BleedingChipsSlowly
BleedingChipsSlowly
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May 6th, 2014 at 8:44:09 PM permalink
Quote: sodawater

The astronaut can't see it at all... he is too far away.

Assume I want the answer from the flag's point of view.

Here's a related question that might help you.

Say you're in a hot air balloon over Earth and hold a steel broom vertically out of the basket. You let go of the broom stick from the top of the stick. How long does it take for the head of the broom (the bottom) to start falling?

Instantaneous, since gravity is causing the action and acting uniformly on the broom stick. Gravity is not a factor per your problem statement.
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
sodawater
sodawater
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May 6th, 2014 at 8:48:11 PM permalink
Quote: sodawater

Say you're in a hot air balloon over Earth and hold a steel broom vertically out of the basket. You let go of the broom stick from the top of the stick. How long does it take for the head of the broom (the bottom) to start falling?



Quote: BleedingChipsSlowly

Instantaneous, since gravity is causing the action and acting uniformly on the broom stick. Gravity is not a factor per your problem statement.



this is incorrect
ChesterDog
ChesterDog
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May 6th, 2014 at 9:03:11 PM 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?



I think any motion through the steel would travel at the speed of sound in steel, which is about 6000 meters/second. So, about 50,000 years is my guess.
sodawater
sodawater
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May 6th, 2014 at 9:03:45 PM permalink
ChesterDog is correct. Nice job.
MathExtremist
MathExtremist
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May 6th, 2014 at 9:07:48 PM 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?


I think it's a trick question: either the pole is made from some magical, massless steel or the pole is itself a major source of gravity. Depending on the diameter of the pole, its mass would be within a few orders of magnitude of the mass of Earth. So the question is sort of like asking how long it takes the Earth to move when you do a push-up.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
sodawater
sodawater
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May 6th, 2014 at 9:12:04 PM permalink
Quote: MathExtremist

I think it's a trick question: either the pole is made from some magical, massless steel or the pole is itself a major source of gravity. Depending on the diameter of the pole, its mass would be within a few orders of magnitude of the mass of Earth. So the question is sort of like asking how long it takes the Earth to move when you do a push-up.



Why would it matter how massive the pole is? The astronaut is strong enough to push it. Gravity has nothing to do with the problem.
MrWarmth
MrWarmth
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May 6th, 2014 at 9:44:06 PM permalink
Maybe ...

The question says "push," so assuming the pole is a perfect rigid body, the flag moves at the same time as the rest if the pole. If it's not perfectly rigid, as that's an impossible condition, then the energy wave of motion would propagate at, I think, the speed of sound through the material. This is not to say, however, that the motion of the flag would be detected right away, so whether the pole was perfectly rigid or not, it would appear to "bend." And, of course, without detecting the motion, you have no reason to think there's any at all. So, perfectly rigid is time from speed of light, imperfectly rigid is time from speed of sound thru steel plus that of light for detection.
sodawater
sodawater
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May 6th, 2014 at 9:50:31 PM permalink
Quote: MrWarmth

Maybe ...

The question says "push," so assuming the pole is a perfect rigid body, the flag moves at the same time as the rest if the pole. If it's not perfectly rigid, as that's an impossible condition, then the energy wave of motion would propagate at, I think, the speed of sound through the material. This is not to say, however, that the motion of the flag would be detected right away, so whether the pole was perfectly rigid or not, it would appear to "bend." And, of course, without detecting the motion, you have no reason to think there's any at all. So, perfectly rigid is time from speed of light, imperfectly rigid is time from speed of sound thru steel plus that of light for detection.



Yes, your last answer is correct. I specified that the pole was steel so we know that it is not perfectly rigid. Although not plus the speed of light because I specified that the clocks are synchronized from the moment the astronaut pushes through a pre-arranged method.
1call2many
1call2many
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May 7th, 2014 at 10:29:24 AM permalink
Assuming there is zero compression between molecules within the pole, then it will take zero time for the other end to move and you have just invented faster than light speed messaging. Move the flag once for yes and twice for no.
MathExtremist
MathExtremist
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May 7th, 2014 at 10:40:55 AM permalink
Quote: sodawater

Why would it matter how massive the pole is? The astronaut is strong enough to push it. Gravity has nothing to do with the problem.


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.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563

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