A ball of mass is attached to a string of length R and negligible mass. The ball moves clockwise in a vertical circle, as shown. When the ball is at point P, the string is horizontal. Point Q is at the bottom of the circle and point Z is at the top.
a) Draw and label all forces on the ball at points P and Q.
b) Derive an expression for , the minimum speed the ball can have at point Z without leaving the circular path.
c) The maximum tension the string can have without breaking is . Derive an expression for , the maximum speed the ball can have at point Q without breaking the string. Answer in terms of M, R, T, and fundamental constants.
d) Suppose that the string breaks when the ball is at point P. Describe the ball’s velocity and acceleration after the string breaks.