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A sphere with a moment of inertia 0.658mr2 and mass m and radius r rolls without slipping along the track shown on a planet where the acceleration due to gravity is g. It starts from rest at a height h = 4.87R above the bottom of the circular loop of radius R.

(For simplicity, neglect the size of the sphere relative to the radius of the loop R and the height h, i.e. r << R, h. Also, while static friction is responsible for the rolling motion, it does no work since it acts through no displacement.)

a) What is the magnitude of the normal force that acts on the sphere at the top of the circular loop as a fraction or multiple of the sphere's weight mg?

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