Chapter 10, Problem 10.68P

CP A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down a track (Fig. P10.68). Points A and B are on a circular part of the track having radius R. The diameter of the shell is very small compared to h₀ and R, and the work done by rolling friction is negligible. (a) What is the minimum height h₀ for which this shell will make a complete loop-the-loop on the circular part of the track? (b) How hard does the track push on the shell at point B, which is at the same level as the center of the circle? (c) Suppose that the track had no friction and the shell was released from the same height h₀ you found in part (a). Would it make a complete loop-the-loop? How do you know? (d) In part (c), how hard does the track push on the shell at point A, the top of the circle? How hard did it push on the shell in part (a)?

Figure P10.68