Pulley question...

Doc Al

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

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

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

[a)]

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

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.

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

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

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.

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

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

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![:D]

russ_watters

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

Doc Al

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. [:D] I now believe that my initial answer (quoted below) is correct:
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? [8)]

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!)

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

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

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. [:D]

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... [:D]

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.