Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 81

A particle can move along only an \(x\) axis, where conservative forces act on it (Fig. 8.49 and the following table). The particle is released at \(x = 5.00 \text{ m}\) with a kinetic energy of \(K = 14.0 \text{ J}\) and a potential energy of \(U = 0\). If its motion is in the negative direction of the \(x\) axis, what are its (a) \(K\) and (b) \(U\) at \(x = 2.00 \text{ m}\) and its (c) \(K\) and (d) \(U\) at \(x = 0\)? If its motion is in the positive direction of the \(x\) axis, what are its (e) \(K\) and (f) \(U\) at \(x = 11.0 \text{ m}\), its (g) \(K\) and (h) \(U\) at \(x = 12.0 \text{ m}\), and its (i) \(K\) and (j) \(U\) at \(x = 13.0 \text{ m}\)? (k) Plot \(U(x)\) versus \(x\) for the range \(x = 0\) to \(x = 13.0 \text{ m}\). Next, the particle is released from rest at \(x = 0\). What are (l) its kinetic energy at \(x = 5.0 \text{ m}\) and (m) the maximum positive position \(x_{\text{max}}\) it reaches? (n) What does the particle do after it reaches \(x_{\text{max}}\)? Force Data Table: Range \(0\) to \(2.00 \text{ m}\): \(\vec{F}_1 = +(3.00 \text{ N})\hat{i}\) Range \(2.00 \text{ m}\) to \(3.00 \text{ m}\): \(\vec{F}_2 = +(5.00 \text{ N})\hat{i}\) Range \(3.00 \text{ m}\) to \(8.00 \text{ m}\): \(F = 0\) Range \(8.00 \text{ m}\) to \(11.00 \text{ m}\): \(\vec{F}_3 = -(4.00 \text{ N})\hat{i}\) Range \(11.00 \text{ m}\) to \(12.00 \text{ m}\): \(\vec{F}_4 = -(1.00 \text{ N})\hat{i}\) Range \(12.00 \text{ m}\) to \(15.00 \text{ m}\): \(F = 0\)