Serway & Jewett — Energy of a System: Problem 33.

A force acting on a particle moving in the \(xy\) plane is given by \(\vec{F} = (2y\hat{i} + x^2\hat{j})\), where \(\vec{F}\) is in newtons and \(x\) and \(y\) are in meters. The particle moves from the origin to a final position having coordinates \(x = 5.00\text{ m}\) and \(y = 5.00\text{ m}\) as shown in Figure P7.31. Calculate the work done by \(\vec{F}\) on the particle as it moves along (a) the purple path, (b) the red path, and (c) the blue path. (d) Is \(\vec{F}\) conservative or nonconservative? (e) Explain your answer to part (d).