How much work is done by the towrope on a waterskier moving due west?

[renegade05]

Homework Statement

The tension in the horizontal towrope pulling a waterskier is 240N while the skier moves due west a distance of 54m. How much work does the towrope do on the water-skier?

Homework Equations

W=F(deltaR)(cos(theta))

The Attempt at a Solution

I just have a quick question. I am wondering if this is a trick question since the rope does not do any work, it is the engine that does the work. Or am I wrong about that?

If i am wrong, is the answer: 12960 Joules? 240N x 54m = 12960 Joules. or is it negative?

 

[PhanthomJay]

There is no trick here, work done by a force is the product of the component of the force in the direction of the objects displacement times the displacement (W = Fdcostheta). When force component and displacement act in the same direction, work is positive since theta is 0; when they act in opposite directions, theta is 180 degrees, so work is negative. Note that since the engine must pull both the boat and itself and the waterskier, it must provide greater force than the rope, and hence more work is done by the engine than is done by the rope.