Two identical smooth balls

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum

Problem

Two identical smooth balls, each of mass 0.50 kg0.50\,\text{kg}, lie on a frictionless horizontal track. Ball AA moves with speed 4.0 m s−14.0\,\text{m s}^{-1} towards stationary ball BB. Evaluate the change in total kinetic energy for the following three separate collision cases and arrange them in order of increasing energy loss. (i) Collision is perfectly elastic (e=1e = 1). (ii) Coefficient of restitution is e=0.5e = 0.5. (iii) Collision is perfectly inelastic; the balls stick together after impact. (iv) Rank the three cases in ascending order of kinetic energy loss, clearly justifying your answer with calculated values.

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