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Question 1

A sphere with radius r and moment of inertia  compresses a spring with spring constant k a distance x.

(a) How far must the spring be compressed so that the sphere rolls around the interior of a circular loop of radius R, depicted in the figure above, while always remaining in contact with the track? (10 points)

(b) In the case described in part (a) what height will the sphere reach at the end of the track? (5 points)

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