How Long for a 186,000-Mile Rod to Move?

[coolpup32]

A co-worker asked me a question this morning that has been bothering me all day. So, here it is.
Numbers are rounded for conversation, asuming we're in a vacuum and no other outside forces.

Lets say I create a straight 'Rod' with the length of 186,000 Miles long, let's also say this rod cannot be bent. If i push on one end of the 'Rod' how much time, if any, would pass before the other end moves?

I agree with the person asking the question that information cannot be transmitted from point A to B faster than the speed of light. While other co-workers argue that the "Rod" is a single point in space that you are accelerating.

I'm poor at explaining without drawing so maybe this helps


Force applied-----> |A|-----------------------|B| (result?)

Anyway, Its been bugging me. Could someone help?

 

[russ_watters]

We should have a sticky on this question, we get it about once a week.

The answer is two-fold:

1. There is no such thing as a perfectly rigid rod.
2. In real life, the impulse travels at the speed of sound in the rod. So if the rod were made of steel (sonic velocity, 15,000 fps), the other end would start to move in about 18 hours.

 

[tony873004]

It's a great question though. I used to wonder this too. I'd use the cable in my bicycle's brakes as an example. The speed of me pulling might be only a few m/s, but the "signal" got from the handle bar to the brake pads instantly.

But it actually wasn't instantly. It was no faster than the speed of sound through the metal the cable was made of. That's rather insignificant considering the short distance, but much slower than the speed of light.

 

[coolpup32]

We should have a sticky on this question, we get it about once a week.

The answer is two-fold:

1. There is no such thing as a perfectly rigid rod.

Yes I understand this... just in theory

2. In real life, the impulse travels at the speed of sound in the rod. So if the rod were made of steel (sonic velocity, 15,000 fps), the other end would start to move in about 18 hours.

I'm not suggesting a vibration... but an actual force to move the rod ie: A gentle nudge.
With your example I could have the same scenario with a 50 pole, push the rod quick enough, and wait to see the result on the opposite end.

Edit: Even better, Let's say I pust point A toward B at twice the speed of sound... with your example i'd be at point B 9 hours before it changes position. There i'd witness point A and B in the same location before watching B shoot off 9 hours later.??


Ok, think of it this way. (Same setting)
I have a train at rest that is 186,000 miles long, no slack in the couplings between cars... When the locomotive departs the station, when does the last car move... It can't be instantly can it?

 

[russ_watters]

Yes I understand this... just in theory

That's the thing, though - if we are allowed to make unphysical assumptions, we can get any answer we want. We can assume the tooth fairy pops out of the other end of the rod when you push on it!

I'm not suggesting a vibration... but an actual force to move the rod ie: A gentle nudge.

It is the same animal. All motion starts with a pressure wave traveling through the object. You just only get half the sine wave until you stop the rod. Consider the water hammer effect: http://en.wikipedia.org/wiki/Water_hammer

Edit: Even better, Let's say I pust point A toward B at twice the speed of sound... with your example i'd be at point B 9 hours before it changes position. There i'd witness point A and B in the same location before watching B shoot off 9 hours later.??

Accelerating the rod quickly to faster than the speed of sound in the rod requires a force large enough to permanently deform it. This is why when you strike a stake with a hardened steel axe head, you put dents in it. If you accelerate the rod slowly, however, the pressure wave builds up (the rod acts like a giant spring) and eventually the entire rod gets to moving at that speed.

I have a train at rest that is 186,000 miles long, no slack in the couplings between cars... When the locomotive departs the station, when does the last car move... It can't be instantly can it?

Correct. It's the same question and has the same answer.

The reason people have trouble with this is that the wave moves faster than human perception. But if you can accept that it is just the speed of sound, you can picture in your head how this works with a spring.

 

[coolpup32]

wow! I guess I just had just assumed that the motion would have been at or close to c. Resulting with a 1 second delay at the other end.

Thanks for the explanation guys! Love the forums.