# Physics Pulley question

1. Dec 3, 2003

### suyver

It seems like a simple question, but I get the feeling that there is a catch: You are standing on a plate attached to a pulley. The rope through the pulley is attached to the ceiling with one end and you pull on the other end. Can you lift the plate and yourself?

a. Yes, but only the strongest people can do this.
b. No, this is principally impossible.
c. Yes, most people can do this.

My feeling is that this is impossible because you continue to 'push' against the plate while trying to lift yourself. However, I am not really sure. Any thoughts?

By the way: I translated the question myself, so let me know if it is incomprehensible. I can always make a small picture to illustrate the question.

2. Dec 3, 2003

### Staff: Mentor

Assuming the plate is not too heavy (neglect its weight), why not?

The pulley makes it easier. The amount of force you need to pull on the rope with is just half of the total weight. (Of course, to lift yourself 1 foot, you'll have to pull 2 feet of rope.)

So, assuming the average person has the grip strength to hang half their weight from a rope, I see no reason why they wouldn't be able to lift themselves up. I say the answer is C.

3. Dec 3, 2003

### HallsofIvy

Doc Al!! I'm shocked!
This isn't true. IF the this were a "double" pulley- a line attached to the pulley goes down to the platform, through a pulley attached to the platform, back to the top pulley and then back down to where you are pulling on the line, so that there are two lines supporting the platform, then you would have a mechanical advantage- you need to apply a force equal to half the weight lifted, but the line you are pulling on doesn't "count" toward mechanical advantage.

That said, in order to lift yourself this way, you would have to be able to lift your weight plus the weight of the platform. Some people can do that but most of us weaklings can't!

4. Dec 3, 2003

### Staff: Mentor

Whaaa????

There's only one way to settle this, Halls. That's right, I'm talking physics DEATHMATCH!. Let's go. You and me. Step into the octagon...
You so crazy, Halls! Think of it this way. You will agree that there is some tension in the rope? And, taking the "platform + person" as the system, will you not agree that the rope attaches to said system at two points? Thus the force exerted by the rope on the system is twice the tension. And the force exerted by the person, who is pulling on just one rope, must equal the tension in that rope?
While it is quite true that I possess the strength of ten ordinary men, such power is certainly not needed with this arrangement.

On the other hand, perhaps I'm wrong? Bah!

5. Dec 3, 2003

### LURCH

I think the average person could probably do it. If you can pull yourself up a rope, you can lift the device described.

I did experiments with a similar device as a child; attaching one end of a length of rope to my belt and throwing the other end over a truss in my familly's pol,e barn. I had little difficulty raisiong myself up to the rafters, even with the added friction of the rope sliding over rough-cut lumber rather than a pully.

6. Dec 3, 2003

### Staff: Mentor

My first reaction as well. But then I thought about it some more - and he's right!

He just explained the tension issue - the distance is a little tougher. But think about it - if you pull down on the rope by a foot, do you raise yourself up by a foot? Nope: the rope is doubled over, so you only raise yourself by 6".

7. Dec 4, 2003

### suyver

But that device is precisely reversed from the one that I was describing: in your case the pully is attached to the ceiling, while in my case the pully is attached to the plate on which you are standing. I keep getting the feeling that there is a difference. But then, I am just not sure...

Obviously, we assume that the plate, pully and rope have no mass and that there is no friction at all. In this case it should be relatively easy to write down all the forces, right?

Applied force by person standing on the plate: Fapplied

Fgravity = m g h

Ftension in rope = m g h + Fapplied (?)

Fnormal = m g h + Fapplied (?)

If my equations are correct, than the Fapplied just results in additional tension in the rope. But that would mean that I can't lift myself this way...

Anyway, I made a small picture, just in case you didn't get the idea (yes, I really look like that ):

http://www.phys.uu.nl/~suyver/physics.JPG

EDIT: I tried adding above picture in this post with [ img ] and [ /img ] tags, but that didn't work. If somebody can explain me what I am doing wrong, then I'll correct it.

Cheers,
Freek Suyver.

Last edited: Dec 4, 2003
8. Dec 4, 2003

### Staff: Mentor

D'oh! So that's what you meant?? (You're kidding us, right?)

Well, of course, that's way different. In that case the tension in the rope must support the full weight of the "person + platform". Even worse, the person must pull up on the rope with that much force---he can't just hang his weight from the rope.

(I think this version is much less interesting than the one I read! )

9. Dec 4, 2003

### suyver

For a foreigner it's sometimes hard to get your meaning. Are you being sarcastic?

The picture that I showed in my previous post is the configuration that I tried to describe in my first post of this thread. I am sorry if that wasn't clear from the start.

But if I read your answer correctly, then you seem to suggest that anybody that can pull his own weight (assuming the platform and pully weigh nothing) will be able to pull himself up in the configuration that I drew?

-Freek Suyver.

10. Dec 4, 2003

### HallsofIvy

I may be confused as to how the pulley is set up.

I interpreted this as saying the rope is attached to the platform, then went up through a pulley attached to the top of the "elevator shaft", then back to the person standing on the platform.
Important point: the "mechanical advantage" DOESN'T depend on who is pulling on rope. It could be a motor right at the top of the shaft or a person standing 100 m away: the length of the rope from the final pulley to the "puller" is not relevant.

Say the platform is 10 m below the pulley. The rope is 10 m long, from platform to pulley. If the platform were 9 m below the pulley the rope would be 9 m long- 1 m less. The rope from the pulley to the person must also be one meter shorter. In order to make the platform rise 1 meter, the person must pull one meter through his hands: NO mechanical advantage.

A single pulley system like this only changes the direction of force, it doesn't give any mechanical advantage (I learned that in the eight grade).

NOW, if the rope is attached to the top, goes down to a pulley on the platform, back up to the roof, THEN down to the person pulling on it, that's a different matter!

In this case, with the platform 10 m below the top, the rope would be 20 m long. With the platform 9 m below, the rope is 18 m long.
The "puller", whether a person standing on the platform, or at the top of the shaft, or 100 m away, must pull 2 m of rope. Since energy is conserved and "work = force times distance", the force applied must be 1/2 the weight lifted. The "mechanical advantage" of a pulley system is the number of lines connecting the platform to the top- the "running end" that is pulled doesn't count.

11. Dec 4, 2003

### suyver

I am sorry if I caused confusion. That was of course not my intention.
Just to repeat the setup:
- The rope is attached to the ceiling.
- The pully is attached to the platform.
- I am standing on the platform.
- The rope goes from the ceiling through the pully to me.
Then I pull the rope. What happens?

This is also what I tried to draw. I hope that my picture was clear.

So it makes no difference if this one pully is attached to the platform or to the ceiling? My system would be identical to its reverse:
- The rope is attached to the platform.
- The pully is attached to the ceiling.
- I am standing on the platform.
- The rope goes from the platform through the pully on the ceiling to me.
Then I pull the rope. Is that equivalent?

Feeling dumber and dumber...

12. Dec 4, 2003

### Staff: Mentor

I was just teasing. Didn't mean to offend!

13. Dec 4, 2003

### suyver

Don't worry, I really wasn't offended at all. Just confused.

So, you're saying that the person needs to apply a force greater than the gravitational force working on him? That would mean that the person must be at least strong enough to pull up his own weight. Which is definitely something that strong people can do, but I can't see my 90 year old grandmother do that. So this means that the final answer is A: yes, you can pull yourself up this way, if you are strong enough. Do you agree with this?

14. Dec 4, 2003

### Staff: Mentor

That's exactly how I interpreted the arrangement (which was not what suyver had in mind).
This is incorrect. Realize that the rope is doubled over the pulley! Ingoring the circumference of the pulley, if the platform were 10 m below the pulley, you have 20 m of rope. To raise the platform 1 m, you must pull 2 meters of rope.
Yes, indeed! And that's the situation suyver had in mind.
Sorry, Halls, but you have it exactly backwards! I think we both need more coffee!

15. Dec 4, 2003

### suyver

I don't think so...

In my situation, the rope DOES NOT go back to the ceiling after it went through the pully! From the ceiling it indeed goes to the pully which is attached on the platform that I am standing on. But after that, the rope goes directly to me.

16. Dec 4, 2003

### Staff: Mentor

You are right. Once again, I misread the question!!!

Damn!

17. Dec 4, 2003

### suyver

We're getting nowhere at incredible speeds like this!

18. Dec 4, 2003

### Staff: Mentor

Just so I don't contribute even MORE to the confusion, let me summarize:

In configuration A the rope is tied to the ceiling, the pulley is on the platform, and the person must pull up on the rope. This is the situation that suyver had in mind. (Please say I'm right!)

In this case, given suyver's original choices, I would say the answer is a: yes, but only the strongest people can do it. The person would have to pull up with a force equal to the weight of the person+platform+pulley. Not easy!

In configuration B the pulley is attached to the ceiling, the rope is tied to the platform and looped over the pulley, and the person must pull down on the rope. (This the situation I mistakenly thought that suyver was originally describing.) As I explained in previous posts, the person would only have to pull the rope with half the weight of the platform+person. In addition, all they need is a good grip, since they can just hang off the rope! Much easier!

19. Dec 4, 2003

### suyver

I agree with your statement of the problem.

Yes, the person has to pull the rope up. However, in doing so, he has to exert a force on the platform! This force makes it harder to pull the platform up, which results in the person applying a larger force, etc. etc.

I still think that it is fundamentally impossible. Where is the error in my reasoning?

Last edited: Dec 4, 2003
20. Dec 4, 2003

### Staff: Mentor

Finally, we are getting somewhere.
Now that I've had my coffee, neither do I!
I believe you are correct, sir!

Whatever force the person pulls the rope with will add to the force that the platform pushes up on the person. If strong enough, he can hold himself in position, but he cannot accelerate himself, even a little.

Good one, suyver!

21. Dec 4, 2003

### suyver

When the pully would have been fixed on the ceiling, then it is possible to lift yourself this way (e.g.: rope, attached to platform, goes to pully on ceiling and the to me, standing on the platform). But this way it's fundamentally impossible. Just another neat example of how classical mechanics can fool you!

By the way: this is one of the problems of this years Dutch National Science quiz. There is another nice one dealing with classical mechanics. I'll start a new topic for you to rack your brain on...

Cheers,
Freek Suyver.

22. Dec 4, 2003

### Staff: Mentor

D'oh - me too. Thats twice today.

HOWEVER, Halls, I still think you interpreted it the same way we did and still have it wrong for that interpretation.
Thats true if the person is standing on the GROUND. If the person is standing on the PLATFORM, he essentially becomes a second pulley. Try this - add a second pulley. Put it on the platform. Now you have the rope attached to the platform, going up to a pulley on the ceiling, back down to another pulley, and to the person. All that second pulley does is re-direct the force so the person can pull up instead of down. You still have two lenghts of rope and two attachement points.

If he pulls one foot of rope up through that new pulley or one foot of rope straight down (notice: pulling his arms one foot straight down does NOT mean pulling one foot of rope through the top pulley), the platform moves up SIX INCHES.
Yeah - now you have THREE lenghts of rope instead of two.

Maybe I need to draw a pic and scan it in.

23. Dec 4, 2003

### LURCH

LOL! Well, I would be embarrassed by the fact that I misunderstood the question, but everyone else seems to have misunderstood it in exactly the same way. I prefer to be right whenever possible, but if I have to be wrong I'm glad I can do it in such good company.

Now that I understand the correct configuration (with the pulley attached to the platform), I must say that Russ is absolutely right. In this configuration, pulling two feet of rope through the pulley a man will raise himself one foot off of the floor. Most people would be capable of this, as it requires lifting only one-half of your own body weight. It is rather easy to verify this experimentally with household items. If you have some string or thread, and an object with a hole in it, try the following:

Tie one end of the string to a doorknob or other fixed position. Run the string through the hole in your test object (if you are using thread, you can run the thread through the hole in the spool). Holding the free end of the thread in your hand, raise that hand six inches. The test object will rise three inches.

24. Dec 5, 2003

### suyver

I still disagree with this solution. You are forgetting that in the original problem (look at the drawing on the first page of this thread!) the person is also standing on the platform and therefore he must apply a force to the platform in lifting the rope up. Newton's third law: action = -reaction!

25. Dec 5, 2003

### Staff: Mentor

Now Lurch has done the same thing everyone else has in misinterpreting the setup of the system (Lurch - thanks for agreeing with me, but thats not what I said!). In the way the picture has the system set up, the force is exactly equal to the weight of the person plus the platform as there is only one lenght of rope extending from the platform to the ceiling.

The way pretty much everyone thought it was set up, with the pulley at the top, its half.