
  V’²e  = 13x2GMe/Re 
  V’e  = √13x√2GMe/Re  = √13×11.2  (  √2GMe/Re = 11.2 km/s )
  V’e  = 3.6×11.2  =  40.2 km/s
Hence escape velocity will be V’e  = 40.2 km/s.

 
I will continue this post with more important concept, I hope you have enjoyed learning escape velocity. I want your feedback comments, share and likes. Learn more and grow thanks for sharing.

Dated 20th Jan 2019

gravitational potential energy

Gravitational Potential Energy

Gravitational potential energy is an important concept, This energy is invisible you can not see, so most of the time students confused, But in this topic you will learn some new hidden concept about gravitational potential energy, I ensure you after learning this post your all doubt and concept will be clear, Each and every concept about gravitation potential energy will discuss, What is gravitational potential energy ? How gravitation potential energy is calculate and what is it real meaning ? Why gravitational potential energy value is negative What is potential energy at infinity ? So lets start.

What is gravitational potential energy ? 

Actually gravitational potential energy is not define directly any meaning, it define in terms of change in potential energy, so for change in potential energy calculation, you need to do some work.
Hence gravitational potential energy is define as work done bringing a mass from infinity to a certain point in gravitational field. This gravitational field is created by another source mass. If you don’t know about potential.
Refer my previous post about gravitational potential concept
 
See gravitation potential energy is not for a single body or mass, It is always for a system means between two or more masses gravitational potential energy is stored in the system of masses .If you will ask what is gravitational potential energy for a single mass ? 
 
Well for a single mass gravitational potential energy is always zero. Wait you will see how it is zero ? As i have mentioned that potential energy is work done then who does this work ? Well external agent like you or gravitational force both does this work but when work is done by external agent then work value is positive and when work is done by gravitation force its value is negative.
 


Mathematical expression change in potential energy (∆U) = (-work done by internal conservative force) or Uf – Ui  = ∆U=  (-work done internal conservative force).
Now what is conservative force ? conservative force is that force in which wok done depend upon initial and final position it does not depend upon the path, like gravitational force, spring force are example of conservative force.
 
So Conservative forces only posses potential energy, non-conservative force like friction does not posses potential energy.
you must remember during the work done velocity must remain constant hence kinetic energy must not change.

Concept of gravitational potential energy 

Potential energy at infinity (∞) for any types of mass system or any mass configuration is assumed universally zero by scientist. Hence you use the above formula, Uf – Ui  = ∆U=  (-work done internal conservative force)
So Uf – U∞   = (-work done by gravitational force bringing each mass from infinity) so
Uf -0 = (-work done by gravitational force bringing each mass from infinity)
Uf  = (-work done by gravitational force bringing each mass from infinity) important again i am telling potential energy is not for mass, it is for design or configuration which is bringing from infinity to a certain point. see below picture.
                                                           
Gravitational potential energy


See from the picture initially both masses are placed at infinity, where gravitational field, gravitational potential as well as gravitational potential energy is assumed zero.

Now think for first mass m1 to bring from infinity to location as shown. What do you think does any work will required to bring mass m1 ? Well no any work required because there is no any mass, which will attract mass m1, So when you will just touch the mass m1 at infinity it will start moving with constant velocity obeying Newton’s first law every body in rest and motion continue in rest and motion unless and until an external force is applied.

When m1 reaches at location shown in figure then just touch to stop it will stop, Hence in this manner no any work done by external agent or gravitational force, So bringing m1 from infinity to m1 location does not required any work.

Now consider for second mass m2, for this case see m1 is already at location shown, which is created its gravitational field around it, So m1 will attract m2 with gravitational force, let at any intermediate position x between infinity to m1.
  
Hence gravitational force F  = Gm1m2/x²  this force will increase the velocity of m2 so to avoid increase in velocity you need to apply less little force opposite to this force to move m2 very very slowly, So you have to work in this case.

Now see this force F  = Gm1m2/x² , which is variable for different value of x force will be different, so you can not use direct formula of work 
         →      →
W = force.displacement  because here force is not constant, So for this you need to take a very small point dx where force will be constant hence you can write.
           r
∫dw  = ∫F.dxcos0⁰   why angle cos0⁰  because see the direction of gravitational force and                

 displacement in the same direction, limit initial from infinity to r distance from m1
        r                                        r                                      r
w  = ∫ Gm1m2/x² dx  = Gm1m2∫x⁻²dx     = Gm1m2⎣ -1/x ⎤   = -Gm1m2(1/r-1/∞) =  -Gm1m2/r 

∞                                            ∞                                         ∞

                                                                                 
Hence work done Wg =  -Gm1m2/r , who has done this work this work is done by gravitational force, This work done is stored in the system mass m1 and m2 in the form of gravitational potential energy.

Here negative sign indicate both the masses are now bound with each other with potential energy, If you want to separate them ,then you have to do work.First you need to supply energy Gm1m2/r positive then any one mass will separate from bound system.
So gravitational potential energy is always negative for any masses system or configuration which indicate the system is bounded with potential energy.

You can find gravitational potential energy without integration 

Previous gravitational potential topic which link is given above in first paragraph in which i have discussed work done formula is Wext = m∆V where ∆V is potential difference between two point and m is that mass which is bringing from infinity.
 
Hence in second case from above case you are bring mass m2 from infinity , So you can write Work done by external agent  = m2(Vr – V∞)  now put the value potential at r distance due m1,  Vr = -Gm1/r and potential at infinity V∞ you know it is zero.

 Hence  Wext = m2(Vr – V∞)  = m2(-Gm1/r -0) = -Gm1m2/r , So Wext = -Gm1m2/r  this work done is stored in the system in the form of potential energy, This is very powerful formula for work done by external agent calculation.
Same formula is used in electrostatic for work done calculation but basic quantity is charge there So  Wext = q∆V. 

Important point does this energy belongs to a single mass m1 or m2 answer is no it does not belongs to single mass, This potential energy belongs to system of masses m1 and m2.

What is potential energy mgh ? 

Difference of potential energy between two points which is mgh potential energy, you will see here how mgh is calculated ? see the below picture.
                                                                     

Potential energy mgh

potential energy at two level system at surface system between Earth and mass m potential energy is -GMem/Re  and at height h between Earth and mass m system potential energy -GMem/(Re+h) , can you tell me, which energy value is higher at surface or at height h.
Well at height h level potential energy is high because negative sign associated with energy, So when you go up from the Earth surface there is gain in the potential energy.

Recall i have mentioned above first paragraph potential energy is define as potential energy difference, So the difference in potential energy or gain is given as.
Uf – Ui  = ∆U =   (-GMem/(Re+h) – (-GMem/Re) )

∆U  = Potential energy difference  = GMem( 1/Re – 1/(Re+h) )  = GMemh/(Re+h)Re 
Now h<∆U  = Potential energy difference = GMemh/Re²  = (GMe/Re²)mh 
you recall what is formula (GMe/Re²) this is small g so (GMe/Re²) = g 

Hence ∆U  = Potential energy difference = mgh
Hence this mgh formula is basically derived from basic potential energy of the system formula (-Gm1m2/r), This negative sign indicate the force is attractive .So the work done is negative.
See below numerical question for potential energy of the system.
                                                                         


In first question you have to find potential energy of equilateral triangle mass shown at vertices 2kg, 4kg and 6kg.

You know potential energy of the system U  = -Gm1m2/r in this case three combination is possible (2kg,4kg), (4kg,6kg), (2kg,6kg) So apply the formula.

U = -G2X4/1 + (-G4x6)/1 + (-G2x6)/1  = -8G -24G – 12G  = -44G  = -44×6.67×10⁻¹¹ 
U = 293.48x10⁻¹¹ J so this is the potential energy of the triangle system.

Now for second question square find the potential energy of the system.
Can you tell me how many combination will be in square shown, well there will be six combination (1kg,2kg), (2kg,3kg), (3kg,4kg), (1kg,4kg) and two diagonal (1kg,3kg), (2kg,4kg)
Hence total energy of the system will be.

U = -G1x2/1 + (-G2x3)/1 + (-G3x4)/1 + (-G1x4)/1 + (-G1x3)/√2 + (-G2x4)/√2 
U = -2G – 6G – 12G -4G – 3G/√2 – 8G/√2  = -24G – 11G/√2 =  -24G – 7.8G =  -31.8G 
U = -31.8×6.67x10⁻¹¹   = -212.1x10⁻¹¹ J  is the potential energy of the system.

Remember one formula change in potential energy (∆U) = (-work done by gravitational force)  = Work done by external agent .
So  ∆U = -Wg = +Wext.
                                                                     


See the above picture and find the external work done.
use the above formula change in potential energy of the system is equal to work done by external agent.

∆U  = Wext  so Wext  = ∆U = Uf – Ui  now find final and initial potential energy of the system Uf  = -G1x1/2 + (-G1x1)/2 + (-G1x1)/2 = -3G/2 
Ui = -G1x1/1 + (-G1x1)/1 + (-G1x1)/1 = -3G

Wext  = Uf – Ui  = -3G/2 – (-3G) = 3G – 3G/2  = 3G/2 = 1.5×6.67×10⁻¹¹ =  10⁻¹⁰ J
Wext  =   10⁻¹⁰ J this work will be done.

Q Find how much work done is required to free a mass m from Earth field from the surface of the Earth. This question is for you.  


Dated 13th Jan 2019

I will continue post with more hidden concept, I hope that you have enjoyed to learn  gravitational potential energy. I want your feedback, comments and likes learn more and grow. Thanks for sharing.  

            

gravitational force and gravitational constant

Gravitational force and Gravitational constant

Today our topic is very important and interesting because you will know the fact of gravitational force, which you will be not knowing before,Here you will learn hidden facts of gravitational force,I hope that you will enjoy this topic to know the hidden concepts of gravitational force. Here in this topic your all doubt and confusion will be clear, After reading this complete post, I ensure you will feel that you have learned some hidden concepts about gravitational force, which you were not learned before, so lets start to know gravitation force facts.

                                                                           

Gravitational force 


Gravitational Force law history facts


As you know and learned by your teacher saying that an apple was fall on head of  great scientist Newton, He did not ate that apple but started to think , Why did this apple fell down on the Earth ? And after that this gravitational force law was invented by Newton.
This is wrong story but trended in society, You can think and imagine yourself that due to an apple fall no body can make a big universal truth law. This law was not made by a simple apple fall, You can search on Internet the history of gravitational law, This is documentary type of topic, If i will explain in details then this post will become very long, So in short and important contribution of all scientist to develop gravitational law will discuss.

                                                                      

 
                                                                       

Ancient era before scientist Galileo, peoples believe was that Stars, Sun, Moon and other planet all moves around the Earth. Those time peoples were thinking that  Earth is the centre of universe, But after so many hard works and experiment Galileo found that Earth is not the centre of universe, The Earth and other planets moves around the Sun. This was a great invention given by Galileo.
 
Scientist Tycho Brahe studies about the Starts and its motion, He discovered that all Stars also moves in the universe. This was great invention by Tycho Brahe.
 
Scientist Kepler studies about the motion of planets about the Sun, How different planets moves around the Sun and also find out their time period and path of rotation around the Sun and finally discovered three laws, which you will study latter in this post. But Kepler was unable to explain the reason of planets motion,why all planets move around the Sun and also move in different path ?
 
Latter Scientist Newton came  and explain the significance reason for motion of planets, the Earth, Stars and the Moon, And also explained why apple fell down towards the earth, The reason was well explained by Newton.
So you can not say gravitational force law is given by a single man law, Behind this law two to three century are added, All the above scientist have devoted his time and life behind this law,  Then this law was proposed by Newton by significance reason and proof. 
So this law is called by Newton’s Law of gravitation, But it does not mean that Newton is only behind gravitational force law.

 

Newton’s Law of Gravitation                       

This law states that two point masses apply equal and opposite attractive forces on each other along the line joining them. see the below picture ,


From the above Formula F  = Gm₁m₂/r²  it is clear that if m₁ and m₂ will be heavy then force will be more. Similarly if r value will be large then force value will be small.
take an example if you living far distance from your family, Then your parents remember you less some time call you on mobile, but when you live with your parent at home then they call you all the times, means to say when distance is large attraction becomes less, but when distance is small then force of attraction is more ,Think how natural is this law and applicable for all point masses.

 

Gravitational force important points

This gravitational force is a central force means this force will act along line joining their centre as shown in above picture F12(force on m1 due to m2) and F21(force on m2 due to m1), This force act at the centre of mass and act along centre line important concept for force direction. 
Where r is distance from centre to centre for point masses like m₁ and m₂, G is universal gravitational constant and its value G = 6.67×10⁻¹¹ Nm²/kg² 

2  Gravitational force is always attractive force means two point masses attract each other in the universe. But you can think, why gravitational force is attractive in nature ? So the right  answer for this question is the Almighty God made gravitational force attractive in nature to balance the Universe. If the gravitational force are not attractive in nature then planets, stars, Moon all were not doing motion and balances with each other Due to this attractive nature every things on the Earth are stable  even you.
You must think the Earth is rotating then why not you displace from earth and fall down to other planet and in the universe. 
Gravitational force attractive nature is the reason to stop everything fall down to other planet and in the universe. I hope you have got the importance of attractive nature of gravitational force. 

3  Gravitational force is independent of medium, means between two masses gravitation force measured in air, vacuum, water, oil at moon, you will find the value of gravitational force value will be same, Because G is universal gravitational constant, mass will not change and r will also not change so gravitation force value will not change.

4  Gravitational force is same in magnitude but opposite in direction so it is written as 
→          →
F12  =  -F21 .

5  Gravitational force is only valid for point masses like very very small masses not for big and heavy masses. Now this is important point to think over, which masses is big and which masses are small.
So for this concept you must think with respect to whole Universe, every masses in the universe are point masses. Now take two mass one Earth and other Sun these two masses are big and heavy but  distance between these two masses are very very large, Hence these two are also look like point masses with respect to each other and treated as point masses, So gravitational force F  = Gm₁m₂/r² is valid for Earth and Sun. 
But Suppose this distance become small but two masses are big then this formula will not be valid you must remember this point.

6  Significance of gravitational force is valid for heavy bodies, In day to day life you don’t experience learn many things from gravitational law.
for example two point masses attract each other, Then when you walk on the road and other people are also walking on the road. Hence according to this law you and other men get attracted and collide.
You are sitting in your room many masses are in room like TV, computer, fan, Wall all should attract and collide with each other but this does not happen Why ?
Because these all masses are small and Value of G = 6.67×10⁻¹¹ Nm²/kg² which is very very small, Hence this force value become very very small, which you not notice and feel .
But this force act, now in case of heavy masses gravitational force value become big and noticeable.
So gravitational force significance for heavy masses, but it does not mean  you can not use for small masses, in the examination questions are based on small masses on gravitational force because examiner just want to know your concept of gravitational force.

 

Gravitational force questions

                                                               

                                      
From above first question Q1 .
You know that  F  = Gm₁m₂/r² , how you will take step to solve this question, here both mass is identical given from question, but m is not given, so you have to suppose mass m for both the masses because both are identical and made by same material.

Now you see both the mass are spherical, suppose density for both masses 𝛒  hence you can now find mass m = volumexdensity  = 4𝛑𝙧³/3 x 𝛒 since volume of sphere   =4𝛑𝙧³/3


Now apply gravitational force formula   F  = Gm₁m₂/r²  = Gm²/(2r)²  here m1 = m2 = m and r = 2r distance between centre to centre now put value of m in above equation of force you will get  F = Gm²/(2r)²  = G (4𝛑𝙧³/3 x 𝛒)²/4r² here all G , 𝛑, 𝛑 are constant after simplification  F will be proportional  to r⁴  so (c) is correct answer.

Now from question Q2 you have to check which statement given from a to h are correct .
          →             →       →                               →
(a)   F12  = – F21   F12 = GmM/r²i^ and F21 = –GmM/r²i^ you have already seen this statement is correct, because forces are same in magnitude but opposite in direction.
                                                                               →     → 
(b) Fnet = 0 now you see from from expression   F12 +F21 = 0 this means that total external force on the system is zero F12 and F21 are internal forces so this is also correct statement.
       →      →
(c)  a₁₂  = a₂₁  for this calculate a₁₂ = F/m  = GmM/(mr²)  = GM/r² so a₁₂ = GM/r² now similarly calculate acceleration  a₂₁  = F/M  = GmM(Mr²)  = Gm/r² so  a₂₁ =  Gm/r² hence clearly seen that a₁₂ value is not equal to a₂₁, you can also feel one mass m is small and mass M is big, force on both mass is same which one will move faster obviously small mass will move faster so its acceleration will be more than acceleration of M so this is wrong statement.
       →
(d)  acₒₘ  = 0  that is acceleration of centre of mass, Since Fnet on the system is zero so acceleration of centre of mass must be zero. where as both the mass have different acceleration but centre of mass acceleration will be zero how and why ? this is beauty of Physics .You have already studies in previous post for reference you can refer centre of mass   Why answer is very simple. 
You have already studies when Fnet = 0 means net force on any system is zero then acceleration of centre of mass will be zero.
How for this you have already studies in previous post if you not please refer centre of mass post, where centre of mass formula   acₒₘ = (m₁a₁+m₂a₂)/(m₁+m₂) now you have already calculate a₁ and a₂ value above and here m₁ = m and m₂ = M put the value in equation
acₒₘ = (m₁a₁+m₂a₂)/(m₁+m₂) , you will get  acₒₘ = 0 . So you can understand by any point either by why or by how but result will be same. 
Hence this statement is correct .
     →      →
(e) V1  = V2  = 0  this is clearly seen that both the masses have different acceleration a₁₂ and a₂₁ so their individual velocity will not be zero, So this statement is wrong without any doubt.

(f)  Vcom  = 0  Since  acₒₘ = 0 so velocity of centre of mass Vcom will be constant it will not be zero. hence this statement is wrong.

(g) Vcom = constant , This statement is correct .

(h)  V1  = V2  = constant , This statement is wrong because both the masses have different acceleration  a₁₂  and  a₂₁ so their individual velocity will not be constant.
But centre of mass velocity will be constant.

 

Does the Earth accelerate towards you ?


Does the Earth accelerate towards you, when you jump from a height ? You may find it hard to digest but the correct answer is Yes. You don’t see and feel the acceleration since it is very small, but you do move the Earth just like the Earth moves you due to gravity, let me explain see the below picture.

                                                                         

There are equal and opposite forces on you and the Earth due to Gravitational attraction 

Gravitational force acts between all objects with mass. The simple facts that an object has mass means that will attract with other object with mass. As you have seen the gravitational force magnitude between the objects depends upon their masses.

Larger the masses of objects, larger the force of attraction between objects. Your weight is the attractive pull forces between you and the Earth.
 
You know according to Newton’s third law of motion. The magnitude of force on you due to the Earth pulling on you, is the same magnitude as the force on the Earth due to you are pulling on it. Means to say there are two forces acting and they are equal in magnitude, one acting on you and other acting on the Earth.
 
When you jump, falling towards the ground. When you are falling, you are accelerating towards the Earth due to the pull force of the Earth on you. Since there is also an equal force on the Earth, It starts to accelerate towards you.
 
However the effect of these two forces on you and the Earth are rather different and this is due to the relative difference in the mass of you compared to the Earth.

 

Earth accelerate towards you  

 

 The mass of the Earth is approximately 6,000,000,000,000,000,000,000,000 kg. that is 6×10²⁴ kg , Now the average human has a mass of 62 kg. So the mass of the Earth is relative to you is very very very large.
Now you know from Newton’s second law, for a given forces F = ma on an object the acceleration reduces as the mass of the object increases. 
Hence it is easy to see that the acceleration of the Earth compared to you, When you are falling is incredibly small. However the Earth still accelerates towards you even if it is very small.

 

Gravitational force application

                                                                     

Gravitational force application

From the above picture two body of mass 10kg and 5kg are initially at infinite distance and both are at rest. After releasing both the masses start to move towards each other due to gravitational force of attraction.

At any time it is found that the velocity of 10kg mass is 4m/s, then what will be velocity of mass 5kg ?

How you will solve this types of question, apply the concept there are two state one is initial and other is final. Now see the net external force in both the cases is zero, You must remember that gravitational force is internal forces between two masses not external force.

Hence Fnet = 0 so acceleration of centre of mass acom =0, Then velocity of centre of mass Vcom = constant. Big concept Vcom is constant means if it is initially zero then finally it will be also zero. So find out initial Vcom = (m₁v₁ + m₂v₂)/(m₁ + m₂) but as you see initially both the masses are at rest so v₁ = v₂ = 0 , Hence Vcom = 0  (Initially).

This means that final Vcom will be also zero because Vcom must be constant, So now find final Vcom  = (m₁v₁ + m₂v₂)/(m₁ +m₂)  for final case v₁ = 4m/s and v₂  =v and m₁ = 10kg and m₂ = 5kg also Vcom = 0, now put in above equation you will get.

0 = (10*4 + 5*v)/(10+5)  or  v = -40/5  = -8 so  v  = -8m/s .

Understand Concept individual both masses will have acceleration and velocity but acceleration of the system will be zero and velocity of the system will also be zero as Vcom is zero.  

Superposition of Gravitational forces

Superposition of gravitational forces means, You know that among every two point masses gravitational forces acts, but think if there are more than two masses then what will happen ? how gravitational forces will acts on the system of point masses.
This is done by superposition principle. According to superposition principle, you take a single mass and rest all masses of the system will attract that single mass, Add all the gravitational forces by vector addition rule on a single mass due to other point masses.
This is superposition principle, see the below question.
                                                                             

                                                                     
 From the above picture, you have to find the net forces on mass m and 2m. From the question it is given triangle is equilateral having side length a. So each angle of triangle is 60º.

Now first calculate net force on 2m, as shown in the figure on 2m two force are acting due to two masses m. So the net force on 2m  is F and F angle between them is  60º., so now you can calculate by using vector resultant formula.

Fnet  = √(F² +F²  +2*F*Fcos60º)  =  F√3, Hence net force on 2m will be √3F
Now you know for gravitational force F = Gm*2m/a², So Fnet  = 2√3Gm²/a².

Similarly net force on mass m, here also two forces acting on m, F1 and F so F1  = Gm*m/ a². or Gm² / a²., F = Gm*2m/ a²  = 2F1 .
Hence again use the resultant formula Fnet  = √(F1² +(2F1)² +2*F1*2F1cos60º) =  √7F1 
Net force on m  = √7*Gm²/a². So in this way you can find out net force on any mass by using superposition principle.

 

Why Gravitational force is applicable  only for point masses ? 

According to Newton gravitational force formula is only applicable for point mass, Everywhere i have mentioned point mass.

Now this is time to understand feel of point mass important concept about gravitational force, You will learn the best concept for point mass here.
See the below question to explain the concept of point mass for gravitational force.       
                                                                     

Gravitational force acts on point mass 

From above picture, How you will try to solve gravitation force between rod of length L and mass M and a point mass m.

Think rod is not a point mass its mass is distributed over the length L so what you will do to solve, The whole mass of the rod will be at centre of the rod, So you can suppose the whole mass of the rod at centre M, Now the distance between M and small m will be (L/2 +a) because length of the rod is L.

So gravitational force between rod and small m will be  = Fg  = GMm/(L/2+a)² 
Hence gravitation force Fg  = GMm/(L/2+a)²  if you have done this then you are WRONG 
now you will ask why this is wrong ?

Applying centre of mass concept is wrong here because every mass of the rod is not attracting the small mass m with equal force.
Remember gravitational force formula  F = GmM/x²  inversely proportional to x this means that the distance x is less force of attraction is more.
See from the picture mass divided into small dm, dm₁, dm₂ ……  If all this mass get attracted with same force then your logic of centre of mass was correct but you see here all mass will attract with different force because distance x will be different for different dm,dm1,dm2,dm3………. dm will be more attracted than dm1, dm2 …. and so on .

So some masses near small m are attracting more and some masses are far small m will attract less. Hence rod one side more attraction and other side less attraction so your logic for centre of mass is wrong here because x is inversely proportional.

But your logic was correct in case if the distance was directly proportional for example in case of potential energy U = mgh¹ here h power 1 . Hence here your logic will be correct .

So how you will solve this question, applying the concept of small mass dm so Newton explained that gravitational force formula is only valid for point masses.
Now i hope your concept for point mass is clear.

So from the picture a dm mass taken at a distance of x hence gravitational force on dm due to m mass will be Fm  = Gmdm/x² , now this formula is valid because dm is very vey small mass like point mass. 

So divide M of length L in many small dm masses, Now according to superposition principle if there are many point masses then net force will be vector some of all the forces.
Hence Fnet will be  like this.               
→         →        →         →                          
Fnet  = Fdm₁ +Fdm2 +Fdm3 +……………….                           
All small dm will attract mass m in the same direction so simply add all forces removing vector symbol   Fnet  = Fdm₁ +Fdm2 +Fdm3 +……………….  
Now you know how to add this types of small quantity tell me, I hope your answer will be by integration so use integration.

∫dF   =∫ Gmdm/x²   now check limit first dm start at distance a and last dm end at distance (L+a) so limit will be from ‘a’ to (L+a) hence .

          L+a                       L+a
∫dF   =∫ Gmdm/x²  = Gm∫dm/x²   now there is a problem you can not integrate dm with x² so
          a                           a
for this you have to change dm in term of x, use unit mass concept for L length mass is M so for dx length will be dm  = M/L*dx so put this value in above equation .
                  L+a                L+a 
Fnet  = Gm∫dm/x²   = Gm∫M*dx/L*x²
                 a      L+a               a            L+a
Fnet  = GmM/L ∫ dx/x²  = GMm/L⎜-1/x⎥
                        a                                   a
After putting value of limit you will get  Fnet   = GmM/(a(L+a))  

This will be gravitation force on small mass m due to rod of length L and mass M                   Now i hope you got the concept of point mass importance for gravitational force.                                                                 


Now for this moment i hope you have enjoyed learning gravitational force and gravitational constant. I will continue Gravitation post with more concepts and questions wait. 
I also want your feedback through comment like and shares Thanks.  

Dated 3rd Dec 2018

         

conservation of momentum

conservation of momentum

Conservation of momentum is very important topic of Physics because conservation of momentum concept state second law of Newton.We will see how Newton’s law was derived from conservation of momentum.In our previous post we have already studies about conservation of momentum formula and its basic concept, You can refer the previous post for basic concept and definition of conservation of momentum concept for conservation of momentum. In this topic we will cover the application of conservation of momentum as well as its numerical problems.So lets start.

Conservation of momentum for a system

Linear conservation of momentum, we know that any rigid bodies system is made by collection of many small particles, Take an example of rotating wheel of a car, Another example rotating ceiling fan.


When we observe this rotating bodies, Then we found that there are many small particle, Which are rotating with different speed in different radius.
If anybody ask find the speed of the rotating wheel,Then what will be your answer, Which small particle speed you will answer this is really difficult, So to make this simple, we answer the speed of center of mass of the rigid body.
Because whole mass of the rigid body is concentrated at the centre of mass. we have already learn in previous post . So whole body is consider as a system and its internal small particle conservation of momentum gives the whole body conservation of momentum.
We will see how these two conservation of momentum is same, just wait see the below picture.
                                                                     
Conservation of momentum
 
In Centre of mass post we have studies that how to find the centre of mass for small point mass, So i am just using that concept.
We know that centre of mass general formula is given as rcom (centre of mass) .
 
rcom  = (m₁r₁+m₂r₂+m₃r₃+………………….+mₙrₙ)/(m₁+m₂+m₃+…………….+mₙ)
Now  differentiate this equation with respect to time on both side then we will get 
d(rcom)/dt  = (m₁dr₁/dt+m₂dr₂/dt+m₃dr₃/dt+…………..+mₙdrₙ/dt)/(m₁+m₂+m₃+……….+mₙ)
we know  dr/dt  = velocity = v so we can write the above equation as 
Vcom  = (m₁v₁+m₂v₂+m₃v₃+…………..+mₙvₙ)/(m₁+m₂+m₃+……….+mₙ)
 Now arranging the equation we can write like this.
(m₁+m₂+m₃+……….+mₙ)Vcom  = m₁v₁+m₂v₂+m₃v₃+…………..+mₙvₙ
 
 (m₁+m₂+m₃+……….+mₙ) = total mass of rigid body =M as shown in above picture  so we can write as 
MVcom  =  m₁v₁+m₂v₂+m₃v₃+…………..+mₙvₙ now as shown in above motion picture momentum of different small particles m₁v₁, m₂v₂, m₃v₃  hence If we want to write momentum of the system can write  Psystem  = MVcom . p = mv


Whenever we want to write momentum of a rigid body then we take whole mass of the body and velocity of centre of mass product as state above.Hence now we can write 
→               →  →  →                            →
Psystem  = p₁+p₂+p₃+……………………+pₙ
 
Hence total momentum of a body is equal to vector sum of momentum of individual particles.
                                                            

*** Conservation of momentum definition by centre of mass

 We have just written the equation 
Vcom  = (m₁v₁+m₂v₂+m₃v₃+…………..+mₙvₙ)/(m₁+m₂+m₃+……….+mₙ) 
Now if total external force on the system is zero then Fnet = 0
What does it mean individual force on the particles are zero ? answer is Big no it indicate that total force on the system is zero.
It also indicate that centre of mass acceleration is zero that is if Fnet = 0 then acom = acceleration of centre of mass = 0 .
It also indicates that Vcom = velocity of centre of mass is constant 
 
Now from the equation  
Vcom  = (m₁v₁+m₂v₂+m₃v₃+…………..+mₙvₙ)/(m₁+m₂+m₃+……….+mₙ)  = constant so arrange 
m₁v₁+m₂v₂+m₃v₃+…………..+mₙvₙ = (m₁+m₂+m₃+……….+mₙ)*constant 
here mass total mass is also constant so finally we can write 
m₁v₁+m₂v₂+m₃v₃+…………..+mₙvₙ  = constant
p₁+p₂+p₃+……………………+pₙ  = constant or we can write 
Psystem  = constant 
 
Hence this prove that if total external force on a system Fnet =0 is zero then momentum of the system remains constant.
So momentum will remain conserved and this is called conservation of momentum. I hope you have got the concept behind conservation of momentum.

Conservation of momentum for internal particle 


Don’t be confuse internal particle momentum can change one ball will hit other ball and there momentum can change, But the whole system momentum will not change, It will remain constant forever if external force on the system is zero.

Conservation of momentum by Newton’s second law 

Newton’s second law state that rate of change of momentum is equal to net force 
Fnet  = ma  = mdv/dt = dp/dt  ( we know p = mv or dp = mdv partial differentiation )  
Fnet  = dp/dt  ( This is applicable for a single particle as well as for a system )
 
Now if external force Fnet = 0 then we can also write dp/dt  = Fnet = 0 so 
dp  = 0 or p = constant or Psystem = constant.
Hence Newton’s second law conservation of momentum.

Conservation of momentum application 

When we fire a bullet conservation of momentum is apply here before firing bullet gun and bullet momentum is zero, as we fire bullet then bullet got a momentum with high speed to cancel this momentum gun get backward same momentum so that momentum is conserved.
How momentum is produce ? force is cause to produce the momentum without force momentum can’t be produce.
Rocket lunch also work on conservation of momentum it thrash the smoke back to get momentum forward so that the momentum can be conserved.
There are so many application of conservation of momentum.

Numerical problems based upon conservation of momentum.

See the picture below and find the velocity of mass M.
                                                                         

                                                          

As from the question nuclei was initially at rest no any external force acting on nuclei system hence its initial momentum will be zero . Now as the alpha particle will come out so it will get momentum in forward direction,now to remain momentum conserve remaining nuclei will get jerk in backward direction. 
So we can apply the conservation of momentum as net external force Fnet =0 on the nuclei.
Hence initial momentum = final momentum  or Pi = Pf  so we can write here Pi =0
0  = mv -Mu (here direction of velocity of nuclei is in opposite so it is minus )so u = mv/M this will be velocity of remaining nuclei in the backward direction.
Similarly you can use conservation of momentum for gun case initially gun was at rest so Pi = Pf here Pi =0 hence use the equation .
0  = mv -Mu or u  = mv/M 
I hope you have got how we use here conservation of momentum.

How to solve question by Conservation of momentum

                                                                   
 


From first question car is already moving with velocity v, It is not necessary always system or body will be in rest position, here car and cat to be consider as system.
Cat drop on the roof of moving car with very slowly u =0 or zero velocity. So here momentum of the system will remain constant.
Hence apply conservation of momentum Pi = Pf now Pi is initial momentum of the system Pf is final momentum of the system. 
Pi = initial momentum of cat + initial momentum of car = m*0 +M*v  = Mv
Pf =  final momentum of cat and car together = (m+M)u here u is velocity of car after landing of cat on roof of car. Some momentum of car will be taken by cat so some momentum of car will decrease. 
now equate the initial and final momentum Pi = Pf   
Mv  = (m+M)u or u  = Mv/(m+M) this will be new  speed of car after landing cat.
 
Now from second question trolley and man are initially at rest. As shown from the picture man is standing on trolley.
there is no any external force on the system hence momentum of the system will remain constant, so we can apply conservation of momentum.
Pi = Pf  here Pi =0 because initially system is at rest 
Pf = final momentum of man + final momentum of trolley .
Here i will ask what do you think about final momentum of man ? is it will be mass of man and product of its velocity that is 20*2 = 40 ? Big no
If you think like that then you are wrong but why ?
Here speed of man given with respect to trolley and if suppose trolley will move with velocity u in backward direction it will be with respect to ground.
So two different frame of reference you are doing calculation which is wrong . So we will have to take same frame of reference for trolley and man ground as frame of reference. 
 
Hence we need to calculate velocity of man with respect to ground which will be (2-u)  because man is moving with 2m/s forward on trolley but trolley is moving backward with u velocity with respect to ground.
Hence a person standing on the ground and observing velocity of man observer will observe slow speed of man and that will be (2-u).
Hence we can find the final momentum  Pf  = 20*(2-u) -10*u  = 40 -20u-10u  = 40-30u
 
Pi = Pf  = 0  = 40-30u or  u = 40/30  = 4/3  = 1.33m/s 
So this will be speed of trolley in backward direction.
Hence this is the concept you will solve question by conservation of momentum.
                                                                
From the above picture question is given as 
 
Q m slide on 10m without any friction and 10m is kept on frictionless surface . Find the velocity of m just reaches the bottom surface.
 
Solution Think and tell me we can apply here conservation of momentum .Is net force on the system is zero ? Answer is no net force is not zero, normal contact force between mass m and 10m is zero but mg external force is acting on the mass m which is external force.
 
So it is clear that external net force is not zero. Then what do you think now we can apply conservation of momentum yes or no.
Answer is yes we can apply conservation of momentum how ? see mg external force is acting along y axis but net force along x axis is zero so we can apply conservation of momentum along x axis, this is concept remember, momentum is a vector quantity so Conservation of momentum can apply along any particular direction whenever net force along that direction is zero.
 
Now suppose when m block reaches at bottom its velocity is v with respect to ground and this block pushes 10m in back direction hence 10m velocity is u in backward direction with respect to ground.
 
Conservation of momentum along x direction.
Pix = Pfx  initially system is at rest hence Pix = 0   now final momentum 
Pfx  = mv – 10mu = 0 or v = 10u  now here two variable v and u but only one equation so we will find one more equation.
 
Now think when block reaches at bottom point then mass m has kinetic energy and 10m has also kinetic energy, from where this kinetic energy has came. So we see that block m lost its potential energy and that potential energy converted into kinetic energy.
So we can apply conservation of mechanical energy. Yes we can apply conservation of mechanical  energy here because mg force is conservative force but you should remember that conservation of mechanical  energy is apply only where all forces must be conservative and no any external non conservative force acting on the system.
 
So we can apply here conservation of mechanical energy Mi = Mf 
Ui +KEi  = Uf +KEf 
mgR +0  = 0+ 1/2mv² +1/210m*u²  
gR  = v²/2 +10u²/2   now replace u  = v/10 and put g = 10m/s², R = 22m and solve the equation
v² = 20*20  v  = 20m/s  this is velocity of mass m at bottom.
 So you have got the concept for conservation of momentum use in problem.      
 
Now we will continue in next post. I hope you have enjoyed learning Conservation of momentum. If you like comment and share, thanks for reading and sharing learn and grow.
 
Dated 17th Nov 2018    
 
                 

What is meaning of collision in physics

What is meaning of collision in Physics?

Collision is important and interesting topic of physics, If you have already studies previous post like centre of mass, conservation of momentum and your concept is clear then you will enjoy learning collision. We will study from basic concept of collision to depth concept of collision step by step in easiest way so that you can understand complete concept of collision, don’t worry your all doubt and confusion will clear about collision and you will learn some new concept of collision in this post. If you don’t know about conservation of momentum then i will suggest you to refer post conservation of momentum concept  so lets start collision.


What is meaning of collision in details?  

The meaning of collision in Physics is not like that two bodies collide together.The real meaning of collision is if any one body velocity effect the other body velocity or one body momentum effect other body momentum, it is not necessary to collide with other body but effect the momentum of other body is called collision. 
But in our syllabus all question will be based upon the collide cases in which the momentum will exchange.So collision is an event in which two bodies strike each other applying large force for a small time.
So all the story of collision will be based upon the momentum, Hence any kind of collision you will apply conservation of momentum to the system, Why system ? because a single body can not collide itself at least two body required so two body system.
Hence the initial momentum of two body will be same as final momentum of two body and will also be same in between initial and final position.
So momentum remains conserved throughout the collision 
We see example of collision in day to day life like when we drop a ball on the ground it reaches the ground and strike the ground then bounce back to some height. The time at which ball strike the ground that event is called collision see below picture.

                                                                 

Collision

    

                                                         

What happens during collision ? 

In collision elasticity comes into play, see how elasticity work ? when ball strike the ground then ball compress like spring, then inside the ball elasticity forces is produce and to restore the ball shape elongate like spring and ball bounce back some height, This happens in every collision and body separate away in this way after collision.
 
What are changes during collision ? mass of the body does not change, Velocity of the body changes it may decrease or increase depend upon the collision condition.
Now related to velocity we study in Physics two important quantity momentum (mv) and kinetic energy (1/2mv²) so there may be changes in momentum or there may be changes in kinetic energy and on the basis of this we study and have done classification of collision.             

Why necessary to study collision ?

Collision study is necessary because in our daily life, we see many objects collide with other objects so around us many thing are colliding and collision is happening.
These collision may be for very small particles like air particle, Which we are unable to see but these air particle collide. We feel that air comes from one side and collide with wall after that we don’t see what happens ?.


 
So after study collision, we will see what can happens after collision. In this way big object also collide.
Hence small and big both object collide, What will be their result that is we are going to study in collision.
Now see the above picture, When a ball is drop from some height h1 to ground its velocity increase with time time due to acceleration of gravity, When the ball approaches ground this velocity is called relative velocity of approach, Then ball hit the ground and bounce back with some velocity now this ball is separating from ground this velocity is called relative velocity of separation. If relative velocity of approach and relative velocity of separation values becomes same then ball must bounce back the same height but we observe normally this not happens, Ball bounce less height so it is clear that relative velocity of separation becomes less than relative velocity of approach.

 

Hence in any event of collision there is a relative velocity of approach then collision occur and then relative velocity of separation .
These relative velocity of approach and relative velocity of separation may or may not be same  So we made a quantity to measure this value which is called coefficient of restitution.
 
Which is define as ration of relative velocity of separation to relative velocity of approach,
e = Coefficient of restitution = (Velocity of separation)/(velocity of approach)                                                                                     

                                                                 

Now from above picture value of e may be 0, e≤1, maximum 1 and based on it we categories collision types which we will study now.   

Types of collision

There are mainly two types of collision, which we will study in this topic.


1 Elastic collision 

In Collision there are three quantity involve, first is momentum (mv) second is kinetic energy (1/2mv²) third is total energy.
(a) In this collision momentum of system is conserved that is m₁u₁+m₂u₂ = m₁v₁ + m₂v₂.
(b) Kinetic energy is also conserved that 1/2m₁u₁² +1/2m₂u₂² = 1/2m₁v₁² +1/2m₂v₂².
(c) Total energy is also conserve.
 
Important point kinetic energy does not remain constant through the collision at the time of collision kinetic energy loss in deformation of body and again regain the original shape of body then kinetic energy regain, Hence initial and final kinetic energy will be same in elastic collision.
We assume that this is perfectly elastic collision. now we will solve momentum equation and kinetic energy equation to derive important facts about elastic collision.
 
m₁u₁+m₂u₂ = m₁v₁ + m₂v₂ arrange this equation m₁ one side and m₂ other side so we can write as  m₁( u₁- v₁)  = m₂(v₂- u₂)  say this equation number 1.
Now take kinetic energy equation 1/2m₁u₁² +1/2m₂u₂² = 1/2m₁v₁² +1/2m₂v₂² cancel 1/2 and arrange same like  m₁ one side and m₂ other side then we can write 
m₁( u₁²- v₁²)  = m₂(v₂² –u₂²) or  m₁(u₁- v₁)*(u₁+ v₁)  = m₂(v₂- u₂)*(v₂+ u₂) say this equation number 2,
 
Now divide equation 2 by equation 1 we will get like this
m₁(u₁- v₁)*(u₁+ v₁)/m₁( u₁- v₁)  = m₂(v₂- u₂)*(v₂+ u₂)/m₂(v₂- u₂) 
(u₁+ v₁)  =  (v₂+ u₂)  or arrange this  ( u₁-  u₂)  =  (v₂- v₁)  this is very important equation .
 
 u₁-  u₂) is called velocity of approach 
 (v₂- v₁)  is called velocity of separation 
Hence in case of perfectly elastic collision velocity of approach = velocity of separation or 
 
(v₂- v₁)/u₁-  u₂)  =  velocity of separation/velocity of approach = 1 =e

                                                               


As from the first question we have to find v₁ and v₂ after collision, We assume that this is perfectly elastic collision.
Hence use the equation u₁-  u₂ =  v₂- v₁ now put the value of  u₁ and u₂ in this equation we will get  5- 2  = v₂- v₁  or 3  = v₂- v₁ say this equation number (1).
Now here two variable v₁ and v₂ hence two equation required to solve the value of v₁, v₂.
So use one momentum equation m₁u₁+m₂u₂ = m₁v₁ + m₂v₂ because momentum is conserved so we can write .
2*5 +3*2  = 2v₁ +3v₂  or  16  =  2v₁ +3v₂ say this equation number (2) .
 
Now using equation (1) and equation (2) from (1)  v₂ = 3+v₁ , now put the value of v₂ in equation (2) we will get   16 = 2v₁ +3(3+v₁)  or  16  = 2v₁+9+3v₁ 
16 – 9  = 5v₁ or  7 = 5v₁  or  v₁ = 7/5 =  1.4  or  v₁ = 1.4m/s 
Now put the value of v₁ in  v₂ = 3+v₁ so  v₂ = 3+1.4  = 4.4 hence v₂ = 4.4m/s.
So this is velocity of ball after collision.
 
Now for second question we have to find mass m which is at rest .
This is also elastic collision hence we can apply similar equation to find the value of m.
u₁-  u₂ =  v₂- v₁  now put the value here u₁ = u , u₂ =0 , v₂ = v , v₁ = -u/3  see from the above picture given value put in the equation  u₁-  u₂ =  v₂- v₁ .
u-0  = v-(-u/3)  or  u  = v+u/3  or  3u = 3v+u or 2u  = 3v  say this equation (1)
Now use the equation of momentum conservation 
1*u +m*0  = 1*(-u/3) +m*v  or  u =  -u/3 +mv or  mv = 4u/3 say this equation (2) 
 
Now from equation (1) v = 2u/3 put v value in equation (2) we will get 
m*2u/3  = 4u/3  or m =2kg this is mass of second body at rest.

Elastic head on collision case

Now take the equation u₁-  u₂ =  v₂- v₁  (1) and  m₁u₁+m₂u₂ = m₁v₁ + m₂v₂   (2)
from (1) we can write  v₂ = u₁-  u₂ +v₁  now put value of v₂ in equation (2) so we will get
 
m₁u₁+m₂u₂  = m₁v₁ +m₂(u₁-  u₂ +v₁)  or 


m₁u₁+m₂u₂  = m₁v₁+m₂u₁ –m₂u₂+m₂v₁  now arranging we can write u₁ one side and v₁ other side 
m₁u₁ – m₂u₁ + m₂u₂ + m₂u₂  =  m₁v₁+ m₂v₁  or 
u₁(m₁-m₂) +2m₂u₂   = v₁(m₁+m₂)  
v₁   =  u₁(m₁-m₂)/(m₁+m₂) +2m₂u₂/(m₁+m₂)   say equation  (3)
Now putting the value of  v₁ then we will get the value of v₂
v₂  =  u₂(m₂-m₁)/(m₁+m₂) +2m₁u₁/(m₁+m₂)  say equation   (4)
 
Now we will apply conditions  if mass of two bodies are same m₁ = m₂ = m then see what will happens v₁ and v₂ in equation (3) and (4)
 v₁ =  u₂  and  v₂  =   u₁  this is important result for elastic collision here we see that velocity is exchange after collision if mass of two body are same.
 
Now second condition if  m₂>>> m₁  and  m₂ is initially at rest then what will happen  find out v₁ from equation (3)  here m₂ is at rest means u₂ = 0 and m₁→0 comparison of m₂ so we will get  v₁ = – u₁  this indicate will return with same speed in opposite direction 
example for this case a heavy truck is at rest and one person on bicycle going to hit the track then what will happen truck will not move at all, but the bicycle person will return back with same hitting speed.
Now you find  v₂ it will becomes zero v₂ = 0 its clear that truck will not move.
 
Now take opposite condition if  m₁>>> m₂ and m₂ is at rest ( u₂ =0 ) then find v₁ and v₂ .
This case is like a person are standing or is at rest and truck is hitting the person what will happen here you calculate  v₁ = u₁ and  v₂  = 2u₁ this indicate that truck will move with same velocity but standing person will get twice velocity of truck.
 
So this is conclusion  that heavier mass has no effect of change of its momentum  when it collide with lighter mass in both the cases lighter mass has got effected.
 
So i hope that you have got the answer when air particle collide with wall what will happen ?


2 In-elastic collision 

(a) In this collision momentum is conserved m₁u₁+m₂u₂ = m₁v₁ + m₂v₂
(b) Kinetic energy is not conserved 
(c) Total energy is conserved 
 
Now we will continue in next post. I hope that you have enjoyed learning  What is meaning of collision in physics. If you like comment and share thanks for reading and sharing. Learn and grow.
 
dated 23rd Nov 2018 

         

Electromagnetic Waves Best Examples Physics Theory

Electromagnetic waves  Physics Theory is a special gift of nature. So You are going to learn here the best concept of Electromagnetic Waves in simple and with Easy Examples. 
What is Electromagnetic waves ?.
How does electromagnetic waves is created ? As well as Types of electromagnetic waves . And Application and uses of electromagnetic waves.
How electromagnetic waves propagate in the space ? History and depth concept of electromagnetic waves.
Keep reading the most important concept for Electromagnetic Waves. Which you will never forget. 
This is very important topic of Physics and really very interesting, I hope and ensure you will enjoy to learn electromagnetic waves.
This will be long post but i will suggest you to read complete post, so that you will never forget about electromagnetic waves.
so lets start, What is Electromagnetic Waves.

Electromagnetic waves is a special gift of nature



This world work on nature principle, Today you are able to talk 1000 km far distance with other peoples sitting in other countries,
Even you can see them. You can go other country in few hours. You can get any information within second.
You can know and get information about planets, stars which are very very far distance from you with the help of science.
You know from Physics concept nothing is at absolute rest or in absolute motion in this universe, always taken one body with reference to other object,
So rest and motion is always relative, Now you will ask if Earth is moving then why not my home location change ?
your home always find at a fixed location this is because you and earth are in same reference frame,
in more details i want to say your home location is not changing with respect to surrounding. 
so you feel your home is at rest and is fixed at a point but if you will see from the Sun then you will find your home location is changing due to the Earth rotation.
For more details about relative motion your can refer the previous post Relative motion concept
When reference is change then speed of object is change but this is not valid with light speed it does not depend upon reference frame and light is an electromagnetic wave.
Electromagnetic wave
See the figure every body in the universe radiate electromagnetic wave and its frequency depends upon f  = c/𝛌
 where f  is frequency of vibration and c = speed of light  = 3×10⁸ m/s, which is constant for all medium  and 𝛌 is wavelength.
Now high frequency wave are having more energy than low frequency wave,
You can calculate for Sun light  f  = c/𝛌  f  = 3×10⁸/500×10⁻⁹  = 6×10¹⁴ HZ for visible light 𝛌 = 500nm. 
Now calculate the radiation coming from a person body assume the body temperature of the person normally 37⁰C  so f  = c/𝛌  = 3×10⁸/9.35×10⁻⁶  = 3.2×10¹³ HZ.
 amazing the radiation coming from your body has frequency  32 times trillion per second,
How does it happens see the atoms of your body and skin do vibration  32 times trillion per second and do radiation electromagnetic wave.
So on the basis of this radiation electromagnetic wave is categories  in many different types of electromagnetic wave on the basis of frequency range.
wait i will discuss it later in this post.

What is electromagnetic waves ?



First you should understand what is wave ? then  i will explain electromagnetic wave,
hence wave is define as a disturbance or energy transfer from one place to other place through a medium, that medium may be air, water,
metal, gas but electromagnetic wave is special it does not required any medium to transfer disturbance or energy from one place to other place
it transfer disturbance or energy through vacuum by the help of changing electric and magnetic field in space.
very beauty symmetry Change in electric field create magnetic field and also
change in magnetic field create electric field and this create a wave propagate forward with speed of light 3×10⁸ m/s,
remember electric field, magnetic field and wave all are perpendicular to each other, light is special example of electromagnetic wave.
Now you will ask how change in electric field is done ? You know a stationary charge create a electric field, which start from (+)charge and terminate at (-)charge,
But when this charge is accelerated back and forth it create a changing electric field,
this electric field is curly type it always change its direction and due to this electric field change create magnetic field see below picture.    
Electromagnetic Wave

 


Electromagnetic waves theory history 



It is very important to know the electromagnetic wave theory,
So that in this theory many important concept is hidden, as i have already stated above that changing electric field create magnetic field,
Now you will see here its proof how changing electric field create magnetic field,
so for this you have to understand concept of Displacement current and to understand displacement current you need to understand Ampere’s  law according to this law.
                        → →
Ampere’s law ∫ B.dl  = 𝞵₀iₑₙ  now you will understand this law meaning in depth,
what Ampere’s law states by this mathematical expression so see the below picture all cases step by step.
Displacement Current
Take first case a current i is following in the wire as shown, Now you take a loop as shown and apply Ampere’s law, as you know Ampere’s law is valid for closed loop.
→  →
∫ B.dl  = 𝞵₀iₑₙ   
For left hand side I have taken a loop but for right hand side expression you have to take a surface
so i have taken a flat surface. iₑₙ represent the current cutting and passing through that flat surface, so here i is current cutting and passing through that flat surface.
                                                   → →
Hence you can write Ampere’s ∫ B.dl  = 𝞵₀iₑₙ  = 𝞵₀i  this is for first case.
Now take second case,
As shown in figure same process but this time with different surface that is hemispherical now again apply Ampere’s law for this case you will get.
 → →
∫ B.dl  = 𝞵₀iₑₙ = 𝞵₀i  same value as previous  case value, so you can take any surface for Ampere’s law, here loop is same hence result is same.
Now take third case as shown in figure now apply the Ampere’s law for this case.
→ →
∫B.dl  = 𝞵₀iₑₙ  now for the left hand side take a loop but for right hand side 𝞵₀iₑₙ you have to take a surface which is again flat,
see clearly in this case iₑₙ is zero, how ? see the same amount of current is cutting the surface and same current return back as shown in figure, hence iₑₙ is zero.
                             → →
So  Ampere’s law ∫B.dl  = 𝞵₀iₑₙ  = 0.
Now take forth case as shown in figure with same loop but hemispherical surface and apply Ampere’s law,
now in this case current is not cutting hemispherical surface, hence iₑₙ is also zero in this case.

                             → →

So you can write  ∫B.dl  = 𝞵₀iₑₙ  = 0 , now see the case third and forth value is same that is zero
but the reason in both case is different, you can see in third case same current cutting the surface and same current return back,
but in forth case current has not cut any surface, without cutting the surface current has returned back.
But anyway value of equation are coming same, whatever you are choosing the surface. 
Now take fifth case as shown in figure, where two plate of capacitor are shown, basically this is a RC circuit,
Now again take a loop for the wire, take a flat surface as shown  and apply Ampere’s law.
→ →                                                                                             → →    
∫B.dl  = 𝞵₀iₑₙ  see here i current is cutting the flat surface  so ∫B.dl  = 𝞵₀iₑₙ  = 𝞵₀i which is correct .
Now take for sixth case as shown in figure take a loop and consider a hemispherical surface
here it is important see iₑₙ is not cutting the hemispherical surface, Now apply Ampere’s law 
       → → 
So  ∫B.dl  = 𝞵₀iₑₙ  = 0  because iₑₙ is zero .
Important conclusion 
→ →
Now you compare fifth and sixth case, in fifth case value ∫B.dl  = 𝞵₀iₑₙ  = 𝞵₀i  where as in 
                   → →
sixth case  ∫B.dl  = 𝞵₀iₑₙ  = 0 now this is contradiction different surface have different value
where as you are taking same loop, but in rest cases first, 2nd, 3rd and 4th value was coming same for different surfaces.
hence it is clear that for fifth and sixth case Ampere’s law is WRONG. it must give the same value but not like this.
Actually when Ampere’s law was given at those time scientist were checked case first and third,
no body was thought about case fifth and sixth but later a great scientist Maxwell thought about this case.
Hence Maxwell realized that Ampere’s law is not correct fully,  so different value are coming for fifth and sixth case, hence Maxwell correct this equation and given the correct equation as given below.
Ampere’s Maxwell Law 
→ →
∫B.dl  = 𝞵₀iₑₙ + 𝞵₀𝝐₀d𝛟ₑ/dt  Maxwell added new term 𝞵₀𝝐₀d𝛟ₑ/dt in the previous Ampere’s law hence this equation was called Ampere’s Maxwell law.
Now see the term d𝛟ₑ/dt this is electric flux, note flux may be electric as well as magnetic but here suffix e denote this flux is electric flux.
Now you can apply Maxwell law for all the above cases.
For first and second case there is no any electric field hence electric flux will be zero so the term  𝞵₀𝝐₀d𝛟ₑ/dt will be zero
hence equation will be same as Ampere’s law and is correct as shown.
For third and forth case iₑₙ is zero as well as electric field is also zero so electric flux also zero hence.
→ → 
∫B.dl  = 𝞵₀iₑₙ  = 0 
Now for fifth case see there is a capacitor hence capacitor will charge and there will be electric field due to charge accumulation in between capacitors as shown in figure.
So what will be value of that electric field, Perhaps you know E = Q/𝝐₀A .
Now you see there is electric field lines but this field lines are not passing through the Ampere’s loop, electric field are between the capacitor hence flux through this surface is zero so  𝞵₀𝝐₀d𝛟ₑ/dt will be zero.
             → →      
Hence  ∫B.dl  = 𝞵₀iₑₙ   =   𝞵₀i.
Now for sixth case see there is electric flux electric filed is passing through hemispherical surface to the capacitor so how much electric flux ? this will be  𝛟 =EA now from above 
EA = Q/𝝐₀ so  𝛟 =  Q/𝝐₀ now differentiate this with respect to time.
d𝛟/dt  = 1/𝝐₀*dQ/dt  = i/𝝐₀ , now put in equation  𝞵₀𝝐₀d𝛟ₑ/dt value of  d𝛟/dt you will get 
 → →
∫B.dl   = 𝞵₀i
                                                                                                           → →
Now you see the magic in case fifth and sixth value is same that is ∫B.dl   = 𝞵₀i  .
now you can see when you were using Ampere’s law, the value was different for fifth and sixth cases, but using Maxwell law equation are giving same value.
So Ampere’s Maxwell law is correct because this law is correct for all the above cases .
→ →

∫B.dl  = 𝞵₀iₑₙ + 𝞵₀𝝐₀d𝛟ₑ/dt  =  𝞵₀(iₑₙ + 𝝐₀d𝛟ₑ/dt) , Now see the dimension of  𝝐₀d𝛟ₑ/dt is current dimension. well  iₑₙ is called conduction current and  𝝐₀d𝛟ₑ/dt is called displacement current this name was given by Maxwell.

Now see the sixth case of circuit carefully, where capacitor plate having charge (+Q) and (-Q), As the current will flow through circuit the value of charge at capacitor (+Q) will increase, and due to this charge there will be a electric field between capacitor as shown and i have stated this earlier.

Now the term 𝝐₀d𝛟ₑ/dt is associated with electric field, because  d𝛟ₑ/dt is electric flux, see the term  𝝐₀d𝛟ₑ/dt is displacement current name given by Maxwell but actually this is not current, This is simply associated with electric field as shown in sixth case, whereas Maxwell given this name as current, because its dimension is same as current.

Now  you can write the above expression  𝞵₀(iₑₙ + 𝝐₀d𝛟ₑ/dt) =  𝞵₀(ic +id) where ic is conduction current i which is flowing in the circuit as shown.id is displacement current 
id current is in between the capacitor as told by Maxwell.

Now important concept  conduction current is due to flow of charge, but when Maxwell is saying displacement current is in between the capacitors then there is flow of charge between the capacitor plate, Is it correct ? BIG  no.

It is clear that there is no any charge flow between the two capacitor plate. So you must understand that displacement current does not mean flow of charge. Then what is meaning of displacement current here ?.
Well displacement current meaning here is changing in electric field. But how ? see as the current will flow through the circuit, then charge (+Q) will accumulate at capacitor plate so charge (+Q) will increase and hence electric field will increase.

So it is very simple displacement current is due to changing electric field, you can see the mathematical expression for displacement current id  = 𝝐₀d𝛟ₑ/dt , where d𝛟ₑ/dt is electric flux .


BIG Important Concept for displacement current 



Due to changing electric field produce displacement current, Now you think electric field is a vector quantity, Hence electric field can change by two ways first either by changing its magnitude or second way by changing its direction only keeping magnitude constant, So here this is case of due to changing both magnitude as well as direction of electric field hence electric field are changing here due to both magnitude as well as direction, so finally changing electric flux. 

For second case keep charge magnitude constant and accelerate that charge back and forth in this case electric field direction will change, so this is also changing electric field hence displacement current will also be there without flow of charge.
Now third case take a stationary  charge will it change electric field ? No because neither electric field direction changing nor its magnitude is changing.

Hence a stationary charge will not change electric field, so no displacement current will be due to stationary charge.
Mathematically you can see if electric field is constant then electric flux will be also constant and hence d𝛟ₑ/dt will be zero, Hence displacement current will be zero.


Conduction and displacement current create magnetic field


Both current ic and id create magnetic field see below picture.
Conduction and displacement current

From the first figure conduction current ic carries charge so at positive plate  Q will accumulate and value of Q will go on increasing, Hence electric field will also increase as shown in figure. Hence changing electric field so create displacement current as shown.

Now you see the second above picture, As you know conduction current carrying in a wire create magnetic field as shown in red loop.
Similarly due to displacement current between the capacitor plat will also create magnetic field lines as shown in second picture. So as due to conduction current magnetic field lines are created in the same way due to displacement current magnetic field lines are created.
Note Electric field and magnetic field are perpendicular to each other, Now you can think due to displacement current (id) magnetic field are creating (B), and displacement current are created due to changing electric field (E).
So it is confirmed that when changing electric field create magnetic field and vice versa is also true changing magnetic field also create electric field how beautiful gift of nature electric and magnetic field.   

How does electromagnetic wave is created ?



Source of electromagnetic wave is accelerating charge, Due to this accelerating charge electric field is changes and due to electric field changes magnetic field is created, Hence due to electric and magnetic field changes electromagnetic wave is created. 
Hence to make accelerating charge you need a LC oscillation circuit where L is inductor and C is a capacitor in this case once inductor will charge and capacitor will discharge, in next time capacitor will charge and inductor will discharge, Hence charge will keep oscillation left and right. 
But nature has many ways to create electromagnetic wave and it has been observed, but how you will understand this is electromagnetic wave.
Well in every electromagnetic wave weather it is created by LC oscillation or by nature but one property will be same that is velocity of electromagnetic wave is always a constant and it is equal to speed of light C = 3×10⁸ m/s.
So we assume that light is an electromagnetic wave in which electric and magnetic field are present.
Now you must understand charge properties in different states.
1 A static charge create a electric field around it, This electric field apply force on a static electric charge.
2 A moving charge with constant velocity (electric current) create magnetic field around it, This magnetic field exert force on a moving charge. but this magnetic field can’t exert force on a static charge. This is as simple as that a moving charge will experience force in magnetic field but static charge will not experience any force in magnetic field.
3 An accelerating charge create electric field as well as magnetic field and push ahead both electric and magnetic field. So this accelerating charge create electromagnetic wave.
Now think what will do this electromagnetic wave ?
Wherever  this electromagnetic wave will fall, it will accelerate charge, Hence this electromagnetic wave comes in antenna and accelerate charge of antenna.
Now this acceleration create force and this force create work and energy, But think from where this energy is coming in electromagnetic wave.
Well think at the time of LC oscillation circuit we use battery source energy to create electromagnetic wave from this battery source energy is taken and carries this energy in the form of electromagnetic wave and finally deliver this energy to antenna.
Hence in this way electromagnetic wave carries energy and transfer to your mobile antenna.

Properties of electromagnetic waves


Is there momentum in electromagnetic wave ? As you know that momentum mathematical formula is p = mv that indicates if any particle having velocity as well as mass has momentum, Now you think light has no mass, so it should not has momentum, but it has. because momentum concept is changed  after Albert Einstein.
light is packet of photon and photon has mass but can’t measured, so for that momentum concept was changed rather than mass concept.Hence momentum defined as again .   
Momentum is a property of a moving particle, which will not change when moving particle will go from one point to other point, so momentum is conserved.
So momentum is a physical property, which is conserved between two location. Hence anything having velocity and energy has momentum.
So electromagnetic wave has velocity and energy so it has momentum.
Hence momentum p = Energy/Velocity , So energy with photon = E = h𝝼 ,
now velocity of electromagnetic wave c = speed of light so momentum p  = h𝝼/c 
you also know  c = 𝝺𝝼 so put in momentum p = h/𝝺  where 𝝺 is wavelength of electromagnetic wave and h is plank’s constant.
Electromagnetic wave create pressure, because due to change in momentum create force and force per unit area is pressure but it value is so small that you don’t feel.  

Electromagnetic waves equation 


See below wave equation varying with time magnitude of electric field as well as magnetic field change,according to displacement and time.
You should remember that electric field and magnetic field are always perpendicular to each other and wave propagation equation also perpendicular to both electric and magnetic field                                                                 

Wave Equation

where 𝛚 is angular frequency, k = 2𝛑/𝛌  is called wave constant or wave number .
E₍ₓ,ₜ₎  = Eₘcos(kx-𝛚t +𝛟) ,   B₍z,ₜ₎  = Bₘcos(kx-𝛚t +𝛟) , This is the equation of electric and magnetic field.
questions are asked on the basis of this equation, compare and find the required parameter 𝛌 , 𝛚 , 𝛋  and 𝛎 , 𝛟  So remember the equation to find the asked value above relations. 


Electromagnetic waves  source


The source  of electromagnetic wave is electric charge, You know there are two basic characteristics of material one is mass and other is electric charge. Mass is that characteristics, which creates gravitational field. you can refer gravitational field concepts.  

Charge is that characteristics, which creates electric field around it. there can be three state of a charge.
1 A stationary charge   ( Velocity is zero )
2 A moving charge       ( Velocity is constant )
3 An accelerating charge  ( Velocity is variable )

According to this velocity there is effect around it. A stationary charge create stationary electric field. And a moving charge create electric field as well as  magnetic field.

Sample of moving charge is current in a conductor see below picture.

Electromagnetic wave source

Conductor carrying current is not charge body because every time number of proton and number of electron in conductor is same, so it is not a charge body.So it can’t create electric field.
see at one end electron inter in conductor and same time other end  electron out from conductor hence net charge on conductor is always zero, electron in motion but number of electron and proton are always same on conductor body.
So current in a conductor only create magnetic field. Hence current in a conductor does not create electromagnetic wave.

Accelerating charge as shown in figure q create electric field, due to motion of charge create magnetic field and due to increase in charge velocity both electric and magnetic field are pushed forward. 
So electric and magnetic field start moving forward. Hence accelerating charge create electromagnetic wave. 


Electromagnetic waves propagation 


Propagation means spreading in all the directions, motion word is not used because normally motion word is used for one particular direction, But for a point source electromagnetic wave goes in all the directions, So you use the word propagation.
 
Propagate means spread out, Now how this electromagnetic wave spread out ? well you have learned, when an electric charge accelerate or oscillate a magnetic field is created and oscillating charge also create a varying electric field.
You know if there is a positive and negative charge then electric field direction is from positive charge to negative charge like this .
       E 
(+q)→(-q)  see below picture.
I will continue this post with more important concept. I hope you have enjoyed learning electromagnetic wave. I want your feedback, comments, like and share, learn more and grow thanks for sharing.
Dated 16th Dec 2018  

Acceleration due to Gravity Formula

Today post is all about acceleration due to gravity formula.
Because this is very basic concept of Physics , how everything is attracted towards the Earth.
So this is important for you and need to know EVERYTHING acceleration due to gravity formula.
Are you ready to know mystery about acceleration due to gravity experiment.
So In this post you will learn, what is exactly meaning of acceleration due to gravity ?
As well as how, acceleration due to gravity formula varies planet to planet. 
So let’s start from very basic questions and concept, So that you can better understand. 
Now dive in, what you are going to learn here today.  
  • What is acceleration due to gravity formula ?
  • How to calculate  value of acceleration due to gravity any point ?
  • What’s acceleration due to gravity on mars ?
  • Acceleration due to gravity experiment by Newton
  • acceleration due to gravity derivation formula
And many more important concept like, examples of acceleration due to gravity.
If you want to these all questions facts keep reading. You’ll learn here some new concept. Which nobody will tell you.   
Well, Do you know ? How its value is 9.8 m/s² ? and  acceleration due to gravity has fixed value.
 Why and how its value varies at different point location and due to Earth rotation ?
How acceleration due to gravity is a gravitational field, You will learn all concepts about of acceleration due to gravity, so lets start.
But before going to discuss in details. I like to answer some FAQ. Which is given below, So go through this FAQ.   
[faq title=”Frequently Asked Questions (FAQ)” open1st=”0″ openAll=”0″][faq_item title=”What is the acceleration of gravity?
” number=”1″]The acceleration of a body, in free fall condition under the influence of Earth’s gravity. Which’s rate of increase of velocity per unit time as approaches the ground or Earth. So due to increase in velocity an acceleration is created and its value is 9.8 meter per second square. And this’s called acceleration due to gravity.[/faq_item][/faq]
[faq title=”” open1st=”0″ openAll=”0″][faq_item title=”What is the formula for acceleration due to gravity?” number=”2″]Using two most important formula given by Newton F = ma and F = GmM/R*R formula for acceleration due to gravity is calculated g = G*M/R^2. Where g = a = acceleration due to gravity, G is the universal gravitational constant, M is mass, and R is radius of Earth. Note this value is on the surface of the Earth.[/faq_item][/faq]
[faq title=”” open1st=”0″ openAll=”0″][faq_item title=”What does the acceleration due to gravity depend on?” number=”3″]Acceleration due to gravity depends on the mass of the planet. And the distance from the center of planet mass. G is universal constant and Its value is = 6.673 x 10-11 N. [/faq_item][/faq]

What is acceleration due to gravity  Formula ?  

Gravity is a force with which Earth attract every other object towards it centre.
Earth has created this gravity around its surrounding. This property of the Earth is due to heavy mass of the Earth.
Because compare to the Earth mass, all other objects masses are small near its surrounding, Hence all other masses falls towards centre of the Earth.

So from the figure above Earth is pulling you with force mg, you also know from the law of gravitation force between two masses.
Therefore you can refer previous post for Gravitational force the value of force between Earth and man shown in figure will be F= GMₑm/(Rₑ + h)².
Because here value of h is very small compare to radius of Earth Rₑ so h is neglected.
Hence F =  GMₑm/Rₑ² , Now both force will be equal as per statement.
GMₑm/Rₑ²  = mg   or  g =    GMₑ/Rₑ² , this is important formula where G is universal gravitational constant G = 6.67×10⁻¹¹ Nm²/kg², Rₑ is radius of Earth approx Rₑ = 6400 km.
Rₑ = 6.4×10⁶ m , Mₑ is mass of Earth approx Mₑ = 6×10²⁴ kg .
Now after putting all the values in above formula g =  6.67×10⁻¹¹x6×10²⁴/(6.4×10⁶)²
g  = 9.8 m/s², remember this value of g is near the earth surface only.
Now suppose if h is very high then you can’t neglect value of h, so in this case g =  GMₑ/(Rₑ + h)², Now as the value of h increases then value of g will decreases, So you can’t say value of g is constant.
And  acceleration due to gravity dimensional formula is [ L/TT].
On increasing the value of h from the surface of the Earth value of g will decrease. You will see how the value of g decreases as moving from the surface of the Earth in this post later.
Now see below picture and find weight.
How you’ll calculate  acceleration due to gravity on mars.
you can do acceleration due to gravity experiment on different planet, the value will be different. 

As from the question, You have to find the weight of same man at Mars, his weight is given at Earth is 70 N. 
So very Interesting now scientist are planing to move to Mars booking are going on for Mars journey, But at present very costly in million $, which is not possible for a average men.
Because you should know what will be your weight at Mars ?
You know weight at Earth is mg w = mg, now weight at Mars will be w’ = mg’ here g will be different from Earth so take as (g’).
w’/w  = mg’/mg  = g’/g  ( You know that mass is not changed anywhere in the universe )
w’/w  = g’/g   you have calculated g value at Earth surface g  = GMₑ/Rₑ² , Similarly for Mars 
g’  = GMₘ/Rₘ²  put this value of g and g’ in the expression.
w’/w  = g’/g  =  (GMₘ/Rₘ² )/(GMₑ/Rₑ²)  =  (Mₘ/Mₑ)x(Rₑ/Rₘ)²  now from question given that Mars mass is 10 times less than Earth so Mₑ = 10Mₘ and radius of Mars is 1.8 times less than radius of Earth Rₑ = 1.8Rₘ , now put this values in above expression you will get.
w’/w  = (Mₘ/Mₑ)x(Rₑ/Rₘ)²   =  (Mₘ/10Mₘ)x(1.8Rₘ/Rₘ)² =  3.24/10 = 0.324 
w’/w  =  0.324   =  w’ = wx0.324 = 70x0.324  = 22.68 N .
Hence weight at Mars for same person will be w’ = 22.68 N  which is approximately  3 times less than weight at Earth .
So you will feel less attracted at Mars, you will feel more free. At moon your weight will be 6 times less than weight at the Earth, So acceleration due to gravity varies.

Acceleration due to gravity formula Variation in gravity (g) as you go above Earth surface.

Here’s acceleration due to gravity derivation formula, how it’s calculated at different point of the Earth.

Variation in g above Earth Surface
So from the above figure mg’  = GMₑm/(Rₑ+h)²  or  g’  = GMₑ/(Rₑ+h)²  see as you will go above the Earth surface, value of h will increase and hence value of g’ will decrease.
and it is also logical that as you will be far distance from Earth surface gravity g field effect will be less on you. So it is clear that above the Earth surface gravity g will decrease.
Now compare the value of g’ with original value of g at Earth surface, So you know the value of g at Earth surface g  =  GMₑ/Rₑ²  now from here you can write GMₑ = gRₑ²  now put this value in the new g’ expression .
g’  = GMₑ/(Rₑ+h)²   = gRₑ²/(Rₑ+h)²  =  g/(1+h/Rₑ)²  after arranging the expression you can 
So in terms of height, you can write new value of g’ like this.
g’  =   g/(1+h/Rₑ)²  now it is important ,if the height from the earth surface value of h is about 1km up to 100 km value of g’ will be nearly g, So no effect of gravity value is change near the Earth surface within this range.
But when you will go up to 500 km and more then value of g’ will change and its effect will seen. Now i will make some assumption see below
If  h<< Rₑ   you can write  g’  = g(1+h/Rₑ)⁻²  now you know from binomial expansion  
(1+x)⁻ⁿ  = (1-nx)  if   x<<1 font=”” h=”” of=”” similarly=”” value=””>Rₑ <<1 span=””>
So you can write g’  = g(1-2h/Rₑ) . See below the question. 
Now examples of acceleration due to gravity.
Q Find the height above the Earth surface, where gravity ‘g’ drops to 25% of g at surface . 
Solution for any numerical question, first you should understand well the question then you relate the given parameter So as from the question it is given that new value of gravity g’ 25% of at Earth surface hence  g’  = gx25/100 =  g/4   (1)
You also know that  g’  =  g/(1+h/Re)²    (2)
hence equate expression (1) and (2) so you can write .
g/(1+h/Re)²  = g/4  or    (1+h/Re)²  = 4 or  (1+h/Re)  = 2 
h/Re  = 2-1   = 1  or  h  = Re  So at radius of Earth height value of gravity g’ will be 25% of Earth surface.

acceleration due to gravity experiment Variation in gravity as you go below the Earth surface. 

Variation of gravity g inside the Earth
From figure you are h depth inside the Earth and now you are r distance from the centre of the Earth.
Now from the law of gravitation you can write mg’  = GM’m/r²  understand the concept, the mass of the Earth with which now Earth will attract you will be M’ not Mₑ.
only inside circle mass will attract, outer mass will not attract you, Because due to Gauss theorem in a shell gravitational field is zero.
This is also important outer shell mass will not pull you out side because gravitational field is zero inside a shell whether it is solid or hollow in both the cases gravitational field will be zero inside a shell.
Now from expression mg’  = GM’m/r²  or g’  = GM’/r² 
Suppose Earth is a uniform sphere means equal mass distribution everywhere but it is not like that just we assume.
now the density of Earth is 𝛒  everywhere assumption hence M’ = volume x𝛒.  =  4𝛑r³/3x𝛒
M’  = 4𝛑r³/3x𝛒
g’  = GM’/r²  =  Gx4𝛑r³/3x𝛒/(r²) =  g’ =  G𝛒4𝛑r/3  here you see g’ is directly proportional to r its mean that as you will come from the centre of the Earth towards the surface of the Earth value of r will increase and hence value of g’ will increase.
At the surface of Earth it will be maximum.
Now you can calculate the density of Earth   𝛒 = mass/volume = Me/4𝛑Rₑ³/3 put this value in above equation  g’ =  G𝛒4𝛑r/3 = GxMe/4𝛑Rₑ³/3x4𝛑r/3 =  GMₑr/Rₑ³  here it is also clear that g’ is directly proportional to r.
You remember for always g = GMₑ/Rₑ² at the surface of Earth this is standard formula use everywhere in this topic, So from here G = gRₑ²/Mₑ , now put this value in g’ expression 

g’  =   GMₑr/Rₑ³  = (gRₑ²/Mₑ)x(Mₑr/Rₑ³ )  =  (g/Rₑ)r or  g’   =  (g/Rₑ)r
Hence it clearly show as you will go inside the Earth surface value of gravity g will decrease  you have seen here g’ directly proportional to r.
Now you have to write this formula in terms of h so for this see the figure, I can write 
Rₑ = r+h  or r   = Rₑ-h, put this value in above expression 
g’   =  (g/Rₑ)r  =  (g/Rₑ)x(Rₑ-h)  = g(1-h/Rₑ)  or  g’  = g(1-h/Rₑ) .

Now one question are generally asked, what will value of gravity g at the centre of the Earth ?

So you are looking the formula  g’  = g(1-h/Rₑ)  at the centre of Earth h = Rₑ hence g’ =0 

Hence it is very much clear that at the centre of Earth g’ will be zero, and as move from the centre it will increase and at the surface it will be maximum g’ = g = GMₑ/Rₑ², now from surface to above height again value of g’ will decrease, you have already seen above. 
So acceleration due to gravity is maximum at Earth Surface.

Acceleration due to gravity on mars Variation with distance 

See below the graph plotted variation of gravity with respect to distance, here you can easily see how value of g is changing with respect to distance.  
Variation of gravity g with distance 

Variation in gravity g due to Earth rotation 

Due to rotation of Earth value of g decreases but its value is very small due to angular velocity value is very small 𝛚  = 2𝛑/T = 2×3.14/(24x60x60) = 6.28/86400 = 7.28×10⁻⁵ rad/s
Every point on the Earth surface will have different circle of rotation, and due to centrifugal force on body, the effective value of g will decrease.
Important point due to rotation, effective g is not along the centre of the Earth, it will deviate slightly from the centre of the Earth.
After calculation g effective value will be g’ =  (g-Rₑ𝛚²cos²ϴ) now at equator put ϴ =0 then
g’ =  (g-Rₑ𝛚²) , now at pole ϴ = 90⁰  So g’ = g. refer below picture.
Variation of gravity due to Earth rotation
 The reason of gravity g different at pole and equator is due to rotation of the Earth as you have seen above.
Hence finally you have seen that gravity g varies above the Earth surface, inside the Earth and due to rotation of the Earth, In all the cases gravity g decreases, at the centre of Earth g value is zero.
and at the surface of the Earth maximum g = 9.8 m/s²  , not a constant value.   

#Conclusion:

If you know the basic concept, then it is easy to understand Physics. I hope you have enjoyed learning acceleration due to gravity formula .I will continue post with more hidden concepts, I want Your feedback, comment, likes and shares. If  you’ve any doubt ask me, always here for your support.Thanks for sharing, learn and grow.  
 Dated 23rd Dec 2018.       

Gravitational Field And Intensity is Important Topic

Gravitational Field And Intensity is important topic.  If you are looking for gravitational field meaning. Then you are at best place. Because i am explaining gravitational field, in  simple and easy way. So that you are never forget. Gravitational field and intensity is very important concept of Physics.
Because it help to understand, many other topic of physics easily. Hence for example gravitational potential ,Gravitational energy and many more. So if your concept for gravitational field is clear. Then this topic is become easy for you. Now lets start, what is gravitational field concept ?

What is Gravitational Field simple meaning ?


Well you are here to learn, gravitational field and intensity in this post. So what is field ? and how this field is created. As well as what is strength or intensity of this field. Hence this is new concept of gravitation and very interesting.
In the previous post. you have learned in details about Gravitational force. If you are not seen that post. Don’t worry. I am providing that post link, in this post below. where you can check. Now the concept of point mass is use here to better understand. What is  gravitational field ?
so you should also refer first Gravitational force introduction. Now lets start and learn some new concept for gravitational field.
 
Gravitational field and electric field are similar.  Gravitational field concept is apply in electric filed also. So only difference is that, in gravitational field mass is source of field.  But in electric field charge is source of electric field.
Hence gravitational field is always attractive in nature.  But electric field is attractive as well as repulsive in nature. So it depend upon charge nature. If charge is positive. then it is repulsive.  And if charge is negative.  Then it is attractive.
Therefore you are learn latter about electric field.  Here our topic is gravitational field. 

Best example of gravitational field explanation 


 

See the above picture.  Suppose a room is completely vacant. Now you released a very small mass. Then that mass automatically, start to moves towards a particular direction as shown in picture.

 
Now you are start thinking. How this mass is moving ?. Because nothing is pushing the mass. But it is moving. Hence the thing, which is invisible but effect are showing that mass is moving. Then i told you that. there is an imaginary field.
Therefore Someone has made this field.  And due to which this small mass is pulling. After that you remove the screen, and found that wow. There is a big mass. Now you are clear that definitely this big mass is pulling.  That small mass by law of gravitation.  
 
Hence this big mass is created gravitational field. Since the big mass is not seen. But its effect you seen So this is an imaginary field. Because it  is a hypothetical concept story. But in actual nothing is imaginary field .
Hence it is important, if there is a field . Then there is also  a source for that field. In this case big mass is source for gravitational field. And small mass, on which you do experiment is called test mass .
Therefore Condition for test mass is limit lt m→0 .
So test mass is always taken as small. Because it can also create its own field. which is disturbing main source field. And this is creating inaccuracy for field strength measurement.   
 
Hence gravitational field is a space around a body. Such that in which gravitational force is experienced. So there are two method to apply forces.  One is through contact.  which is called  contact forces. And other is without contact, which acts in nature. And these are called field forces. 

What does gravitational field do ?


 
Now field do two important work. So first whenever any mass body comes in field region.  Then it inform the source mass. Such an information, that someone is entered in the field. And second it attract that entered mass in its field. So for practical example.
when a criminal live in a particular area.  Then he is creating an effect among the people. Which is field in that area. Because people of that area fear from him. whenever he moves people don’t want to see and meet him. 

 

 
Hence when other criminal enter in this area.  Then again first criminal came to know, that somebody is entered in my area.  And start fighting with small criminal.  Therefore finally captured by big criminal. Same as  big mass overcome on small mass.

What is Gravitational field intensity or strength ?

Gravitational field strength is define as force per unit mass Eg  = F/m, understand the concept field is not a measurable quantity, actually field strength is measured, field is just a feel, which a small mass experience due to a big mass field created. 
Gravitational field is a vector quantity so it has also direction hence the direction of field will be same as direction of force acting on small mass ,If you want to measured the field strength, then just put a small mass at that location and check the force experienced by that small mass and just divide that force with small mass you will get the strength of the field at that location. 
                                                                           →      →
Mathematically gravitational field is express as Eg  = F/m , Now see the picture below to understand better concept.
Gravitational Field strength

 

See the above first picture the Earth and same mass of 1kg experienced different forces of attraction by the Earth at different location, But question is why ? the same mass of Earth and the same mass of 1kg but different location, 1kg mass experienced different force.

What is gravitational field  formula of earth ?

You will get the answer of why wait ? but first you notice that gravitational field depend upon the location, As you see changing the location force value on 1kg mass is changing.
 
You know from previous post gravitational force between two masses F  = GMem/r² .
now from above formula  Eg  = F/m  = GMem/mr²  = GMe/r².
 
Eg  = GMe/r² N/kg which clearly shows that gravitational field depend upon r position as the distance will increase from the source mass Me field value will decrease.

 

 
Now you see second Earth image for answer why ?
Gravitational field work just like spring, see the image of ball near the Earth, Three spring are pulling that ball towards the Earth so its gravitational field strength at this location will be more. Similarly when the same ball is moved some distance above the Earth then see only two spring is pulling the same ball at different location, So here less field strength at this location.
Again move the same ball some more distance away from the Earth then see only one spring is pulling the same ball hence more less attraction, So here field strength will be more less, Hence in this way field strength varies according to location. Now i hope you have understand the concept of gravitational field and its strength.

Gravitational field intensity unit

As you have seen the definition of gravitational field strength  Eg  = F/m  now put the unit of force in this equation, unit of force is kg*m/s² .
Eg  = kg*m/s²*kg  = m/s²  wow this is unit of acceleration due to gravity g , So gravitational field strength is acceleration.
Hence remember field strength is always calculate per unit mass at any location in space.

Principle of superposition gravitational field 

Principle of superposition state that if there is more than one mass at a location and you want to find the gravitational field strength at a point, due to all masses then vector sum of all fields due to each masses, this will give the total field strength at that point.
See the picture below, find field strength.

 

 




How to find gravitational field strength at a point ?

From the first question to find out gravitational field strength at point P due to mass m1 and mass m2, You will put a unit mass at point P and you will see, this unit mass is attracted by m1 and m2 as shown in figure.

Hence direction of gravitational field is clear by mass m1 and m2, Now you know that gravitational field is a vector quantity hence it will add as vector sum, So total field at point P will be like this.
→      →      →
Eg  = E1  + E2   at point P, You know magnitude of E1  = Gm1/r₁² , similarly magnitude for E2  = Gm2/r₂² .

Now if you want to write in vector form to sum the actual value of E1 and E2 then take component of E1 along x and y axis, Hence in vector we can write as.

E1  = -E1cos45i^ + E1sin45j^  ( minus due to negative direction of x component) 


E2   = E2cos45i^ +E2sin45j^ now for total field at point 
→       →      →
Eg   = E1  + E2  =  (E2cos45 – E1cos45)i^ + (E1sin45+E2sin45)j^ , now put the magnitude of E1 and E2

Eg    =  (Gm2/r₂²*1/√2 –  Gm1/r₁²*1/√2)i^  + (Gm1/r₁²*1/√2+ Gm2/r₂²*1/√2)j^

Now after putting all values of G, m1 and m2 you can find the total field strength at point P in vector form, for magnitude take square root of i^ and j^ vector.

Now for second question equilateral triangle, find  field strength at point P centre of the triangle as shown in figure.

As you see in this case three masses of same magnitude are placed at vertices of the triangle. Now do the same process put a unit mass at the centre of triangle and analyse all the three masses will attract that unit test mass placed at the centre.

Hence the direction of field will clear to you as shown in figure. Now total field due to all three masses will be vector sum of three field .
→       →     →     →
Eg   = E1 + E2 + E3  now it is given that all three masses are same and distance from centre to all masses are same hence field due to all masses will be also same without doubt. So  E1 = E2 = E3 , now all three field are in different direction so it will cancel to each other, Hence net field at centre of the triangle will be zero.
      →      →     →     →
So  Eg  = E1 + E2 + E3  = 0   


How to solve Numerical questions

You can prove it also first you take base side two masses see the x component magnitude are same and in opposite direction, so it will cancel. now its y component vertically downward and its magnitude 2Ecos60 = E (downward) and by third mass top vertices E upward hence both will cancel each other, So total field at point P at triangle centre will be zero.

Hence it is clear that whenever symmetrical mass distribution is given and asked to find the field at centre point of that geometry shape then field will be zero at centre point.

Now you can also check this for square and ring , put the same mass on the square corner and find the field at centre of square it will be zero try yourself this case. 


Why Gravitational field intensity is applicable for point mass only ?


 

You must remember that gravitational field intensity formula Eg  = GM/r²  is only valid for point mass, not valid for distributed masses, How you will find gravitational field strength for distributed masses. See below some question, Which will clear your concept.

 For first question Q1, suppose x distance from m field strength will be zero, then field due to m will be E1  = Gm/x², now field due to 4m will be E2  = G4m/(12-x)² , since field will be zero its mean that vector sum of both field will be zero.
→      →
E1  + E2   =0 or  E1  = E2  hence equate both field magnitude 
Gm/x²   =   G4m/(12-x)²
(12-x)²/x²   =  4 or  (12-x)/x  = ±2  if take positive value then (12-x)  = 2x or 3x  = 12 
x  = 12/3  = 4  hence  x = 4cm.

Now take negative value of x, then expression will be (12-x)   = -2x or x  = -12cm now see for this case x = -12 which will lie left of m at this point both the direction of E1 and E2 will be in right direction , so E1 and E2 will add, Hence this value is not possible.

Hence x = 4 value is lie in between them so final value of x will be x = 4 at this point field strength will be zero.   

Now for second question Q2, Which is not a point mass it is distributed over the semi circle, here you can not apply directly point mass formula because it is distributed mass, so for this you can do one thing divide this semi circle in small dm mass then you can apply formula for point mass because dm mass will be very small like point mass.

Now see here Eg at a point mass dm as shown Eg  = Gdm/R²   now along y axis it is symmetric so its x component will cancel each other Ex  = Gdmcosϴ/R² , but its y component will not cancel so Ey  = Gdmsinϴ/R² , now to add this types of all small masses you have to integrate this small dm.

∫ dEy     = ∫Gdmsinϴ/R² =  G/R²∫sinϴdm , now for dm in terms of ϴ  we can use mass per unit concept .

dm/Rdϴ  = M/𝛑R  or dm =  M/𝛑 now put this value in main equation 

G/R²∫sinϴdm  = G/R²sinϴ*M/𝛑  = GM/𝛑sinϴdϴ , limit will be from 0 to 𝛑

𝛑
GM/𝛑sinϴ
0                      𝛑
Ey  = – GM/𝛑R²⎡ cosϴ⎤   = – GM/𝛑R²(-1-1) = 2GM/𝛑R² 
                                   0
Ey  = 2GM/𝛑R²  direction will be vertically upward this will be gravitation field at point P.

If you want to learn more about Physics hidden concept. Then refer my previous post. This link is given below.

 

Now i hope you have enjoyed to learn gravitational field and intensity. Your feedback is important for me. And more new post is in progress. So learn here best concept for you. I want your feedback, through comment, share and likes learn more and grow, thanks for sharing.    

 
Dated 9th Dec 2018 

gravitational potential energy

Today’s our topic is about gravitational potential energy. And is is really very interesting topic.

Because you know that energy is everything. Only its form is change everywhere.

So  you’re going to learn here best concept for gravitational potential energy.

Are you ready to know the best part about gravitational potential energy ? If yes, 

Lets dive in.  

What is gravitational potential energy ?

 

Gravitational potential is very important concept because the same concept is used in electric potential.

So potential is a general concept, Which you need to understand the concept behind potential. Whenever you see gravitational potential then you must remember, the existence of gravitational potential is due to mass.

 
If mass is not present then gravitational potential will not exist, Can you think why ? well if there is no mass then there is no gravitational field and if no gravitational field then there is no gravitational potential.
So you can think potential depends upon field, which may be gravitational field or electric field or magnetic field in general but here you will learn about gravitational field potential.
 
If you have not studies gravitational field then i will suggest you first to learn about gravitational field in my previous post so that you can better understand gravitational potential concept, You can refer link Gravitational field.
 
When you see electric potential this is due to charge, but the potential concept for both the cases is same. Hence you will learn in this topic, what is potential ? and how it is calculated, why need to learn potential ? and then potential energy.   

What is gravitational potential energy derivation? 

Potential word itself has not got any defined meaning, whereas potential difference is defined as “the difference in potential between two points that represents the work involved or the energy released in the transfer of unit quantity of mass from one location to the other location”. So it is clear that potential is a characteristics of location or point.
 

 

Suppose there are two points A and B and a small mass m is kept at point B, now this small mass m bringing from point B to A, now you need to do some amount of work that amount of work is called potential difference between B to A.
                                                                                                                                  ←m
Mathematically written as  Va – Vb  = (Work done B to A)/m             A         W            B  
with no change in kinetic energy, means when you are bringing mass m from point B to A the speed of mass does not change during the journey from B to A.then only this formula is valid.
 

Gravitation Potential definition at a point 

 
As i have stated potential itself is not a defined meaning in Physics, So we have taken a reference point, such that the potential of reference point will be zero. Now you can compare any new point potential from that reference point, like how much is potential at new point.   
Hence reference point was take at infinity () so potential at infinity is zero, now you are able the compare any new point potential respect to infinity potential. But remember point does not have energy but whenever you bring a mass near to that point then energy is stored in mass.

So it is clear that energy is available in mass but potential at point or at location indicate how much energy will be available at that location in the body or mass, which is bring to that point. You must remember every point has some potential, If you bring a mass then energy is stored in mass, If you don’t bring the mass then energy is not stored, but potential is always there.


You generally listen the peoples use potential word like, there is potential in this business, what do you understand by using this word ? Well that person is indicating about money in that business, Hence money is form of energy in Physics.

So potential indicate about energy of at point or location but when you bring a mass.         
 
Now from the above two point, which you have taken A and B put point B at infinity that is B(∞), now put a small mass m at infinity and bring this mass to point A, the work done will give you the potential at point A.
 
Now you can write mathematically  VA – V∞  = (Work done infinity to A)/m  put V∞ = 0 then you will get  VA  =  (Work done W infinity to A)/m .
what is VA ?  this is potential at point A.
 
Actually potential at a point does not exist, we are just comparing from infinity point potential so you are able to define potential at point A.
Hence potential at a point is define as work done per unit mass bringing  from infinity to that point A, such that without changing the kinetic energy of mass m means mass moving very very slowly from infinity to point A.
 
Now i hope your concept about gravitational potential energy and potential difference is clear.

Gravitational potential due to a mass M

Gravitational potential

 

 As from the above figure Earth has created its gravitational field surround to it in all direction as shown in figure, gravitational field g its direction is directed towards the Earth centre, So any mass comes in gravitation field attracted and fall towards the centre of the Earth.Now you can find gravitational potential at any point near and above the Earth surface due to mass of Earth.
All different location in field gravitation potential will be different. 
 
Now suppose there is no any mass and you want to find potential at a point P, then what will you do ? as per definition of potential a small mass m will bring from infinity to that point P and the amount of work done per unit mass will be potential at point P.
 
But think if there is no any mass then you will required to do any work to bring small mass m from infinity to point P, See the definition of potential at a point state that the amount of work done per unit mass required to bring small mass to point P will be potential at point P. 
 

 

But first of all you need to check whether that work is required or not, So can you tell me in this case work is required or not ,well answer is BIG no think why ?
 
See when you will touch the small mass m at infinity then according to Newton’s first law every object try to continue in rest or uniform motion unless and until external applied force is zero.Hence see in this case there is no any external force on small mass m, So it will start motion after touching very very little force and it will continue in uniform motion.
 
Also there is no any attractive force for small mass m because there is no any mass.
two important point first it should reach the point P and second its speed must not change during the journey from infinity to point P.
Hence you see both the point are valid in this case, It will reach itself point P without doing any external work as well as without changing the speed.suppose the friction and air resistance is neglected. I hope you got about gravitational potential energy.
 
Now when you are not doing work to bring small mass m, then how it will stop at point P, for this you just touch and stop at point P it will stop easily, this stooping and touching force will be very very small and consider as negligible.
 
Hence potential at point P will be zero, So it is not necessary that all point will have some potential, it depends upon mass. See the below picture.
Gravitational potential at a point

 

From the above figure see the second case, there is now a mass M so small mass will be attracted towards the heavy mass M due to gravitation force.
 
Now you have to work to bring this small mass m slowly otherwise the speed of mass m will increase which we don’t want ,so you have to apply force against this gravitation force and this work done will be by external agent.
 
Now suppose point P is at a distance r from the heavy mass M Hence in this case potential at point P will be  Vp  = -GM/r potential is a scalar quantity, negative sign indicates here small mass m is bounded by big mass M so sign is negative.
 

 

In other words you can say the work done by external agent is negative how ? well see you are applying the force against gravitational force and displacement is in opposite direction so the work done by external agent will be negative.Gravitational potential is always negative. 
 
So mass create potential at any point. If mass will not be present then potential will not be available at any point .Now i hope your concept is clear about gravitational potential due to a mass. 

Derivation of potential due to mass at a point

Suppose a heavy mass M as shown in above picture case 2, you want to find potential at point P at a distance r from heavy mass M.
let at x distance bring small mass m from point P then gravitational force between M and m will be  GMm/x² , see here gravitational force is variable depending upon x so you know that variable work done is calculate as.
∞ ∞ ∞ 
W  = ∫F.dx  = ∫ Fdxcos180   = -∫GMmdx/x²  = -GMm∫x⁻²dx  =GMm/r now this work done 
                     r                         r                                r
from Point P to ∞  hence work done from ∞  to point P will be  -GMm/r 
W  = -GMm/r 
 
Now potential at point P is defined as Vp  = ( work done from ∞ to P )/m so 
Vp  =  -GMm/mr = -GM/r so Vp  = -GM/r.
Now condition for heavy mass M is that it must be a point mass.

Now see below questions.
 
Now from question Q1 find the potential at point P due to all three masses .

Ans you know that due to mass m potential formula is given as V  = -Gm/r , where r is distance from mass to point p.

So first calculate the distance AP = BP = CP ,  now from triangle APcos30 = a/2 

APx√3/2 = a/2  or AP =  a/√3 , Hence BP = a/√3, CP = a/√3 now potential due to single mass m at point P will be V = -Gm/(a/√3) = -Gm√3/a .

potential is scalar quantity so due to all three mass potential will be same at point P

Hence total potential at point P will be three times  Vtotal  = -3xGm√3/a  = -3√3Gm/a .


Now from question Q2 above picture, You have to find the work done during moving small mass m from point A to point B.


Ans Here m<

VB – VA  = (work done from A to B)/m.
Hence  (Work done from A to B)  = m(VB- VA) ,  VB = -GM/4x , VA = -GM/2x so put the value to find work done.

(Work done from A to B)  = m(-GM/4x – (-GM/2x)) = mGM(1/2x – 1/4x)  = mGM/4x


(Work done from A to B)  = mGM/4x .


See the numerical question below.

As from question this is ring so it is not a point mass, but whatever formula derived for potential is only  applicable for point mass.
Remember in this case you can’t assume the whole mass of ring concentrated at centre of ring, because it is extended mass and formula for potential is inversely proportional to distance.

Hence to solve the problem you have to divide ring mass in many small masses as shown dm and after that for addition of this all masses, you know just integrate whole masses.


So potential at point P due to dm mass will be ∫ dVp  = -G∫dm/(√R²+x² )  

Now here R and x are also constant and ∫dm = m
So  Vp = -Gm/(√R²+x²) .

Now suppose if this point is very very far distance just feel then ring will look like a point mass, because radius will not look so R→0 so in this case Vp  = -Gm/x .


Now what will be potential at centre of ring, gravitational field will be zero but potential will not be zero, at centre of ring put x =0 then you will get Vp  = -Gm/R .


So in this way you can solve numerical problem, If there may be two ring separated with some distance and ask the potential at axis of ring you can find at any point due to both rings.

Relation between gravitation field (E) and gravitational potential (V)  


In previous post i have discussed in details about gravitational field and link is given above in first paragraph, you can refer. Gravitational potential energy discussed in this post, Now you will see the relation between these two quantity. This is important relation you must remember it will also help you to solve numerical problems.

                            →
Gravitational field E  is a vector quantity and gravitational potential V is a scalar quantity.
Gravitational field is property of a Mass whereas potential is a characteristics of a point or location. Now the relation between gravitational field and gravitational potential is given as 

E  = -dV/dr  where  dV/dr indicate differentiation of gravitational potential with respect to position vector. You can also write Ex  = -𝜕v/𝜕x,  Ey  = -𝜕v/𝜕y , Ez  = -𝜕v/𝜕z partial differentiation of potential along x, y, and z axis because gravitational field is a vector quantity.

Potential is not along x,y and z direction because you know potential is a scalar quantity so it has no any direction. Now you can check the above formula.

You know potential at a point P, x distance due to mass M  Vp  = -GM/x.
use Ex  = -𝜕v/𝜕x = -𝜕(-GM/x)/𝜕x  = GM𝜕(x⁻¹)/𝜕x = -GM/x²  Ep  = -GM/x  here negative sign in field indicate direction is towards the mass M centre.
           →
Hence E  = -dV/dr is correct formula. 


See from the figure E a gravitation field, you know that in a field if you place a mass then gravitational force mE will act on mass towards the field direction as shown.


Now to move the mass m from point A to B, you have to apply very little greater force in opposite direction Fext (external force) -mE negative sign indicate opposite direction.


Now work done by external force  Wext  = force*displacement = -mEr , this work done bringing mass m from point A to B.

Again recall potential difference  VB – VA  = (work done A to B)/m , now put the value of work done, so you will get.

VB – VA  =   -mEr/m  = -Er , Now if i told you A is very very close to B then r will be dr and VB – VA will be dV , hence  you can write .

dV  = -Edr or E  = -dV/dr hence it proved. 

#conclusion:

         
I will continue post with more concept. I hope you have enjoyed learning gravitational potential energy. I want your feedback through comment, like and share, learn and grow thanks for sharing . 

 
Dated 6th Jan 2019 

Motion Of Centre Of Mass

Today Topic is Motion of centre of mass.

So i’m going to show you in this article what’s is meaning of motion of centre of mass EXACTLY.
Because most of students are confused to understand motion of centre of mass due to lack of true concept.
So after finishing this post you’ll learn all about exact concept and meaning of motion of centre of mass.
And this is very very important topic of Physics.
So today your all doubt and confusion will be clear here.
You will get best concept for motion of centre of mass in this article.
Let’s continue with me and dive in right now.

Motion Of Centre Of Mass Class 11 Concept

Well, in previous post you have already studies about basic concept of center of mass.

For example what is centre of mass of a body.

And how to calculate centre of mass.

As well as importance and application of centre of mass.

If you have not read previous post then i’ll suggest you to check that link first So that you can better understand.

And i’m providing here the link you can refer the previous post Centre of mass Physics .
Now in this topic we will learn what Physics says about motion of centre of mass like velocity, acceleration.
So this’s right time to explain motion of centre of mass
Here is the deals:
When two bodies moving separately then what effect on motion of centre of mass so lets start.

                                                                       

Motion of Centre of mass

                                                            

A system has n particles and mass m1,m2,m3,m4……………………………..mn

 

As from the figure we see that if there are many point masses in the system then its centre of mass is  defined as rcom.

 

And position r1,r2,r3,r4………………………………rn
Then sum of all moments is define as  
rcom  = (m₁r₁+m₂r₂+m₃r₃+m₄r₄………………………..+mnrn)/(m₁+m₂+m₃+m₄+………..+mn)
 
now rcom is the position of centre of mass with respect to origin.
If you want velocity of centre of mass then differentiate this equation with respect to time on both side we will get velocity of centre of mass.
 
Hence Vcom  = (m₁v₁+m₂v₂+m₃v₃+m₄v₄…………………….)/(m₁+m₂+m₃+m₄………..)
 
Now for acceleration of centre of mass again differentiate the above vcom equation with respect to time on both side we will get acceleration of centre of mass.
 


acom  = (m₁a₁+m₂a₂+m₃a₃+m₄a₄+………………………..)/(m₁+m₂+m₃+m₄)

Application of motion of centre of mass

 
From the above figure two ball of mass 1kg each having velocity 5m/s and 10m/s respectively.Considering as a system find the velocity of centre of mass.
 
Here velocity of both ball at an angle of 37⁰ so we have to take separate component for velocity along x axis and along y axis.
Now velocity of first ball along x axis  = 5cos37⁰   =5*4/5 = 4m/s
similarly velocity of second ball along x axis  = 10cos37 = 10*4/5 = 8m/s
Now apply formula Vcom =( m1v1+m2v2)/(m1+m2)
 
Hence velocity of centre of mass along x axis = Vcomx = (1*4+1*8)/(1+1) = 12/2 = 6m/s
Similarly velocity along y axis for first ball = 5sin37⁰ = 5*3/5 = 3m/s for second ball  -10sin37⁰ = -6m/s 
 
Vcomy = (1*3-1*6)/(1+1)  = -3/2 m/s
 
We have already learn vector in details previous post if you have problem refer vector post.
Hence velocity of centre of mass Vcom = Vcomxi^ +Vcomyj^  = 6i^ -3/2j^
So net velocity of centre of mass will be Vcom = √6²+(3/2)² m/s
 
Now for angle tanϴ = Vcomy/Vcomx  = -1.5/6 
As from the question initially both mass are kept then its initial centre of mass will be as shown.
If mass of 10kg will move toward right them centre of mass will adjust itself and will try to move left.
But from question centre of mass should remain stationary 20kg mass have to move left that need to find.
 
You know that centre of mass rcom = (m₁r₁ +m₂r₂ )/(m₁+m₂)
now partial differentiate this equation you will get 
 

 

drcom  = (m₁dr₁  +m₂dr₂)/(m₁+m₂)  this equation is very very important remember forever.

 
Here drcom is change in centre of mass but in this case no any change centre of mass remains stationary.
so drcom  = 0 so put the value in above equation
drcom  = (m₁dr₁ +m₂dr₂)/(m₁+m₂)  here dr₁ = 2cm
0   =  10*2 +20dr₂ 
0  = 20 +20dr₂ or  dr₂ = -20/20 = -1cm hence 20kg mass need to move 1cm towards left .
Which is opposite of the movement of 10kg mass to remain centre of mass remains stationary.  

Important point for motion of centre of mass

This is very important concept for motion of centre of mass.
You know that acceleration of centre of mass for large number of point masses is defined as.
 
acom  = (m₁a₁+m₂a₂+m₃a₃+……………..+mₙaₙ)/(m₁+m₂+m₃+……….+mₙ) 
Now after arranging the denumerator  we can write as.
 
(m₁+m₂+m₃+……….+mₙ)acom  = (m₁a₁+m₂a₂+m₃a₃+……………..+mₙaₙ)
 
Here it is clear that in Newton’s second law Fnet = M*acom
where acom is acceleration of centre of mass or Fnet =M*acom  = m₁a₁+m₂a₂+m₃a₃+…………..+mₙaₙ 
 
→        →  →  →                   →
Fnet   = F₁+F₂+F₃+……………+Fₙ

***** Important conclusion for motion of centre of mass

Is this possible the net Force on system is zero, But individual particle of the system is doing motion ?
What is your opinion ?
Well, the correct answer is yes.
lets understand this important point.
If Fnet  = 0 it does not mean all forces F1, F2 ,F3 …… are zero.
it may be F1,F2, F3 are having some values but after adding this value in vector method Fnet becomes zero.
acom = Fnet/M hence it clear that if Fnet is zero then centre of mass acom will must be zero.
This is 100% true if the Fnet acting on system is zero then acceleration of centre of mass must be zero.
If acceleration of center of mass is zero then it does not mean that each mass of the acceleration a₁, a₂,a₃…….. are zero.
  Because individually each acceleration will have some value but after adding it becomes zero.
Now if acceleration of Center of mass acom is zero.
Its mean that there is no change in velocity of centre of mass.
So velocity of centre of mass is constant.
But it does not mean that every individual particle velocity is constant .
Because their acceleration is not zero hence it velocity may change.
Are you getting ?
 
So these all above points are very very important for key concept about motion of centre of mass.
But it will take sometime to digest you.
So understand  carefully and practice key concept.

#Conclusion:

 
Centre of mass position is conserved during a motion. “If no external force is applied”. Internal force within the system. And external force which comes from outside of the system. For example Earth Moon system . There will be a centre of mass closer to Earth because mass of Earth is heavy than Moon. So both Earth and Moon is consider as a system. Because centre of mass is always closer to heavier mass. But Remember “centre of mass never rotate”. Earth and Moon rotate about centre of mass freely.  We will continue in next post. I hope you have enjoyed to learn motion of centre of mass if you like comment and share thanks for learning and sharing keep reading more and more.
 
Dated 4th Oct 2018          
 
 

center of mass physics

Today i ‘m going to explain what’s center of mass Physics

Because it’s very important concept in Physics.

So you need to know everything about center of mass Physics

 Without understanding concept of center of mass Physics, It will not be easy for you to understand better Physics.
So try to understand center of mass physics.
And in previous post you have already study center of mass basic concept for continuous mass distributed body.
So you can refer previous post Center of mass formula .
But here we will study center of mass for hollow and solid hemisphere with easy concept.   


What is center of mass Physics ?

So Center of mass of  a body is that point where whole mass of the body is concentrated.
And it can lie within the body or outside the body depends upon the shape of the body.

But Why you need to study center of mass Physics

Because in Practical every rigid body has some shape and size .
If the body comes in motion then every point on rigid body have different velocity and acceleration. 
Suppose a rigid body of some mass m is rotating about its axis as well as translate.
Every point on rigid body will have different velocity and acceleration.
So It is really difficult to calculate velocity and acceleration of all point on rigid body.
Hence there is a single point where whole mass is concentrated is called center of mass.
And that point velocity and acceleration is consider as whole body velocity and acceleration.
Hence that special point is called center of mass.
you know that Newton’s second law . Fnet = ma, p = mv. Here in this case “a” and “v”  is acceleration of center of mass  and “v” velocity of center of mass.
If any body do combined motion rotational and translational then its path analysis will be easy.
When you sit on center of mass and analyse body other particle motion.

How do you find the center of mass in physics?

Generally center of mass path is easy like (straight line, Circle, Projectile)       
Hence you can think the importance of center of mass.
Fnet  = ma equation has two important condition
Here “a” is acceleration of center of mass and m is a point mass.
This is reason we need to study center of mass physics.

Practical uses and Application of center of mass Physics 

The center of mass plays an important role in astronomy.
The barycenter is the point between two objects where they balanced each other. 
And It is the center of mass where two or more celestial bodies orbit each other.
When a moon orbits a planet or a planet orbits a star, both bodies are actually orbiting around a point that lies away from the center of the large bodies.
So for example the moon does not orbit the exact center of the Earth.
But a point on a line between the center of the earth and the moon, approximately 1710 km below the surface of the earth.
Where their respective masses are balanced. This is the point about which the earth and moon orbits.
Also Automotive applications  engineers try to design sport car so that its center of mass is lowered to make the car handle easy.
Also uses in aeronautic, high jumping .
Now i think you have understand the importance of center of mass.

How to find hollow hemispherical center of mass ? 

                                                               


Center of mass hollow hemisphere

center of mass calculus

From the figure it is clear that mass is distributed over the surface area of hollow hemisphere.
and One thing is clear that hollow hemisphere is symmetric about x axis.
Which means positive x axis (right side) and negative x axis (left side) mass distribution is same. 
Hence Xcm will no need to calculate it will be at origin for Xcm.
Along y axis its mass is different for different value of y.
 
Let total mass of hollow hemisphere is M and its radius is R, Now taking a elemental ring of mass dm.
now the thickness of elemental ring will be Rdϴ as shown in figure.
And the radius of elemental ring is Rcosϴ  as shown above figure. Now the Ring above the origin that is y = Rsinϴ as shown in figure.

 

Ycm  = ∫ ydm/∫dm  now put the value of y  =  Rsinϴ 
Now dm can’t be integrated, Because  dm is not written in terms of y, Hence we need to find out the mass of elemental dm first.
So to find out the mass of elemental ring, we have to consider surface mass density.
which is define as mass per unit surface area, It is denoted by 𝞼 .
Hence  𝛔  = M/A = M/2𝛑R²   Since mass is only distribute on surface area of hollow sphere 
So we can write 𝛔 =dm/dA or dm  = 𝛔dA.
 
Now we can calculate the area of elemental ring and it will be area .
of elemental circle of radius Rcosϴ and thickness Rdϴ.
Hence Area = 2𝛑Rcosϴ*Rdϴ So for elemental area  dA =   2𝛑Rcosϴ*Rdϴ  hence from here dm = 𝛔*2𝛑Rcosϴ*Rdϴ.
 
Now use the equation for Ycm  = ∫ ydm/∫dm  = ⎰Rsinϴ *𝛔*2𝛑Rcosϴ*Rdϴ/M 
 
Here ∫dm = M  since total mass is M.
 


Ycm  = R³*𝛔*𝛑*1/M⎰2sinϴ*cosϴdϴ now putting value of 𝛔 and 2sinϴ*cosϴ = sin2ϴ then 
 
Ycm  = R³xM/2𝛑R²x𝛑/Msin2ϴdϴ now take limit from 0 to 𝛑/2 total mass will be cover hence after simplification we will get .
                   𝛑/2 
Ycm  = R/2sin2ϴ
                  0
                               𝛑/2
Ycm  = R/2⎡-cos2ϴ/2⎤   now put the value we will get 
                                  0
 Ycm  = R/2 (2/2) = R/2  , Ycm = R/2 
 

Center of mass for solid hemisphere  

 
Solid hemisphere can be made by many hollow hemisphere so you will use this technique to find the center of mass for solid hemisphere.

                                                           

This is 3-D because it is solid lets suppose an elemental strip is taken from origin at a r distance.
then just we have seen in case of hollow hemisphere its center of mass is at r/2 distance from origin.
Hence this elemental strip center of mass will be at r/2 distance from origin as shown above figure 
Now apply center of mass formula  Ycm  = ∫ ydm/∫dm .
Here it is clear y = r/2 
now this is solid so its mass density will be mass per unit volume and it is denoted by 𝛒 
  𝛒  = M/V  = M/(2x𝛑r³)/3 = 3M/2x𝛑r³  since half volume of solid sphere 
Ycm  =  ⎰r/2dm/⎰dm  = ⎰r/2dm/M  ⎰dm = M.
 
Since total mass is M
now for dm mass dm/dv  =𝛒  or dm  = 𝛒dv 


now for dv  = Area x thickness  = 2𝛑r²xdr
dm  = 𝛒2𝛑r²dr  now put the value in above equation we will get 
Ycm  = ⎰r/2x𝛒2𝛑r²drx1/M  =  put  𝛒 = 3M/2𝛑r³
            R
Ycm = ⎰r/2*3M/2𝛑r³*2𝛑r²dr/M  after simplification and integration you will get 

 

           0
Ycm  =   3R/8 

#Conclusion:

Now we will continue in next post. I hope you have enjoyed learning Center of mass Physics .If you like comment and share thanks for learning and share.
 
Dated 3rd Nov 2018                                 
    

Different Forces in the world around us

Today i’m going to explain here everything about different forces in the world around us.

So you’ll learn in this article the hidden concept about forces.

Which’s is invisible to you different forces in the world around us.

But are working in the nature.   

So after finishing this article your concept and doubt about all forces will be clear. 

Because you are going to know how many types of Forces in the World around us true meaning here today ? 
So let’s dive in right now.

 what is force simple meaning ?

Force is a notion experience or feel of push or Pull.
you found force in the world every place most important point about force see force always come in picture between two bodies.
So one body apply force and other body receive force without two body force can’t come in picture.
Here some example of forces is given below in picture see in every forces there is two body. 
                                                     
Different Forces in the world
Here the motive is to understand different types of forces in the Nature around us.
And its Properties and its source. there are many forces just overview of forces take some example.

Different Forces in the world around us

Gravitational force 
When you take a ball in our hand and just released and told to ball stand here.
But ball not stand falls down towards earth the we say earth apply a force on ball and this force is gravitational force.
Friction Force :  
Whenever you put one object over other and try to push then you have to apply more forces to push the body.
Then you told there is friction between bodies.
Tension in Spring :
Now you fixed one end of spring roof ceiling and other end stretched and some mass is tied and release the mass.
what happen mass will move upward tension in spring.
Buoyancy Force : 
when you jump in swimming pool then water apply a force on our body which is called buoyancy force.
Viscosity Force :
And a ball of iron is drop in oil container ball goes slow to the bottom of container this is called viscosity force.
Inter atomic Force:
This force arises between two atom and chock is best example of this.
Because one end of chock is hold and other end of chock does not fall on the earth.
The reason each atom of the chock is tightly bounded by inter atomic force.
Electromagnetic force :
When you on our TV through remote you press button of remote.
And this force goes in the form of electromagnetic force and press our TV on button this is called electromagnetic force.

Examples of different forces in the world around us

Hence these are some example of forces there can be 100 example in the world for forces.
Then how many force you will study it will become very large study for this.
Because our physics has given a Principle that is called Unification.
which is already explained before it explain that maximum number of phenomenon can be explain through a single laws.
now we try to search the sources of force and think over it perhaps.
Because you are doing study of similar forces at two or more different places and wasting your time.
And making the study large means to say that one forces working at two, three more or all different places.
Now good scientist accept that in the world there is only one force and it is working at different places appear in different form.
Because there is only one force which is running in the world.
 But it is easy to say easy to listen but when asked what is and where is that single force running the world.
So till date we have not found may be our knowledge is insufficient.
And we have not found till in spite of this we try to find minimum number of forces.
Now scientist try to find out the source of different forces a car is running on the road due to friction force.
you walk on the ground due to friction force, earth rotate around sun why earth not move in a straight line.
Because sun pull the earth towards it own and earth rotate in an elliptical path.
This is gravitational force ball fall on the earth due to gravitational force.
Similarly after study so many force it was found that there is a single force for many phenomenon.
Like friction force, viscosity force, buoyancy force, tension in string, electromagnetic force.
So all these forces source is electron this all force arises due to exchange of electron.
And it is kept under categories electromagnetic force so scientist studies each forces and search their sources.
So that they can found out fundamental force and finally found four fundamental forces present in nature.
which drive the all phenomenon in nature then it became somehow easy for our study.
After all scientist are trying for one single force.
which drive the whole universe and latter it will be possible because we have seen that nothing is final in science.


Fundamental Forces in Nature :  

1 Gravitational force 
Gravitational force causes due to mass this force is in categories of macroscopic.
means we can see through eye the phenomenon of gravitational force ball falls on the ground .
Example of this force any body having mass has gravitational force heavy mass body.
And having large gravitational force due to this gravitational force.
All masses of body are stable and fixed on the earth, stars,planets, galaxy motion are control by this force so this is popular force.
this force acts on mass, nature of this force is attracts,range of this force is infinite comparative strength weak than other fundamental force.  
2 Electromagnetic force 
 This forces cause due to electric charge whether it is static, moving or accelerating.
this is also in categories of macroscopic we can see through eye it effect.
example of this force is magnet two opposite charges attract each other its forces are limited.
so it is not popular. this force acts on electric charge if body is not charge.
this force will not act.nature of this force is attract as well as repel, range of this force is infinite.
comparative strength is very strong 10^27 times gravitational force.example of this force is friction, magnet etc.  

what are the four main types of forces

3 Strong Nuclear force 
This causes due to nuclear sub particle electron, proton, neutron.
this is place in categories of microscopic we can’t see the phenomenon of  strong nuclear force through eye its phenomenon happens inside nucleus.
So nature of this force is attract as well as repel,range of this force is 10^-15m, .
comparative strength 10 times stronger than electromagnetic force.example inside nucleus electron, proton, neutron. 
4 Weak Nuclear force 
This causes due to nuclear particle when they come out from nucleus .
when nuclear is blast radioactive element come out alpha, beta, gama at that moment a force among these particle is called weak nuclear force.
this is in categories of microscopic we can’t see the phenomenon though our eyes.
weaker than strong nuclear force and greater than gravitational force scientist have no more ideas about this force it is under research. 
 
if you study about any force it will come under any one of these fundamental force.
latter we will see in more details about each force.
 

different forces in the world around us Conservation Laws: 

 Conserve means to hold safely, When the universe was made by God.
whatever things was made by God is safe till date not destroyed anything.
whatever that things is you need to understand here that is well define mass and energy.
the whole universe is made by mass and energy by God.
mass is the material light from sun is energy sound is energy when you observe whole universe.
you will find only mass that is particle or energy.
wait just count the whole universe particle it will be some quantity and similar count the whole energy of universe.
So it will also be some quantity hence this quantity of particle and energy will never be change.
Hence this is called conservation laws we are talking about world mass and energy.

There are many conservation laws in nature: 

         
1 Conservation of mass and Energy this is fixed by God and will be fixed forever unless the universe is not destroyed by God
2 Conservation of Charge this is also fixed charges transfer from one body to other body.
it can’t be destroyed as well as created take an example when battery of our cell is discharge our cell goes off.
now what we do put cell on charging process and our cell battery  get again charge.
how it happens. when our cell work electron travel from one end higher energy level to lower energy level.
when all electron reaches in lower energy level then our battery goes down electron has no energy.
but are present at low energy level. when we connect through external charge source.
that lower energy electron from cell is drawn and energetic electron is putted in the battery of the cell and our cell battery again get charged .
here charge is transfer from external source to cell battery but not destroyed and created. 
3 Conservation of mechanical energy this energy is potential energy(standing body energy).
 And kinetic energy(moving body energy) this energy can be transfer one location to other location.
as well as one body to other body but can’t be destroyed and created.
4 Conservation of momentum what is momentum this is how fast a body is moving this is also transfer from one body to other body.
but can’t be destroyed and created.this is very important laws on the basis of this laws we study whole physics.

Different types of forces and their examples

Every system in this world want to spend minimum energy this is universal and general truth.
every body of this world want to stay in minimum energy level.
so that the body or system will be stable if the body will have high energy it will be unstable.
take a practical example if someone given you 10000$ suddenly what will happen you will be unstable.
you will go for marketing, party with friends you will not stay in home at all in other sense.
if you have no money you will continue in home you will be stable. feel yourself a running man want to stand.
a standing man want to sit, a sitting man want to sleep why because standing man spend less energy.
than running man, sitting man spend less energy than standing man, sleeping man spend less energy.
than sitting man so every body or system want to spend less energy.
physical action or any system of nature wish to continue with minimum energy level. our physics study is based on this principle.

Principle of Symmetry:  

 The principle of nature are symmetrical what does it mean lets see One lakh years ago winter came after 365 days.
today what happens after every 365 days winter came so one lakh years winter season was same as well as today.
so after changing time nature principle is not change.
we change our principle but nature never change its principle.
water always flow from higher energy level to lower energy level due to minimum energy level .
And concept it is truth for whole nature in India it will flow from higher energy level to lower energy level.
it will also be same in America today is happening and it will also be happen after one lakh years.
so principle of nature never changes with location and time this is called principle of symmetry.
Here the speed of light is 3*10^8m/s if we go to mars and calculate this is same or if we go to out of sun.
there will be also same, if we go to other galaxy there will be also same this is symmetry of nature.

Conclusion:

I hope now your doubt is clear about different forces in the world around us. If this article is helpful for you then like comment and share on social media. Thanks for reading Different Forces in the world around us.

center of mass formula

Center of mass Formula

Today our topic is for center of mass formula for continuous distribution of mass of the body. This topic is conceptual but important for whole topic in physics. So we will learn from basic concept to depth .Once you will learn the basic concept, Physics will be easy for you in every topic and your concept will developed the way to think about problems. In previous post we have study about basic concept of center of mass, When body is discrete, Means two or more body masses are separate. You can refer post center of mass But in this topic we will study center of mass formula, When body mass is distributed continuously, Hence the previous post formula will not be applicable, So have to drive new center of mass formula, So lets start and enjoy learning center of mass formula.


integration meaning 

As we have discussed here body mass will be continuous distribution over a shape and length, not in discrete manner. So we required here concept of Integration meaning.
So that you can well understand without any doubt.
Hence first see the Integration meaning, Then will continue for center of mass formula derivation.
                                                                     

Integration Meaning





calculus is the important branch of mathematics, greatest invention for mankind  and invented by Issac Newton .when he was stuck at a point where normal mathematics was not supporting to carry out his experiment and derivation after rigorous hard work for two years, Newton finally invented Calculus and you know without knowledge of mathematics we can’t understand physics well . mathematics is tool of physics or backbone of physics so we need to understand calculus application here .calculus is amazing branch of mathematics simple and complex both, but we are studying here physics so we will not study here in depth as per our need we will see application.

Now come to the Integration meaning. You generally see two symbol is frequently use in Physics and mathematics one Delta(∆) and other is d. Now see the meaning of both.





∆→ Meaning change for large number, When written as x means change in x, but its value will be large.
d→ meaning change for very very small, When written as dx means change in x, but its value is very very small.
Here this concept will be use to calculate center of mass formula. In this topic you will learn how to take very small value to calculate mass of uniform distributed body. Apart from here this concept will be use in rotation mechanics also and everywhere in Physics as well as in mathematics.

So this concept is very important,Hence lets start.

Center of mass formula continuous mass distribution  

                                                                   

Here the center of mass formula derive Xcm = ∫xdm/∫dm is for continuous mass distribution.Hence if continuous mass distributed then you can not apply individual or discrete center of mass formula Xcm = (m1x1+m2x2+m3x3+………..)/(m1+m2+m3…….).

Similarly Ycm  = ∫ydm/∫dm  or for z axis  Zcm  = ∫zdm/∫dm .

Now one important point what is meaning of ∫dm, This is sum of all small masses and it will be equal to total mass. So we can write ∫dm = M
Xcm = ∫xdm/M.

Now problem here in this above equation ∫xdm/M is that there are two variable x and dm of different type one is length and other is small mass so it can’t not be integrated unless you not convert into same type. 
Hence to do integration above equation we have to change one type of variable,So we will have to change dm value in the form of x to do this one new term is introduce see below.

Linear mass density

Linear mass density is important concept try to understand this concept will be use in physics many topic. It is denoted by (𝞴) its meaning is mass per unit length.


𝞴 = M/L (mass/length) now important concept 𝞴 is always constant for uniform mass distribution, uniform means equally mass distributed over the length.
Hence for small dm above shown its length will be dx so we can write 𝞴  = dm/dx or 
dm = 𝞴dx now we have got small mass dm value dm = 𝞴dx this was the key point of concept. Now put value of dm in above equation we will get.

Xcm  = ∫xdm/M  = ∫x𝞴dx/M  here 𝞴 is constant so it will come out from integration hence
Xcm  = 𝞴∫xdx/M now limit will be from one end of rod 0 to other end of rod L
             L                             L 
Xcm = 𝞴∫xdx/M  = 𝞴/2M*⎡x² ⎦   now put value of 𝞴 = M/L and limit after simplification we will
            0                             0
Xcm  = L/2 this is the value of center of mass formula for uniform mass distributed rod .






Now mass distribution of rod can be uniform or non uniform both if non uniform then mass density will be not constant, Means value of 𝞴 will be not constant.
Question for you suppose non uniform mass distribution of same rod and its mass density is given 𝞴 = 2x then find center of mass.Try yourself if you have got the above concept it will be solve easily.

Center of mass formula for semicircular wire  

                                                                 

Since it is a wire hence one dimension, So its linear mass density 𝞴 = M/L = M/𝞹R because it is a semicircle.

Again 𝞴  = dm/dx  or dm = 𝞴dx now problem is that here dx is not know, So for that just see the small triangle dm arc. We know for small value of d𝞱  we can write Rd𝞱 = dx small length of mass.

So our small mass dm = 𝞴Rd𝞱 now put dm value in Ycm above equation we will get.

Ycm = ∫ydm/∫dm , put y = Rsin𝞠 in this equation we will get finally
                                                          𝞹
Ycm = ∫Rsin𝞠𝞴Rd𝞠/M = R²*M/𝞹R*M∫sin𝞠d𝞠 f after integration we will get finally 
                                                         0
Center of mass formula for semicircular wire Ycm = 2R/𝞹.This is important formula try to remember this formula.

Now we will continue in next post.I hope you have enjoyed to learn Center of mass formula for uniform distributed mass. if you like comment and share thanks for reading and sharing keep reading more and more.
Dated 24th Oct 2018.     
                                                                                 

conservation of momentum formula

conservation of momentum formula

Today our topic is conservation of momentum very important topic. We will discuss this topic from basic concept to depth concept of conservation of momentum.First we will discuss what is momentum and then how momentum of a system is conserved by taking practical example.
In previous topic we have already learn about centre of mass of a system, So that concept of centre of mass also be use in the conservation of momentum.
So i will suggest you to go through topic of centre of mass for easy understand, You can refer previous post Centre of mass important point  to understand concept of centre of mass. Now lets start conservation of momentum.  


What is momentum ?  

                                                                     


                                                     Conservation of momentum        
                                                                     
As from the above figure momentum. Bicycle and truck are moving towards you as shown  then which one you will try to stop.
I am sure you will try to stop bicycle not truck.But why the reasoning behind this is momentum. The momentum of truck is more than bicycle.
Momentum is simply mean mass in motion. Momentum of truck is more because it is very massive. Now momentum of bicycle is less because it has less mass. But it does not mean that momentum only depend upon mass. It depend upon velocity also.

Hence momentum mathematical relationship with mass and velocity is define as  momentum = mass*velocity or denoted p = mv.
Where p is momentum m is mass in kg and v is velocity. 
You should remember that velocity is define as speed with direction, If an object has large speed it also has large velocity. we know velocity is vector quantity so momentum is a vector quantity. 

From the above momentum equation  p = mv we see that if you vary the mass and velocity momentum will change.
If you increase either of variable mass or velocity momentum will go up. So truck momentum is more than bicycle. This also means that an object at rest does not have momentum. Velocity of an object at rest is zero so no movement.

So in order to an object having momentum it must be moving. I hope you have understand momentum.
Now let me discuss more interesting about momentum, An important point to note about momentum. It is a vector quantity this means that it has magnitude as well as direction.


The direction of momentum is same as the direction of velocity vector. But in order to fully describe the momentum of an object must include direction.

Now look at some  example of momentum for better understanding. An object of any size can have large momentum whether its size is large or small but can have large momentum.
Because its depends upon the speed of an object as well its mass.
If its speed is more then its momentum is more and if its mass is large its momentum is large. Now you think that all object which have greater mass have greater momentum but it is not true for all cases .

Let us discuss in this case a super tanker ship is coming to the port not be travelling very fast through the water but it is massive so it will be easy to stop at port safely.

Lets understand momentum with daily life example . A truck of full load has a large mass and must slow down long before a stop light because even with a small velocity, It has a large momentum and is difficult to stop.
A bullet, although small in mass, has a large momentum because of an extremely large velocity.

What is Conservation of momentum ? 

As we have seen mathematical relation of momentum p = mv now differentiate this equation on both side with respect to time then will get.
dp/dt  = mdv/dt  here mass is taken as constant, Now we know that dv/dt is acceleration but remember which acceleration this is centre of mass acceleration if you are not digesting refer previous centre of mass post.
Hence we can write dp/dt  = ma and from Newton’s second law ma is Fnet or we can write 

dp/dt  = Fnet  now try to understand physical meaning of this equation.
Rate of change of momentum is net force on the system. Its physical meaning is if force is applied on a body then its momentum will be greater in the force applied direction.
                                                               


See the Above picture for conservation of momentum suppose we have a system as shown in which there are some objects which are moving as shown in figure.
As we have learn the system will have a centre of mass as shown by pink mass and it will also have a velocity which is known as velocity of centre of mass Vcm.

Now we are saying that the external force on the system is zero Fnet =0, Internally the object or particle can have apply force. But externally there is no any force acting on the system.
So as external force is zero its mean that acceleration of centre of mass is also zero acom =0, Then Vcm will be constant Vcm = constant, magnitude as well as direction constant.
Hence its mean that momentum of the system is constant.

So it is very important conclusion derived, If external force on the system is zero that is Fnet =0 then momentum of the system is conserved or constant means initial and final momentum of the system will be same.

Conservation of momentum definition 

Principle of conservation of momentum states that if external force on a system is zero,Momentum of system remains constant or conserved.

Now we will see some numerical questions so that your concept and doubt may clear, how to apply conservation of momentum formula. see below questions.
                                                                     

From the question considering two men together as a system and it is given initially the system is at rest. So it is clear that external force on the system is zero hence Fnet = 0.

Hence total momentum of the system should remain constant that p = constant ,so we can write Pf = Pi 
Now initial momentum of the system is zero both men are in rest initially 
so  Pi  = 0+0 = 0
Now final momentum of the system is Pf =  100*v – 50*10  ( negative for 50kg because momentum is vector quantity consider with sign it is in negative direction)


Now equate Pf = Pi, Hence  100v-500 =0 or  v = 500/100 = 5m/s  v= 5m/s in right direction.

So you have seen that if external force is zero then momentum is conserved, and how to apply to solve the numerical question.
                                                                        

From the above picture question Q1.
We have to find velocity of car when man is walking above the car with 2m/s suppose friction between ground and car is negligible .

Here external force is zero, Fnet = 0 so momentum will remain conserved.
Final momentum = Initial momentum 
initial momentum is zero Pi = 0 because initially man is standing and car is at rest 
now for final momentum let v be the velocity of car, important point is consider velocity with respect to ground.

Pf = m*2  -10m(2-v) = 2m – 20m-10mv  = -18m -10mv  Hence 

Pf = Pi
 -18m -10mv  = 0
v  = -18m/10m  = -1.8m/s.

Now you can try for second question Q2 .
Hints before one mass is moving and other mass is at rest and after collision both stick together then find final mass velocity.

Now we will continue in next post . I hope that you have enjoyed learning conservation of momentum formula. If you like comment and share thanks for sharing and reading learn and grow.

Dated 9th Nov 2018   



centre of mass important points and numerical

Centre of mass important points and numerical

Today our topic is about centre of mass important points and numerical. This topic is important because we will discuss in this topic key point of centre of mass. If your theory concept is not clear you can’t solve the numerical problem. So it is very important to clear your theory concept first to solve the numerical problem.

So we are going to discuss here key theory point for center of mass and then solve the numerical problem easily.
In the previous post we have already discussed about motion of center of mass. If you have read that post i will suggest you to go through that post before learning this post.
Because we have already discussed basic and important point about centre of mass, You can refer that post motion of centre of mass.

Centre of mass important point you must know


                                                           
                                                 Center of Mass important point

Centre of mass always for a rigid bodies, Centre of mass is a point and the specialty of this point we suppose that whole mass of the rigid bodies lies on that point.
Center of mass point may lies inside the rigid  body or  may lies outside the rigid body depends upon the shape and size of body
This is an imaginary point can be anywhere.
If Centre of mass is taken as origin then its all particle moment or effect is zero about the origin or moment about centre of mass is always zero.
∑mⱼrⱼ  = 0 this is very important result used in rotation. 
Our laws of motion are applicable for point mass, Now in rigid body or system of particle no point mass because in system of particle every particle has mass.
Now we want to apply laws of motion so we can’t directly apply laws of motion on system of particle. Hence to apply laws of motion we consider centre of mass for system of particle.
                                                            
Conservation of velocity of centre of mass 

If no external force is applied on the body then path of centre of mass is conserved.
See below the question.
                                                                 

As from the figure shown consider system of mass m1 and m2 we know that from Newton’s gravitation law two masses attract each other with equal and opposite forces as shown F on each mass m1 and m2.


Now tell me what will be the net force on the system. Of course Fnet on system will be zero because forces on m1 and m2 are equal and opposite.
Hence Fnet =0 so its mean that acceleration of centre of mass acom will also be zero acom =0,But tell me acceleration of m1 and m2 will be zero Big no, m1 and m2 will have some acceleration separately and moving towards each other with acceleration, don’t confuse acceleration of centre of mass of the system will be zero, because the net force   Fnet over the system is zero.  
It indicate velocity of centre of mass vcom will be constant because acom is zero. Now tell me velocity of m1 and m2 will be constant Big no m1 and m2 are having acceleration hence their velocity will be variable not constant, But the velocity of center of mass will be constant.

***** It is clear that if system is initially at rest then system will be finally at rest. If the system is initially in motion then system will finally in motion.
This is the meaning of velocity of centre of mass constant Vcom = constant if Fnet =0 this is very very important concept.

It also clear that centre of mass remain at rest drcom = 0 .

Now see the below question for centre of mass.
                                                                   

As from first boat question since given system is initially at rest when Rajesh moves from one corner to other corner. What will be displacement of boat ?

Apply the concept Fnet on system is zero, acom =0 Vcom = constant but given initially at rest then Vcom = 0 , Hence centre of mass will be at rest no change.

Man and Boat can move internally but centre of mass will not move will be at rest you are getting my point this is the concept.
Now apply the equation for two body centre of mass.

rcom  = (m₁r₁  +m₂r₂ )/(m₁+m₂)  now differentiate this equation partially we have already discussed this equation in previous post.

drcom  = (m₁dr₁+m₂dr₂)/(m₁+m₂) now centre of mass at rest hence drcom = 0 put this value in above equation we will get.

0 =  m₁dr₁+m₂dr₂  Now one concept here always take displacement with respect to ground .


Now as from question when Rajesh will move to other corner on boat then he will travel distance 4m with respect to boat.
Now suppose boat move x distance in opposite to Rajesh then actual displacement of Rajesh with respect to boat will be (4-x) = dr₁, Similarly dr₂ by boat will be ( -x ) because in negative direction.
Hence put the value in above equation we will get.

0  = 60(4-x) +40(-x)  or  24 – 6x -4x  = 0 
10x  = 24 or x = 24/10  = 2.4m or   x = 2.4m in left direction.

Now from monkey and baloon second question in above picture, Monkey is climbing on baloon rope then baloon will come down.
Q By what distance the baloon shift downward when Monkey reaches at top most point neglect baloon height.

Now similarly to first question here Fnet is zero and initially the system is at rest hence centre of mass will remain at rest. So we can use the equation 

m₁dr₁+m₂dr₂  = 0
m(L-x) +M(-x) =  0  here we have suppose that baloon shift x distance downward 
mL -mx – Mx  =0  after simplification
(m+M)x  = mL
x = mL/(m+M) This is the displacement baloon will shift downward.

Now we will continue in next post. I hope you have enjoyed learning centre of mass important points and numerical.  If you like comment and share thanks for reading and sharing learn and grow.


Dated 7th Nov 2018

center of mass concepts

center of mass Concepts

Today our topic is about center of mass very important topic for physics, If you will understand this topic well then you can command over the mechanics complex and difficult problems, With the help of Center of mass concept, You can solve the numerical problems easily. This center of mass concept is used broadly in rotational and transnational mechanics, Center of mass has great importance to understand concept of mechanics, Hence lets start center of mass basic meaning and its concepts.

center of mass definition physics  

Center of mass meaning mass of center not the geometric center only mass center, Hence center of mass is that point, Where we suppose whole of the mass is concentrated, Which can be lies inside the body or lies outside the body. some important facts about center of mass.


Some important facts about Center of mass 

1 Center of mass is an imaginary point ( Why imaginary point ? because it is not necessary there may be something it may free space, Hence center of mass point can be free space no anything at that point so it is called imaginary point )
2 Center of mass may or may not be located on system (why it lies outside system ? because every body or system want stability and minimum energy, hence Center of mass lies outside to balance system )
3 Whole mass of the body system can be assumed to be concentrated on center of mass ( why that ? because when body pass with any process considering as whole mass the output result will be same as when considering pass through center of mass).
                                                                 
Center of mass Concepts

                                                          

Why Center of mass need to study ?    

All rules are valid for point mass only, There are so many rules in Physics which is only valid for point mass , As for example Newton’s second law F = ma, This rule is valid only where m is point mass,And a is acceleration of center of mass, We also use equation p=mv where v is velocity of center of mass Second example Newton’s law of gravitation where force of attraction between two masses F = Gm1m2/r²  This law is also valid only for point masses.
But in general practical life example any body has some geometrical shape and big size except particle electron,proton and neutron all body having some shape and size which can’t be like point mass because it occupies big space, So we need a point of mass such a way that where whole body of mass is concentrated, Replacing big body as point of center of mass such that the behavior of body should not change . Hence we need to study Center of mass.So in Physics rules a big body we have to assumed a point of mass, Which is consider as center of mass, then we have to find the location of center of mass, where  whole body of mass is concentrated.Hence concept of center of mass came in picture, So we need to find the location of center of mass in this topic as above picture shown.


from above picture of table a piece of paper is kept if we want to lift the paper vertically, tie four string on the corner of square size paper, and hence we can lift the paper vertically, But other second method find the center of mass of the square paper and apply directly force vertically at center of mass, paper will be lifted vertically without changing it behavior using only a single point called center of mass. This is the application of center of mass.

How to calculate center of mass ?    

Now here we will see how to calculate or find out center of mass for any body or point mass it is written in short COM(Center of mass).
Suppose there are many masses like m1,m2, m3……..  then we need a Cartesian plan to find out the center of mass of the system see below picture.
                                                               

  


   Now technique for finding center of mass try to place the body on  Cartesian plan, So that we get maximum number of zeros or maximum symmetry so that it will be easy to find out center of mass of the body or system.

How can guess center of mass position of a body ?    

As we have discussed position of center of mass of a body depend upon shape of the body.
The position of center of mass will shift towards heavy mass of the body,So you will get center of mass towards heavy mass of the body.
Center of mass divide length in opposite ratio of mass this is important point about center of mass.Center of mass shift closer to heavy mass.
Center of mass is independent of coordinate system, In other words center of mass of the body does not change with respect to body,Whenever coordinate system is change.
Try to find symmetry to find center of mass, See below picture for above mentioned point.

centre of mass problems

                                                                 

  


 Here for Equilateral triangle we have to find center of mass first find out coordinate of all three mass point A, B, C .
As from figure coordinate of A(0,0) , B(a,0) for coordinate of C apply geometry x coordinate will be a/2 now for y coordinate sin60⁰ = y/a so y = asin60⁰ =   √3*a/2 hence coordinate of point C(a/2, √3*a/2) .
Now use the above discussed formula 
Xcm = (m1x1+m2x2+m3x3)/(m1+m2+m3) = (m*0+m*a+m*a/2)/3m =  a/2
Ycm = (m1y1+m2y2+m3y3)/(m1+m2+m3) = (m*0+m*0+m*√3*a/2)/3m = a/2√3 .
Hence Center of mass for equilateral triangle is (a/2, a/2√3).

Try to use symmetry to find center of mass

With the help of symmetry complex problem can be solved by easily so whenever any system of mass is given and asked to find the center of mass then try to use symmetry as possible lets see below hexagonal problem.
                                                               
From the above hexagon question applying symmetry see how it is easily solved, so you have to use the symmetry to find center of mass.
Now after applying symmetry all masses located on a single axis x, Where coordinate of all masses are now known, Hence to find center of mass we can apply formula.

Xcm  = (m1x1+m2x2+m3x3+m4x4)/(m1+m2+m3+m4)
Xcm  = (m*0+4m*a/2+2m*3a/2+2m*2a)/(m+4m+2m+2m)

Xcm  = (0+2ma+3ma+4ma)/9m = 9ma/9m = a

Hence center of mass of this hexagon will be COM(a,0) here y coordinate is zero .
Here center of mass located on x axis at a distance a from origin.  

We will continue this topic in next post, I hope that you have enjoyed learning Center of mass, If you like please comments and share on social media,Thanks for reading and sharing keep learning more and more.
Dated 19th Oct 2018         

centripetal force formula technique

Centripetal force formula technique

Today our topic is about derivation of centripetal force in previous post we have use this force formula but in this topic you will learn short derivation technique for centripetal force rather than traditional derivation in different books i hope you will enjoy to learn derivation of centripetal force before start this derivation i will suggest you to go through previous post centripetal and centrifugal force concept so that you can understand better concept.

Centripetal force derivation by two method

we will derive formula for centripetal force by two different method one we called traditional method and other is short technique method first we will see traditional method for centripetal force formula derivation and then for short method you should know both the method for depth concepts for centripetal force derivation.

# 1 centripetal force formula derivation by traditional method


                                                       

Centripetal force formula technique
                                                                   
              
From the above picture let V1 and V2 is velocity of particle at two different time now we assume that particle is doing uniform circular motion its mean that magnitude of velocity or speed is constant | V1 | = | V2 | = V =constant.
only its velocity is changing due to change in direction, Here in circular motion every time velocity direction is changing hence there is change in velocity and we know that due to change in velocity acceleration is created and we have already learned in previous post  due to change in direction an acceleration is generated which is centripetal acceleration hence from Newton’s second law centripetal force is acting in circular motion its direction is towards the center of the circle along the radius.
since velocity is always tangent to circular path means angle between radius and velocity V1 and V2 is always 90 degree angle between r and r is ϴ for large value of ϴ triage is given where angle between V1 and V2 is ϴ but how it is simple we see that in circle two tangent  V1 and V2  the perpendicular radius making an angle ϴ  hence its tangent line angle will be also ϴ since magnitude of V1 and V2 is same so its length will be equal in triangle hence from from triangle apply vector we can write.
→     →      →        →      →    →
V1 + ∆V  = V2  or  ∆V  = V2 – V1  this is change in velocity which create acceleration called centripetal acceleration.
now we say this is for very less time dt then angle ϴ will be also very small and taken as dϴ in reality then velocity change will also be very small hence  ∆V  = dv.
now for dt time linear distance will also be very small ds hence taken other triangle ds now dv and ds triangle are similar because all three side of both triangle will be equal for very small value of dϴ  hence ration of side will be same so from here we can write as 

dv/v = ds/r  now divide by dt on both side we will get note v1 = v2 = v
dv/v*dt  = ds/r*dt  or  (dv/dt)*1/v  = (ds/dt)*1/r   ( dv/dt = a𝒸  = centripetal acceleration) ds/dt =v in above equation

a𝒸/v  =  v/r  or a𝒸 = v²/r  or  a𝒸 = v²/r now we can also put v = 𝛚r then we will get

a𝒸   = 𝛚²r²/r = 𝛚²r now for centripetal force we can write F𝒸 = ma𝒸 = mv²/r 

F𝒸  = m𝛚²r this is centripetal acceleration.

Centripetal force very important point why centripetal acceleration direction is towards center of the circle ?

Ans if centripetal acceleration and velocity is perpendicular then take component of centripetal acceleration along the velocity then it will be a𝒸cos90 which will be equal to zero then this acceleration will not increase or decrease the speed of particle hence it will be uniform circular motion. if centripetal acceleration not perpendicular to velocity the speed of particle will not be constant which will not be uniform circular motion proved.

# 2 centripetal force formula derivation technique 

Assumption Speed constant | v | = constant for uniform circular motion in uniform circular motion only centripetal acceleration no tangential acceleration only velocity direction change no change of magnitude of velocity.

we have already studies in previous post v =  𝛚r  if you have not seen this post you must read that post because we have discussed in details about this relation your concept of circle motion will be complete clear all doubt please refer this post Circular motion hidden concepts 


now come to our equation v =  𝛚r  here v velocity will not change r will also not change hence 𝛚 will also not change so it is very important in uniform circular motion v is constant as well as 𝛚 is also constant note it .

v =  𝛚r  now differentiate this equation with respect to time on both side see what we get
dv/dt = 𝛚(dr)/dt +r(d𝛚)/dt  = 𝛚(dr)/dt +0  here 𝛚 is constant (using by parts method)

now here velocity can change by two method either by changing by magnitude or by changing by direction so above we have already made assumption velocity magnitude is constant hence only direction is change here and we know due to change in direction centripetal acceleration is created hence dv/dt = a𝒸 it is clear

dv/dt  = 𝛚(dr)/dt  ( here dr/dt is linear velocity v )

a𝒸  = 𝛚v  ( now put the value v =  𝛚r from above in this equation )

a𝒸 = 𝛚*𝛚r = 𝛚²r  or centripetal force  F𝒸 = ma𝒸 = m𝛚²r  = mv²/r  hence it is again proved 

F𝒸 = ma𝒸 = m𝛚²r  = mv²/r  centripetal force formula .
i will suggest you to refer method first for your 11th exam but for competition you can refer method second.
we will continue in next post read and learn more and more all the best.
i hope you have enjoyed learning centripetal force formula technique if you like please share thanks for learning and sharing.
dated 10th Oct 2018.  

Friction in Physics static and kinetic

Friction in Physics static and kinetic 

Friction in Physics is important topic as we have already studies  about many forces like normal force, tension force, spring force gravitational force in previous post friction is also same type of force but this is new type of force we will study about new type friction force in this topic you can refer Newton’s law of motion   .


Friction force is more complicated  than other forces so it required more attention and concepts friction force is of two types one is static friction and other is kinetic friction first we will see kinetic friction and then static friction see picture below for visualization.
                                               

   from the above picture it is clear that friction force acts between two surfaces which is shown in the figure between two surfaces but question arises why friction force acts between two surfaces ?answer when you will see with microscope surfaces you will find small holes in both the surfaces it will look like rough surfaces normally you will see smooth but actually it is not smooth now when block moves with velocity v then block small holes trap in other surface small holes and velocity of block decreases and hence a kinetic friction force acts upon the block in opposite direction of block motion hence we can say “friction acts due to roughness of the surface”.
value of kinetic friction from above FBD of block fr = 𝛍N where 
normal reaction force and 𝛍 is coefficient of friction N = mg hence fr = friction force = 𝛍mg, 𝛍 value is constant its value depends upon the roughness of the surface if roughness is more then value of 𝛍 will be more and if roughness is less then value of 𝛍 will be small for example you have played carrom board in childhood we use powder on carrom board surface to reduce roughness of the surface for making smooth surface  then friction force value is reduce see below some question.
                                         

    from above picture question 1 we will calculate the value of friction we know that friction force fr = 𝛍N = 𝛍mg = 0.5*5*10 = 25N now from question 2 here 10N force is also acting in downward direction so first calculate normal reaction force write the vertical force equation mg force will be vertical downward and normal will be upward hence N = 10+mg = 10+5*10 = 60N now use friction force formula fr = 𝛍N = 0.5*60 = 30N hence friction force is 30N in this case compare question 1 and question 2 value in first case 25N friction force but in question 2 friction force value is 30N why ? answer in second case 10N more force pushing block downward hence the small holes between two surface will trap more so its friction force value will be more this is physical significant.


now for question 3 we can solve similarly taking vertical force and horizontal force suppose block is moving in right direction with acceleration a here you have to take 100N force component in both direction vertical and horizontal now breaking the component horizontal component will be 100cos37 and vertical component will be 100sin37 now we can balance vertical component 
N+100sin37  = mg or N = mg -100sin37 
now horizontal equation 100cos37 – fr = ma or 100cos37-𝛍N =ma now put the value of N and m we will get value of acceleration easily.
Static friction force is define as tendency of relative motion its mean that motion is just about to start it also mean body is at rest no motion suppose a heavy mass is laying on a ground two children of your colony are trying to move it after applying by two children total force the heavy mass is not moving then where does this force gone of course this force applied by children is adjusted by friction force which is not seen again two more children come and join this group to move this heavy mass but still it is not moving again some children come and join this group to move this heavy mass suppose 10 children join and applied force then heavy mass just start to move this is the limiting force adjusted by heavy mass and this is called static friction hence at rest friction force applied is called static friction force but limiting.
friction force acting during body motion is called kinetic friction force kinetic friction force value is less than static friction force i hope that you have enjoyed learning Friction in Physics static and kinetic thanks for reading.
dated 19th Aug 2018        

Motion law for constraints

Motion law for constraints

Motion law for constraints is very important topic for physics complex motion problem solving technique and concept it has some important point must need to understand that point for concept of constraints motion, first point is net force on a massless body is zero because you apply Newton’s motion second law Fnet = ma here m is zero hence Fnet is zero to understand basic concept of constraints motion you can refer constraints concept here we will discuss important motion law for constraints see below picture.


                                                 

 Constraints motion best example is in your childhood your father hold your hand and walk on the road means your motion was guided by your father as your father will move you will follow the path of your father hence your motion is called constraint motion.
if two block A & B are attached together and we are applying force on block A then block A & B will move together then we can say displacement of block A & B will be same because both are attached moving together from here we can write xa = xb where xa displacement of block A and xb displacement of block B now differentiate this equation with respect to time we will get 
d(xa)/dt  = d(xb)/dt 
va  = vb ( velocity of block A & B are also same ) again differentiate with respect to time 
d(va)/dt  = d(vb)/dt ( acceleration of block A & B are also same)
hence these equation are called constraints equation.
above are simple pulley question where we solve easily but for complex question we need some important method to solve question so one method is virtual work method by which we use to solve pulley constraints question see below picture.


                                           

 Now we will learn virtual work method for solving difficult problem virtual work method made easy to understand complex problem you can use this method for complex problem suppose two block are attached through single pulley as shown in figure.  
                                               

From above second picture lets big pulley has tension T in rope big pulley is fixed as shown now small pulley has tension T1 in rope small pulley is movable its mean that small pulley will work but big pulley is fixed hence it will not work now apply work done by each pulley so for big pulley suppose small pulley moves up by displacement xp now we can write equation for big pulley rope
T*xa+T*xp = 0 ( Net work done by rope is zero )
xa +xp  = 0
now for small pulley since pulley is massless hence tension in rope will be T/2 small pulley upward tension in rope is T hence downward tension in rope will be T/2 
now apply work done 
-T/2*xb -T/2*xp -T/2*xp = 0
-xb -xp-xp = 0
xb = -2xp or xp = -xb/2 put in above equation we get.
xa -xb/2  = 0
xa  = xb/2 ( this is our constraint equation relation )
now we can write this equation in short form also work done by rope first and work done by rope second will be zero  w1+w2 =0
(T*xa+T*xp) + (-T/2*xb-T/2*xp-T/2*xp) = 0
see here pulley term is going to cancelled its mean that if we don’t write pulley work or forget then result will be correct this is important point to remember 
xa  = xb/2  i hope that you have enjoyed learning Motion law for constraints and your concept is now clear thanks for reading.
dated 12th Aug 2018

centripetal force and centrifugal force easy concepts

centripetal force and centrifugal force easy concepts

Today is most important topic Centripetal force and centrifugal  force so far in circular motion previous post we have studies only about kinematics part which deals with angular displacement,angular velocity,angular acceleration,centripetal acceleration,tangential acceleration you can refer previous post centripetal and tangential acceleration but in this topic dynamics of circular motion which deals with centripetal force and centrifugal force means we will find out the cause of circular motion and we know from Newton’s laws cause of motion is force so here in circular motion centripetal force and centrifugal force we will study very interesting and easy concepts.


                                             
centripetal force and centrifugal force easy concepts

                                                                         

any particle of the world do circular motion its velocity changes every time due to change in direction whether its speed is constant or speed may change but condition for circular motion its velocity direction always be change its magnitude may change or may not change but direction always be change and we know that due to change in velocity acceleration is created hence it is clear that if body is doing circular motion then acceleration is there and we know that due to change in velocity direction acceleration is created and this is called centripetal acceleration and its direction is always towards the center of the circle along the radius it is denoted as a𝒸  in previous post we have already studies formula for a𝒸 = v²/r = r𝛚²  where v is tangential velocity r is radius and 𝛚 is angular velocity now important point can you tell me which quantity create acceleration answer is force create acceleration or acceleration create force this is just like question which one first came on the Earth hen or egg hence the correct answer is force create acceleration because when we apply force then body start accelerate and due to acceleration velocity change hence in circular motion if centripetal acceleration is there so it is clear that centripetal force created centripetal acceleration i hope that you should not have any doubt about centripetal force concept now and this is vector quantity hence it has direction so from Newton’s second law we can write

→     →
F = ma  hence direction of force will be same as direction of acceleration so centripetal force direction is always towards the center of the circle along the radius as shown in above figure and its direction always changes and always towards the center of the circle hence this is power of dynamics which tell us the cause of centripetal acceleration created due to centripetal force now what will be formula of centripetal force hence from above formula 
F = ma put here a = a𝒸 = v²/r = r𝛚² so F𝒸 = mv²/r or F𝒸 = mr𝛚²
so whenever there is circular motion anywhere in the world there may be a centripetal force but wait and wait there is no any centripetal force existence in the world this is truth you can refer my previous post for different forces in the world   you will get here all force in the world no any force name centripetal force then you will think what is this and which is centripetal force ? then answer is actually some other force made centripetal force or some other force which behaves as centripetal force for example a bob is tied in a string and rotate the bob with hand the bob will rotate in a circular path a tension will develop in the string towards the center this tension is called centripetal force hence its actual definition is “the net force towards the center is called centripetal force” very important point note is  the resultant force towards the center is given the name centripetal force take other example Earth and Moon we know that Moon rotate around Earth means Earth attract Moon with gravitational force this gravitation force towards the earth will become centripetal force you can’t apply a new force name as centripetal force the net resultant any force towards the center will be given name as centripetal force now question arises is this force is imaginary or real correct answer is this is real force if it will be imaginary then no any body or particle can do circular motion actually we have made the concept that the net force acting towards the center given name as centripetal force i hope now your concept is clear for this force see below some question.


                                             

As from the above arrangement we have to find tension in all string T, T1, T2 hence lets start from 3kg block see FBD T2  tension in string acting towards center hence it will be equal to centripetal force in radius of 3m important point angular velocity for all three masses will be same and is 2 rad/s because all three are moving same angle in same time but remember linear velocity for all three masses will be different because v =r𝛚 here radius for all three block is different so F𝒸 = T2 = mr𝛚² = 3*3*2² = 36N
now for 2kg block see the FBD here net force towards the center will be centripetal force F𝒸 = T1 – T2 and it is moving in 2m radius so F𝒸 = mr𝛚² = T1 – T2
2*2*2²  = T1 – 36
16 = T1 – 36  or T1 = 16+36 = 52N  T1 = 52N
now for 1kg mass similarly we can use equation from FBD
F𝒸 = T-T1
mr𝛚²  = T – 52
1*1*2²  = T -52
4 = T-52 or T = 4+52 = 56N hence T = 56N 
hence we can calculate applying concept of centripetal force net force towards center.
Centrifugal force  : it is a pseudo force we know that pseudo force acts in non inertial frame of reference now non inertial frame of reference is that frame of reference where observer is observing from an accelerated frame of reference means acceleration of frame of reference is not zero where Newton’s second law of motion F = ma is not valid because this law and formula is only valid for inertial frame of reference means non accelerated frame of reference acceleration is zero this frame of reference is called inertial frame of reference in non inertial frame of reference pseudo force always acts opposite to original acceleration direction you can see the first figure where observer is sitting inside car  
on circular motion will feel a centrifugal force opposite to center of the circle and its value will be same  ma where m is mass of the observer and a is acceleration of rotating frame of reference and centrifugal force direction will be opposite to original direction of acceleration hence formula for centrifugal force = ma  = mv²/r = mr𝛚² and direction is away from the center and observer is sitting on rotating frame of reference this is all about the centrifugal force its value is same as centripetal force only frame of reference is changed in centrifugal force now we will continue in next post i hope you have enjoyed learning centripetal force and centrifugal force easy concepts thanks for reading and sharing.
date 27th Sep 2018 

   

Circular Motion hidden concepts

Circular Motion hidden concepts

Circular motion hidden concept in this topic we will learn the concept for circular motion which we have not learned before as from the name we know that circular motion means related to circle motion but not only this more than circle motion is circular motion all concept for different parameter use in this motion we cover in depth concept its definition and derivation in first post we have learn the basic concept for circular motion you can refer post Basic concept circular motion here we will see depth concept of circular motion this motion is 2-D motion because both x and y coordinate position changes from reference point when a particle or body do circular motion see the picture below.


                                               

                                                

Angular displacement is 𝛳 this is measure in two unit one is called degree and other is radian (S.I unit) as we know that degree to radian is converted like one complete rotation means 360 degree.
360⁰   = 2𝛑  rad        45⁰ = 𝛑/4 rad
180⁰   = 𝛑 rad           60⁰ =  𝛑/3 rad
90⁰     = 𝛑/2 rad        30⁰  = 𝛑/6 rad
above is radian to degree converter so SI unit is radian 
Angular displacement 𝛳 is a vector quantity and it is a axial vector means along axis its direction will be away from the plan use right hand thumb rule put your finger in motion direction and curl your finger thumb pointing will give the direction angular displacement dimension is M⁰ L⁰ T⁰  it is dimensionless quantity it has unit radian but no dimension rear quantity now relation with angular displacement and linear displacement we know 
2𝛑 (Angular displacement)  = 2𝛑r (linear  displacement )
𝛳(angular displacement )  = r𝛳 (linear displacement )
let s = linear displacement then s = r𝛳 (this can’t be written in vector form because 𝛳 and s direction are not same now come to angular velocity as we know linear velocity is v = ∆s/∆t hence angular velocity will be 𝛚(omega)  =𝛳/∆t  angular velocity 𝛚 is a vector quantity having direction same as angular displacement its SI unit is rad/s  dimension M⁰L⁰/T .
Vavg  = ∆s/∆t  for long time period for small time Vins = ds/dt similarly 𝛚avg = 𝛳/∆t for long time period, for small time 


𝛚ins = d𝛚/dt .
take an example 𝛳 = 2t² +2 then find 𝛚 in 2 s and at 2s
𝛚avg in 0 to 2 sec put t=0 then 𝛳 = 2, put t=2s then 𝛳= 2*2*2+2 = 10
hence 𝛚avg = 𝛳/∆t = (10-2)/2  =8/2 = 4rad/s 
now at 2s means 𝛚ins = d𝛳/dt  = 2*2t+0  = 4t now put t=2
𝛚ins = 4*2 = 8rad/s.
Now relation between linear velocity and angular velocity 
we know that linear velocity V = ∆s/∆t and 𝛚 = 𝛳/∆t and we have seen s = r𝛳 or 𝛳 = s/r put in above equation 𝛚 = 𝛳/∆t = ∆s/r/∆t
here r is radius and constant 𝛚  = 1/r*(∆s/∆t) = v/r hence v = 𝛚r
𝛚  = v/r concept which below equation is correct 
→    →
v  = 𝛚r  or  v = 𝛚r  here vector equation is wrong because direction of v and direction of 𝛚 is not same 𝛚 direction is along the axis and v direction is always changing in circular path tangent to radius so scalar equation is correct.
now  v = 𝛚r is only correct for circle not for all angular velocity cases in circle one condition is very unique angle between v and radius is always 90⁰ means it is clear that the equation v = 𝛚r velocity must perpendicular to radius to use this formula very important point or 𝛚 = v/r = velocity perpendicular/r 
see below question to understand the concepts.
                                         

    when particle is at point p then angular velocity will be 

𝛚  = v(perpendicular)/r = 10/4 = 2.5 rad/s but when particle will be at point B then radius will be OB and we have to take v(perpendicular component ) to OB now we need calculate OB and perpendicular component of velocity to find angular velocity now from triangle OB = 5  now take perpendicular velocity component to OB it will be 10cos37 hence 𝛚 angular velocity at B = 10cos37/OB =  10*4/5*1/5 = 8/5 = 1.6rad/s hence it is clear that for angular velocity perpendicular component of velocity is taken for using formula 𝛚 = v/r and other important point linear velocity is constant but angular velocity is changing is decreasing means angular velocity is not related to circle it is a general term use anywhere see the below question for angular velocity.
                                                 

 here from first question angular velocity at point B with respect to 0 𝛚 will be 𝛚 = velocity perpendicular/OB = 10sin37/OB 
𝛚 = 10sin37/4 = 10*3/5*1/4 = 6/4 = 1.5rad/s.
for second question take perpendicular linear velocity component to OB it will be angular velocity 𝛚 with respect to 0 
𝛚  = 20sin37/4 = 20*3/5*1/4  = 3rad/s  
now if 0 and B both point are moving then you have to take  relative perpendicular velocity component and divide distance this is angular velocity concept hence you write in circular motion  
𝛚 = v/r 
→     →    →     
v    = 𝛚  × r      this equation is correct 
because radius is always perpendicular to velocity i hope now your concept for angular velocity is clear 
Frequency : this is define as number of revolution in one sec it is denoted by f in one complete revolution angular displacement =2𝛑 hence in one sec 𝛳 = 2𝛑 f now 𝛚 = 𝛳/∆t = 2𝛑 f/1sec = 2𝛑 f
𝛚 = 2𝛑 f  this is relation between angular velocity with frequency.
Time period : this is define as time taken to complete on revolution
if frequency is f then time period will be 1/f hence T = 1/f hence we can write 𝛚 = 2𝛑 f = 2𝛑/T now we will continue in next post i hope you have enjoyed learning Circular Motion hidden concepts 
thanks for reading.
dated 9th Sep 2018
    

Motion with constraints concept

Motion with constraints concept

Motion with constraints are restrictions applied on the movement of body by various method or in other language motion confined body have to move in the confined direction brought by constraint forces  for example we may restrict the body to move along a straight wire see an example below picture.
                                       


 Above first picture shows that two block are connected with string which is not stretchable if block A moves with speed 5m/s then block B will also move with velocity 5m/s because of connected with string hence same velocity for both the block while in second case where A moves with velocity 2m/s then as shown arrangement what will be velocity of block B ? as block A moves block B will moves on ground horizontally not in air along attached string but string is common for both the block hence string velocity will be 2m/s hence we have to take component of horizontal velocity Vb along string because this string is causing motion for block along horizontal so take component Vbcos37  = 2 or Vb = 2/cos37  = 10/4 = 2.5m/s hence velocity of block B along horizontal Vb = 2.5m/s. velocity of any two point along the string must be same otherwise string will break so for common string velocity is same for every point.
below given example of constraints motion.
                                 


    from the above first Q1 we have to find Va the actual movement of A will be horizontal towards right hence take a component of Va along string velocity so Vacos37  = 2 or Va = 10/4  = 2.5m/s hence Va = 2.5m/s towards right.
in second Q2 Velocity of block A is 5m/s towards left now take a component of 5m/s along string velocity along string = 5cos37 = 4m/s now this string is common for block B so same velocity of block B along string that is 4m/s now take a component of Vb along string Vbcos53  = 4 0r Vb = 20/3m/s.
now take example for pulley cases.
                                             

    now see the picture below for more pulley cases and concept to solve problem.
                                           

     now from the above question we have to find velocity of block c for this start from pulley P2 we know that general formula for P2 pully  va+vb  = 2p2 here vb =0 so  0+4 = 2p2 or P2 = 4/2 = 2 m/s  direction is below hence P2 is moving with velocity 2m/s down hence P3 will move with 2m/s up hence apply now formula at P3 pulley  vb+vc  = 2*2 here vb = 3m/s put in this equation  
3+vc = 4 vc = 4-3  = 1 m/s hence vc = 1m/s.
now you can solve more question using this concept i hope you have enjoyed   Motion with constraints concept thanks for reading 
dated 5th Aug 2018                           

Static friction force

Static friction force

Friction force is of two types one is kinetic and other is static in this topic we will study about static friction force we have already learn in previous post about kinetic friction force you can refer for basic concept about friction force here Friction force concept  actually kinetic friction force is easy to understand but static friction force required concept to understand its rule student generally confuse in static friction force don’t worry it is not so hard you can understand this after discussion of concept of static friction we will study here every concept and question for static friction force which will clear your all doubt you will learn here static friction force hidden concept. 


Static friction force important point  
Static friction force apply when body will be at rest when there will be tendency of relative motion actually body at rest no relative motion started, static friction force value is variable it is denoted by fs but its value is not constant like kinetic friction force fk = 𝛍kN static friction force is also called “self adjusting” static friction force value lies between 0≤ fs≤Flimiting  fs is static friction
minimum zero and Flimiting  = 𝛍sN 
don’t confuse there is no formula for static friction force because it is variable its value change hence it has a method not formula and 𝛍sN is Flimiting maximum self adjusting force direction will be opposite to the tendency of relative motion where 𝛍s is coefficient of static friction or coefficient of limiting friction see picture below.
                                            


from above question is clear that static friction force value is variable and self adjusting force hence if body is at rest then friction force will be equal to applied force which is justified body will be at rest not equal to the Flimiting force otherwise body will move opposite to applied force which is not possible logically this is important point to remember about static friction force now see the below question 
                                                      
  from above question it is clear that body is in motion and friction acting upon body is kinetic friction so we can now find the acceleration using Newton’s law of motion Fnet = ma using this equation  20-8 = ma or 12 = 2a or a = 12/2 = 6m/s².
                                                

From the above question and FBD mg force try to slid the block on wall so first we will calculate Flimiting force = Static coefficient*Normal   here normal force will be equal to 40N because pushes the wall and wall will push with same force to block as normal force hence Flimiting = 0.3*40 = 12N now here applied force is mg force so mg = 1*10 = 10N now Flimiting is greater than mg force hence block will not slid so block will be at rest hence friction force will be 10N equal to mg force since block is at rest hence acceleration will be zero this is the concept for static friction force.
from the figure angle of friction is define as at the time of Flimiting the angle made between resultant contact force and normal reaction force is called angle of friction and it can be calculated as 
tan𝚹  = Flimiting/N  = 𝛍sN/N = 𝛍s , tan𝚹= 𝛍s this is angle of friction you can solve more question based upon the concept learn here now i hope you have enjoyed to learn Static friction force 
thanks for reading.
dated 26 Aug 2018

Physics circular motion equations

  Physics circular motion is today topic for you . Because it’s very important and interesting topic of Physics. 

So you’ll enjoy to learn Physics circular motion hidden concept keep reading.  
You will study here from basic concept of Physics circular motion to the hidden concept of circular motion.
So lets start first question what is circular motion ? which’s easy for you right.
My simple Answer, when any body or particle moves on a circle or circular path this type of motion is called circular motion.
But this motion is found in whole universe everywhere you can see and analyse the picture below.

Physics Circular Motion hidden concept is here

From above picture planets moves around sun in circular motion, moon moves around Earth in circular motion.
Even electron moves in atom around the nucleus in circular path.
So that here all above examples are doing circular motion .
But important point is heavy mass like Earth, planet and Moon as well as light mass like electron are doing circular motion.
Hence it is clear that big body as well as small particle are doing circular motion everywhere.
so it is very obvious if you want to understand the world.
Then first important to understand circular motion. so it’s very interesting.
So you are going to study in this topic Physics circular motion .
But at the same time mechanics start from circular motion concept.
Therefore Physics circular motion is important topic for you.
I hope, you got my point why it’s important ?
Because mechanics is going to some complicated branch of Physics but don’t worry .
Only you need  to understand carefully.
all the points in this discussion you have already studies kinematics topic.
so you can understand well circular motion because circular motion will related with kinematics you can refer Kinematics concept
you can do small question of circular motion from the concept of kinematics very easily see below questions.

Physics of Circular motion

   In above simple question we have just uses to answer the basic concept of kinematics which we have already studies .
so it is important to refer kinematics concept first then study circular motion you will understand better.

Angular variables

when an object moves on a curve its position vector always changes from reference point .
Which’s origin and its direction is also changes here position vector is represented by r and direction is represented by 𝜃 .
Hence using by this two variable any particle moving on a curve path angular position can be found and this is called angular variables see below in picture.

So from the above picture all three cases, it is clear that general motion is curve motion.

where r position vector and angle both changes one dimensional straight line motion is special case of curve motion.
Again where angle is constant only r position vector changes.
  similarly  circular motion is a special type of motion where r position vector is constant only and angle is changing.
so here you will compare in more details between one dimensional motion and circular motion .
Because our circular motion understanding will more develop now see below the comparison.

 

Physics Circular motion equations

Here from above comparison between two motion you will see the below point in one dimension linear position x = +2m or x= -2 m .
while in circular motion angular position 𝜃 = 𝛑/3 rad or 𝜃 = –𝛑/3 rad
linear displacement 𝚫x = Xf-Xi m while in circular motion angular displacement 𝚫𝜃 = 𝜃f-𝜃i rad.
linear velocity = dx/dt = v m/s while in circular motion angular velocity = d𝜃/dt = 𝛚 rad/s.
Q find 𝛚 of  second and minute hand of a clock .
So it is very simple question first 𝛚 of second hands = angular displacement/time = 2𝛑/60 = 𝛑/30 rad/s now 𝛚  for minute hand = 2𝛑/60*60 = 𝛑/1800 rad/s.
You know linear acceleration = dv/dt = a while in circular motion angular acceleration = d𝛚/dt = 𝛂 whenever 𝛂 is positive its mean that angular velocity 𝛚 is increasing.
whenever 𝛂 is negative it mean that angular velocity 𝛚 decreasing when 𝛂 =0 its mean that 𝛚 is constant you can experience.
when fan is on then 𝛂 is positive and angular speed is increasing after sometime 𝛂 becomes zero then angular speed is constant.
when fan is off it is reverse of first case you can notice it is best example.
In linear motion at constant acceleration we have three motion equation  v = u+at, v² = u²+2as , s = ut+1/2at².
similarly in circular motion we have equation 𝛚f = 𝛚i+𝛂t  , 𝛚²f = 𝛚²i+2𝛂𝜃, 𝜃 = 𝛚t+1/2𝛂t²
Now you can use this formula to solve the numerical problem for circular motion questions .
So i will continue in next post more concept details keep reading every post.
I hope you have enjoyed learning Physics circular motion equations.
If this article is helpful for you like, comment and share.
Having any doubt ask me always here for your support Thanks for 
Dated 3 Sep 2018.
 

Newton’s law of motion and law of inertia

Newton’s law of motion and law of inertia

Newtons’s law of motion and law of inertia state about the cause of motion the main point of discussion of this topic is why and how a body moves or changes its position and its physical state Newton found the reason of the motion and physical state changes is due to Force hence depth analysis about force in this topic hence Newton given three laws of motion based upon the force analysis refer for different types of forces .


This is branch of Mechanics in which there are two parts one is kinematics and other is dynamics in kinematics we study about distance, displacement, velocity,speed,acceleration which we have already studies you can refer Kinematics  in this topic we have to study about dynamics means cause of motion means if an object is moving with constant velocity why ? if an object moving with constant acceleration why ? if an object is at rest why ? all the reason or cause we will study in dynamics and Newton’s laws of motion to understand Newton’s laws of motion it is very important to understand  “force”  in day to day life we listen force word so first try to understand force so lets talk about force.
force is a push or a pull example on a office door you can apply a push or pull force next point living or non-living things can apply force most of the time students confused only living things can apply force wrong non-living air can apply force on tree or anythings you feel when force acts two objects are involved one object force apply and other object force receive example when you push the door then you are applying force and door receive the force we also know force is a vector quantity and its point of application is also important now we will discuss Newton’s laws of motion.
Newton’s laws of motion:
1st Law (Laws of inertia) it state that if a body is at rest or moving it will continue in its same state unless any external force is not applied only external force can change its initial physical state this is also called laws of inertia if net force on a body is zero acceleration of body will be zero change in velocity is zero or velocity is constant means magnitude and direction is constant
                                   

 From above three picture state clearly Newton’s first laws of motion state if velocity is not constant then acceleration is there and hence net force will not be zero if net force is zero it does not mean that velocity is zero velocity will be constant and body will be in motion.

2nd Laws : rate of change of momentum is equal to the force applied on the body by external agent that is ∆p/∆t = (p₂-p₁)/(t₂-t₁) now for very very small time we write dp/dt =d(mv)/dt  now differentiate with respect to time dp/dt = mdv/dt +vdm/dt here mass is taken as constant for this laws so dm/dt = 0 hence equation becomes dp/dt = mdv/dt = ma 


                                             

  

  Newton’s third law : if we apply force on a body then that body also apply same force in opposite direction.
                                           

See the picture above block is on ground  apply a normal contact force on earth N and earth also apply same normal reaction force on block N contact force has two important point first its always acts normal to contact surface and second its direction compress the object this is important point for contact forces.
Newton’s third law of motion is action reaction pair of forces every action has reaction this is law of nature both the forces action and reaction nature should be same.

important point where is reaction of mg force normal N force is not reaction force because mg force is gravitational force and N force is electromagnetic force hence it can’t be reaction force because both the forces nature should be same see below some question.
Free body diagram state that show all the forces acting on a body according to their direction to analyse acceleration forces easily on the body   
                                                     

from above FBD we can write Newton’s laws of motion second equation Fnet  = ma along x axis see below
50 – N1  = 2a (1) this is for 2kg block
 N1  = 3a (2)  this is for 3kg block now put the value of N1 in equation (1) then we can write  50-3a  = 2a or a = 10 m/s*s this is acceleration of both block move with same acceleration now N1  = 3*10  = 30N this is normal force between block.
Important concept  alternate solution for above question since both block moves with same acceleration we can add two masses and take as single mass that is 2kg +3kg = 5kg single block external force will be same 50N now we can write a single equation Fnet = ma  50 = 5a so a = 10m/s*s and this acceleration will provide contact force N1 = ma = 3*10 = 30N                   

i hope that you have enjoyed learning Newton’s law of motion and law of inertia thanks for reading and sharing. 
dated 21st Jul 2018
                                                

centripetal acceleration and tangential acceleration

centripetal acceleration and tangential acceleration is topic for today.
If you REALLY want to understand, the basic concept for centripetal acceleration and tangential acceleration.
Then you’re at right place. Because here i’m going to explain EVERYTHING, you need to know about  centripetal acceleration and tangential acceleration.
So Keep reading the whole article to buildup your concept for this topic.
I ensure you’ll definitely learn new concept for this topic in this article.
So are you ready to learn some new concept, I hope your answer is YES.
Let’s start without more waiting.    

centripetal acceleration and tangential acceleration

 centripetal acceleration and tangential acceleration in previous topic we have covered basic concepts of circular motion .
And its parameter involved in circular motion like angular displacement, angular velocity angular acceleration time period frequency.
So i will suggest you before going to study this topic first you study previous post basic concept of circular motion.
Lovely article very interesting and hidden concept elaborated in depth.
Why i’m forcing you to learn that post because the concept discussed will be use here. So you must refer that article to buildup concept from basic.
Even providing you this link below “hidden concepts circular motion” 
So this’s the best and easy way to understand circular motion link hidden concepts circular motion .
But today we will discuss acceleration in circular motion that is called centripetal acceleration.
 today you will learn here there is no only one centripetal acceleration in circular motion.
actually there are four acceleration in circular motion we will study here all types of acceleration involved in circular motion so far we have studies. 
  •  (linear displacement)  s = r𝛳(angular displacement)
  • (linear velocity)  v = r𝛚(angular velocity) r is radius of circle
  • (linear acceleration) a = r𝛂(angular acceleration)
now here we will learn four acceleration step by step and its concepts very first centripetal acceleration meaning and its concepts.
centripetal acceleration(a𝒸) 

                                               

                              
whenever a particle rotate on circular path its velocity always changes.
But can you tell me why ?
Well, because its direction of motion changes hence it is clear that velocity will be always variable
whether the magnitude of velocity is constant but velocity will be variable.
So due to change in direction hence you know when velocity is variable the acceleration must be there hence centripetal acceleration comes in picture.
And due to change in direction of velocity very important point since centripetal acceleration is a vector quantity.
Hence its direction is always towards the center of circle along the radius as shown in above figure where its value is a𝒸  = v²/r where v is speed and r is radius.
Now if you have seen from previous post we have study v = r𝛚 for circular motion only see the first post .
where we can’t write v = r𝛚 so put value of in above equation we can also get a𝒸 = r²𝛚²/r = r𝛚² so we can also write  a𝒸  =r𝛚²  where  𝛚 is angular velocity.
So now i hope you have got how centripetal acceleration comes in picture now its formula derivation we discuss in next post don’t worry.

Tangential acceleration(a𝓉) 
                                             


And this acceleration arises due to change in speed of particle or change in magnitude of velocity.

Hence if a particle velocity magnitude is changing due to this a acceleration will come in picture.

which is called tangential acceleration this is also a vector quantity hence its will have definitely direction now direction depend upon the velocity magnitude.

If velocity magnitude is increasing then direction will be along the velocity direction and if velocity is decreasing then direction will be opposite to velocity direction tangent to the radius.

As shown in above picture now its value is define as a𝓉 = d|v|/dt remember this is change in speed .

upon change in time concept it is not change in velocity upon change time  v = velocity and | v |   = speed  .

So in tangential acceleration has a condition if velocity is constant then  d|v|/dt = 0 because constant differentiation is zero .

Because in this case a𝓉 = d|v|/dt =0 so only centripetal acceleration will be there no tangential acceleration .

Hence sometime   centripetal acceleration is also called normal acceleration or perpendicular acceleration.

Because it is perpendicular to the surface and  tangential acceleration is called parallel acceleration because it is parallel to surface as shown above figure .

Net acceleration(a𝓷𝓮𝓽) .

this is due to total change in velocity due to direction and velocity magnitude both it is called net acceleration.

now its value is   a𝓷𝓮𝓽 = |dv/dt|  now its direction will not be in velocity direction because a𝒸 and a𝓉 are always perpendicular.

hence a𝓷𝓮𝓽 resultant will be  a𝓷𝓮𝓽  = √a𝒸²+a𝓉² now for direction use triangle law tan𝝰  = a𝒸/a𝓉 now we will see some questions to clear concepts.

Centripetal acceleration question 

Q if tangential velocity v= 2t and radius r =9m find a𝒸,a𝓉 and a𝓷𝓮𝓽 at t =3s.
Ans for velocity v= 2t put t=3 v =2*3 =6m/s
centripetal acceleration a𝒸 = v²/r = 6*6/9 = 4m/s²
tangential acceleration  a𝓉 = d| v |/dt = 2m/s²
net acceleration a𝓷𝓮𝓽 = √a𝒸²+a𝓉² = √4²+2² = √20
Q2 if  𝛚 = 2t and radius r =2 find a𝒸,a𝓉 and a𝓷𝓮𝓽 
now you can solve this problem yourself using v = r𝛚 .

Angular acceleration(𝛂 )  change in angular velocity divided by change in time 𝛂avg  = ∆𝛚/∆t  or  𝛂inst = d𝛚/dt 
Q if  𝛚 = t² +1 find 𝛂 in 0 to 2s and at 2s.
Ans angular acceleration in 0 to 2s put t=0 𝛚0 = 1 now put t=2s 𝛚2 = 2*2+1 = 5 ∆𝛚 = 5-1 = 4 hence 𝛂avg  = ∆𝛚/∆t = 4/2 =2 rad/s²
now for 𝛂 at 2s 𝛂inst = d𝛚/dt  = 2t = 2*2 = 4 rad/s²
now one relation in angular acceleration and linear acceleration 
a𝓉  = r𝛂  where a𝓉 is tangential acceleration .

Q if | v | = constant in a circular motion then find 𝛂, a𝓉,a𝒸 which will be constant ?
Ans since | v | is constant then 𝛚 = v/r here both v and r constant then 𝛚 will be constant hence 𝛂 = dw/dt = 0 which is constant now for a𝓉 we know a𝓉  = r𝛂 = 0 which is also constant now for a𝒸 = v²/r here v and r are constant then a𝒸  magnitude will be constant but a𝒸  is a vector quantity and its direction is variable all the time in circular motion hence it will not be constant it will be variable remember this is important concept this is all about today topic we will continue in next post i hope you have enjoyed learning centripetal acceleration and tangential acceleration  thanks for reading.
dated 16th sep 2018

Projectile motion equations and formula | explanation with real examples

Today I’m going to explain EVERYTHING about Projectile motion formula. As well as projectile motion examples.

Which you need to know, what is horizontal projectile motion, and projectile motion problem in this article. 

So lets start from very basic concept. 

Projectile motion best definition is here . Because projectile motion is easy, but conceptual.  And this is best example of 2D motion. So very first, what is projectile motion and its equation equation ? . Hence it is define as, any body or particle having m mass but negligible  size.

Therefore if you through any body vertically upward.  Then that body moves in a straight line. Which is a vertical line.  Similarly if you through a body, along horizontal line. Then  again that body moves along horizontal straight line.

So both motion are straight line.  But when you through a body between horizontal and vertical plan, making some angle with horizontal line.  Then that body moves in a parabolic shape of path.  So this is called projectile motion.  And the path travel by projectile, is called projectile motion equation.

[faq title=”Frequently Asked Questions (FAQ)” open1st=”0″ openAll=”0″][faq_item title=”What is the equation of projectile motion?” number=”1″]projectile motion is best example of 2D-motion, this motion occure in two plane (x,y). And acceleration only in the vertical direction. Which is called acceleration due to gravity (g). Equation of path of projectile motion is called trajectory. And path of this trajectory is y = (tan θ0)x – gx2/2(v0cosθ0)2 .With this equation, you’re able to calculate all parameter for projectile motion. for example maximum heigh, time of flight, velocity.[/faq_item][/faq]

[faq title=”” open1st=”0″ openAll=”0″][faq_item title=”What are examples of projectile motion?” number=”2″]Example If you throw a ball vertically upward, and it falls vertically downward, You kick a ball at an angle with horizontal with some speed. And let it fall, So all these’re example of projectile motion. Anything free fall is also under projectile motion.
[/faq_item][/faq]

[faq title=”” open1st=”0″ openAll=”0″][faq_item title=”What are the three types of projectile motion?” number=”3″]1 Horizontal projectile, Which is any ball throw horizontal with some speed from certain height.2 Vertical projectile, This is anything free fall under gravity is called vertical projectile. 3 Oblique projectile, If anything throw at an angle with horizontal is type of oblique projectile.
[/faq_item][/faq]

 


What is the formula for projectile motion ?


This motion is also called free fall motion. Because when you project a body, then only gravitational force acts upon the body. And no any other forces act on the body.  Hence this is called free fall motion. 
Because all fundamental concept is applicable for projectile motion.

What is projectile motion formula with an example ?


However important about projectile motion. This is plan motion 2-D.  But you analyse this motion, by separate two straight line motion.  Hence one along x axis, and other along y axis. Do you know why ? .
Because we have no any equation of motion . Which is available for plan 2-D motion  till date . So you use two separate straight line motion.  For solving equation of projectile motion. And other important point is velocity, along x axis  which is ucosα.
Similarly velocity along y axis is usinα. Now you tell me, which velocity component is responsible, for projectile to achieve height.   Well in air obviously usinα is responsible.  Because this is the only velocity, due to which projectile travel maximum height.
Hence this velocity is also variable, acceleration due to gravity along y axis.  Which is acting vertically  downward. So initially velocity decrease, and at maximum height, its become zero. Then the projectile starts falling down.

What is plane motion explain its importance in horizontal projectile motion ?


But note at maximum height, total velocity is not zero.  Because velocity along x axis is present. Therefore velocity along x axis is, always remains constant throughout the motion. If you calculate velocity along x axis, Then every point is same.
But why so,  This is because of, there is no any acceleration along x axis. And this indicate acceleration along x axis is zero.  Hence velocity along x axis is constant. So using this all component velocity, and acceleration.  You can find out projectile parameters by using trick.
  • initial velocity along x axis  = ucosα
  • initial velocity along y axis  = usinα
  • acceleration along y axis  = -g
  • acceleration along x axis  = 0
where u is velocity of projectile, and  α is angle of projection with x axis.  Now as i explain above . So by using straight line motion, in two separate axis x and y. You are able to find, all projectile parameter.  Hence you can refer, straight line motion.

How do you explain 2D motion ?


So here are three equation. Which is given below  
v = u+at, s = ut +1/2at²  v² = u²  +2as.
Now for projectile motion. You just use this equation to find its parameter .
So Time of flight is define, as total time taken by projectile in air. Hence You want to find time of flight.
Simply apply trick, you know that velocity along y axis is responsible, to kept in air.  hence use velocity along y axis to find time of flight.
And you  know that, initial velocity along y axis  =  usinα,  and velocity along y axis at maximum height is zero.  hence use this equation .
v = u +at  where a = -g.
0  = usinα -gt after simplification  t = usinα/g this is also call time of accent.  time taken to travel maximum height, and same time taken to decent from maximum height to ground. hence total time in air will be T = time of accent +time of decent  = usin𝛳/g + usin𝛳/g = 2usin𝛳/g so T = 2usin𝛳/g.

What is  2D motion explain its importance ?

Alternate method you can use 2nd equation  s = ut +1/2at² here you can use concept displacement along y axis is zero after reaching projectile on the ground this will give total time projectile in air so put all value  0 =  usin𝛳t – 1/2gt² = t(usin𝛳-1/2gt)  = 0
now t = 0 and t  =    2usin𝛳/g here t = 0 gives when projectile was start throwing and t =2usin𝛳/g  gives when projectile reaches at ground so t =2usin𝛳/g is time of flight.
Maximum height   we know that for maximum height velocity along y axis is responsible hence use third equation  v²  = u²  +2as
now we know that at maximum height velocity along y axis will be zero so  0 =  (usin𝛳)²  -2gh after simplification  H =  (usin𝛳)²/2g this is maximum height.
Range    this is define as horizontal distance travel along x axis by projectile for this we know that velocity along x axis is responsible to travel distance along x axis and acceleration along x axis is zero hence again use 2nd equation  s = ut +1/2at² 

How formula is calculate for 2D- projectile motion examples ?

R  =   ucos𝛳*time of flight  – 1/2*0 =  ucos𝛳*2usin𝛳/g = u²2sin𝛳cos𝛳/g  = u²sin2𝛳/g  hence  R  =  u²sin2𝛳/g now for maximum range sin2𝛳 = 1 so 𝛳 = 45⁰
Q1 sometime asked question for which two value of 𝛳 Range will be same for this if one angle is 𝛳 then other angle will be (90-𝛳) for same range 
Q2 Find the speed of projectile after time t.
for this question how you can approach after time t we have to find speed we know that projectile having velocity in both component along x axis and along y axis we also know that velocity along x axis remain constant and is equal to  ucos𝛳
velocity along y axis is variable depend upon time hence can be written as  v  = u+at  =  usin𝛳 -gt hence total velocity will be 

How to solve numerical problems ?

V   =  ucos𝛳i^ + ( usin𝛳 -gt )j^  now for speed take modulus 
|v|  = √(ucos𝛳)² +( usin𝛳 -gt )² this is speed of projectile after t time.
Q3 A particle is projected from a tower height 20m from ground with a velocity of 20m/s at an angle of 30⁰ with horizontal find  maximum height from ground, total time of flight,find range, find final speed of hitting ground.   
for any projectile question first you have to take separate two motion along x axis and y axis for this question we already know maximum height formula H = (usin𝛳)²/2g  put the value 
H = (20*sin30)²/2g  = (20*1/2)²/2*10 = 100/20 = 5m
hence maximum height from ground = tower height + maximum height  = 20 + 5  = 25m
for total time of flight you have to approach by trick velocity along y axis is responsible for projectile to be in air or time of flight first you calculate time taken for maximum height use equation 
v  = u +at  final velocity along y will be zero hence t  = usin𝛳/g
t = 20*sin30/10 = 20*1/2*1/10  = 1s 
now after maximum height projectile will fall down and travel 25m distance vertical and initial velocity is zero hence use equation 
s = ut +1/2at²  put all value  = 25  = 0+1/2*10t² after simplification t  = √5  so for time of flight total time = 1+√5 .
now for range we know that velocity along x axis is responsible for range hence use same equation s = ut +1/2at² for range here a =0
R = 20*cos30*time of flight  = 20*√3/2*(1+√5) 

Numerical examples for projectile 

now for final speed we know that velocity along x axis will be same hence velocity along x axis = 20*cos30 now velocity along y axis use equation  v = u+at  initial velocity along y axis at maximum height is zero so v = gt = 10*√5  hence speed will be take modulus of total velocity along x and y axis that is 
V   =  10√3i^ +10√5j^  now take modulus of this.
 
|V|  = √(10√3)² +(10√5)²  m/s will be speed with which projectile will hit ground .
now sometime asked trajectory this is the path of projectile which is parabolic shown above in picture we can find out this equation lets see how write the 2nd equation   s = ut +1/2at² use separately for x axis and y axis for x axis  x  = ucos𝛳t +0  =  ucos𝛳
for y axis  y  = usin𝛳t – 1/2gt² now from x  =  ucos𝛳t so t = x/ucos𝛳
put t =  x/ucos𝛳 in y equation we will get equation of trajectory.
If you want to learn more topic of Physics. Then refer my previous post. This link is given below.
now using this concept you can solve any type of projectile problem i hope you have enjoyed learning  Projectile motion equations and formula thanks for reading and sharing.
dated 14th Jul 2018.

Velocity definition and acceleration definition in graph

Velocity definition and acceleration definition in graph


Velocity definition and acceleration definition is our topic for today through graphical representation, you can visualize the meaning of velocity and acceleration graphical method is very important to understand concept of velocity and acceleration, students generally confused in graph due to lack of concept and trick but honestly graph questions are very easy and simple important point is you should know the concept and trick to solve the question today i will teach you that concept and trick so that your all doubts in graph will be clear and you will be able to solve complex questions very fast and easily with confidence, trick and concept is also simple don’t worry after following this concept you will be master in graph question lets start we know from previous classes graph always between two parameter hence in physics there are only three type of graph which are given below.you can refer displacement,velocity,acceleration


Graph
1 (x – t) graph  (distance/displacement – time)
2 (v – t) graph  (speed/velocity – time)
3 (a – t) graph  (acceleration – time)  

basic point for graph representation in coordinate system, why coordinate system is used ? because coordinate system is a reference point or frame of reference through this frame of reference we analyse motion of body or particle with respect to time so coordinate system is required for graph representation now  time is always taken as positive and along x axis.
x→displacement, v→velocity, a→acceleration taken as positive and negative both along y axis.
                                            


    first the basic point is describing about graph so that you can get idea about graph, i will provide you trick in the last section don’t worry in the above picture example how to construct graph from given problem. you must remember in (x-t) graph this is displacement verses time graph and slope of this graph is define as 
Slope = (y2-y1)/(x2-x1) = (x2-x1)/(t2-t1 ) = ∆x/∆t = v = tan𝛳  
here on y axis displacement and in x axis time.
as slope will be greater velocity will be grater because slope is equal to velocity in (x-t) in above figure shown velocity is greater slope is also greater important point slope of (x-t) gives velocity if slope is less than 90 degree slope is positive and hence velocity is positive angle always taken from positive x direction we know that to find slope of any curve at any point we draw a tangent to curve on that point and slope of that tangent line give slope of curve at that point hence two basic important point for (x-t) graph if slope is increasing then velocity is increasing and if slope is decreasing means velocity is decreasing and second point is angle if angle say 𝛳< 90 degree then velocity is positive and if 𝛳>90 degree then velocity is negative angle always taken from positive x axis this is already shown in above picture velocity increasing and decreasing case this is actual velocity definition how velocity how velocity increases and decreases and direction changes if 𝛳 is constant its mean that velocity is constant after knowing this basic point now we will do some question see picture below Velocity definition and acceleration definition  


                                             

here two question for (x-t) graph lets solve one by one take first problem analysis as from question we have to find velocity in region OA, AB, BC.
we know that in (x-t) graph slope gives velocity hence slope of OA will give velocity in region OA we also know that slope is equal to


Slope of OA  = (y2-y1)/(x2-x1)  = (10-0)/(5-0) = 10/5 = 2 m/s and angle of OA is less than 90 degree hence positive so velocity in region OA is 2 m/s constant in positive direction now similarly for region AB slope  put the value of y coordinate and x coordinate slope  = (10-10)/(15-5) = 0/10 = 0 m/s hence velocity in AB region is 0 m/s its means that body is at rest no displacement also seen in picture body has no any displacement during region AB now for similarly BC region put the value of y coordinate and x coordinate in slope equation hence slope  = (15-10)/(20-15) = 5/5 = 1 m/s slope for BC is less than 90 degree hence positive now you can analyse as  velocity in OA region is greater than velocity in region BC hence slope of OA is greater than slope of BC it is clear from figure.
Now for second question see figure trapezoid similarly we can calculate velocity so velocity of region AB = slope = (10-0)/(5-0) = 10/5 = 2 m/s 
velocity of region AB = slope = 0 now velocity of region BC 
slope = (0-10)/(20-15)  = -10/5 = -2 m/s here it is clear that slope of BC is greater than 90 degree so velocity is negative so it is very clear that in (x-t) graph find slope for velocity magnitude and find angle for velocity sign hence for any type of graph in (x-t) you can easily find out velocity in case of curve find velocity with same process but see whether slope is increasing or decreasing if slope is increasing then then velocity is increasing and if slope is decreasing then velocity is decreasing for sign angle less than 90 degree positive and if greater than 90 degree negative this is basic fundamental point for (x-t) graph with the help of this concept you can solve any problem in (x-t) graph.now it is clear that in (x-t) graph either it will be straight line or curve or both so for all cases the process for checking velocity and its sign will be same now for curve velocity will be variable hence acceleration will be there so for acceleration sign just check velocity is increasing or decreasing if velocity is increasing then acceleration will be positive if velocity is decreasing then acceleration will be negative second method to check acceleration sign if concave of graph is up then acceleration will be positive if concave of graph is down then acceleration will be negative it is important point for acceleration sign.
(V-t) graph
                                         

   In (v-t) graph slope of curve gives acceleration as in above figure given now for acceleration positive or negative same process for angle means slope is used and area under this graph gives displacement this is two important point for (v-t) graph now from Q1 we have to find acceleration in region OA, AB and also displacement lets solve first we will find acceleration hence slope of OA = (10-0)/(5-0) = 10/5 = 2 m/s² and angle is less than 90 degree so positive now for acceleration in region AB it is clearly seen that velocity is constant means slope is zero but how slope of AB  = (10-10)/(10-5) = 0/5 = 0 so acceleration in region AB is 0 now for displacement during OA we know that for displacement find area under curve (v-t) here it is triangle so area of tingle = 1/2*5*10  = 25 m now for displacement during AB it is rectangle hence area of rectangle = 10*5 = 50 m so for total displacement during OAB  = 25+50 = 75 m 
now for Q2 find displacement and distance we know that area under curve (v-t) gives displacement but remember above x axis area will be positive and below x axis it will be negative now you can find area and displacement hence above x axis area = displacement = 1/2*5*10  = 25 m similarly below x axis area = 1/2*5*10 =  25 m but it is negative hence total displacement = 25-25 = 0 now for distance both will be added  = 25+25 = 50 m because weather body moved forward or backward distance will be total addition.
now from this concept you can convert (x-t) graph to (v-t) and vice versa using concept of both graph now last graph is (a-t) graph
(a-t) graph 
(a-t) graph slope gives Jerk that is da/dt = Jerk m/s³  area of this graph gives change in velocity.
Trick for solving graph questions.
(x-t) graph  ↓
(v-t) graph  (Slope)
(a-t) graph
remember this series from top to bottom means to say that if (x-t) graph is given and asking for velocity so find slope if (v-t) graph given and asking for acceleration find slope similarly

(x-t) graph
(v-t) graph (Area) 
(a-t) graph ↑
remember this series from bottom to top means to say if (a-t) graph is given and asking for velocity then find area if (v-t) graph is given and asking for displacement and distance find area.
Now i hope that you have enjoyed to learn Velocity definition and acceleration definition and you have learn the concept for graph thanks for reading we will continue in next post.
dated 7th July 2018.       

3 Equation of Motion in Physics for Kinematics

                 3 Equation of Motion in Physics for Kinematics

3 equation of motion in kinematics is our topic for today. we will study in details about kinematics equation and application this is important to understand derivation of equation and its basic application to better understand kinematics you will really enjoy to learn this topic to understand kinematics of physics lets start see picture below.
                                           


Student always confused in kinematics problem because they not focus on concept of kinematics they only remember 3 equation of motion and think that kinematics is finished but when question of kinematics is asked then fail to solve the problem generally because concept is not clear so i recommend you first learn basic concept of and parameter involved in kinematics for basic concept and parameter refer this post first kinematics concept .
kinematics topic is conceptual we actually analyse motion of body or particle in kinematics suppose a car was running on road at a certain time driver seen a breaker on the road and applied break on the car then what will happen after some time car will stop then we analyse motion about this parameter. what was initial speed of car before applying break, how much distance covered by car, how much time taken to cover this distance,how speed of car was increasing with time hence only four parameter relation involved in kinematics motion equation that is s,v,t,a.
s→ distance or displacement
v→ initial, final speed, velocity
t→ time taken to complete journey.
a→ acceleration or retardation 
hence using this parameter 3 equation of motion for kinematics is derive relation between them but don’t think only this equation of motion is kinematics this is only a little part of kinematics as mentioned above we have already studied basic kinematics concept now we will see some conceptual problem lets start and understand concept for kinematics.
Q1 equation of motion is given x = 2t² find the speed at 2s and find average speed at 2s.
Ans this equation relation is between distance and time now from basic kinematics concept and parameter we know that dx/dt =v if you have not study differentiation refer  differentiation post  .
from equation x = 2t² when we put t =0 then x = 0 its mean that particle start motion from origin now we know that instantaneous speed and velocity is same in magnitude only difference is velocity has direction so for speed at 2s is instantaneous speed and we know that how to calculate instantaneous speed that is  v = dx/dt so 
differentiate the given equation x = 2t² dx/dt  = 2*2t that is v = 4t
hence if we put t = 0 then speed is zero its mean that at t=0 particle is at rest but according to question speed at 2s hence put t=2 in equation v =4t = 4*2  = 8 hence speed at 2s is 8m/s.
now for second query average speed we know that average speed is total distance/total time now again put t= 0 then x =0 put t=2 then x = 2*2²   = 8 hence average speed = 8/2 = 4m/s . you can see in this question speed is variable every time speed increasing this is case of accelerated motion in our above picture. 
Q2 equation given x = 4t – t² find distance traveled by particle in 3s
Ans think how we take step to solve this type of problem.
first put t=0 then x=0 its mean that particle start from origin now differentiate to find speed dx/dt =v  dx/dt  = 4d(t)/dt – d(t²)/dt = 4-2t hence v = 4-2t now put t =0 then speed v = 4m/s initial speed 
here you can analyse speed is decreasing with time 
now find when speed will be zero put v =0 then  4-2t  =0 so
t = 4/2  = 2s now find the distance travel at 2s 
x  = 4*2 – 2²  = 8 – 4  = 4m  hence at 2s velocity of particle is zero and will return back but has traveled 4m distance now put t = 3s then particle position x = 4*3 – 3²  = 12  – 9 = 3 so at this time particle position is at 3m hence 1m has returned back so total distance will be 2s distance 4m and 3s distance 1m back so total distance  = 4+1 = 5m concept is don’t put directly t =3s in equation it will give you displacement but question asked for distance so for distance first check particle round back.


Q3 equation given x  = t² – 6t  find average speed in 5s.
Ans similarly put t = 0 , x = 0 again differentiate dx/dt = v
dx/dt  = d(t²)/dt – 6d(t)/dt  = 2t – 6  now put t =0 v = -6 moving in negative direction this indicate speed is decreasing now check when speed will be zero for this put v = 0 then 2t – 6 =0 or t  =3s hence at 3s particle speed will be zero for distance put t = 3s
x  = 3² – 6*3  = 9 – 18 = -9m at this point particle will round back now put t = 5s then x = 5² – 6*5  = -5m this is particle position hence total distance  = 9+4  = 13m so average speed = 13/5  = 2.6m/s .                                            →
Q4 velocity of particle is given as V  = 2i^ +2tj^  at t = 0 particle position was (0,0) find distance travel by particle in 2s.
Ans how you will attempt this question here velocity vector are given this is good question first tell me this motion is 1-D or 2-D ask yourself try to understand concept this is 2-D motion means motion in a plane not on a straight line how 2-D because velocity is not constant it is variable dependent on t if in same question if velocity was constant then it was 1-D motion or straight line motion but current velocity it is 2-D motion, you can also find trajectory which will help to find out motion from question x = 2t, y =2t² you can put t = x/2 in y, y = 2x²/4 or y = x²/2 which is equation of parabola hence it is curve and 2-Dnow think how we will calculate distance we know that
→         →
dr /dt  = v     =  2i^ +2tj^  now integrate with respect to t
 r →           2          2 
 ∫ dr    = 2i^∫dt +2j^∫t^dt   after simplification we will get 
0                0          0
→ 
r     = 4i^ + 4j^  if we take modulus then |r|  = 4√2 m .
what do you think this is distance big no this is not distance this is displacement but in question asked for distance then how we will calculate distance think distance is scalar quantity hence take mode of velocity then it will be speed and we know that speed is define as  v = dx/dt  hence  | v |  = 2√1+t²  now integrate this so 
∫dx = ∫ | v |dt
x           2
∫dx  =  2∫√1+t²  
0          0
after simplification this will give you distance.
                                       →
Q5 position is given as r    = 5(1-cos2t)i^ +5sin2tj^ find distance travel in 10s.
Ans again distance travel in 10s how you will solve this question first differentiate and find out velocity then take modulus of velocity it will be speed and again integrate this you will get distance so lets see how will do.   → 
after differentiate velocity vector  v    =  10sin2ti^ +10cos2tj^
x             10
∫dx   =∫ | v | dt  now put the value and solve distance  = 100m .
0        0 
Equation of motion for uniform acceleration.
3 equation of motion derivation 
first we will understand what is meaning of uniform acceleration we know that acceleration is define as a = (v – u)/t that is change in velocity divided by time means (v – u) is change in velocity which should remain constant with equal interval of time means in every second time interval change in velocity (v-u) must be constant
                    50m/s                  40m/s                  30m/s                  20m/s
            ←←🚙←←←←←🚙←←←←←🚙←←←←←🚙 

                   t=4s                  t=3s                   t=2s                t =1s
here it is clear that every second velocity is increasing with 10m/s 
so in every time interval velocity increment is same and acceleration is uniform constant and equal to 10m/s²
now we know that instantaneous acceleration is define as 
dv/dt  = a now from here we can write taking integration on both 
        v         t  
side  ∫dv  = ∫adt  after simplification  v – u  = at or we can write as        u        0     v  = u + at  this is first kinematics equation where u is initial velocity v is final velocity and a is uniform acceleration and t is time now for second equation we know that instantaneous velocity is written as ds/dt so from first equation we can write as 
ds/dt  =   u + at now integrate on both side 
s        t          t 
∫ds  = ∫udt + ∫atdt  now after integration on both side we will get
0       0         0 
s  = ut +1/2at² this is second equation of kinematics where s is displacement not distance note it u is initial velocity a is uniform acceleration and t is time
now for third kinematics equation square on both side first equation as  v²  = ( u + at )² simplify this equation then we will get
v²   = u² + a²t² + 2uat  v² – u²  = 2a(ut +1/2at²)  = 2as hence 
v² – u²  = 2as  putting value (ut +1/2at²)  as s hence this is third equation of kinematics.
now we will see how this kinematics equation of motion is apply in case of free falling body as we know that when we through a ball vertically upward then it goes up in a straight line path with decreasing velocity and at maximum height its velocity becomes zero and then that ball start falling down on the same straight line now every time its velocity is increasing with constant value of g during free fall hence this is case of uniform acceleration motion so we can apply all 3 equation of motion here.
upward case :
when we through ball vertically upward in this case velocity and acceleration due to gravity is in opposite direction then here a = -g
then our equation will be .
v  = u – gt 
h  = ut – 1/2gt² 
v²  = u² – 2gh .
free fall downward :
in this case velocity is increasing every second and direction of velocity and acceleration due to gravity is in same direction the equation will be like this.
v  = u + gt
h  = ut + 1/2gt²
v²  = u² + 2gh
one more equation is there distance travel in nth second for this distance calculation we use above displacement equation as
S𝑛th  = S𝑛 – S𝑛-₁ putting value of n and n-₁ in place of t in equation s = ut + 1/2at² then we get equation S𝐧 = u +a/2(2n-1) so using this equation we can solve numerical problems.
Q6 A body is thrown vertically upward with velocity u find time taken to reach maximum height, maximum height, time taken to reach on initial point.
Ans this is simple question here initial velocity given u and is positive at maximum height final velocity will be zero a = -g now apply equation  v = u – gt put v = 0 then t = u/g this is time taken for maximum height now for maximum height use formula 
v²  = u²  – 2gh here v = 0 so h = u²/2g which is maximum height now for time taken to reach at initial point concept when body will reach its initial point its mean that displacement will be zero then apply equation s  = ut – 1/2gt² now displacement is zero hence put s =0 then ut – 1/2gt² = 0 now from here t =0 or t = 2u/g here t = 2u/g is time taken to reach on ground.
Q7 A stone is dropped from a tower height 20m find time taken to reach on ground and find speed just before hitting ground.
Ans simple basic question here stone is dropped means initial velocity u =0 here h = -20 and a = -g then apply equation  s  = ut – 1/2gt² now put u =0 then h = 1/2gt² now from here t  = √2h/g now put value of h = 20m and g = 10 we will get √4 hence t = 2s.
now for final velocity v  = u -gt  = 0 -10*2  = -20 hence speed will be 20m/s.
now you can practice more problem like that i hope that you have got the concept involved in this topic and enjoyed learning kinematics for 3 equation of motion we will continue in next post thanks for reading.
dated 24th Jun 2018 

Kinematics one direction motion in physics

Kinematics one direction motion in physics

This topic is very important to understand motion concept this is also called as 1-D motion or straight line motion, 2-D motion or plane motion, 3-D motion or space motion in this topic every basic concept for motion will be covered you will enjoy to study this topic this is first topic of motion so here first we will study 1-D motion hence in this topic we will only study 1-D motion or rectilinear motion  student always confused to understand the different parameter involved in kinematics so i will provide you each and every concept use in kinematics so that your doubts will be clear to understand well,  after study this topic your all doubts and concept will be clear, so lets start this topic.what is meaning of kinematics ? 


meaning of “kine”→motion, meaning of “matics”→math whatever math involved in kinematics like how to calculate distance, displacement, speed, velocity, acceleration of body or particle at the time of motion whether body has any type of motion but we need to calculate all the above mentioned parameter.
Motion in 1-D or straight line motion or rectilinear motion 
Meaning of motion if any body or particle is moving then it is called that body or particle is in motion, like if you are walking then you are in motion if you are sitting at position then you are not in motion you will find motion example in the world everywhere so motion is very important take some example of motion to understand concept, Moon is moving around the Earth so moon is in motion, Earth is rotating about its axis so Earth is in motion, Air is blowing so air is in motion,in Sea water is in motion, Aeroplane is moving ,train is in motion,watch needle in motion, in room fan is in motion so everywhere is motion, infect where you are not seeing motion, there is also motion like a lady is sitting on a chair you will say there is no motion because she is at rest but think in lady body blood, heart and kidney are in motion lady taking breath air is coming in and out so air is in motion. now in your room wall is at rest you will say there is no motion but think in wall there is many many atoms inside atoms there are many many electrons which are in motion so think how much of electrons are in motion inside the wall so everything in motion big body and small particle all are in motion hence aim of physics is to understand natural world so it is very important to understand motion hence we want to learn motion so “kinematics is a branch of physics in which we study how to describe motion”.
Here we are studying straight line motion its mean that body or particle will move in a straight line only not on a curve path.
Trajectory :    Path of an object like electron revolve in an atom in circular path hence trajectory of electron is circular.
Meaning of dimension  see below picture for dimension.


                                             

Kinematics one direction motion in physics
  Now from above figure 1-D object is a pencil so for one dimension motion only one axis is sufficient to analyse motion for every point on straight line similarly for 2-D motion badminton  object or any play ground on earth surface is two 2D here for any point motion two axis is required to describe motion now for 3D object is truck two analyse any point motion we required three axis like whenever any football player running on ground is 2D motion but sometime jump to hit the ball in air now this is 3D motion.
Now for 1D motion object will move in a straight line either along x axis or along y axis but we generally represent 1D motion by x axis see below picture.
             f         e          d                  a        b        c    
-x←←-3←←-2←←-1←←0→→1→→2→→3→→+x
right side taken as positive and left side taken as negative 
Variables in kinematics or math in kinematics:
  • Position
  • Displacement
  • Distance
  • Instantaneous Velocity  
  • Average Velocity
  • Instantaneous Speed
  • Average Speed
  • Acceleration
  • Jerk
Position: Position is a vector quantity, position means “address” if we want to locate someone address then we have to locate district name colony name and house number then we finally reach at that address or position similarly for any body or particle address location we need Cartesian coordinate that is xy plane to locate address or position of a body or particle here we are studying 1D some one plane only x axis is taken.position vector is line joining from origin to given point which position want to determine.      
now if we want to write position vector of point a then we can write
→                      → 
Ra   = 1i^, for b Rb   = 2i^ similarly for for d and e
→               →
Rd  = -1i^ , Re   = -2i^  but this is one dimension motion hence it will be always along x axis so we neglect i^ and written always as
Xa  = 1, Xb  = 2,  Xd  = -1,   Xe  = -2 
Displacement : this is define as change in position vector is called displacement, now change word is very very important in physics to understand concept now any quantities change means final minus initial or can write as change  = final – initial here it is position vector so “change in position vector”  =  “final position vector” – “initial position vector” this is displacement it is a vector quantity because position is a vector quantity hence its change will be a always vector quantity now displacement is minimum length vector from final position to initial position joining straight line initial position to final position, vector along shortest path whether body has travel by any path but its shortest path straight line joining initial to final position is only displacement.
Distance:  this is define as length of path travel or length of trajectory in which body or particle travel it is scalar quantity 
                                       
   Distance is greater than and equal to displacement                                
hence distance is path dependent but displacement is only straight line joining initial point to final point and direction from initial to final point.

 velocity: this is define as rate of change of position with respect to time and just we have study change of position is displacement hence displacement with  time is  velocity and this can be written as 
→      →       →     → 
V    = D/t  or (r2  – r1)/t   direction of velocity will be same as direction of displacement Concept in general question asked find the velocity of a body at a point.remember to find out velocity minimum two point is required that change in position initial and final point unless there will be no displacement we can’t find velocity. we can’t find velocity at a single point then why question is asked find velocity at a point ? actual meaning of this is define as we take very close to that point two point one left and other right 
      →dx←
           p
         | 🚶 |    hence velocity is define as v= dx/dt hence if ask to you 
     → dt ←

find the velocity at a point its meaning that take very close to point a left point and a right point then we calculate like above v  = dx/dt otherwise at a single point velocity can’t be find out.
Instantaneous velocity: now it is define as take displacement as much of smallest that is displacement→0 or dx→0 very very small then that velocity will be instantaneous velocity means velocity at a instant or a particular time and written as v  = dx/dt 
Average velocity:  When we take displacement larger distance like two point at far distance picture below point A and B 
                           ∆x
A→→→→→→→→→→→→B   

                           ∆t                     
hence Average velocity is define as =   ∆x/∆t  this is know as average velocity both are velocity hence both are vector quantity
now for direction average velocity direction is always same as direction of displacement means initial point to final point but for instantaneous velocity its direction is tangent to the asked point towards initial to final point.
Instantaneous Speed : this is define as smallest distance between two point with respect to time, same as instantaneous velocity modulus means scalar quantity and define as |v|  = |dx/dt| here in smallest case displacement and distance is same. 
Average Speed : this is define as total larger distance path travel with respect to time and define as average speed = distance/t = d/t here in this case displacement and distance are not equal and speed is a scalar quantity.
Acceleration: this is define as rate of change of velocity with respect to time and denoted by a = dv/dt that is change in velocity a  = (v2 – v1)/t acceleration is a vector quantity now if velocity and acceleration are in same direction then speed will increase and if velocity and acceleration are in opposite direction then speed will decrease.
Now time for some basic question on this topic.
Q1 A circle having radius R one person travel on circumference from one end to other end and other person travel on radius from one end to other end find the distance travel by both person and their distance ratio.
Ans this is very simple question   ab see the circle from question, distance travel by person through circumference = 𝞹R
distance travel by second person on diameter = 2R
now ration =   𝞹R/2R  = 𝞹/2 .
Q2 A cube of side having length 4cm a bee is at point A after some time it fly and A to B and B to point D though side length now find the distance travel by bee and also displacement made by bee from A to D                                                                      
                                          D
                                      A                       B                                           Ans here bee fly by side wise and reaches at D hence distance will be = 4+4+4 =12cm
 now for displacement recall vector addition for three dimension already study in previous post vector topic displacement is a vector quantity hence will be added by vector rule cube is xyz plane
here AB is along x positive so we can write 4i^ now from B opposite to z direction so -4k^ now in positive y direction so 4j^ hence for final displacement add displacement along all axis 
d   = 4i^ + 4j^ – 4k^ now for magnitude take modulus 
|d|  = 4√3
Q3  three velocity of a particle are given below find the type of motion. for each velocity 
→               →                        →
V1   = 2i^ , V2  = 2i^ + 3j^ , V3  = i^ +5j^ – 2k^
Ans very easy V1 is along x direction so it is 1-D motion 
V2 is in xy plane so it is 2-D motion
V3 is in xyz plane so it is 3-D motion 
your concept is wrong it is not like that all three velocity are straight line V1 is along x axis ok straight line V2 velocity in xy plane but straight line similarly V3 is in xyz plane but straight line then how to recognize 1-D, 2-D, 3-D motion simple when particle is moving in straight line it is 1-D motion, when particle is moving on curve path in a plane like xy,yz,xz then it is 2-D motion, when particle is moving in curve path in two different plane then it is 3-D motion now i hope your concept is clear.
Q4 A boy  walks 6m east in 3s and 3m west in 1s find the average speed and average velocity during journey.
Ans first understand question simple.

West←←←←←←←←←0→→→→→→→→→→East  
  we know that average speed  = total distance/total time 
  Average speed = (6+3)/(3+1)  = 9/4 =2.25m/s
Now for average velocity = total displacement/total time 
Average velocity = (6-3)/(3+1) = 3/4  = 0.75m/s
hence it is clear that average speed is greater than equal to average velocity.
Q5 A man goes from point A to B with 60m/s and returned from point B to A with 40m/s find average velocity and average speed.
Ans simple question see below.

A→→→→→→→→→→→→→B
from question A to B speed is 60m/s and B to A speed is 40m/s
now average velocity  = total displacement/total time here total displacement is zero because finally returned to point A so average velocity = 0m/s
now for average speed = total distance/total time here neither distance nor time is given so let d is distance between point A to B
now speed is given so we can calculate time taken from A to B
T1  = d/60 ( using constant speed formula s= vt similarly time taken from B to A T2  = d/40 hence apply the formula 
average speed  = total distance/total time  = 2d/(d/60+d/40)
average speed = 2*60*40/(60+40)  = 48m/s.
Now you can practice yourself more question like this for numerical problems. thanks for reading. 
  Kinematics one direction motion in physics .
dated on 17th June.

Vector addition subtraction and component

Vector addition subtraction and component

Today we will study different operation for vector in last post we have study some addition method for two vectors only but in this topic we will learn how to add more than two vector through component method also some powerful use of unit vector for vector problem solving technique you can refer previous post two vector addition method and some concept refer  this topic will give you vector power lets start given below picture is three different frame 1-D, 2-D, 3-D we can find any point position in three different frame using vector method and can add and subtract any vector easily as we are talking about vector its mean that magnitude and direction must be provided for any operation of vector.

                                            

Vector addition subtraction and component
Subtraction of vector: i will suggest you first go and study concept of addition of vectors above mentioned link because to understand subtraction you must understand addition of vector because subtraction of vector is actually addition of vector understand concept vector follow only addition operation no subtraction operation nothing is subtraction in vector has no meaning then why we study subtraction method the reason behind this is only due to direction magnitude is fixed in any vector but direction can be change and may be in any direction take an example to understand concept suppose i told John has moved 5m here 5m is magnitude here it is not specified in which direction John has moved it can be left , right, up, down or some angle in any of the direction from the original position or origin 5m is scalar until direction is not specified now suppose i told John has moved 5m in right now it is vector because direction is specified here if i take this direction positive then opposite of this means left will be negative now for vector representation.

→                                    →

A right is positive then  -A vector will be in left direction. suppose there are two vector A and vector B given below direction.
               →                                            →               
               A                                            -A
→→→→→→ (+ve direction)   ←←←←←← (-ve direction)  
          →                                               →
          B                                                -B
→→→→→→ (+ve direction)   ←←←←←← (-ve direction)
now do the operation for two vector  A and B let R is result 
→      →     →
R    = A   +  B   ( operation is addition )
→      →      →      →       →
R    = A    –    B  = A   +  (-B)   (operation is addition B vector -ve)
hence it is clear that only operation performed in both the cases is addition whereas we say second case subtraction but it is actually addition so vector can only be added not subtracted.
hence it is called negative of vector magnitude remains same but direction changes opposite of original direction. 
Two vector addition at some angle.
                                    

here from triangle ∠BOA = 𝛳 then in triangle ∠AOM = 180-𝛳 
OM is -B vector opposite of B vector so for A-B vector operation extended OM and using parallelogram method tail- tail addition for resultant and here resultant for vector A- B will be 
R²  = A² +B²+2ABcos(180-𝛳) now we know that cos(180-𝛳) = -cos𝛳 here important to understand that -B is always taken positive because in parallelogram A and B are side of parallelogram it can never be negative always put positive value and take angle between -B vector and A vector hence final resultant is 
 R²  = A² +B²-2ABcos𝛳.
now we will do a small numerical question .
Q A car run at 10 m/s east then take a sharp turn towards north and continue with 10 m/s find the change in velocity of car.
Ans (a )10√2 SW  (b) 0 SE  (c) 10√2 NE  (d) 10√2 NW
here four option is given every option have same magnitude but direction is different why direction because velocity is a vector quantity. here we have to find the change in velocity we know that change in velocity.


∆v  = final velocity – initial velocity = 10 -10 = 0 we can’t do like this because velocity is a vector quantity we have to do here vector operation see figure below .
                                        N
                                        ↑                                 
                                        ↑ 10 m/s final
                                        ↑
                    W←←←←↓→→→→→E
                                        ↓      10 m/s  initial 

                                        ↓ 

                                        ↓
                                        ↓
                                        S 
  →        →    →       →        →
 ∆v     = V₂ – V₁   = V₂  + (-V₁ )  ( addition operation)
use formula for magnitude calculation
     ∆v²  =   V₂²  + V₁²   -2V₂V₁cos90  here angle between V₂ and V₁
    ∆v²  = 10² +10² -0 so ∆v = 10√2  now for direction V₁ vector is east  V₂ vector is north hence -V₁ vector direction will be west hence change in velocity vector ∆v will be NW so answer is 10√2 NW m/s not NE proper follow vector direction.
Resolution or component of vector :
just we have study that combining two vector makes a single resultant vector similarly whenever a vector acting at an angle can be resolve in two component in any plan along x axis and along y axis concept even a single vector acting along x axis has two component where as its y component is zero our motive is to break any vector along two component for vector addition in plane by this method we can add many vector easily by adding all component along x axis and y axis separately and for final resultant add total component of x axis and total component of y axis by vector method and this will give final resultant or result whenever a vector acting along x axis and along y axis no need to break component because it is already component along x axis and y axis only we need to break those vector component which are not along x axis and y axis but acting at some angle. see picture below for vector component.
                                             

 As stated above any angled vector can be resolve in two component and then add easily many vector see in picture five force vector we will add and find the resultant here five vector are OA, AC,CD,DE,EG now follow the vector component rule to add all vector first we will take all five vector x component then y component hence Fx denote component along x axis see how we calculate take magnitude and angle of cos

Fx  = 1Cos30i^ +2i^+ 3cos30i^ + 0  – 3i^ here 0 its component along x axis is zero -3 along negative direction i^ is unit vector along x axis now simplify

Fx  = √3/2i^ +3√3/2i^ -i^ = 4√3/2i^ -i^ = 2.464i^
now similarly take component for all vector along y axis

Fy  = 1sin30j^ +0 +3sin30j^ + 3j^ +0  here j^ is unit vector along y axis now simplify

Fy   = 1/2j^ +3/2j^ +3j^ = 5j^
hence total resultant R
→     →    →
R   = Fx  +Fy  = 2.464i^ + 5j^ hence for magnitude

∣R∣  = √(2.464)² +25  = 5.57 N since this is force hence it has direction so for angle apply tan𝛳 = 5/2.464.
now through this method any number of vector can be added easily 
we will see more question of vector in every topic thanks for reading
Vector addition subtraction and component
   dated 10th Jun 2018

Basic Units and Measurement concept

Basic Units and Measurement concept

Hello Friends,
Good Morning every body so far we have studies Physical World you should study step by step every concept is related with each other for better understanding go through each post.
Today our topic is important and interesting second chapter Physics.
Units and Measurement:   

Very first we have to discussed about physical quantity here we study about nature in physics and nature is around us whatever object we see and interact with this we see in nature different object have different characteristics.Each and every component of nature having different characteristics like chock, board, light,earth, air, water many more each and every component we sense around nature.


                                                   
Basic Units and Measurement concept
 This natural component has to nomenclature on the basis of their characteristics and we want to measure that characteristics because in some component it is large value and in some component small value of that characteristics, take some example if we put a chock in our hand and feel force on your hand very small but second time put a 5kg mass then feel force on your hand it will be large so what we observe here both of this object having a single characteristics small chock is pushing my hand very little but heavy mass 5kg pushing my hand large so pushing is a single characteristics in both object with different values. similarly for small size object and large size object it will be characteristics of same with different values so characteristics of nature which can be measured is called “physical quantity”.
Now we will nomenclature the physical quantity for measurement according to their characteristics example when we take a chock it easily confined in my fist but when we take a long stick it is not confined in fist so for this characteristics measurement we use length and latter this length will be use in many places like distance, height, width, thickness,volume in all places length will be use.now we will see other characteristics of nature take example we will take same length of two object in our both hand in left hand take a chock and in right hand take iron rod then we observe that in left hand chock pushes my hand less but right hand iron rod pushes my hand more whereas length of both object is same so this is other characteristics rather than length hence we nomenclature this natural characteristics mass so in similar fashion we observed more natural characteristics and nomenclature means putting their name and this is called physical quantity. hence we observed in nature and start to making characteristics 1,2,3,4,5,7,8,,9,10,……..100000 lakh of characteristics now it become problem for us shortage of name also it become difficult to remember name of each characteristics and its properties then we started to think over this characteristics if there should be only one characteristics then it will be good for us to study scientist tried to make a single characteristics through which all the other characteristics can be explain when we taken same length of chock and iron rod and try to explain through single characteristics length but it fail because length is same but pushing characteristics of both object is different hence there must be a another characteristics and it was nomenclature as mass hence if one quantity is not able to explain other characteristics then we have to consider another quantity. take an example length, width, height tell me these three are different characteristics or same characteristics wait this is same one quantity can explain these three characteristics when length is rotated with 90 degree it become height now length is again rotated with 90 degree it become width so our basic quantity is length through which we measure characteristics of  physical quantity length.now using length technique measurement we can measure width and height no separate technique required to measure width and height.now i ask you that in the evening you had gone to your friend home how much distance is your friend home this is another quantity which is present in nature now we need to study this distance characteristics and it will be a new quantity big no because distance is also length between two point and we have already basic quantity length for measurement now take another question when i ask you what is speed of your motorcycle you reply 20 m/s here motorcycle is new component of nature and speed is its characteristics this is another new quantity ? big no because  it is define m/s that is length per unit time so we see here height, width, distance, speed, volume in all these measurement we are measuring length all these quantities having same characteristics which is length basic physical quantity. how easy it become you learn one technique length measurement and measuring all above quantity on the basis of this we made two group one is Fundamental/ basic quantity and other is derived quantity. hence length is fundamental quantity and derived quantity from length are width, height, distance, area, volume, speed and many more which involve length.so we can say that in the world there is only one basic quantity length our answer is big no just above we have seen mass where length fail to explain chock and iron rod characteristics so we can’t explain length in terms of mass and similarly mass in terms of length so these two are separate basic quantity. hence we know heavy mass body has more pushing characteristics so from mass derived quantity are force we know force depend upon mass, momentum, energy. now we learned basic quantity through which we will measure characteristics of the nature and are happy but wait a boy came to ask a physics question we simply told him today we have learnt basic quantity please come tomorrow another boy came to ask question again told you come after two days, third boy came to ask question again told him you came after one week now what is this can we measure the length first boy will come, can we explain with mass no then what is this new characteristics we say everyday after 24 hr sun arises.hence we nomenclature this new basic quantity time. so time is that quantity which can not be express by length and mass. so our third new basic quantity is time similarly temperature which can’t be express by length, mass, time so after observing all the characteristics of the nature we finally found seven Fundamental/Basic quantities hence these are seven fundamental quantities length, mass, time, temperature, electric current, amount of substance, luminous intensity, plane angle, solid angle (plan and solid angle are supplementary added latter ).


Why we want to measure Physical quantity ?
Nature is a science of measurement nature is all about measurement how we say today is hotter on the basis of measurement two friend are discussing one say today is hotter and other say yesterday was hotter no one is agree to accept then go to third person and ask yesterday was hotter or today is hotter then third person measure temperature and say yesterday temperature was 45 degree Celsius today is 50 degree Celsius then they agreed otherwise fighting continue so science is measurement take an another example of land two person are fighting one say my land is from this pillar to 10th pillar other say 10th number pillar is in my land then what is solution measurement so physics is all about measurement which measurement nature because physics is study of nature what we want to measure characteristics so finally we measure nature characteristics.
Now how we will measure any physical quantity ? we will have to make a unique system.
Unit measurement of a quantity is a standard measurement which is given a particular name its value should not change with time, place and other physical conditions.Now we will apply unit we know that a physical quantity length use to measure size all scientist sit together and decided that stretch your hand and cut a iron rod length of your hand and nomenclature  this one meter again cut 50 iron rod of this size and distributed in every country for measurement named one meter and hang one sample in lab. now every country has got a iron rod length one meter now again the country will make more iron rod of same length and distributed in all city and announce that this length is one meter from this we will use for measurement of one meter written on this iron rod whole over the world our unit of length is ready now for us this became a standard for meter wait but as the season changes in summer this iron rod length increase by some length and in winter it become some shorter then it created problem among people and lead to continue fighting so for this reason our standard should be like that it should not depend upon season, location and any physical condition then it will be a standard unit hence what are characteristics of a standard unit, value should not change with time,should not destroyed with time in case of iron rod after time passes it get to rust and after cleaning it became smaller. it must be well defined its definition should be so accurate so that any other can’t create controversy on its definition an example we made a standard that when ice is converted to water and water is converted to ice that temperature is zero degree but a person claim on this when we increase the pressure and decreases the pressure it become ice before and after zero degree temperature now it not a standard then we again correct our definition that when water converted to ice its pressure should be normal at sea level now it became standard so any type of confusion should not create upon standard unit. take an example when we talk about light speed and its frequency which light color we consider because light every color frequency is different then we mention that orange color we are considering so in this manner our definition should be clear so in science we always correction required and changes take place. standard unit must be reproduce whenever needed easily means to say that suppose earth quack happen and lost our meter length then again it should be created easily that should be unit standard.next point should be proper size neither to big nor too short now it is very interesting we have to made mass unit how we will choose the standard unit suppose all people giving their opinion some given small size mass next given larger than this other given larger than this and so on then how we will choose the standard unit of mass how much big mass want to make unit, what is unit means one ?  now we think over it we will make unit of that mass which comes in our daily use so that there can not involve too much mathematical calculation we made the mass unit kilogram then how much mass will be one kilogram how we will decide one kilogram mass then we started to search daily use of our life that daily food daily we go to market and brought vegetable how much vegetable daily brought from market for a normal family daily brought one kg vegetable so what most we do measurement daily that is our food so we fixed the mass which we use daily buy then we fixed that mass one kg then it became one kg in the world. now for big mass we compare from our standard unit one kg like 5kg five times of one kg for 10 kg we use ten times of one kg and so on suppose if kg was not our unit some other unit were there then how we told buy vegetable told shopkeeper give me 500 unit vegetable, give me 1000 unit vegetable and so on it was awkward now it seen it is ok for daily life necessity but when we brought material from outside to truck it is how many of kg 100 kg, 1000 kg, 10000 kg so it become also awkward then we again change for heavy mass name and nomenclature 1000 kg approx one tons now it became easy 1, 2, 3, 4,……20 tons for truck so for the sake of simplicity change the unit. now we got to buy gold then we can’t say shopkeeper give me .0012 kg of gold this is some awkward so again change this unit to milligram and easily say 5 mg , 10 mg, 50 mg unit change for our simplicity so important point for unit is of proper size wherever we use similar for liquid we fixed litter but when more quantity of water taken they we say i want 5 bucket of water now our unit is bucket so it became practical unit should be proper size of  measurement so when i say what will be mass of the sun if you calculate in kg it will be a very large number not easy to told then there should be a big unit for sun mass similarly for distance also distance from sun to earth if we measure in meter it will be very difficult to told here should be a big unit for length that is light year so every unit has standard and practical unit both now i hope we have understand clearly about unit we will continue for measurement in next post.
Thanks for reading Basic Units and Measurement concept
                           

basic system of units concept

Basic system of units concept  

We will Study here measurement of units that time every country was developed their own measurement and unit, India, France, America, Britain all were doing their own measurement like in India we were using hand for length measurement in India Land measurement unit use “Katha”, Bigha in different area and convert to other unit and all this unit does not recognize each other this become problem for us. 
The main problem was that all country were using their own measurement system this was a communication gap of language so in international trade unable to trade, take an example suppose in India Petrol rate is 60 Rupees/litter but in America suppose 6 $/gallon if we purchase form Russia suppose 8 ruble/pound now question arises which one is costly among these three unit this became a problem for scientist.