Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 76

We move a particle along an \(x\) axis, first outward from \(x = 1.0\text{ m}\) to \(x = 4.0\text{ m}\) and then back to \(x = 1.0\text{ m}\), while an external force acts on it. That force is directed along the \(x\) axis, and its \(x\) component can have different values for the outward trip and for the return trip. Here are the values (in newtons) for four situations, where \(x\) is in meters: Situation Outward Inward (a) +3.0 -3.0 (b) +5.0 +5.0 (c) +2.0x -2.0x (d) +3.0x² +3.0x² Find the net work done on the particle by the external force for the round trip for each of the four situations. (e) For which, if any, is the external force conservative?