Speed of pressure?

[Daecon]

Suppose you have a rod of material that was 1 light-hour long (whatever distance that would be) and at one was was you, and another end was a big red button...

 

If you pushed the rod from your end, would the button at the other end be pressed instantly, after an hour, or after an even longer amount of time?

 

How long would it take the pressure to travel from your hand to the button?

[Flashman]

It would essentially be determined by the speed of sound in that material.

[CaptainPanic]

Although I agree that what Flashman said sounds logical, I must say that there exist pressure waves that travel at speeds that are greater than the speed of sound... These occur for example when high explosives detonate. So it's more complicated than what Flashman proposed.

 

Since I am no expert on the field myself, I will just recommend this wikipedia page, which shows a formula to calculate the speed of a P-wave as a function of modulus of incompressibility, μ is the modulus of rigidity and ρ the density (also with links to those 3 concepts).

[swansont]

To address another part of the question — one of the implications of relativity is that there can be no infinitely rigid bodies. The delay in the movement of the other end would have to be at least L/c, i.e. 1 hour in this case

[Daecon]

So from the action pushing one end of the rod, it would be at least an hour before the equal and opposite reaction of the other end moving?

 

How would the speed of my pushing affect things? If I was able to push "my" end of the rod at a speed of 0.5c for example?

 

Would I need to wait an hour for the momentum to "fill up" all the mass of the rod before any part of it started to move, or would my end simply be compressed while the other end remained stationary?

[Cap'n Refsmmat]

So from the action pushing one end of the rod, it would be at least an hour before the equal and opposite reaction of the other end moving?

That's not really an "equal and opposite reaction", more of your force being transmitted all the way down the rod.

 

Would I need to wait an hour for the momentum to "fill up" all the mass of the rod before any part of it started to move, or would my end simply be compressed while the other end remained stationary?

Probably the latter. The key is that the material can't be infinitely rigid or incompressible -- when you push, it's compressed at least slightly, which slows down the travel of your push.

[Daecon]

How would it work if the force of pushing was greater than how much the material could be compressed, like if the rod was made of diamond or something?

 

Where would the extra force go?

[iNow]

I wouldn't think it matters. No matter how rigid your material, the force must still transmit atom by atom down the line like a wave.

 

Per your question on the "extra force," I would guess much of it would create instability and dissipate as heat.

[swansont]

I wouldn't think it matters. No matter how rigid your material, the force must still transmit atom by atom down the line like a wave.

 

That's exactly it. A single impact would transmit a compression pulse. A continuous push would have a "leading edge" of compression; in front the rod will not have started moving but behind, it would be moving.

[Mr Skeptic]

Like others have said, you are pushing the atoms on one end, which via the electromagnetic force push the atoms nearby them, etc, which can't go faster than the speed of light since the speed of electromagnetism is the speed of light. I think that the impulse would travel at the speed of sound in that material, but if you applied force faster than that, you would likely break the rod (though if it were shorter you could transmit a shockwave faster than the speed of sound and might not break it).

[Martin]

It would essentially be determined by the speed of sound in that material.

 

I agree!

 

There is some confusion about P-waves and S-waves. Sound normally travels by P-waves. P-waves are faster. I think you can take the speed of sound in the medium as the upper limit for waves in the medium. I don't mean like shrapnel from an explosion that is material debris, I mean waves.

 

Although I agree that what Flashman said sounds logical, I must say that there exist pressure waves that travel at speeds that are greater than the speed of sound...

 

Since I am no expert on the field myself, I will just recommend this wikipedia page, which shows a formula to calculate the speed of a P-wave as a function of modulus of incompressibility, μ is the modulus of rigidity and ρ the density (also with links to those 3 concepts).

 

I'm not sure about this. I think what you call P-wave speed is the speed of sound. so P-wave would not be traveling faster than sound.

 

Maybe someone else will step in, I have to go.

 

P means primary (not "pressure") and S means secondary

 

Here is another wiki page if you'd like

 

http://en.wikipedia.org/wiki/S-wave

[granpa]

think of the rod as a long spring.

 

if you pushed hard enough it would become degenerate. like white dwarf material.

[Baby Astronaut]

This got me thinking, a rod about a light-hour long would have a lot of mass. What if a rod were long enough to have higher mass than a black hole? Would its length prevent it from becoming one (due to the weak gravity between its ends)?

 

As for Transdecimal's question, I can't answer it but nevertheless -- awesome question!

[Klaynos]

This got me thinking, a rod about a light-hour long would have a lot of mass. What if a rod were long enough to have higher mass than a black hole? Would its length prevent it from becoming one (due to the weak gravity between its ends)?

 

As for Transdecimal's question, I can't answer it but nevertheless -- awesome question!

 

B lack holes, are not just mass defined, but mass within a certain volume, which if it was 1 light hour long then it wouldn't be...

[CaptainPanic]

"When a shockwave is created by high explosives such as TNT (which has a detonation velocity of 6,900 m/s), it will always travel at high, supersonic velocity from its point of origin." (source wikipedia)

 

So, a shock wave can travel faster than sound (supersonic).

 

But: have a read here (again wikipedia) about the Chapman-Jouguet condition.

 

Among some other things which I am not sure I understand, it states that due to a compression, the speed of sound changes. Inside a shock wave, there is a part where the wave becomes subsonic, even though the wave as a whole travels supersonic. I am not sure at all if this can be applied in a solid material.

[swansont]

Inside a shock wave, there is a part where the wave becomes subsonic, even though the wave as a whole travels supersonic. I am not sure at all if this can be applied in a solid material.

 

This is just a guess, but if you can compress the material, I'd say yes. It's just going to be harder to do in a solid.

[Sedit]

Ah here it is im a little rusty so i had to resort to my old physics book here but i think the paragraph answers your question if im not mistaken

 

 

" It has been shown that for a longitudinal wave, when a force is applied to a material, the material is distorted and a force opposing this distortion is created in an attemp to restore the status quo. This restoring force is a function of the elasticity of the material. The velocity depends upon the elasticity and density of the material in which the wave is being propagated"

 

 

v=sqr(E/d)

 

where

d = density(lb/ft2)

E = Elasticity(lb/ft2)

v = velocity (ft/s)

 

 

So after one determined the property of the material that the rod was made of this problem of Time would become childs play.

 

PS. can someone show me how to use that math function that draws the eqations how there suppose to look. thank you

Edited December 15, 2008 by Sedit
typo