Walker, Halliday & Resnick — Potential Energy and Conservation of Energy: Problem 14

14 (a) In Problem 4, what initial speed must be given the ball so that it reaches the vertically upward position with zero speed? What then is its speed at (b) the lowest point and (c) the point on the right at which the ball is level with the initial point? (d) If the ball’s mass were doubled, would the answers to (a) through (c) increase, decrease, or remain the same? Reference from Problem 4: Figure 8-20 shows a ball with mass \(m = 0.382 \text{ kg}\) attached to the end of a thin rod with length \(L = 0.498 \text{ m}\) and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed there.