Suppose that Amy and Bob are two astronauts floating deep in outer space, where

Question

Suppose that Amy and Bob are two astronauts floating deep in outer space, where there is no gravity or friction to interfere, and they decide to have a tug of war. They agree that the loser of this is the one who first crosses over the midpoint between them. Bob has a larger mass than Amy, but Amy is stronger than Bob, so her maximum pulling force is larger than his. They begin not moving relative to each other. Assume that they keep a firm grip on the rope. Also assume that the rope is massless, which means that it is under the same tension force at both ends and everywhere in between. Who will win this tug of war? or is it impossible to determine that? or is it a tie? Explain.

Explanation / Answer

It doesn't matter who has greater pulling force, since the forces are necessarily equal and opposite. Instead, consider where they will meet. In this closed system, the center of mass does not move, so, barring the application of any external forces, they will meet at the center of mass, which is necessarily closer to bob (he "has a larger mass than Jill"). Assuming that we define the "winner" as the person who pulls the opponent over the centerline, or middle point, then Bob wins.

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