A solid sphere of mass m and radius r rolls without slippingalong a slanted ladd

Question

A solid sphere of mass m and radius r rolls without slippingalong a slanted ladder that eventually hits flat ground. Imagine aninvisible loop at the bottom of the slanted ladder where it hitsthe flat ground. The invisible loop (with radius R) represents thetrack of the solid sphere after it reaches the bottom of theladder. The solid sphere starts from rest with the lowest point ofthe 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 thesphere completes the loop?

b) What are the force components on the sphere at a point P(somewhere on the loop) if h=3R?

Explanation / Answer

Is there a diagram that goes with this problem? All this "invisibleloop" stuff is sort of hard to imagine. I don't know if I'mvisualizing what I'm supposed to.

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