Explain how momentum gets conserved in collision of two bodies?
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Solution
Momentum
The momentum of any object is the product of its mass and velocity.
According to the law of conservation of momentum, when two objects or bodies collide with each other the total momentum before the collision is equal to the total momentum after the collision.
The mass of the system must remain constant during the interaction.
Conservation of momentum
Let us consider two objects A and B (as shown in the figure) with mass mA and mB respectively moving with initial velocities uA and uB.
If these two objects collide with each other for time ‘t’, object A applies force on object B, that is FAB. Similarly, object B applies force on A, that is FBA.
Here FAB is an action whereas FBA is a reaction. According to Newton’s third law, every action has an equal and opposite reaction . -------- (1)
If vA and vB are the velocities of the objects A and B after collision respectively, then according to Newton's second law, a force to be equal to change in momentum (mass times velocity) per change in time. and
Hence Eq. (1) can be written with the values of FAB and FBA as
The above equation shows that momentum gets conserved in a collision of two bodies.