Why Does Gravity Affect Work Done in a Simple Pulley System?

[leehufford]

Hello,

This problem seems so simple yet I cannot find the right answer:

Problem:

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 pulling the bucket up?
b) How much work does gravity do on the bucket?
c) What is the total work?

I'm assuming constant velocity. I reason the tension force in the rope must equal that of the weight of the bucket, because there is no acceleration. And since the applied force is in the same direction as the displacement, it should simply be W=Fd. (Since cos (0) = 1)

So I try W = (6.75kg)(9.8m/s^2)(4.00m) = 264.6 J. The book answer is 3.60 J.

For part B, I assumed it would be negative, so -3.60 J. But the book answer is -0.900 J, making the total work 2.70 J. What incorrect assumption am I making?

Thanks in advance,

Lee

 

[Dick]

Hello,

This problem seems so simple yet I cannot find the right answer:

Problem:

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 pulling the bucket up?
b) How much work does gravity do on the bucket?
c) What is the total work?

I'm assuming constant velocity. I reason the tension force in the rope must equal that of the weight of the bucket, because there is no acceleration. And since the applied force is in the same direction as the displacement, it should simply be W=Fd. (Since cos (0) = 1)

So I try W = (6.75kg)(9.8m/s^2)(4.00m) = 264.6 J. The book answer is 3.60 J.

For part B, I assumed it would be negative, so -3.60 J. But the book answer is -0.900 J, making the total work 2.70 J. What incorrect assumption am I making?

Thanks in advance,

Lee

I don't think the book's answers make any sense at all. I agree totally with 264.6 J for the first one.

 

[leehufford]

Should the work done by the person and work done by gravity be equal and opposite? The book has different numerical values for each. (3.0 J, -0.9 J)

 

[Dick]

Should the work done by the person and work done by gravity be equal and opposite? The book has different numerical values for each. (3.0 J, -0.9 J)

Sure. That's just part of why the book's answer doesn't make any sense. The numbers are way off too.

 

[Nickie]

Dear Lee,

Thank you for sharing your problem and thought process. It seems like you have a good understanding of the concept of work and the forces involved in this scenario. However, there are a few key points that may help clarify the discrepancy between your answer and the book's answer.

Firstly, when calculating work, it is important to use the net force acting on the object. In this case, the net force would be the applied force (from pulling on the rope) minus the weight of the bucket. This is because the tension force in the rope is balancing out the weight of the bucket, so it does not contribute to the net force. Therefore, the correct equation would be W = (applied force - weight of bucket) * distance.

Secondly, the work done by gravity on the bucket is not negative. This is because gravity is acting in the same direction as the displacement of the bucket, so the angle between the force and displacement is 0 degrees (not 180 degrees as in the case of a negative work). Therefore, the work done by gravity would also be positive.

Using these corrections, the correct answers would be:
a) W = (applied force - weight of bucket) * distance = (applied force - 6.75kg * 9.8m/s^2) * 4.00m = (F - 66.15N) * 4.00m = 4.00F - 264.6J
b) W = weight of bucket * distance = 6.75kg * 9.8m/s^2 * 4.00m = 264.6J
c) Total work = W + W = (4.00F - 264.6J) + 264.6J = 4.00F = 4.00(applied force - 66.15N) = 4.00(applied force) - 264.6J

I hope this helps clarify the problem for you. Keep up the good work!

Best,