A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assume that the total energy of the ball-Earth system remains constant.
(a) What is the tension in the string at the bottom? (Use the following as necessary: m for the mass of the ball, g for gravitational acceleration, vb for the velocity at the bottom, and R for the radius of the circle.)
(b) What is the tension in the string at the top? (Use the following as necessary: m, g, vt for the velocity at the top, and R.)
(c) How much greater is the tension at the bottom? (Use the following as necessary: m, g.)