F=ma 2025 Problem 11

Physics · mechanics

Problem

When two objects of very different masses collide, it is difficult to transfer a substantial fraction of the energy of one to the other. Consider two objects, of mass mm and M≫mM \gg m. --- Question: Now suppose that instead, the heavier object is initially at rest, and the lighter object collides elastically with it. What is the approximate maximum fraction of the lighter object's kinetic energy that could be transferred to the heavier object? (A) m/Mm/M. (B) 2m/M{2m}/M. (C) 4m/M{4m}/M. (D) m2/M2{m}^2/{M}^2. (E) 2m2/M22{m}^2/{M}^2.

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