What is an elastic collision?

The product of a particle's mass and velocity is called momentum. The term "momentum" refers to a quantity that has both a magnitude and a direction. The temporal rate of change in momentum is equal to the force applied on the particle, according to Isaac Newton's second law of motion.

When two body collide to each other then momentum of the system remain conserved while energy may or may not be conserved.In case of elastic collision

Internal kinetic energy of the system remain conserved.

In collision the forces are generated in the form of action-reaction force. So the net external force on the system remains zero.The force is defined as rate of change of momentum.So, when net force is zero , change in momentum will be zero or momentum will remain conserve.

\(\begin{aligned}{F_{net}} &= \dfrac{{\Delta P}}{{\Delta t}} = 0\\\dfrac{{{P_{final}} - {P_{initial}}}}{{\Delta t}} &= 0\\{P_{final}} - {P_{initial}} &= 0\\{P_{final}} &= {P_{initial}}\end{aligned}\)

Hence, in an inelastic collision momentum of the system remains conserved.

The value of coefficient of resititution (e) as the ratio of velocity of separation and velocity of approach. In case of elastic its value is 1.

\(e = 1\)

As the value of coefficient of restitution for elastic collision is 1, so there is no loss in the total kinetic energy of the system.

It means the objects regain their shape after the collision and they is no heat generated in such type of motion.

Hence , the total kinetic energy in the elastic collision remains conserved.