Work Done on a Bucket in a Well

[kinthos]

"A rope exerts a force on a bucket as the bucket is raised up a well." Is the work done on the bucket positive or negative?

Now, I know that the is a tension force in the rope that must overcome weight to accelerate the object up the well. Also, work is positive if the force exerted is in the same direction as displacement but negative if in the opposite direction. If the net work is positive, then the object speeds up and work is done on the object, but if it is negative, the object slows down and work is done by the object on something else.

Newton's Third Law would make the force exerted by the bucket on the rope equal in magnitude but opposite in direction to the force exerted by the rope on the bucket. What I'm not sure about, though, are the signs of each. I think that, in case of question, the force exerted by the bucket on the rope would be negative because the bucket is subject to the tension force of the rope, but I'm not sure...

 

[AlephZero]

Does the bucket have more or less energy at the top than it did at the bottom?

That should give you a big clue as to whether the work done on the bucket is positive or negative.

 

[kinthos]

Ah, no, this is our class's first day on the topic of work, and I haven't looked at energy yet. I think, instead, that the work would be positive because the force is exerted on the bucket by the rope. If that is true, then would the work done by the rope on the bucket be negative? The tension force is in a positive direction (as is the additional applied force, if any, that causes the bucket to accelerate upward), but the rope is pulled downward (on the other side of the pulley/wheel--that doesn't really have much to do with the problem, does it?)...Mmm, it seems reasonable to me now, but would this be correct?

 

[PhanthomJay]

Ah, no, this is our class's first day on the topic of work, and I haven't looked at energy yet. I think, instead, that the work would be positive because the force that is exerted on the bucket by the rope acts in the same direction of its displacement. If that is true, then would the work done by the rope on the bucket be negative? You mean the work done by the bucket is negative, don't you? The tension force is in a positive direction (as is the additional applied force, if any, that causes the bucket to accelerate upward), but the rope is pulled downward (on the other side of the pulley/wheel--that doesn't really have much to do with the problem, does it?)...Mmm, it seems reasonable to me now, but would this be correct?

See comments in red above. The tension force does positive work in this case, but that is true regardless of whether the bucket is accelerating or moving at constant speed. And yes, the bucket does negative work since its force is acting down on the rope, and the direction of its movement is up. Now if you want to look at the other side of the pulley, the tension force is acting down, but what is the displacement of that force on that side of the pulley? Is the work done by the rope still positive?

 

[AlephZero]

Ah, no, this is our class's first day on the topic of work, and I haven't looked at energy yet.

Ahhh... Hang on in there, with luck you will soon be talking about energy and then things will be clearer. One definition of "energy" is "a measure of the ability to do work" so work and energy are rather closely related

If you want to work done on the bucket, you need to draw a diagram (called a "free body diagram") showing the forces acting on (or applied to) the bucket. It's called a free body diagram, because you can then ignore everything else like the rope etc and just think about the bucket, floating free in space, with those forces acting on it.

Remember force and displacement are both vector quantities (the direction matters as well as the magnitude). To calculate

Work done on the bucket = force applied to the bucket * displacement of the bucket

you must measure positive force and positive displacement in the SAME direction. It doesn't matter which direction you choose as positive. Either you multiply two positive numbers or two negative ones, and the answer is the same either way you do it.

In your problem the force on the bucket due to the rope is upwards and the displacement is upwards, so force * displacement is positive and the work done is positive. When you learn what "potential energy" is, you will understand what my first comment was about