extremely long stick additional questions?

Submitted by Unnombrepls t3_10rqr48 in askscience

Hi,

Let's suppose we have a very long stick with astronomical length in the range of light years or similar.

This question has been proposed before but I wish to hear clarification on some facts that aren't clear to me.

If we push the stick 10 cm, does it mean the stick is 10 cm shorter before the push reaches the other end?

Is the strength we would have to apply to do that only the strength necessary to move the stick with its given length and mass or is it also needed to add additional force to transiently deform it if the previous question is yes?

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Naive_Age_566 t1_j6ycicb wrote

if you apply force on an object - technically, you only apply that force on the outermost layer of atoms. so you push the outermost layer against the next layer, which itself pushes on the next layer and so on.

there is a maximum speed with which that force can propagate through the object. it is the speed of any pressure wave. the most common pressure wave is a sound wave - so usually, we call this speed the speed of sound. in a rigid object, sound is much faster than in air. the actual value for this speed is dependend on the material. if you have a wooden stick for example, if you push on one end, that force is transmitted through the wood with a speed of about 3500 to 5000 meters per second. which is quite fast.

if your stick is about one meter long and you push on one end, that force can be transmitted fast enough, that it looks as if that force is transmitted instantaneous. you can't push that stick fast enough to notice any delay. therefore the only force you have to apply is that to move the stick itself.

however - if your stick is considerably longer, you notice that delay between your push on the one end and the movement on the other. the stick can't move away fast enough. so you have to compress the stick - or apply the force very slowly. if you compress the stick, you have to apply extra force - you not only have to move the mass of the stick (which is now very high). if you push slow enough, you only have to compress the stick a little bit before that pressure can move through the whole stick.

now take a stick that is long enough to reach to our moon. our moon is about 400 000 kilometers away. the speed of sound in wood is about 5 kilometers per seconds. so - if you push on one end of that stick, it takes about 22 hours (!) until the other end moves. if you push the stick about 10 cm on one end, you have to compress the wood - which takes quite some force. but never mind - that stick would be so heavy that moving it at any speed is an astronomical feat.

have you ever seen a stick of wood about one kilometer long? me neither. no wonder, all of this is not quite intuitive.

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Smurfopotamus t1_j6yfqxu wrote

The thing is, we can see similar things with roughly 1 meter wooden sticks: baseball bats. This article talks about how hitting home runs when the bat breaks at the handle (or even "hitting" home runs when you've let go of the bat) aren't much different from a regular home run from the ball's perspective, because the wave is still traveling down to where the bat will break by the time that the ball leaves contact.

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Alfred_The_Sartan t1_j6ym2ll wrote

This is a fantastic explanation. I was thinking it would all move together and was trying to figure out how a light years long stick would react. I was thinking that the whole thing would move at once and therefore information would travel faster than the speed of light.

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DesignerAccount t1_j6yo5lv wrote

That's true for an ideal "rigid" stick/body, which is just a body for which shocks transfer instantaneously. Reality is that no body is perfectly rigid, obviously, and the shocks propagate depends on th density of the object. Hit a long stick on one side and feel the hit with a delay.

OPs question becomes even more interesting if you start making assumptions about the stick being super light, so really low density, so a normal human could potentially move it. Haven't figured out the answer, a convincing one, though.

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lankymjc t1_j6z63dc wrote

I used to think that I had theoretically cracked FTL communication through the use of really long sticks (though the engineering would be its own impossible issue). Took me ages before finding out about compressing objects, which made me feel better because I was sure someone must have already thought of it and disproved it, I just couldn't find the answer until a few years ago!

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saxn00b t1_j70ximj wrote

Not to tease you but it makes me giggle thinking about your thought process “surely Einstein didn’t think about sticks”

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zakabog t1_j6yqxrv wrote

This is the right answer, I would also suggest u/Unnombrepls watch this video on the speed of motion by AlphaPhoenix since I always wondered the same thing about transmitting data faster than light by moving a long cylinder between two points. I knew it would be impossible, I just didn't know why it would fail (ignoring the engineering problem with creating a long enough cylinder to test this.)

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swordsdancemew t1_j6z87c2 wrote

Would it be like pushing a very heavy block, where you 'pour' weight/strength into it before it starts to move? Then the furthest part and the closest part can move at the same time?

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TheThiefMaster t1_j70uxmi wrote

No that's because of contact friction.

Basically at interstellar scales everything is jelly. It doesn't all move together because it squidges and bends before that could happen.

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Unnombrepls OP t1_j71p2zo wrote

Thank you, it is a really detailed answer.

I can't help but see it as a short of "bug" of the universe since it is counterintuitive.

Now I understand it better.

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Naive_Age_566 t1_j72qlbz wrote

the universe is under no obligation to be intuitive. it just is. as a matter of fact, it is quite remarkable, that we can make sense of it in some cases at all.

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bolshiabarmalay t1_j6yjse4 wrote

what if your stick is at absolute zero? your molecular movement would then be stopped. would the stick finally be able to move instantaneously?

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Silver_Agocchie t1_j6ymzvu wrote

No because the energy of you pushing of the stick is still transmitted as an energy wave as described above regardless of the current state of the atoms in the stick. By adding energy with the push, the atoms of the stick will no longer be at absolute zero.

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HeraldOfNyarlathotep t1_j6yntsz wrote

Absolute zero just means there's absolutely no heat energy in the material; getting near that can cause weird things to happen in some materials, but it doesn't mean the entire object goes supernaturally rigid. (I think that's sorta what you were picturing, anyway.) Inertia and mass and such aren't changing. Causality too, given we're talking about moving light-years-long sticks instantaneously.

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bolshiabarmalay t1_j6ypw3d wrote

that's what I was picturing, I understood absolute zero to be where molecular movement stopped attaining supernatural rigidity. The last time I thought about it was highschool physics, so a very simple comprehension of the science as a whole. Interesting to think about tho, thanks for the reply.

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HeraldOfNyarlathotep t1_j6yrvpz wrote

Happy to help friend. Agreed, I love these sorts of questions. They're like logic puzzles, but figuring out the answer usually involves learning something more broadly interesting than "ah, it's that particular sequence of steps to solve it".

XKCD's What If? Articles and books are fantastic for this, if you aren't already aware of them. There's about 160 of em on his site, currently.

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Coomb t1_j783kny wrote

Even if it were true in general that at absolute zero there were no thermal motion of atoms, that wouldn't make things infinitely rigid.

When you push on something, your outer electrons are repelling the electrons of the other object (whether this repulsion happens because of the Pauli exclusion principle or electromagnetism or both is irrelevant for this reasoning).

Anything with mass, like an atom, doesn't move instantaneously when a force is applied. Instead, it accelerates. Therefore, it takes some finite amount of time to move the first layer of atoms back to their equilibrium position (i.e. how far away from your hand, or tool, or whatever, they would be if the two surfaces were just in contact). Similarly, it takes some finite amount of time to move the row of atoms, and the row after that, and the row after that. This is entirely independent of random thermal fluctuation of the atoms.

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things_will_calm_up t1_j6znrpn wrote

This is similar to asking how fast it moves if there was no time. It doesn't make much sense. If there is no molecular movement, then nothing pushes anything and force doesn't propagate.

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eglue t1_j739ije wrote

What if the material is a super conductor?

Could be a situation where the amount of force to move it 10 cm would shatter it before it fully transmitted the pressure?

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Naive_Age_566 t1_j743eh8 wrote

the ability to transfer electricity has nothing to do with the speed, with which a pressure wave is transmitted. so - super conductor behaves the same as normal conductors or isolators.

and yes - if you apply more force on an object than this object can handle, it will shatter/bend/deform/vaporize/whatever.

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eglue t1_j74i7ms wrote

Oh ok. I was thinking about the molecules settling closer to each other would have an impact. Thanks.

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Ceofy t1_j7gjtjt wrote

Is the speed of the pressure wave always equal to the speed of sound in a given medium?

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Naive_Age_566 t1_j84iicj wrote

sound *is* a pressure wave. what other speed should sound have?

so - yes

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Most_Engineering_992 t1_j6yb6zd wrote

This would be similar to pushing a, say, 100m stick against a concrete wall since the inertia of a stick multiple LYs in length would be comparable. Sure, you could push the end 10cm, but it would just crumple or bend.

Fun with math: If the 'stick' was a steel rod about a cm square, it would weigh around 7,400,000,000,000 tonnes per light year. That's only 1/10,000,000th the weight of the moon, but it's still substantial.

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rogert2 t1_j6yc952 wrote

"Give me a place to stand and with a lever I will grunt and strain to no effect." -- Archimedes (kind of)

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Sargotto-Karscroff t1_j6yroq7 wrote

The way I look at it which is kinda overly simple is you are creating a ripple in the medium you are pushing or pulling and that ripple is moving at the speed of sound for whatever the medium is made of.

Big enough objects over large enough space/time act much like liquids do, both with movement acting like a fast moving ripple and the natural slow movement/flow( takes thousands to many millions of years slow) on its own driven by its own gravity I believe like the Earth's deep layers.

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unskilledplay t1_j6zcoqr wrote

Yes, there is a speed of motion and the front end of an object will start to move before the back end does.

So let's look at your thought experiment. Imagine an extremely long metal rod in space. We know metal is highly resistant to compression and not very elastic. If you apply too much force at the front, the rod will deform. If you apply a force that is sufficiently low such that it avoids permanent deformation and that force is applied over a long enough time, and the rod is sufficiently long enough, yes, you will achieve your 10cm of compression in motion where the front of the rod will have moved 10cm before the back of it will experience any motion.

The length of the rod to achieve this effect would largely depend on the bulk modulus (resistance to compression), strength of the material (you don't want to deform it), and the speed of sound in the material (which is really the speed of movement).

Here is a great video where an experiment is created to answer this exact question. I highly recommend a watch all of the way through.

https://www.youtube.com/watch?v=DqhXsEgLMJ0

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intuser t1_j7123i6 wrote

Ok, now suppose you accelerate the stick closer to the speed of light, towards my barn.

Because of relativity, objects accelerating towards you are smaller than they would if they were stationary. If I'm in the barn and the stick is going fast enough, too me it could be smaller than the length of the barn.

If I close the door once the stick is fully inside the barn, What would happen to the stick. Does it expand? Can it really fit in the barn?

This was from a physics exam back in college 😅

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Pharisaeus t1_j76dlcb wrote

> If we push the stick 10 cm, does it mean the stick is 10 cm shorter before the push reaches the other end?

Consider that this "stick" is not really a rigid body, but rather a large "spring", and it can compress (at atomic scale). So yes, the stick would be, from certain point of view, shorter while the push is being propagated.

> additional force to transiently deform it

Again, since it's a spring, there is no additional force needed, because the energy is conserved (aka: the spring will uncompress, releasing this "deform" energy) back.

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[deleted] t1_j6z1t4l wrote

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hercola t1_j6z4z75 wrote

You have to refine your model of what constitutes “pushing” when you consider atomic or subatomic scale. It would be different from the macroscopic view of pushing.

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