# Work and Energy - angular force with friction

1. Oct 5, 2011

### estafusis

1. The problem statement, all variables and given/known data

A cart loaded with bricks has a total mass of 13.8 kg and is pulled at constant speed by a rope. The rope is inclined at 20.8° above the horizontal and the cart moves 30.4 m on a horizontal floor. The coefficient of kinetic friction between ground and cart is 0.7 . The acceleration of gravity is 9.8 m/s$^{2}$ . How much work is done on the cart by the rope?

2. Relevant equations

I'm clearly missing something I need because I can't really get close to a solution.

F$_{friction}$ = $\mu_{k}$ * F$_{normal}$
ω = F$_{rope}$ * Δx * COSθ

3. The attempt at a solution

I've gotten this far, but there must be something I'm missing because I still can't get any kind of solution out of it.
F$_{g}$ = 135.2N
F$_{rope}$x = F$_{friction}$
F$_{n}$ = F$_{g}$ - F$_{rope}$y
F$_{rope}$x = F$_{rope}$ * COSθ
F$_{rope}$y = F$_{rope}$ * SINθ

ω = F$_{rope}$ * 30.4 * COS(20.8)
F$_{rope}$ = ?

I've got about 15 more problems just like this to be done tonight so quick responses would be awesome and I REALLY hope its just some small equation or equality that i'm missing.