Can You Lift Yourself on a Pulley?

[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.

 

[Doc Al]

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.

 

[HallsofIvy]

Doc Al! I'm shocked!

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.)

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!

 

[Doc Al]

Originally posted by HallsofIvy
Doc Al! I'm shocked!

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...

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.

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?

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!

While it is quite true that I possesses the strength of ten ordinary men, such power is certainly not needed with this arrangement.

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

 

[LURCH]

Originally posted by HallsofIvy

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!

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.

 

[russ_watters]

Originally posted by HallsofIvy
Doc Al! I'm shocked!...

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".

 

[suyver]

Originally posted by LURCH
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.

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: F_applied

F_gravity = m g h

F_{tension in rope} = m g h + F_applied (?)

F_normal = m g h + F_applied (?)


If my equations are correct, than the F_applied 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.

 

[Doc Al]

Originally posted by 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...

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! )

 

[suyver]

Originally posted by Doc Al
D'oh! So that's what you meant?? (You're kidding us, right?) )

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.

 

[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.

 

[suyver]

Originally posted by HallsofIvy
I may be confused as to how the pulley is set up.

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.

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).

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...

 

[Doc Al]

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

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

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?

No, not at all! Please read my answer again.

 

[suyver]

Originally posted by Doc Al
I was just teasing. Didn't mean to offend!

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

Originally posted by Doc Al
No, not at all! Please read my answer again.

Gladly!

Originally posted by Doc Al
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.

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?

 

[Doc Al]

Originally posted by HallsofIvy
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.

That's exactly how I interpreted the arrangement (which was not what suyver had in mind).

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.

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.

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!

Yes, indeed! And that's the situation suyver had in mind.

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.

Sorry, Halls, but you have it exactly backwards! I think we both need more coffee!

 

[suyver]

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!

Originally posted by Doc Al
Yes, indeed! And that's the situation suyver had in mind.

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.

 

[Doc Al]

Originally posted by 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.

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

Damn!

 

[suyver]

Originally posted by Doc Al
You are right. Once again, I misread the question!

Damn!

We're getting nowhere at incredible speeds like this!

 

[Doc Al]

Originally posted by suyver
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?

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!

 

[suyver]

Originally posted by Doc Al
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!

I agree with your statement of the problem.

However, I do not agree with your answer!

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?

 

[Doc Al]

Originally posted by suyver
I agree with your statement of the problem.

Finally, we are getting somewhere.

However, I do not agree with your answer!

Now that I've had my coffee, neither do I!

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 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!

 

[suyver]

Originally posted by Doc Al
I believe you are correct, sir!

Originally posted by Doc Al
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!

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.

 

[russ_watters]

Originally posted by Doc Al
D'oh! So that's what you meant??

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.

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.

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.

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!

Yeah - now you have THREE lenghts of rope instead of two.

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

 

[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.

 

[suyver]

Originally posted by LURCH
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.

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!

 

[russ_watters]

Originally posted by 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!

Now Lurch has done the same thing everyone else has in misinterpreting the setup of the system (Lurch - thanks for agreeing with me, but that's 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 length 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.

 

[LURCH]

OOps! Sorry, it was not Russ, it was Doc Al. Anyway, try the following thought experiment based on the diagram provided:

Imagine the platform is at its lowest possible position, at the end of the rope. We can call this position "A". The person on the platform grabs the free end of the rope and begins to pull until reaching the point shown in the diagram. He then continues to pull upward without repositioning his hands on the rope. As you can see from the diagram it is possible, given the height of the person and the distance to the ceiling, for this person to reach up and touch the free end of the rope to the ceiling.

The free end of the rope has now traveled the entire distance from position "A" to the ceiling. The platform has traveled only half the distance.

 

[Doc Al]

Originally posted by LURCH
OOps! Sorry, it was not Russ, it was Doc Al.

Hey, don't drag me back into this! Once we saw a picture of what suyver was talking about (what I called "configuration A" in a previous post) I think we all (russ, suyver, and I) agreed about what would happen (or not happen!).

Imagine the platform is at its lowest possible position, at the end of the rope. We can call this position "A". The person on the platform grabs the free end of the rope and begins to pull until reaching the point shown in the diagram.

Ah... but there's the rub! Read the previous posts. The person will not be able to pull himself up.

The free end of the rope has now traveled the entire distance from position "A" to the ceiling. The platform has traveled only half the distance.

Even if we pretend that the person could pull himself up, I think your reasoning is incorrect. The rope is not doubled! To raise the platform 1 meter you must pull 1 meter of rope through the pulley. Note that this configuration is quite different from that of "configuration B" (pulley on the ceiling). In that case, the rope is always doubled over the pulley, and to raise yourself 1 meter, you must pull 2 meters of rope.

 

[LURCH]

Originally posted by Doc Al

Ah... but there's the rub! Read the previous posts. The person will not be able to pull himself up.

I know that's what the previous posts say, I'm just not in agreement with them. But I think I can state my reasons better if I envoke relativity, to remind us that relativity states that there is no preferred frame of reference. So let's switch our usual frame of reference to look at the situation from that frame which is shared by both the platform and its occupant (and, of course, the pulley).

I stand on the platform and pull on the rope. That is, my hands exert an upward force on the rope, while my feet exert a downward force on the platform. Given the exertion thus distributed, let us ask ourselves the question, "can I now exert a downward pull on the ceiling?". The obvious answer is, Yes.

So don't think of it as pulling myself up to the ceiling; think of it as pulling the ceiling down to me!

 

[russ_watters]

Hey, anyone see that Eagles vs Dallas (sucks) game on Sunday?

 

[Doc Al]

Originally posted by LURCH
I know that's what the previous posts say, I'm just not in agreement with them.

I’m not sure I can appreciate your reasoning, but guess what? I’ve given this problem some more thought and I have changed my mind. Who knows, perhaps now we agree. I now believe that my initial answer (quoted below) is correct:

Originally posted by Doc Al
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!

Somehow I had convinced myself that any additional rope tension exerted by the person would just translate into additional force against the platform (it would), but now realize that that is irrelevant.

Consider the equilibrium case: the tension (T) in the rope equals the weight of the platform + person. The forces on the person are the rope tension and weight (acting down) balanced by the normal force of the platform (acting up). The forces on the platform are its weight and the normal force (N) of the person (acting down) balanced by the tension in both ropes (pulling up).

Can the person increase the tension on the rope, thereby lifting the platform and himself? I see no reason why not, if he is strong enough. To exert additional rope tension ΔT, the person would need to push ΔT harder against the platform. But the ropes pull up on the platform with twice ΔT. Thus, there will be a net increase in force on the platform (and on the person).

The dynamics are as follows:
ΔT = m_total a (forces on total system)
2ΔT – ΔN = m_platform a (forces on platform)
ΔN – ΔT = m_person a (forces on person)

Suyver, what do you think?

 

[suyver]

To be honest: I don't really understand LURCH's relativity-argument. Sorry...

However, I do have a question regarding Doc Al's reasoning (you haven't convinced me yet!)

Originally posted by Doc Al
Consider the equilibrium case: the tension (T) in the rope equals the weight of the platform + person. The forces on the person are the rope tension and weight (acting down) balanced by the normal force of the platform (acting up). The forces on the platform are its weight and the normal force (N) of the person (acting down) balanced by the tension in both ropes (pulling up).

I think a agree with this, so far...

Originally posted by Doc Al
[...]To exert additional rope tension ΔT, the person would need to push ΔT harder against the platform. But the ropes pull up on the platform with twice ΔT. Thus, there will be a net increase in force on the platform (and on the person).

And here is the part I disagree with!

We are still talking about ONE pully, so I do not see where the doubling of the applied force would come from. If I pull with additional force ΔF, then this force would be devided over the two parts of the rope and not added to the two parts individually. This will cause your ΔT to be exactly equal to the extra ΔF that was applied. So, we are still in equilibrium and nothing will happen. (I think)

 

[Doc Al]

Originally posted by suyver
To be honest: I don't really understand LURCH's relativity-argument. Sorry...

Me neither.

However, I do have a question regarding Doc Al's reasoning (you haven't convinced me yet!)

I had enough trouble convincing myself.

We are still talking about ONE pully, so I do not see where the doubling of the applied force would come from. If I pull with additional force ΔF, then this force would be devided over the two parts of the rope and not added to the two parts individually. This will cause your ΔT to be exactly equal to the extra ΔF that was applied. So, we are still in equilibrium and nothing will happen. (I think)

There is one pulley, true enough. But, just like in any pulley arrangement, the rope pulls on it twice. When you pull with an additional force, that force goes to increasing the tension---it better, how else can you exert a force on the rope? The force is not divided over different parts of the rope: the tension is the same throughout the rope.

Take another look at the equations I gave and it might make more sense. To lift himself, the person must exert slightly more than the total weight of the system.

 

[suyver]

Doc Al,

I am not ignoring your reply, but I am thinking about it. Intuitively, I disagree with you. But I am thinking of a clear formuation that will also prove that you are incorrect. ... Or maybe that I have been wrong all along...

 

[LURCH]

Dang! And here I thought I had stated my position so much more clearly.[b(]

Well, the main gist of it was that it's not a question of how much force you exert against the rope in your hand, or the platform under your feet, or the pulley. It is entirely a question of how hard you are pulling on the ceiling. If that force is greater than your own body weight, you will pull the ceiling down to your self (which is the same as to say you'll pull yourself up to the ceiling).

BTW, this will go to experiment during the holidays, and then we will all have a definitive answer.

 

[Moose352]

Doc, can you please draw a FBD of the system so we can better understand your reasoning?