From Newton's third law of motion we know that whenever a force is applied on a body there will be an equal and opposite reaction. Action and reaction forces result in change in velocities of both the bodies which in turn change the momenta of these bodies.
In an elastic collision the initial momentum of the bodies before collision is found to be equal to the final momentum of the bodies after collision.
Thus Newton's second and third laws of motion lead us to the very important law of mechanics, the law of conservation of momentum.
Law of conservation of momentum states that - if a group of bodies are exerting force on each other, i.e., interacting with each other, their total momentum remains conserved before and after the interaction provided there is no external force acting on them.
The following example will help us to understand clearly the law of conservation of momentum.
Two bodies A and B of masses m1 and m2 are moving in the same direction with initial velocities u1 and u2. They make a direct collision. Let us assume that after collision they continue moving in the same direction. Let the collision last for a very short interval of time 't' seconds.
During collision, A exerts a force on B. At the same time, B exerts a force on A. Due to these action and reaction forces the velocities of A and B get changed. After collision, let v1 and v2 be the velocities of the bodies A and B respectively.
The force exerted on A = m1 a1[Accord
ing to Newton's II law of motion]
According to Newton's third law of motion, these two forces are equal and opposite.
i.e., total momentum before collision is equal to the total momentum after collision, which is nothing but law of conservation of momentum.