Chapter 7, Problem 19P

(a) A force $\stackrel{\to }{F}=(4x\hat{i}+3y\hat{j})$, where $\stackrel{\to }{F}$ 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 m. Find the work $W={\displaystyle \int \stackrel{\to }{F}\cdot d\stackrel{\to }{r}}$ done by the force on the object. (b) What If? Find the work $W={\displaystyle \int \stackrel{\to }{F}\cdot d\stackrel{\to }{r}}$ done by the force on the object if it moves from the origin to (5.00 m, 5.00 m) along a straightline path making an angle of 45.0° with the positive x axis. Is the work done by this force dependent on the path taken between the initial and final points?