Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 7

7 Figure 8-23 shows a thin rod, of length \(L = 2.00 \text{ m}\) and negligible mass, that can pivot about one end to rotate in a vertical circle. A ball of mass \(m = 5.00 \text{ kg}\) is attached to the other end. The rod is pulled aside to angle \(\theta_0 = 30.0^\circ\) and released with initial velocity \(\vec{v}_0 = 0\). As the ball descends to its lowest point, (a) how much work does the gravitational force do on it and (b) what is the change in the gravitational potential energy of the ball–Earth system? (c) If the gravitational potential energy is taken to be zero at the lowest point, what is its value just as the ball is released? (d) Do the magnitudes of the answers to (a) through (c) increase, decrease, or remain the same if angle \(\theta_0\) is increased?