Suppose an object of length l between point A and B, and of material M. At time t, a mechanical force is applied in the orientation of AB at point A. At time t+x deplacement of point B is observed. What is the value of x?
(In English now)
Let’s say I’ve got an iron rod one light year in length. I give the rod a shove. How much later does an observer at the other end see it move?
a)instantly b)one year later c)depends on the speed of light in the medium d)none of the above
On preview, I’ll also take D, and say it depends on the speed of sound in the medium that matters. Think of it a bit differently, instead of shoving one end, you hit it with a hammer, how long will it take for the sound of you hitting end A to reach end B. Striking A will compress the material and send a sound wave through the material to point B. When the wave finally makes it to B, that point will begin to move from your action at A.
A shove will not propagate any faster through the material than a hammer strike, they are essentially the same thing in this regard.
I’ll grant you that the speed of sound answer is the most plausible. However, the thing that got me wondering about this was watching trains.
So imagine a train 1km in length. Not only is it a perfect train in that it has no loose joints, parts, or such, but it’s also remarkably fast, going from 0 to 100km/h in no less than 3 secs. Incidently, 3 secs is also the time it takes for sound to travel the length of the train. (I know, in air, but it’s for the purpose of the example.) So when the locomotive lurches forward, the rear end of the train starts moving roughly 3 seconds later. Right? In that time, the front of the train is already ~42m ahead.
So what really stumps me is what is happening at the molecular level to make the train (or rod) stretch in such a way.
So. . . The WB cartoons were right after all! A car does stretch when you step on the gas!
Nothing in this world is perfectly rigid - even steel rods expand and contract if you push or pull on it. Your example is rather unrealistic though. Speed of sound in a rigid solid is much faster than the speed in the air, for one thing. And a train is not perfectly elastic - stetch it enough and it will snap, your train will stretch a bit, then the locomotive will break off the train. If anything, your example illustrates why a train can’t accelerate that fast.
By the way, trains are purposely built to have lots of slack in its joints. That way the locomitive doesn’t have to accelerate the whole train at once - the locomotive can first get itself started, then start the car behind it, and then the one behind that, etc.
There IS a way to make a train faster - put a motor on every car and send an electrical signal to start the motors. Or better yet, use a timer to start all the motors. You can start the entire train with zero delay. (Or to be eact, the delay will be determined by the distance between adjacent motors, not the length of the whole train.)
The train doesn’t stretch at all. You just perceive the back part to be starting 3 seconds late, assuming you’re watching from the front end of the train. While there may be some stress on joints etc., there is no way a 1 kilometer train would stretch 42 meters. Or even one meter, for that matter.
Maybe I’m dense, but what the hell does the speed of sound have to do with anything? I always thought seeing and hearing were two rather distinct things.
There is no way a 1 kilometer train would stretch 42 meters. There’s also no way that a train that heavy could go from 0 to 100 kph in 3 seconds. Yeah, if you plug in ridiculous numbers, you’re going to get a ridiculous result. Also, I believe that the speed of sound in steel is 3-4 times what it is in air (but don’t quote me on that). Using the speed of sound in air may be okay for an order of magnitude calculation, but not nearly exact.
What does the speed of sound have to do with this? Well, I’ve never heard this explanation given, but it makes a lot of sense, I think. If you hit one end of a bar, how does the other end know that you did it? Because the molecules at one end interact with the molecules nearby them, and they cause a chain reaction all the way down the line. This is the same phenomenon as the propogation of sound, so it would make sense that both processes happen at the same speed. And I don’t think the perception bit comes into play here. We can say that the train example is nonrelativistic.
So if it’s the speed of sound, then I’d think it would follow that it’s impossible to fire a projectile with initial velocity greater than mach 1 without smooshing it, because the back of the projectile would have moved past the front before the front had begun to move.
That doesn’t sound right to me. Am I missing something?
I liken it to electricity, which if I remember right flows instantly, since it is the movement/displacement of electrons.
I picture a tube full of marbles end to end, you take a new marble and push<pushing the rod> it into one end, in that same instant a marble will fall out the other<seeing the rod move on other end>.
DOes that sound better?
The tube of marbles analogy is a pretty good one for some purposes, but the answer is still not instantaneous. Youve got a bit of circular reasoning there: You’re saying that a physical object (the rod) would react instantly because electrons in a wire react instantly, and the electrons react instantly because another physical object (the marbles) do. In actuality, the electrons aren’t smooshed together as tight as they can be; what happens when you push one in is that it squishes the next one, then that one moves an squishes the one after it, and so on. With electrons in a wire, it works to be the speed of light in the material, not the speed of sound, but in any event, the answer is never more than c.
And Ring, not only did I find the neutron star bit interesting, but I asked my advisor about that exact phenomenon the last time this came up here.
…Assuming we get a “perfect” rod 1 light-year long (from the same store we got all those friction-less, mass-less things used in Dynamics and Physics class) and we push it one foot in the direction of it’s length, the other end will register that movement in one years time?
Discussions of this question tend to confuse two questions:
(1) Can a mechanical impulse (ie, sound vibrations, a “push”) be transmitted through some medium instantaneously?
(2) Can such an impulse be transmitted through some medium such that it arrives at the other terminus “faster than light?”
As to #1: The rate of propagation of a mechanical impulse (I) through a material (M) is proportional to the rigidity of M. Other considerations aside, this alone rules out instantaneous propagation, as no conceivable material (even “neutron matter”) could be absolutely rigid.
But Question #2 seems more interesting. Although in general extremely elongated objects manifest the rigidity deficiencies of the composing material in a more obvious way, there is no definite connection between length and rigidity. No law of science or logic (or Einstein) prohibits the existence of a “rod” one lightyear in length and as rigid as you please. This seems to imply that the rate of propagation of “I” could be as fast as you please.
As I don’t expect I’ve outwitted generations of theoretical physicists, I’d be content to receive a clear and simple explanation of where my chain of reasoning went astray.
Air is a fluid, and not a terribily viscous one as fluids go. A metal projectile, having a considerably lower smooshability quotient and not taking any shit from mere atmospheric gasses, move the air out of its own way. Fire that bullet into water, and different things happen depending on bullet shape. A fully jacketed spitzer rifle bullet will just slow down quickly with almost no deformation but a soft or hollowpoint projectile will smoosh big time even if it’s subsonic for the medium.
thinksnow, if it’s a perfect rod (with infinite rigidity and all that), then no, the other end will register the movement instantaneously. Fortunately, perfect rods are few and far between…
Ring, I’m amazed. I thought no one else used O&R! Hmm… so what happens when you have an anomalous material where for some frequencies the group (and maybe also phase) velocities are greather than c? With what speed do the electrons move then?