# Work and energy of pulleys

1. Oct 4, 2009

### sonutulsiani

1. The problem statement, all variables and given/known data

A box of mass m can be lifted using a rope and two pulleys, as shown.

http://bcs.whfreeman.com/WebPub/Physics/tiplerphysics6e_bridge/question_bank_images/6-36.png?1341

You exert a force of magnitude F on the free end of the rope. Give your answers in terms of h and w.

1. Through what distance does the force move, if the load moves up a distance h?

A. 2h
B. ½h
C. h2
D. 0

2. How much work is done by the rope on the load, if the load is lifted at constant speed?

A. wh^2
B. 2wh
C. wh/2
D. wh

3. How much work do you do on the rope?

A. wh
B. wh/2
C. 2wh
D. wh^2

2. Relevant equations

W= 1/2mv1^2 - 1/2mv2^2
W= F x

3. The attempt at a solution

2. Oct 4, 2009

### kuruman

The answer to question 1 is crucial. If you pull the rope down so that the piece on the left increases by 2 meters, the middle and right pieces together have to get shorter by 2 meters. By what length does each of these pieces alone become shorter? That is the amount by which the load rises. So what is the answer to question 1?

3. Oct 4, 2009

### sonutulsiani

So it is 1/2 h?

4. Oct 4, 2009

### sonutulsiani

And what about the 2nd and 3rd one? Help me with that also please.

5. Oct 4, 2009

### sonutulsiani

Wait if the load moves up by h, then the distance by which force moves is 2h right?

6. Oct 4, 2009

### kuruman

How do you find the work done by force?

7. Oct 4, 2009

Right.

8. Oct 4, 2009

### sonutulsiani

Work = Force x distance x cos theta

9. Oct 4, 2009

### kuruman

OK. For question 2 what are these three things that you need to multiply to get work?

10. Oct 4, 2009

### sonutulsiani

Distance is h, theta is 0
What is force?

11. Oct 4, 2009

### kuruman

What is the value of cosθ?
What force do you think it should be if the problem asks for the "work done by the rope on the load"?

12. Oct 4, 2009

### sonutulsiani

Value of cos theta which is cos 0=1
I still don't get the force.

13. Oct 4, 2009

### sonutulsiani

Is force 2h?

14. Oct 4, 2009

### sonutulsiani

Or 2w? Or w/2?

15. Oct 4, 2009

### kuruman

What is the name of the force that ropes exert? Hint: It starts with the letter "T".

16. Oct 4, 2009

### sonutulsiani

Oh tension? What about it?

17. Oct 5, 2009

### kuruman

What do you think? Look at the drawing, Imagine a box that encloses just the load and the pulley. What forces act on this system of load and pulley? In other words, how many force arrows will you have to draw on the system coming from the outside?

18. Oct 5, 2009

### sonutulsiani

Ya so, it will be 2F - w=0
which means f=w/2

So for 2nd question, work done by rope will be F X = w/2 * 2h = wh

And 3rd question, work done by us will be = 2F * h = wh?

19. Oct 5, 2009

### kuruman

Yup.
There are two ropes, each exerting force w/2, so the rope force is 2*(w/2). Now we are told that the load moves up distance h. So work = 2*(w/2)*h=w*h, but not for the reasons you say.
Again you have a misplaced factor of 2. The force that you exert is f = w/2, but the rope on your side goes down by distance 2h. So the work done by you is work = (w/2)*2h=w*h.