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A solid sphere of mass m rolls without slipping down a frictionless incline. It starts from rest at a height h. At the bottom of the incline is a frictionless loop with radius R.

(a) Draw energy bar charts for the ball-surface-Earth system at (i) the top of the ramp, (ii) the bottom of the ramp, (iii) the top of the loop.

(b) Find the speed v of the sphere at the top of the loop.

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