Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 21_M

Figure 8.17 shows a pendulum of length \(L = 1.25\text{ m}\). Its bob (which effectively has all the mass) has speed \(v_0\) when the cord makes an angle \(\theta_0 = 40.0^\circ\) with the vertical. (a) What is the speed of the bob when it is in its lowest position if \(v_0 = 8.00\text{ m/s}\)? What is the least value that \(v_0\) can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c) to a vertical position with the cord remaining straight? (d) Do the answers to (b) and (c) increase, decrease, or remain the same if \(\theta_0\) is increased by a few degrees?