Object at rope: work to lift it

[iwonde]

An old oaken bucket of mass 6.75 kg hangs in a well at the end of a rope. The rope passes over a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to raise the bucket slowly a distance of 4.00 m.

So far, I have:
F = force exerted by me
s = displacement
W_F=F x s

How do I find F? Does it have anything to do with the tension of the rope?

 

[Kurdt]

Work done is also the change in potential energy.

 

[iwonde]

I'm sorry, I meant to ask for the work done by me.
So,
H= height
H_1 = 0
H_2 = 4m
Work_total = change of potential energy = mg(H_2 - H_1) = 264.6
and W_total = W_me + mgH_1 = 264.6J
W_me = 264.6 J
Did I do something wrong, because it doesn't seem right.

 

[Kurdt]

Looks Ok to me. What are you having trouble with?

 

[iwonde]

The answer in the book is 3.6 J.

 

[Kurdt]

What was the question in full? Are you sure that's the answer to this question?