Inclined plane with massless, frictionless winch

[r34racer01]

A 100 kg box is pulled up an inclined plane by a massless, frictionless winch to which it is attached by a massless rope. The plane makes an angle of 45° with respect to the horizontal. The coefficient of friction between the box and the plane is μ = 0.25 (with μs = μk). The winch has a radius of 0.25 m and is turned at a constant angular velocity of ω = 3.14 radians/sec.

How much work is done on the 100 kg box by the rope when the winch makes 10 complete revolutions?

(a) 4380 J
(b) 5235 J
(c) 9262 J
(d) 12531 J
(e) 13620 J


So I did d = [2(.25)(3.34)]10 since we need 10 rev. And then...
W = mgh + uNd
W = mg(d sin 45) + u(mg cos 45)d
but I'm not getting the right answer, I think I'm suppose to get 13620J, but how do I get that?

 

[Rake-MC]

I'm not so sure that W = mgh + uNd
Isn't mgh the gravitational potential that is gained by doing the work?

I would sum up the forces that are opposing the pull of the rope (parallel to the plane) and multiply it by the distance it moves