Find Work Done on 230 kg Crate in 12 m Displacement

[Gold3nlily]

Homework Statement

A 230 kg crate hangs from the end of a rope of length L = 12.0 m. You push horizontally on the crate with a varying force to move it distance d = 4.00 m to the side (Fig. 7-43). (a) What is the magnitude of when the crate is in this final position?

Figure:
http://edugen.wiley.com/edugen/courses/crs4957/halliday9118/halliday9118c07/image_n/nt0043-y.gif

(This is just a problem from the back, not homework...)

Homework Equations

W = F*d
W = KEf - KEi
(I'm supposed to solve this without using conservation of energy (that is next chapter), only work, forces, and kinetic energies)

The Attempt at a Solution

Normally I would set the two equations equal to each other, but I don't know either velocity and I cannot find a way to cancel them out of the equation.

I also have a question about the angle between the force and the distance. When I look at the picture it looks like the force is horizontal, but the displacement of the box itself is kind of slanted upwards. I am i supposed to ignore that (the arrow indicating the displacement below the box is horizontal)?

Then about the forces, i think that the tension force and the gravitational force does no work becasue it is perpendicular to the displacement, is this right?

I also found the angle at the top of the figure:
@ = tan^-1 (4m/12m) = 18.435 degrees

I feel a little stuck right now. Could anyone please give me a kick start? Is there an equation I am neglecting? Is there a way to solve this problem without using conservation of energy?

Oh and the answer from the book is: 797 N

 

[Doc Al]

I don't understand the problem. Is the crate in equilibrium in its final position?