Object at rope: work to lift it

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To determine the force exerted to lift a 6.75 kg bucket using a rope over a frictionless pulley, the work done by the person pulling the rope is equal to the change in potential energy. The potential energy change is calculated as mg(H_2 - H_1), resulting in 264.6 J for a height change of 4 m. The user is confused about the discrepancy between their calculation and the book's answer of 3.6 J. Clarification is needed on the specific question being asked, as the calculations seem to align with the principles of work and energy. The discussion highlights the importance of correctly interpreting the problem to ensure accurate calculations.
iwonde
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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?
 
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Work done is also the change in potential energy.
 
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.
 
Looks Ok to me. What are you having trouble with?
 
The answer in the book is 3.6 J.
 
What was the question in full? Are you sure that's the answer to this question?
 
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