Calculating Work on a Bucket Hanging in a Well

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Homework Help Overview

The discussion revolves around calculating the work done on a bucket of mass 6.75 kg that is being raised in a well. The problem involves concepts from mechanics, specifically work, force, and gravitational effects.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between tension and gravitational force, questioning whether the bucket is accelerating when raised slowly. There is an attempt to calculate work done based on the assumption of constant speed and the forces acting on the bucket.

Discussion Status

Participants are examining different interpretations of the problem, particularly regarding the forces involved and the implications of the bucket being raised slowly. Some calculations have been proposed, but there is no consensus on the correct approach or values.

Contextual Notes

There is a discrepancy between the calculated work values and those provided in the textbook, leading to further questioning of the assumptions made in the problem setup.

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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 4.00 m. (a) How much work do you do on the bucket in pulling it up? (b) How much work does gravity do on the bucket? (c) What is the total work on the bucket?

m=6.75 kg, s=4.00 m


Homework Equations


F=ma, W=Fs


The Attempt at a Solution


I know that this should be easy, right? It's just one-dimensional movement... but how do I know what the force of tension is? I drew a free body diagram for the bucket - the only forces are FG and FT, but I only know that FT is greater than FG (if it's accelerating upward). I don't know how to actually find the force of tension acting on the bucket.
 
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Is the bucket accelerating if it's being "raised slowly"? I think that you can presume a constant speed over the 4.00 m.
 
So, if FT=mg then, wouldn't the answer to part (a) be (6.75 kg)(9.8 m/s2)(4.00 m) = 264.6 J? But that would make the total work equal zero, with gravity doing -264.6 J. The back of the book says the answers are (a): 3.60 J, (b): -.900 J, (c): 2.70 J
 
Well, it's a mystery. 3.60 J is enough energy to raise a 6.75 kg bucket about 5.4 cm.
 

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