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## Homework Statement

A cube of sides B sits ontop of a hemisphere of radius R. Determine the conditions such that the cube is in a stable equilibrium.

## Homework Equations

A stable equilibrium is one in that the second derivative of the potential energy function is positive. U = mgh.

## The Attempt at a Solution

I figure that I need to write out the potential energy of the center of mass of the cube as it is displaced from the eq. pt. Also, as the cube is perturbed, the arclength of the circle traversed on the hemisphere is equal to the length from the middle of the one cube's side (originaly contacting the hemisphere) to the point of contact. I am having trouble writing down the vertical position of the c.m. as a function of displacement. Is it just this geometry that I need to think about or is something else missing? thanks

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