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.