How much work is done on a bucket when pulling it up?

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The discussion revolves around calculating the work done on a bucket being pulled up a well. The bucket has a mass of 6.75 kg, resulting in a weight of 66.21 N. The user calculated the work done as 264.84 J based on the formula W = FS, where F is the force and S is the distance. However, the answer key from the textbook incorrectly states the work done as 3.60 J, leading to confusion about the accuracy of the calculations. The consensus is that the user's calculation appears correct, suggesting a potential error in the textbook's answer key.
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Homework Statement


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 4.00m.
A). How much work do you do on the bucket in pulling it up?

Homework Equations


##W = FS##
##W = ΔKE##
##ΣFy = T - mg##

The Attempt at a Solution


First, I assumed the problem was implying that the bucket was in equilibrium when it said it was moving slowly. So since the weight is ##(9.81)(6.75) = 66.21 N##, the tension force must be equal to that.

So, ##W = FS##. ##W = (66.21)(4) = 264.84 J##. This seemed like the correct answer to me, but when I look at the back of the book, it says the answer is 3.60 J.

Where did I go wrong here? Thanks!
 
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I'd say your answer is correct. What book/problem is this from?
 
Doc Al said:
I'd say your answer is correct. What book/problem is this from?
That's what I thought too. It's from "Sears and zemansky's University Physics With Modern Physics, 12th edition".

I guess there was a mistake or something in the answer key.
 
BlueQuark said:
I guess there was a mistake or something in the answer key.
Yep.
 
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