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A wooden cube rests on a rough horizontal surface and a force is applied to it. The condition of whether it begins to slide before it overturns, or overturns before it starts sliding, does not depend on:

1. the location of the point where the force is applied
2. the side length of the cube
3. the mass of the cube
4. the coefficient of friction between the cube and the table

Correct answer: the mass of the cube

Solution

Sliding starts when F = mu mg; overturning starts when F h = mg(a/2), i.e. F = mg a/(2h). Which occurs first depends on comparing mu with a/(2h), so it depends on the side length a, the height h of the force, and mu, but the mass m cancels out. Hence it does NOT depend on the mass of the cube.

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