Question

You know that a collision must be “elastic” if: (1) The colliding objects stick together. (2) The colliding objects are stretchy or squishy. (3) The sum of the final kinetic energies equals the sum of the initial kinetic energies. (4) There is no change in the internal energies of the objects (thermal energy, vibrational energy, etc.). (5) The momentum of the two-object system doesn’t change.

Short answer

3) The sum of the final kinetic energies equals the sum of the initial kinetic energies and 4) there is no change in the internal energies of the objects (thermal energy, vibrational energy, etc.) and 5) the momentum of the two-object system doesn’t change.

Step-by-step solution

Significance of the law of conservation of momentum and elastic collision of a system

This law states that the momentum of a particular system before and after collision is constant if no external force acts on the system.

The total momentum of a system is conserved in an elastic collision and the mechanical energy is also conserved.

Determination of the elasticity of a collision

From the law of conservation of momentum, the momentum of a system gets conserved. Hence, all the bodies should be included while defining a system of bodies. However, when the objects collide and also bounce back between them, a moment redistribution amongst the bodies occurs. Moreover, in the elastic collision, the initial and the final kinetic energy of an object does not change.

Thus, 3) the sum of the final kinetic energies equals the sum of the initial kinetic energies and 4) there is no change in the internal energies of the objects (thermal energy, vibrational energy, etc.) and 5) the momentum of the two-object system doesn’t change.