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A uniform solid sphere with radius r and mass m compresses a spring with spring...

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A uniform solid sphere with radius r and mass m compresses a spring with spring constant k by a distance x The spring must be compressed by minimum distance 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 27mg R r A x 5k B The speed of the sphere at the top of the circular loop must be g R r 10mg R r k C If the surface was made perfectly smooth x required to loop the loop is D in option C above the speed at the top of the circular loop must be R r

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