Question

(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?
(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls?
(c) What are the answers to (a) and (b) for an inelastic collision?
(d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

Answer 1

With reference to the given question, we have to go through elastic and inelastic collision to answer the following question. Conservation of linear momentum states that the momentum of the particles before collision and after collision are equal.

Complete answer:
(a) In the given elastic collision, kinetic energy of the ball is not conserved during the short time of collision.
However, the total kinetic energy before collision of the balls and after collision are the same. At the time of collision, the kinetic energy of the ball gets converted into potential energy.
(b) Yes, the total linear momentum conserved during the short time of an elastic collision of two balls.
Linear momentum of a particle is always conserved whatever the cause may be.
(c) In case of inelastic collision, kinetic energy of the ball is not conserved during the short time of collision.
In fact, in inelastic collisions the total kinetic energy before collision is always greater than after collision.
The total linear momentum is always conserved.
(d) It is given that the potential energy of two billiard balls depends only on the separation distance between their centres which implies that the forces acting on them are also conserved.
Hence, the collision is an elastic collision.

Note:
It must be noted that an elastic collision refers to that collision in which there is no change in the net kinetic energy associated with the collision. Whereas, in inelastic collision there is a change in net kinetic energy as some of the kinetic energy is lost as heat energy, sound energy and others.