Nonuniform ball . In the figure, a ball of mass M and radius R rolls smoothly fr

Question

Nonuniform ball. In the figure, a ball of mass M and radius R rolls smoothly from rest down a ramp and onto a circular loop of radius 0.50 m. The initial height of the ball is h = 0.33 m. At the loop bottom, the magnitude of the normal force on the ball is 2.05Mg. The ball consists of an outer spherical shell (of a certain uniform density) that is glued to a central sphere (of a different uniform density). The rotational inertia of the ball can be expressed in the general form I = ?MR2, but ? is not 0.4 as it is for a ball of uniform density. Determine ?.

Explanation / Answer

The height energy lost = the KE gained

M * g * h = 1/2 * M * v^2 + 1/2 * I * w^2

I =

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