A small, solid sphere of mass 0.4 kg and radius 62 cm rolls without slipping alo

Question

A small, solid sphere of mass 0.4 kg and radius 62 cm rolls without slipping along the track consisting of slope and loop-the-loop with radius 3.2 m at the end of the slope. It starts from rest near the top of the track at a height h, where h is large compared to 62 cm. http://gyazo.com/2366456097669446837384b1b12cbf1e What is the minimum value of h (in terms of the radius of the loop R) such that the sphere completes the loop? The acceleration due to gravity is 9.8 m/s^2 . The moment of inertia for a solid sphere is 2/5m r^2 . Answer in units of m. What are the force component in the horizontal direction on the sphere at the point P, which has coordinates (?R, 0) if we take the center of the loop as origin, and if h = 3 R ? Answer in units of N

Explanation / Answer

The sphere will pass through the entire loop if g = v^2/r --> v^2 = rg. Energy conservation: mgh = 1/2 * m * v^2 + 1/2 * (2/5 MR^2 + MR^2 [from parallel axis theorem]) * (v^2/r^2) + mg(9) [highest point of the loop] place the values to get the answer

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