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 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).
Solution and Explanation
(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision (when they are in contact)?
Answer: No.
In an elastic collision, the total kinetic energy before and after the collision is the same, but during the short contact time some of the kinetic energy is temporarily converted into elastic potential energy due to deformation of the balls. Hence, at the instant of contact, the total kinetic energy is not conserved, although the total mechanical energy (kinetic + potential) is conserved.
(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls?
Answer: Yes.
During the collision, the forces acting are internal (action–reaction pair between the balls), and there is no external net force on the two-ball system. Therefore, the total linear momentum of the system remains conserved at every instant, including during the short contact time.
(c) What are the answers to (a) and (b) for an inelastic collision?
Answer: (a) No; (b) Yes.
In an inelastic collision, some kinetic energy is permanently transformed into other forms such as heat, sound, or internal (deformation) energy, so total kinetic energy is not conserved. However, as long as no external force acts on the two-body system, the total linear momentum remains conserved even in 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?
Answer: Elastic.
If the interaction potential energy depends only on the separation between centres, the force between the balls is conservative. For conservative forces, total mechanical energy (kinetic + potential) is conserved, so the collision is elastic.
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