A solid sphere of mass m and radius r rolls without slipping along the track sho

Question

A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.77. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? (b) What are the force components on the sphere at the point P if h = 3R?

Explanation / Answer

a) for the solid cylinder to complete the full circle the velocity is found using energy conservation as => h = 11R/4 b) using again the principle of conservation of energy we have the force on the cylinder is mg downward and 8mg/3 to the left ( due to normal reaction = centripetal acceleration)

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