Serway & Jewett — Energy of a System: Problem 19.

(a) A force \(\vec{F} = (4x\hat{i} + 3y\hat{j})\), where \(\vec{F}\) is in newtons and \(x\) and \(y\) are in meters, acts on an object as the object moves in the \(x\) direction from the origin to \(x = 5.00\text{ m}\). Find the work \(W = \int \vec{F} \cdot d\vec{r}\) done by the force on the object. (b) What If? Find the work \(W = \int \vec{F} \cdot d\vec{r}\) done by the force on the object if it moves from the origin to \((5.00\text{ m}, 5.00\text{ m})\) along a straight line path making an angle of \(45.0^\circ\) with the positive \(x\) axis. Is the work done by this force dependent on the path taken between the initial and final points?