SOOPOO
Joined: Aug 8, 2010
• Posts: 8437
May 7th, 2014 at 12:27:25 PM permalink
Quote: MathExtremist

You said there was no major source of gravity nearby, but the pole is a major source. That's all, I know gravity isn't related to the problem.

I understand the solution you're going for -- the vibration from the push travels down the pole -- but I think in reality the flag would never move. The minuscule force the human astronaut exerted would be absorbed by the pole, turned into heat, and dissipated into the void of space. Suppose you're an astronaut on the far side of the moon and you do a jumping jack. How long would it take for the flag planted by Neil Armstrong in the Sea of Tranquility to move? I don't think it ever would.

I love ME!
sodawater
Joined: May 14, 2012
• Posts: 3321
May 7th, 2014 at 12:31:33 PM permalink
Quote: MathExtremist

I understand the solution you're going for -- the vibration from the push travels down the pole -- but I think in reality the flag would never move. The minuscule force the human astronaut exerted would be absorbed by the pole

Haha, I said the astronaut was "really strong"!
Dalex64
Joined: Feb 10, 2013
• Posts: 1067
May 7th, 2014 at 1:21:53 PM permalink
You could change it to a 10 foot pole with mirrors facing inward at each end, and laser rangefinders in the middle.

Then, you could push one end of the pole and see if the one side moves towards the rangefinder simultaneously with the other side moving away.
98Clubs
Joined: Jun 3, 2010
• Posts: 1728
May 8th, 2014 at 10:52:59 AM permalink
I had the thought that it was a transfer of energy, and thus instantaneous (at SoL and thus 1 year). Since there is no gravity, any pulse-applied force will travel through the steel rod. As I thought about this, I also thought about the "Closing Scissors" problem in which the point of cutting accelerates to the SoL by the time the scissors are fully closed. I think these two problems are the same. In this case the pulse-applied energy does not travel at a constant rate but accelerates to the SoL at the tip of the pole with the flag. Considering the pole is 1 L.Y. in length it would take 2 years for the pulse to reach the flag. This due to the fact that steel has a flex modulus that can absorb the energy of the pulse and transmit it through the length. So there is a minimum velocity not zero. BTW, said steel pole IS a gravitational influence to all ouside agents (and astronauts).ChesterDog's answer looks very possible, if not correct in that striking the end of the pole with a hammer is the same thing, except the pulse is shorter than the flex modulus time generating a sonic wave through the pole. In my case my answer presumes the pulse wave is longer than the flex modulus time (rebound time) and converts the whole pole to motion, not just a segment.
Some people need to reimagine their thinking.
Canyonero
Joined: Nov 19, 2012
• Posts: 509
May 8th, 2014 at 11:05:05 AM permalink
Keep in mind that at that length the pole would - if observed from great distance - essentially behave like a piece of string. So the movement the astronaut could provide would translate into bends along the length of the pole. Therefore, the flag at the other end would never move.
98Clubs
Joined: Jun 3, 2010
• Posts: 1728
May 8th, 2014 at 11:22:07 AM permalink
The astronaut is very strong, and counters the rebound. But I like that torque idea alot. a 2" pole a light-year long that is still straight. Thats quite possible. But hitting said pole with a hammer might actually induce motion sonically WITHIN the pole.

edit: Retracted, OP is steel.
Some people need to reimagine their thinking.
MangoJ
Joined: Mar 12, 2011
• Posts: 905
May 8th, 2014 at 11:57:04 AM permalink
Quote: sodawater

There's an astronaut floating motionless in an empty part of outer space, nowhere near any major sources of gravity. Floating next to him is a steel pole that is 6 trillion miles (6x10^12) long, with a flag at the other end. The astronaut pushes the pole (he's really strong). How long does it take for the flag to move?

This is not a math question, but a physics question. When the astronaut pushes the one ends pole, a wave of strain and stress is send through the pole. The speed of the wave is the speed of sound in this material. For steel, it is somewhere like 800 miles per hour. When the wave hits the other end with the flag (after 1 million years), the flag wiggles (and the wave is reflected from the poles end).
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5150
May 8th, 2014 at 8:13:42 PM permalink
Quote: MangoJ

This is not a math question, but a physics question. When the astronaut pushes the one ends pole, a wave of strain and stress is send through the pole. The speed of the wave is the speed of sound in this material. For steel, it is somewhere like 800 miles per hour. When the wave hits the other end with the flag (after 1 million years), the flag wiggles (and the wave is reflected from the poles end).

Question: does the temperature of the steel have any effect on the speed of sound traveling through it? I remember that the speed of sound through air is proportional to the square root of the air's absolute temperature.
MangoJ
Joined: Mar 12, 2011
• Posts: 905
May 8th, 2014 at 11:47:40 PM permalink
Well, pressure fluctuations in air (or a gas) are different from pressure fluctuations in a solid, like steel.
In a gas, these are the collisions of all the molecules moving in random directions. Their average speed is proportional to sqrt(T).

In a metal, you are basically pressing on the bound electrons in the host atom matrix (electrons repell each other). The speed of sound is then determined on the density of the electrons, and likewise on the density of the host atom matrix. So the speed of sound is proportional to the density.
MathExtremist
Joined: Aug 31, 2010