Question

Problem 2 – variation of problem 10.76: A thin- walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in the figure. 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 ho and R, and the work done by rolling friction is negligible.

a) What is the minimum height ho, 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 ho 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?

Answer 1

a)As the motion of the shell is circular, it has both translational and rotational kinetic energy Consider the conservation of energy at A and o 2 2 3 2mgR 6 --mgR +2mgR 17 6 b)Let point 2 be B 2 R Consider the conservation of energy at point "B" 2 2 2 gR Consider the equilibrium of forces at point "B" BC BC