A steel ball rolls down an incline into a loop-the-loop of radius R (Fig. 8.52a).

(a) What minimum speed must the ball have at the top of the loop in order to stay on the track?
(b) At what vertical height (h) on the incline, in terms of the radius of the loop, must the ball be released in order for it to have the required minimum speed at the top of the loop? (Neglect frictional losses.)
(c) Figure 8.52b shows the loop-the-loop of a roller coaster. What are the sensations of the riders if the roller coaster has the minimum speed or a greater speed at the top of the loop?

(a) (b)