Solve a Simple Work Problem and Find Out Why You're Wrong

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The problem involves calculating the work done on a 6.75 kg bucket being raised 4 meters using a rope over a frictionless pulley. The correct force needed to lift the bucket is calculated as 66.15 N, leading to a work output of 264.6 J. The claim that the answer should be 3.6 J is deemed incorrect by participants in the discussion. The confusion stems from a misunderstanding of the problem rather than an error in the calculations. The initial calculations for work done are accurate, confirming that the problem is indeed simple and correctly solved.
Laban
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Hello :)
I must have missed something. This problem is extremely simple and yet I can't figure out what I'm doing wrong. Really frustrating!

The problem:
A 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 m.

How much work do you do on the bucket in pulling it up?

My Guess
Since you need to raise the bucket, you need to pull with a force that equals the downwards gravitational force on the bucket. This is 6.75*9.8 = 66.15 N.
Now you pull it a distance of 4 m. This is 66.15*4 = 264.6 J.

But this is wrong! It's supposed to be 3.6 J


What am I supposed to do, and more importantly, why is what I'm doing wrong? This is supposed to be so simple >.<
 
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It is simple and you're doing it correctly. That 3.6 J answer is bogus.
 
You have solved the problem correctly. 3.6 J is incorrect.
 
I sure hope you're both right. Thanks!
 

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