Question

In Fig. 11-35, a solid brass ball of mass m will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R, and the ball has radius r << R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? (b) If the ball is released at height h = 6R, what is the magnitude of the horizontal force component acting on the ball at point Q? State your answers in terms of the given variables, using g where applicable.

Figure: i.imgur. com/ WvU4V.gif
(remove spaces)

Answer 1

first, at the top of the loop, centripetal force <= mg

centriptal force= m v^2/R where v= wR
= m w^2 * R

but rolling energy + Kinetic energy+ potential energy at the top has to be = mgh

so work that out to find h. For I of the solid ball, I= 2/5 mr^2