F=ma 2025 Problem 10

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

m

and

M \gg m

. --- Question: If the lighter object is initially at rest, and the heavier object collides elastically with it, what is the approximate maximum fraction of the heavier object's kinetic energy that could be transferred to the lighter object? (A)

m/M

. (B)

{2m}/M

. (C)

{4m}/M

. (D)

{m}^2/{M}^2

. (E)

2{m}^2/{M}^2

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