Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 8_M

Figure 11.10 shows the potential energy \(U(x)\) of a solid ball that can roll along an \(x\) axis. The scale on the \(U\) axis is set by \(U_s = 100\text{ J}\). The ball is uniform, rolls smoothly, and has a mass of \(0.400\text{ kg}\). It is released at \(x = 7.0\text{ m}\) headed in the negative direction of the \(x\) axis with a mechanical energy of \(75\text{ J}\). (a) If the ball can reach \(x = 0\text{ m}\), what is its speed there, and if it cannot, what is its turning point? Suppose, instead, it is headed in the positive direction of the \(x\) axis when it is released at \(x = 7.0\text{ m}\) with \(75\text{ J}\). (b) If the ball can reach \(x = 13\text{ m}\), what is its speed there, and if it cannot, what is its turning point?