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

21 Figure 8-23 shows a pendulum of length L = 1.25 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 parts (b) and (c) increase, decrease, or remain the same if $\theta_0$ is increased by a few degrees?