A Very Very Long Pole (Physics Question)

[Story]

Say I have a pole, infinitely strong, infinitely light (yes, this is hypothetical) and extends the length of the distance between the Earth and Jupiter.

Say I pull on one end of the pole.

How long will it take to effect the other end of the pole.

And what does this imply? would the pole lengthen.... what other interesting effects could we observe?

 

[lrkun]

The distance between the earth and jupiter ranges from 4.2 AU to 6.2 AU. 1 au is 149,668,992 km.

It will take you a very very long time.

Assuming you pull 1m per second. 1 thousand seconds per 1 km.

1000 X 149 668 992 X 4.2 or 6.2

a. 628609766400 seconds

b. 927947750400 seconds

Hehe

My answer is different from the question. >.< This is how long you will get to the other end if you pull at one meter per second.

What do you mean by effect?

 

[Logic-Nanaki]

i think i know what you are on about. if you have a pole and you pull at it. will it be instantly moved on the other side? if this is indeed your statement...i as well have wondered at this. all tough..my imaginary pole is a light year long one...

 

[Aught3]

Wouldn't the force you applied to the pole propagate at a limited speed?

 

[Nelson]

I think this will depend on some other things that are not yet specified, namely the density of the pole in question. I believe the answer will be directly related to the speed of sound in the material.

As you tug on one side of the pole, you create a gap between the molecules at that end, and their immediate neighbors. The EM potential around these neighbor molecules will change, and so there is some slight lag before the molecules 1 meter away will respond and the lattice in this vicinity resets itself. This will propagate as a lattice wave down the pole until it reaches Jupiter. So if you pull the pole 1m toward you, I think it will take:

time = length / (sound speed)

before the opposite end at Jupiter actually moves toward you. So, lets say we have a diamond tube (which is quite dense and therefore has a very high sound speed). And let's also estimate the distance to Jupiter as ~ 5 AU (Irkun already pointed out that this actually varies).

time = (7.5e9 km) / (12 km/s) ~= 6.3e8 seconds or ~20 years

There are a lot of simplifying assumptions here, but I think this should be correct to within at least an order of magnitude.

EDIT:

I was just thinking about my response and I realized you said "infinitely light". In this case we have zero density, and I don't really know how to answer the question. In fact, I don't really think it is meaningful to talk about waves propagating in a material of zero density. Regardless, hopefully my explanation about a pole with some known density was at least somewhat helpful.

 

[Gunboat Diplomat]

Nelson has it right...

Say I have a pole, infinitely strong, infinitely light (yes, this is hypothetical) and extends the length of the distance between the Earth and Jupiter.

Say I pull on one end of the pole.

How long will it take to effect the other end of the pole.

And what does this imply? would the pole lengthen.... what other interesting effects could we observe?

Even the mere phrasing of the question makes little sense. If this pole is "infinitely light," doesn't that make it massless? That's like describing an empty glass as "having infinitely little water." That you would phrase it like that betrays a lack of understanding of what it is you're trying to ask...

How long it will take to affect the other end of the pole, like the speed of sound, depends on the stiffness of the pole and its density...

That is, if it were an ordinary "pole." However, your magic pole will have many strange properties. For instance, because it's massless, you won't be able to move it (or stop it if it happens to already be moving relative to your reference frame). That's because any attempt to apply a force to it will result in a literally undefined acceleration. So, in answer to your question, it will never affect the other end... whether that's because such an object can't be moved or because no such pole exists is up to you...

Why did you want that qualification anyway? What are you really trying to ask?

 

[Aught3]

Why did you want that qualification anyway? What are you really trying to ask?

Probably means 'light enough so I could move it'.

 

[Laurens]

Speaking as a man possessing of a long pole...

 

[Story]

Speaking as a man possessing of a long pole...

Mine stretches from Earth to Jupiter

I was just thinking about my response and I realized you said "infinitely light". In this case we have zero density, and I don't really know how to answer the question. In fact, I don't really think it is meaningful to talk about waves propagating in a material of zero density. Regardless, hopefully my explanation about a pole with some known density was at least somewhat helpful.

Definitely helpful... curious though. If the pole will be affected at the speed that sound travels through it, then you assert that when I pick up any object (lets say, a bottle), the molecules are affected at the speed that it takes for sound to propagate through it too, and that a lattice travels through that also?

Nelson has it right...

Even the mere phrasing of the question makes little sense. If this pole is "infinitely light," doesn't that make it massless? That's like describing an empty glass as "having infinitely little water." That you would phrase it like that betrays a lack of understanding of what it is you're trying to ask...

Yes, to be honest I don't completely understand the subject I'm asking about, but that's a part of why I'm asking.

How long it will take to affect the other end of the pole, like the speed of sound, depends on the stiffness of the pole and its density...

That is, if it were an ordinary "pole." However, your magic pole will have many strange properties. For instance, because it's massless, you won't be able to move it (or stop it if it happens to already be moving relative to your reference frame). That's because any attempt to apply a force to it will result in a literally undefined acceleration. So, in answer to your question, it will never affect the other end... whether that's because such an object can't be moved or because no such pole exists is up to you...

The reason I said infinitely light was because someone in the chat room instantly said that the pole would break in such circumstances, so I used that to avoid any arguments that just explained how a real pole would break, which wasn't really a part of the question I'm trying to ask.

But lets say >.> infinitely dense then. Still no idea where I'm going, but I'm curious if that would make an object that will have it's lattice propagate at the speed of light.

Why did you want that qualification anyway? What are you really trying to ask?

Well you see, anything that occurs at such massive scales, would obviously still apply at smaller scales also. Take for instance if a lattice propagates along the object at the speed of which sound would propagate through it, then for a material that wasn't extremely dense like <non extreme dense object> then we'd be able to see the effect on a relatively small pole on earth, like for instance, 5 miles of iron bar. Moving one end would take nearly a second for it to effect the other side. If this is true... then clearly God exists. Because who would be moving the other side? hmmm?

I kid... :lol:

This is just a fleeting curiosity of mine.

 

[Nelson]

Definitely helpful... curious though. If the pole will be affected at the speed that sound travels through it, then you assert that when I pick up a any object (lets say, a bottle), the molecules are affected at the speed that it takes for sound to propagate through it too, and that a lattice travels through that also?

I believe so. It's just that sound speeds in solids are absurdly fast relative to everyday sizes. Sound speed in glass is around 4km/s. But, it's also the case that most everyday solids aren't going to have a nice pretty lattice structure throughout, so everything becomes more complicated.

The point is that there is no truly rigid body on the scales of multiple molecules. The various parts of the solid are interacting through EM forces. There will be some delay, but it is tiny fractions of a second, and so the deformations of these things will be quite small and they are basically negligible for average sized objects being moved around at average speeds.

Also, I'm just an astronomer, not a REAL physicist . If someone more qualified to fully answer this sort of question would like to step in and correct me, be my guest.

 

[Gunboat Diplomat]

Yes, to be honest I don't completely understand the subject I'm asking about, but that's a part of why I'm asking.

I'm not saying that you don't know much about solid-state physics or materials science. I'm saying you don't really understand what it is you're asking... It's hard to come up with an analogy but it's sort of like asking about a charged particle that doesn't have an electric field... or (trying to move away from science here) about history that didn't take place in the past... It makes so little sense that it's hard to tell what it is you're trying to ask...

The reason I said infinitely light was because someone in the chat room instantly said that the pole would break in such circumstances, so I used that to avoid any arguments that just explained how a real pole would break, which wasn't really a part of the question I'm trying to ask.

Hold on a second... I missed it the first time but, now that I look at your first post, didn't you specify:

Say I have a pole, infinitely strong, infinitely light (yes, this is hypothetical) and extends the length of the distance between the Earth and Jupiter.

If it's "infinitely strong" then why would it break?

Why did you really make it massless?

But lets say >.> infinitely dense then. Still no idea where I'm going, but I'm curious if that would make an object that will have it's lattice propagate at the speed of light.

If it were infinitely dense then it would be a black hole and not a pole... unless it were infinitely strong, then it would suck up the entire universe and turn everything else into a black hole... that was in the shape of a pole...

Such an object won't have a lattice or any other molecular structure to propagate compression since, being infinitely strong and dense, it's clearly not made of atoms!

This is just a fleeting curiosity of mine.

...but what are you curious about? You've yet to explain this to us...

We could tell you how a real pole would behave but you just said that you're not interested in that. If you're going to hypothesize magic poles with impossible properties then why don't you tell us what they'd do?!


Oh, I forgot to apologize for the post explosion. I've been trying to avoid it but, this time, I was referring to so many specific things written in your post that it ended up being more clear this way...

 

[Story]

STOP USING LOGIC... If I want to have MY thread with MY own magical poles, MY FREE SPEECH rights give me that!

No, but in all seriousness. I was curious about what would happen with a normal pole of that length. Infinite lightness was something someone in the chat suggested, I had no idea of it's implications until you brought them up, but of course a normal pole would break, so I gave it properties that I thought would help it :?

Maybe I gave it too much power, especially since it's already destroyed the entire universe, which is sad because I really liked this universe. :cry:

 

[Story]

Sound speed in glass is around 4km/s.

If that's the case, then a glass pole the length of 12 km would lag for 3 seconds before any force you applied to one end happened on the other?

 

[nasher168]

My answer, based on limited knowledge of physics, would be:
Data can only travel as fast as the speed of light, so since the pole moving at the other end is telling an observer that you are puling it, presumably it would be a few minutes before anything happened out by Jupiter.

 

[Gunboat Diplomat]

No, but in all seriousness. I was curious about what would happen with a normal pole of that length. Infinite lightness was something someone in the chat suggested, I had no idea of it's implications until you brought them up, but of course a normal pole would break, so I gave it properties that I thought would help it :?

Well why didn't you just ask about that? Oh right, because of that chat room guy...

Well he's wrong! Don't listen to him... Why the hell would it break? ...and why would lower density help that?

To the best of my knowledge, you could, in principle, have a pole made of... wood as long as the distance from the Earth to Jupiter. It obviously couldn't be one contiguous piece or that would have been one hell of a tall tree... but it cold be nailed together or glued or whatever. It actually would break if you pulled on it too hard or tried to bend it too quickly. However, you couldn't pull it hard enough to break it with your own muscles and you could bend it gently without it breaking...

The end would feel like a normal wood pole connected to something very sturdy, probably because it would be a normal wood pole connected to something very sturdy; that something being an incredibly long wooden pole!

If the pole were made of steel instead of wood, it would have all the same properties except that it would be made of steel instead of wood. So, it would be harder to break it because steel is so much stronger than wood. It would be more massive since steel more dense than wood. It would probably be harder to break it by bending it since I don't know of any kind of wood that's as malleable as steel...

Sound propagates faster in steel than in wood. The speed of sound differs depending on the type of wood but it can be as high as almost 4000 m/s. Sound travels through steel at about 6000 m/s. However, with either substance, it's unlikely that pulling on one end would be noticed by the other end. That's because the energy used to pull on one end would dissipate as heat due to friction as it propagated down the pole. With astronomical distances like the Earth and Jupiter, all the energy will probably dissipate before reaching the other end. If you try to add enough power to one end so that the energy won't dissipate and you'll likely break the pole...

A question that interests me is if your pole were made out of carbon nanotubes. It has the highest tensile strength known to man and possibly the strongest possible material in principle. It's currently 30,000 times as strong as some of the strongest steel and has a theoretical strength of 150,000 times that. What can you do with materials of that strength?

I don't know. Even everything I said before that is just my personal guess. It would take an actual engineer to calculate all this. When I was in school, all I ever did with calculus was prove theorems about it. Not once did I ever actually calculate anything with it...

 

[sgrunterundt]

However, with either substance, it's unlikely that pulling on one end would be noticed by the other end. That's because the energy used to pull on one end would dissipate as heat due to friction as it propagated down the pole. With astronomical distances like the Earth and Jupiter, all the energy will probably dissipate before reaching the other end. If you try to add enough power to one end so that the energy won't dissipate and you'll likely break the pole...

No, if you keep up the pull it will move. Conservation of momentum.

Sure a sharp jerk in one end will spread out as the wave travels down the pole, so that it will be accelerating much more gently in the other end. But it will still move.

Also a pole of reasonable thickness would behave as string on this scale. Bending it with a radius of curvature of, say, several kilometers will require very little energy, and the distances are so much larger.

 

[Master_Ghost_Knight]

I think some people have wonder of into tangents that are unecessary and doesn't answer the question in the conditions that it were put. The main problem he is a conflict of the physical models that we use in a day to day aproximation with the fine details that are only obvious at large scales.
When we think of a pole what we do is to create in our head a model of an academic perfect case (which is not matched by anything in reality) of a enlongated and perfectly rigid object, and this aproximation works for a large variety of day to day or even simple short scale aplications with almost no noticeable error (but there is an error being commited) by using materials for instance with a large young modulus (check material science; high so when putting a jumbo jet on top of it would create a distortion of 0.01 milimeter, and it makes absolutly no difference for the majority of tasks if it distorts 1mm or 0mm). Of curse for other more refined apliations where a slight distortion of the material influences significatively the outcome, we can no longer use this aproximation (because there are no perfectly rigid materials, all materials deform, only some more than others) and you have to take that factor into consideration.

Of course if you use such a simplifyed model, when you pull at one end, from the implicaions of it follows that the other end responds emidiatly, and that would lead people to question, "hey what about the relativity which says that no information can't travel faster than the speed of light, wouldn't this violate relativity?" And the answer is Yes it would. The problem here is that relativity is a much more refined model, which can not acommodate the aproximations like "perectly rigid bodies" because the slight error that we made by doing that aproximation acumulates over large scales giving an answer that is very destinct from reality or what would a finer model (like relativity) would give you.


I personaly would have discarded the perfectly rigid body by the time it was the lenght of a sky scraper, even if I didn't used relativity at all, but that is just my experience of it.

 

[TheFlyingBastard]

Maybe I gave it too much power, especially since it's already destroyed the entire universe, which is sad because I really liked this universe. :cry:

You pole is OP. It needs a nerf. Or we could buff the universe. Whatever balance change you like.

 

[Nelson]

If that's the case, then a glass pole the length of 12 km would lag for 3 seconds before any force you applied to one end happened on the other?

Something like that, but now we have problems because we are talking about the real world. Let's pretend that we actually have this 12 km glass pole. And we want to move it 1 m, and have someone at the other end measure the 3 second lag. I think it would be virtually impossible to actually get your end to move 1 m in 3 seconds without shattering the pole at some point. This thing is going to be absolutely massive, so you won't me able to get it moving very quickly without very large forces. Basically, a wave of a large enough magnitude will just break your solid.

Maybe we could talk about some much smaller velocity, like 1 cm/s. Even if you can get your 12 km pole moving at this speed, your end will only move 3 cm before the wave travels to the other end and it begins to catch up. At most we will have a distortion of 3 cm over 12 km. This means the pole will be 0.00025% longer. Hardly sounds ridiculous does it?

 

[Pulsar]

A question that interests me is if your pole were made out of carbon nanotubes. It has the highest tensile strength known to man and possibly the strongest possible material in principle. It's currently 30,000 times as strong as some of the strongest steel and has a theoretical strength of 150,000 times that. What can you do with materials of that strength?

I wonder if it would keep its structure under its own gravity.