Question

Answer carefully, with reasons : (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

a)

In the case of an elastic collision of two billiard balls, the kinetic energy is conserved so the total kinetic energy of the balls will be equal to the total final kinetic energy of the balls.

At the time of collision of two billiard balls, the kinetic energy of the balls is not conserved and it will get converted into potential energy.

Thus, the total kinetic energy is not conserved during the short time of collision of the balls.

b)

The total linear momentum of the system always remains conserved in the case of an elastic collision.

c)

In the case of an inelastic collision, there will always be a loss of kinetic energy that means the total kinetic energy of the billiard balls before collision will always be greater than that after the collision.

The total linear momentum of the system always remains conserved in the case of an inelastic collision.

d)

The forces that are involved in the given case are conservative. This is because the forces depend on the separation between the centers of the billiard balls.

Thus, the collision is elastic.