Will it move?
Congratulations! You just bought a brand new iron rod that has a length of 1 lightyear. Now, suppose you pushed one end of the rod. About how much time will pass before the other end moves?
Details
- Note, matter waves move with speeds v ≪ c .
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4 solutions
Discussions for this problem are now closed
Could you please explain why the sudden force will propagate at the speed of sound?
Maybe in a neutron star a "sudden force" at one end of it could propagate quite fast through it, maybe at a reasonable fraction of the speed of light? But most ordinary materials, like air, water, iron, any shock wave in it moves at the speed of sound for that material. Engineers know this, and there's published tables for this. Check this out Engineers Toolbox Note that the speed of sound is slightly faster for beryllium, at 12890 m/sec, than it is for diamond, at 12000 m/sec. Interesting, huh? That's why the new James Webb Space Telescope uses beryllium for its mirrors. It's really STIFF!
All materials basically behave like rubber. It's just a matter of how stiff it is. Tensor analysis was originally developed for this sort of thing.
I'm sorry if this sounds dumb, just had a weird thought. He answer here says more than a 1000 years. Lets just take 1005 years for argument's sake. Suppose i moved one end of the rod 1 lightyear in a 1000 years, will the length of the rod become zero for the remaining 5 years ?
@Akhil Warrier – No. If you move the end of the rod at a speed that is not negligible compared to the speed of sound, the rod will become very compressed. (You would need to push very hard.) Your rod would bend and undergo plastic deformation. If you suppose that it doesn't bend, then the speed of sound would raise with compression, allowing for the wave to propagate faster.
@Akhil Warrier – No. It will not become zero. Just notice the following. Suppose I represent the constituting particles of a rod as "o". And their arrangement is as follows.
o o o o o o o o o
Now I push the rod from its right end. Hence the rightmost particle will move closer to its immediate left particle.
o o o o o o o oo←Impulse
And so the collisions continue.
o o o o o o oo o
Observe that after collision the right sided particle stops instantaneously at its new displaced position.
o o o o o oo o o
o o o o oo o o o
↓
o o o o o o o o o
These would be final positions of the particles. Notice each particle would move one unit to the left. Such is the effect of an impulse applied to one end of the rod.
@Akhil Warrier – In response to Akhil Warrier. The question doesn't say that the rod is fixed on other end. It implies that if u keep moving the rod, it will keep moving , coz its space ………………!!!!
There is an error in the Engineers Toolbox that was mentioned. The speed of sound in steel is said to be greater than that in titanium for m/s, but for ft/s it is said to be smaller.
who said anything about a "sudden force"? Would the same principles apply to a "slow force"?
@Jon Bushman – How slow? It's still an impulse function, the only difference is spread. If I had a rocket 1000 miles long, and when its rockets ignite, it will actually take some time before the guys at the nose would notice anything different.
In fact, "specific impulse" is an important design variable in rocket engines. Have a look at this Specific Impulse
@Michael Mendrin – sir i am a15 yr old girl i tried this question i dont get the answer so i went through your discussions i dindt understand athing can you please help me with this question
@Aaysha Babu – :( why has no one answered you? If you had a pencil on a table and pushed one end, in almost an instant you would see the pencil move. This is because the amount of energy you placed at one end of the pencil moved, very quickly, through the entire pencil. For the pencil to move, the energy has to move through the entire pencil
Picture the pencil as a tunnel and the the energy as a car. The car is very fast and, in the case of the pencil, the tunnel is short. It doesnt take a car very long to travel the length of a pencil, right? When the tunnel is very VERY long however, it takes the car much longer to get to the other side. In this example, 1000 years.
@Jamie Broomfield – This is the best analogy for this specific problem I have read so far. I didnt quite understand either but this makes perfect sense.
@Jamie Broomfield – Hi..you seem like a helpful person.This question is bugging me still >.< I got this question wrong too and i scrolled through the comments for the explanation.I'm no physicist but i kinda grasp what people are trying to explain and I'm trying to relate it into basic physics I've learnt.I understand that energy move from particle to particle as explained and of course it'll take time for the transfer of energy to reach the other end and at some point the rod will be shorter than it is as some people pointed out before it reach the other end.For me it can be translated as watching a football hitting someone's face in super slow-mo when your face scrunched up before it actually move your head in the direction of the force. Since the question says i own a lightyear long rod i'll be assuming that i'm larger than a lightyear and is strong enough to carry it or push it. Who needs logic here.haha. From the quiz,we need to make the rod move. My question is: 1) i know the energy needs to reach the other end before it moves.But wouldn't it be the same at the end you're pushing?because even if there is a compression wave in the particle it's not really visible to the naked eye.For the iron to move shouldn't the particle all be at the same speed as your applied force for it to move as one?Why cant we say that to INITIATE a movement we need more than a thousand years,but for it to actually to have movement at both ends,they are instantaneous? 2)If i'm bigger than the rod,wouldn't the movement of the particle small enough for it to seem instantaneous? 3)And for your analogy about a car moving though a tunnel,if the tunnel is the iron..shouldn't it be moving too?My thought process includes things moving at the same speed.Like the person driving the car is in the same speed as the speed of the car.Say if it is not just a short push,say you're pushing it continuously until the the whole iron rod is at the same speed given by your force,wouldnt it move as a whole at some point?
I'm sorry if my question sounds dumb but i need some answers so that i can sleep well.LOL.Thank you in advance!
@Jon Bushman – yes it would apply
This is because sound needs a medium to travel and speed of sound is maximum in solid or metals
Because the kinetic energy from the thing pushing it will propogate through the rod as a compressional wave with a speed that is relative to the density of the material it is traveling through.
Because sound is just energy (vibrations) moving through particles in the air, and so you are sending a 'vibration through the iron rod which will have to pass through each particle at a time, like dominos until it reaches the end. (At least that's the logic I came to).
it has to be instant. The medium is continuous. is there any experimental proof for this time lag , even on the small scale?
Assuming the rod does not bend due to self weight.
No, it is not "instant". All mechanical processes takes time. Maybe certain quantum behavior is "instant", but things can "go backwards in time" too in quantum mechanics! Kind of like, "Oh, here's other end moving" before anything even touches the first end. Let's forget about that, because that only applies to quantum behavior, not ordinary mechanical processes.
i can understand the quantum behavior, since i am working on it. but if you are creating a vibration by holding the end , then it will behave as if the sound wave propagation.
Here it is about the position and the rectilinear movement. From the Heisenberg (generally), only one thing can occupy single state. No other object or matter can occupy the same state.
so it has got to make the instant movement.
@Siv Sri – This is supposed to be a mechanical process. The rod is PUSHED at one end, and we wait to see when anything happens at the other end. Nothing is said about inducing any quantum behavior. I've offered to look at how an electrical signal could be sent by means of a mechanical shock, but even that cannot travel faster than the speed of light.
If you say that the 1 lightyear long rod can "move instantly", so that messaging would be possible "instantly" across a light year, I suggest you apply for a patent on how that can be done. Lots of people would be very interested in that technology.
@Michael Mendrin – In the mean waiting time , what about the positions of the rod?. where will be the adjacent part of the rod reside? Assuming the purely rectilinear. no vertical shift. No Compression as well
The answers to your Instant messaging- "The Quantum Entanglement". The connected space. this is not the discussion here.
So Lets focus on the Iron ROD.
@Siv Sri – I think the reason it is not instant is because atoms repel each other due to electrostatic forces; they may have fixed positions in solids, but they don't actually touch each other as simple diagrams would have you believe (where the atom is represented as just a circle).
How I imagine it (hopefully it's not completely incorrect):
When the first column of atoms is pushed, it moves over to cause a greater overlap between the electric fields of the atoms in the second column (a simplified diagram would show the circles partially overlapping). This causes repulsion between the columns to increase, causing the second column to also move forward, increasing repulsion between the second and third columns which causes the second to move backwards and third to move forwards and so on, forming a longitudinal mechanical wave (the same way sound is transferred, hence the propagation at the speed of sound). It may seem unusual to take this a step at a time (a particular row moves forwards, then backwards, then forwards, etc., rather than just going straight to the end position), but the process is not instantaneous I think because the electrostatic forces depend on the transfer of electromagnetic exchange particles that cannot exceed the speed of light.
As a force continues to be applied, the wave continues to be produced at your end, meaning that the length of time over which the other end accelerates (after you wait for it to start moving) is the same as the length of time you spent pushing/accelerating your end. After you stop applying a force, the whole rod continues to move at constant speed as one entity (by this I mean that movement at your end is instantaneously transferred to the other end). This is consistent with the idea that speed is relative (the end state is equivalent to the initial state).
@Will Cxp – You gave the first good explanation, thanks!
@Siv Sri – Well, sure, if we treat the iron rod as an abstract object, like a simple mathematical cylinder, with no consideration given for its true physical properties, it'll "move instantly".
@Michael Mendrin – Suppose I grab it in the middle and move it in one direction; what happens? Does one end move faster than the other? Does it's length change?
@Bernard Rzetelny – I think what's happening now is that this subject is becoming more about structural properties of common materials, i.e., the kind of thing engineers have to deal with when designing bridges, for example. Let's forget about that it's a light year long. Now, let's imagine that the iron rod is replaced with a long helical spring. If I grab it in the middle and give it a tug in one direction, what will happen? Eventually, the entire spring will move in the direction and by the amount I tugged it---but it won't happen instantaneously. A compression wave will travel in the direction of the tug, and a decompression wave will travel in the opposite direction, until both reach the ends.
What happens if you move the rod at a speed greater than speed of sound from one end.What will be the speed at other end ? Is the maximum speed at other end always the speed of sound ?
I like that question!
Detonation speeds of explosives can be quite a bit faster than shock wave speeds even in metals, such high explosives to try moving an iron rod faster than iron's speed of sound could be tried. But what's going to happen is that after the detonation wave passes through the explosive and hits the iron rod, it will quickly settle back to the speed of sound in iron. As another example, it's hard to imagine something as sudden as a lightning bolt, generating plasma shock waves of prodigious speeds at the core--and yet, once it hits ordinary air, we still estimate how far away it is by the speed of sound in the air. Really, you know, to a lot of things in physics, like neutrinos, or even neutron stars, solid iron might as well be ratified air.
It will take more than 1000 years for the other end to mimic the motion of the beginning of the rod. The speed of sound refers to the time it takes for the bulk of the wave motion and energy to travel from one place to another.
But there is no reason why the initial response should wait that long. As soon as an electron near the beginning of the rod is moved, its electric field will change position, which in turn will affect neighboring electrons, etc. All of this at the speed of light-- electric field disturbances travel at light speed, and charges respond immediately to local changes.
Isn't that the same thing as sending an electric current down the rod? That should be an interesting physics experiment---have a really long iron rod, hit one end with a hammer, measure how soon an piezoelectric disturbance can be detected at the other end. Not that the other end would MOVE, though, not for a while.
it means that the length of the rod will decrease until the sudden force reach the other end of the iron rod?
That is exactly right! Right on the money.
If you think about it it would be imediatly because dosnt brake any physics rules plus the entire rod will move at the same speed is push too so basicly it will all move at the same time and same speed regardles how far the other end but the object must be solid in order to achieve this
It does break physical laws, though. Ever heard this one? "No information can be transmitted faster than the speed of light in a vacuum." If the rod moved instantly at the other end, that's information, and it's being 'received' at the far end much, much more quickly than the speed of light.
I would prefer the answer 'never' if we're going to take into account the dynamics of the problem. A sudden application of force would just cause the rod to plastically deform - the other end would never even know that the first end moved. Secondly, the sound speed argument makes sense until you consider damping at which point the sound wave (or shockwave, depending how hard you tug the thing) would just dissipate out after a hundred or so meters.
Why not instantly ???????
Impulse is more appropriate rather than force particularly when thinking between rigid and not rigid.
I suppose the answer is instant if you consider the steel rod to be perfectly rigid element. In reality its not and the impluse propagate depends on the rigidity of the material. I just dont know why the answer is more than 1000 years, simply no figure to follow...
I believe that my first answer to this as well as the question itself was tampered with by moderators, so trying to make sense out of this subject by reading the comments here can be confusing. In particular, I don't think it was originally stated that the 1 light-year long rod was "brand new iron rod". But let's assume it is a brand new freshly cold-rolled steel rod at room temperature. The speed of sound in such is about 20,000 feet per second. A light year is roughly 30 x 10^15 feet. Hence, a "shove" at one end will be felt at the other end in about 1.5 x 10^12 seconds, or roughly 50,000 years.
Now, I'm not real sure what happens if the temperature of the steel rod is near the 3 degrees Kelvin due to the background radiation, whether or not that's cold enough to consider quantum effects.
Your logic seems to prevent objects from moving faster than sound, yet they regularly do. I can crack a whip, moving it faster than sound; but by your logic, there would be decompression in the whip, but as the wave propagates through it no faster than the speed of sound, the speed of the end of the whip could never be greater than the speed of sound. Since this clearly goes against observation, there must be a flaw in your reasoning.
yeah, why is the speed of sound propagating the force? I'm not a physics major or anything, but I feel like it would be more like electromagnetic force or one of the nuclear forces that "propagates" the force
Think of it this way, at a microscopic level when you push on one end of the rod, the force propagates through the atoms, i.e the atoms collide with other atoms, which in turn collide with another atoms until it reaches the other end. In principle that is equivalent to the way sound propagates as it travels through a medium...
At the lowest level it is the electromagnetic interaction that's propagating the signal.
@Josh Silverman – yes but the speed of electromagnetic waves in metal isn't the same as the speed of light in vacuum
@Josh Silverman – Indeed, but I was trying to clarify the speed of sound confusion..
@Beakal Tiliksew – I agree with you both @Beakal Tiliksew and @Pierre Dufour . I was pointing out that just because the signal travels at the speed of sound doesn't mean that it's not electromagnetism underlying it all.
What would happen if we push the rod...will the effect be same????plZ answer
If I were to speak to you in a very, .. l---ooow.. voice, would it mean it'll take longer for the sound to get to you? No? Same thing here. If you pushed the rod very...sl----oowly, the effect will still travel down the iron rod at the speed of sound in iron.
So it means that at one point of time,the rod's length will be slightly smaller?
Thanks for that! I'd never considered how sound propagates in a solid object. Still a longitudinal compression wave just like air. Essentially just series of pushes and pulls along the same axis!
I didn't get it the length of rod is constant so if we move it from one end it should move instantly at the other so the length remain constant. I might sound naive but i really wanna understand this concept . Can anyone explain in details.
So when you move something it transfers the force at the speed of sound relative to that matter? I always though it instantly moved as long as your force was greater than the coefficient of friction
I obviously inferred a few principles here that are not in the stated equation, but assuming you pushed the rod 1 inch. The inch would not be static until the energy in the rod came to an equilibrium. The pressure of the push would have to be maintained and the movement would not be complete until long after the the energy passed back and forth through the rod; however, there are a large number of variables in this equation that must be assumed to come to an answer where the energy does reach the other end, including that no outside forces (i.e. gravity) are acting on this impossibly long iron rod. With gravity in the equation the answer maybe near instantly. The distortion of the rod would cause the rod to begin to collapse in to a ball(assuming no other objects gravitational forces are acting on it). I could blather on, but I'll let those that are more knowledgeable than I respond. ;)
Ah, yes, you are correct.
I guessed "instantaneous", because in my thought experiment, I assumed the rod to be infinitely rigid. In such a case, movement would be instantaneous.
My question now: would the other end of the rod EVER move? Or would the length of the rod be so great, that all imparted energy would be dissipated by buckling/elastic deformation, long before vibrations could rtravel to the other end?
That's what the title suggests " will it move?"
Before we discuss about 1 light year long rod I would like to know the time taken by 1 km rod to move at one end when force is applied at other end. I saw many questions and answers on this topic like sound ...quantum etc.. Before all this I would like to rewind the question " how much time will pass before the other end moves when we push it". So first tell how much force a normal person applies...
is not the same result if we use a rod of maybe 10meters? why?
I think there are a lot of good theories here but the way to know would be to actually perform this experiment. Otherwise, every comment here is just a theory. So the correct answer is D: None of the above. Anyone got any iron rods 5,878,000,000,000 miles long layin' around ?
So the rod will be shorter than it actual size for more than 1000 years?
Yes, that's right. Isn't that funny? So, somebody hit me on the head. I'm gonna be short for a thousand years.
If i move one end the it will not move until the other end moves so this means that the other end should move instantaneously
The rod will compress because it is compressible. If is wasn't compressible, the speed of sound in it would indeed be infinite (but that's impossible). Everything is compressible.
The metal rod cannot move instantly, as that would require the force to move through the rod at the speed of light. The way a pushing force actually works is that it moves one layer of atoms forward. This then knocks into the next layer of atoms and pushes that forwards and so on (This is a simplified explanation). This behavior is how a sound wave works, they are both types of compression waves. So the force travels through the rod at the speed that a compression wave can, or the speed of sound through iron, or 5130 m/s.
The rod is 1 light year long, which means that it would take a year for light to go from one end to the other. Because the compression wave doesn't move down the iron at c (speed of any massless particle), it cannot reach the other side in a year. This also rules out any possibility of it taking a week.
Therefore, the only remaining option would be over 1000 years, which could be any amount of time from 1001 years to 1*10^100 years. This is all assuming that the force is applied equally on all points on one side of the rod. Any imbalance will create torque which would build up over time and either move the rod by quite a bit or snap it. It's only 1 light year long, so there would be very little risk of it crashing into anything. Assuming this isn't done in a completer vacuum (even intergalactic space has some stuff there), the rod would slowly loose energy as the wave traverses it, so in reality, a force may never reach the other end.
When you excert a force you create a pressure wave that propagates through the rod.
Pressure waves that travel through a medium, do so at the speed of sound, specific to the density of the medium.
The speed of sound in iron is about 15x faster than that through air. (5130 m/s)
You don't need too much maths to determine it would take (WELL) over a millennia to travel a lightyear
Can anyone explain this: when force is applied at one end, layers of molecules transfer that force at the speed of sound through that material, but when that impact reaches the other end will it be equal to the applied force or will it be less because of losses? And when the impact reaches the last layer of molecules how do they result in movement of object?
I'm not a physicist, but as far as I know the energy at the end would be less than the applied because the vibrating particles always loose part of it to the surroundings. Just imagine yourself getting further away from a sound source, it will be progressively more difficult to hear it.
I think you are all going off at a tangent. I am not a scientist, just an ordinary guy. I do not see what it has to do with the speed of sound! We have no details other than it is an iron bar of almost fixed length, if you assume the speed of light to be fixed. I thought of it as an abstract bar so if I push it at the speed of 1m/s for 1 second the other end will move 1 metre instantaneously. However, being iron, not the strongest medium in the universe the amount of effort required to change the inertia of a lightyears length of bar would probably be so great that the bar would compress at the point of the applied pressure such that the bar would not move at all..
Of course the energy will reduce. And the rod which is this long will have enormous mass & hence enormous inertia. So it will require phenomenal amount of energy to move it even for a centimeter.
You're assuming that it is being affected by gravity. If it is not any pressure would cause movement.
So if you applied 100N force at one end then at other end will it be near to 40 N?
Actually, it's a lot longer than a thousand years. Any sudden force at one end will propagate along the iron rod at the speed of sound in the iron rod, which is about 5000 meters per second. A light year is roughly 1 0 1 6 meters, so you know where this is going.