How Is the Force Calculated in the Hanging Crate Problem?

[demonelite123]

A 230 kg crate hangs from the end of a rope of length L = 12.0m. You push horizontally on the crate with a varying force F to move it a distance d = 4.00m to the side.
a) What is the magnitude of F when the crate is in this final position?
During the crate's displacement, what are
b) the total work done on it?
c) the work done by the gravitational force on the crate,
and
d) the work done by the pull on the crate from the rope?

i can't get part a) at all. the only formulas i know are W = (1/2)m(v² - v₀²) and W = F * d. how do i find the force?

my books answer is 797 N and i have no idea how they got it.

 

[lanedance]

draw a free body diagram of the crate

if i understand the question correctly, the crate will now be off the ground & the rope inclined, you know the sides of the triangle, find the angle the rope makes with the vertical

now balance all the forces, the vertical force will be equal & opposite to the gravtational force, use your trinagle to find the horizontal force, which will be balanced by the push