Astronaut
Quote: BleedingChipsSlowlySometime next year, relatively speaking.
Nope.
I'm calculating the time it would take for the reaction traveling at the speed of light, 186,000 miles a second. Not right?Quote: sodawaterNope.
Quote: IbeatyouracesNever
Haha... why never?
I will specify that at some point after the astronaut pushes the pole, the flag at the other end does move.
Quote: BleedingChipsSlowlyHow about the flag moves one year after the action, since it it is on a one light-year long pole, but it takes two years for the astronaut to see that movement.
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. Assume that through some pre-arranged method (like observing an equidistant third party), a stopwatch at the flag is started the instant the astronaut pushes the pole.
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.Quote: sodawaterThe 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?
Quote: sodawaterSay 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: BleedingChipsSlowlyInstantaneous, 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
Quote: sodawaterThere'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?
Quote: sodawaterThere'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.
Quote: MathExtremistI 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.
Quote: MrWarmthMaybe ...
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.
Quote: sodawaterWhy 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.
Quote: MathExtremistYou 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!
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"!
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.
edit: Retracted, OP is steel.
Quote: sodawaterThere'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).
Quote: MangoJThis 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.
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.
Quote: MangoJThis 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).
I agree it's a physics question. To me, the question should really be how much force (edit: impulse) needs to be applied in order to ensure that the stress wave actually propagates all the way to the flag, one LY away, rather than being entirely turned into heat by friction inside the pole. My intuition is that no human could possibly exert sufficient force to make the flag move. Actually, it's probably the case that attempting to apply the requisite force would shear off the end of the pole...
To the astronaut it would be a lot slower since he is literally motionless. What takes 50,000 years to pass on earth would be like 5 million years to the astronaut.
As you point out, time ir relative. I would assume the time measurement asked for in the problem is relative to the astronaut, and the related time span on Earth or anywhere else in the universe is immaterial. I did point out in a previous post that if the flag motion is relative to the astronaut's observance then you would have to add a year to the time the flag itself actually moves.Quote: JoePloppyDo we forget time is relative? This astronaut is "motionless" in space. Since time is directly related to how fast you are moving, If we observed the flag moving from earth, it may take 50,000 years.
To the astronaut it would be a lot slower since he is literally motionless. What takes 50,000 years to pass on earth would be like 5 million years to the astronaut.
He is moving relative to something even if it's a travelling Martian space ship a trillion billion miles away.
At best he can be at rest relative to the pole, which also cannot be motionless.
