A 0.150 kg ball is going around in a vertical circle of radius R = 0.300 m at constant speed v. The ball is attached to a massless ideal string which is attached to a fixed pivot point. If the tension F in the string is greater than 125 N, the string will break. Gravity acts downward on the ball. Ignore any effects of air friction on the motion of the ball.
(a) Draw free-body diagrams for when the ball is at the top of the circle and when the ball is at the bottom. Derive expressions for the tension F in the string when the ball is at the top of the circle and when the ball is at the bottom of the circle. Explain physically why F is larger when the ball is at the bottom of the circle than when the ball is at the top of the circle.
(b) What is the minimum constant speed of the ball vmin for which the ball goes over the top of the circle while the string is still taut? This criterion means that the calculated F ≥ 0.
(c) What is the maximum constant speed of the ball vmax for which the string does not break?