Pushing a light year-long stick

[Lord Antares]

Imagine a stick of wood that was 1 light year long. There are two people holding it, one on either side of the stick. Before I proceed to my questions about this scenario, I would like to clarify something:

 

In another thread, I was told that one person moving the stick wouldn't be instantaneous on the other end, but move at the speed of sound because of its elasticity. At first, I didn't understand this remark at all but I think I do now. I think what they mean to say that the stick would be very, very thin relative to its length so that it wouldn't be sturdy when held from both ends.

 

I was thinking of a much wider stick. Imagine the length to width ratio of the stick to be that of an average shovel. If it helps further, imagine it to be a cube instead of a stick. I just want to remove the issue of elasticity (if it can be removed, of course). So would the movement on both ends in that case be instantaneous?

 

I will post my questions after that has been answered, as they depend directly on the answer.

[Bender]

You cannot remove the issue of elasticity. The speed of sound in the stick is independent of the width. The speed of sound is also the speed any pressure wave travels through a substance.

[pzkpfw]

No.

 

No substance can be completely inelastic. Your rod could be made of diamond (or whatever), and there'd still be a speed at which a force could move through it, generally the speed of sound, in that substance.

 

 

(

Having said that, I think that even if a hypothetical inelastic substance did exist, you'd still not get instant communication.

 

I tried to explore that here ( https://forum.cosmoquest.org/showthread.php?163576-That-quot-rigid-rod-quot-question-so-often-seen&highlight= ) but few could really get past the above issue, to consider what I was actually asking.

)

[Lord Antares]

So they were right.

But doesn't that mean that the same thing happens when you push a pen, just on a smaller scale? Then both ends of the pen don't move simultaneously, but there is a small delay instead? Doesn't that mean that the pen actually gets a bit shorter until this force gets to the other end?

 

And doesn't that then mean that when a star moves, that both ends of the star don't move simultaneously, but instead this movement travels through the star until this reaches the other end?

If this is true, I've been completely oblivious to it.

[Bender]

So they were right.

But doesn't that mean that the same thing happens when you push a pen, just on a smaller scale? Then both ends of the pen don't move simultaneously, but there is a small delay instead? Doesn't that mean that the pen actually gets a bit shorter until this force gets to the other end?

Correct. You generally don't notice it, because the speed of sound in solids is usually more than 1000 m/s. Imagine pressing an unsupported spring quickly: one end moves while the spring compresses and the other side only follows afterwards. Every solid is a spring.

 

Of course, if you pull something, it gets longer rather than shorter.

 

And doesn't that then mean that when a star moves, that both ends of the star don't move simultaneously, but instead this movement travels through the star until this reaches the other end?

It only works if a contact force is exerted. e.g. a falling object isn't compressed, because gravity acts on all parts at once (although there is a temporary effect that the object shortens because the force holding it up disappears)

Edited February 22, 2017 by Bender

[J.C.MacSwell]

So they were right.

But doesn't that mean that the same thing happens when you push a pen, just on a smaller scale? Then both ends of the pen don't move simultaneously, but there is a small delay instead? Doesn't that mean that the pen actually gets a bit shorter until this force gets to the other end?

 

And doesn't that then mean that when a star moves, that both ends of the star don't move simultaneously, but instead this movement travels through the star until this reaches the other end?

 

If this is true, I've been completely oblivious to it.

Compare a star reacting and accelerating in response to some force applied to one side vs one simply "moving" with constant velocity

You cannot remove the issue of elasticity. The speed of sound in the stick is independent of the width. The speed of sound is also the speed any pressure wave travels through a substance.

Not entirely. There are differences in the bulk modulus, shear modulus, and Young's modulus of a material and they all are related to the speed of sound (or speeds of sound, as there maybe more than one type of wave propagation). But if you can imagine a pressure wave moving along a rod, there would be a different response in a bulk than at less constrained surface (the rod can expand or contract more readily) ...the lesser the width, the more that effect would be present

[Lord Antares]

Correct. You generally don't notice it, because the speed of sound in solids is usually more than 1000 m/s. Imagine pressing an unsupported spring quickly: one end moves while the spring compresses and the other side only follows afterwards. Every solid is a spring.

 

Of course, if you pull something, it gets longer rather than shorter.

 

Hm, this is interesting information for me. What if one person pushes the rod, and the other pulls it? I suppose the issue of general relativity is that they can't pull it simultaneously per se, but if they each pull/push it one year before the other, would this ''shockwave'' meet in the middle? What would happen then?

 

 

It only works if a contact force is exerted. e.g. a falling object isn't compressed, because gravity acts on all parts at once (although there is a temporary effect that the object shortens because the force holding it up disappears)

 

Aha. So I would assume that this elastic effect has a proportional relation with the amount of force with which the object is pushed?

 

 

Not entirely. There are differences in the bulk modulus, shear modulus, and Young's modulus of a material and they all are related to the speed of sound (or speeds of sound, as there maybe more than one type of wave propagation). But if you can imagine a pressure wave moving along a rod, there would be a different response in a bulk than at less constrained surface (the rod can expand or contract more readily) ...the lesser the width, the more that effect would be present

 

What would be the difference in travel time with the most elastic objects and with the least elastic ones? Is such information known?

[Janus]

So they were right.

But doesn't that mean that the same thing happens when you push a pen, just on a smaller scale? Then both ends of the pen don't move simultaneously, but there is a small delay instead? Doesn't that mean that the pen actually gets a bit shorter until this force gets to the other end.

Imagine a wooden pencil 6 in long. You push on one end so that it moves at 1 ft.sec. At the speed of sound through wood, In the time it takes for the push to reach the other end of the pencil (~1/22000 of a sec), your end will have moved ~1/2000 of an inch and the pencil will have momentarily contracted to ~11999/12000 of its original length.

 

In reality its a bit more complicated, because you can't get the end of your pencil from 0 to 1ft/sec in zero time. To even get it up to 1 ft/sec in the 1/22000 of a second it takes for the impulse to travel through the wood would involve an acceleration of 2245 g. In other words, under real life conditions, the other end of the pencil will start moving before you stop pushing on your end and have fully gotten it up to speed, and the actual compression of the pencil will be less than that given above.

[J.C.MacSwell]

 

 

 

What would be the difference in travel time with the most elastic objects and with the least elastic ones? Is such information known?

That was with regard to the speed of sound. This is known for most common materials.

[MigL]

Not at all sure why you keep trying to bring relativity into it...

This has to do with the propagation of a pressure pulse through a material, by contact or minimum separation. In effect the constituent particles have to move, either close enough for inter-atomic forces to move the next particle, or by actual contact.

I'm sure you are familiar with a sonic boom...

That is what happens when you push air molecules faster than the speed of sound. You get a shock wave where there is a very steep discontinuity in speed, supersonic on one side, subsonic on the other, and a huge amount of localized energy. Enough to shatter windows miles away !

 

What do you think would happen to any 'realistic' rod ?

[Lord Antares]

That was with regard to the speed of sound. This is known for most common materials.

 

Oh, sorry, I forgot that the speed of sound is different for different materials. Understood.

 

 

Imagine a wooden pencil 6 in long. You push on one end so that it moves at 1 ft.sec. At the speed of sound through wood, In the time it takes for the push to reach the other end of the pencil (~1/22000 of a sec), your end will have moved ~1/2000 of an inch and the pencil will have momentarily contracted to ~11999/12000 of its original length.

 

In reality its a bit more complicated, because you can't get the end of your pencil from 0 to 1ft/sec in zero time. To even get it up to 1 ft/sec in the 1/22000 of a second it takes for the impulse to travel through the wood would involve an acceleration of 2245 g. In other words, under real life conditions, the other end of the pencil will start moving before you stop pushing on your end and have fully gotten it up to speed, and the actual compression of the pencil will be less than that given above.

 

Thanks for the math. I understand what you mean. It takes time for acceleration as well, so less compression will happen.

 

 

Not at all sure why you keep trying to bring relativity into it...

 

I mentioned relativity once in reply to Bender because it was relevant to the question.

 

 

What do you think would happen to any 'realistic' rod ?

 

I didn't think of it that way. I thought, because the rod is one continuous object, no speed greater than the speed by which you move it would be reached.

[mistermack]

What do you think would happen to any 'realistic' rod ?

You wouldn't get any measureable motion. It would just shatter, no matter what material you chose.

Imagine the mass of a rod that was a light-year in length.

If you tried to push it by hand, it would just feel like a brick wall. If you made it thicker, the mass would increase even faster.

In the end, it would be totally impossible to cause any noticeable motion. Unless you had a few million years to spare.