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