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The very long rope

  1. Mar 17, 2007 #1
    I have a question that popped into my head the other day and I haven't been able to find an answer for it. Keep in mind I'm not a physics student, so if it's an easily solved question, I'm sorry.
    The experiment I am about to describe is very impractical, but it was my original thought, and I think it gets the point across.

    Ok, there are two men floating in open space where there is very little gravity. They have a rope that stretches the distance from Earth to the Sun. There is no slack in the rope and one man is at each end. If one of the men decided to pull on the rope, would it take eight minutes for the man on the other end to see his end of the rope pull away from him? If so, what is happening to the rope during this process?

    *I guess what I am describing is more of a pole, but I always saw it as a rope in my mind.
     
  2. jcsd
  3. Mar 17, 2007 #2
    The 'tug' cannot travel faster than the speed of light- so yes, it would take at least 8 mins. In general, no information can travel faster than the speed of light.

    In practice, the tug would travel at the speed of sound in the rope, which would be much greater than the speed of sound in air, but much much less than the speed of light.
     
    Last edited: Mar 17, 2007
  4. Mar 17, 2007 #3

    AlephZero

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    A typical speed (for conventional materials) would be a few km/sec or less. So the guy at the far end would have to wait a few million years before he felt anything.
     
  5. Mar 17, 2007 #4

    russ_watters

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    You mean a few million seconds. The sun is around 150 million km away. If the speed of sound in that material were 1km/sec, it would take 4.7 years. Of course, the material would have broken by then...
     
  6. Mar 17, 2007 #5

    AlephZero

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    Brain was doing free association between "astronomy" and "light years", while fingers typed "years" not "seconds".

    Units, schmunitz! :smile:
     
  7. Mar 17, 2007 #6
    Ok, say both gentlemen decided to pull their side of the rope for 100 km. Before the energy from both sides reaches a meeting point, is the rope temporarily 200 km longer? Or say the two got on rocket ships and blasted off at Mach 2. Would they ever feel the effects of the others pull? I guess the rope would just break after a while.
     
  8. Mar 17, 2007 #7

    russ_watters

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    Yes...
    No.
     
  9. Mar 17, 2007 #8
    Can you explain further?
     
  10. Mar 17, 2007 #9
    But what if the rope was made out of a completely uncompressable material. Like what if the rope was actually just a huge metal rod that was theoreticaly unable to be compressed woudn't that mean that he would feel it instantaneously. Because the only way for it to go would be to him wouldnt it or am i wrong?

    I also think that with that rope he would feel it almost instantanously due to the fact that you are transfering information but in all actuality your really not sending anything are you?
     
    Last edited: Mar 17, 2007
  11. Mar 17, 2007 #10

    russ_watters

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    I'm not sure what else there is to say - if you pull on one end and the other doesn't move, of course you have lengthened the rope. And if you are moving faster than a wave, of course the wave never catches you.
     
  12. Mar 17, 2007 #11

    russ_watters

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    What we are talking about is why such a thing does not exist. Molecules are held together by electromagnetic forces, which propagate at the speed of light, so the speed of sound in a material can never exceed that.
     
  13. Mar 17, 2007 #12
    Wow how weird... I was actually thinking about this about two days ago, but was too scared that it was a stupid question to post it here. Apparently it was a very valid inquiry.

    If a steel rod stretching one lightyear was to be viewed by on observer was pressed on one end to make the rod move a noticeable amount (to the observer), the rod would look as if it was being compressed? Or is there some concepts of relativity that are being left out?
     
  14. Mar 17, 2007 #13

    Mk

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    You can't normally see sound moving in a steel rod, but, same idea.
     
  15. Mar 17, 2007 #14

    russ_watters

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    You don't need relativity for this - that's just what sound is. Sound is compression waves.
     
  16. Mar 18, 2007 #15
    For an observer in the same reference frame equidistant from both ends of the rod it would look as though it had been compressed at one end until the pressure wave reached the other side, which would take quite a while for a one lightyear long rod.

    What would happen if one end of the rod was given a push so that it was going faster than the speed of the propagation of the pressure wave through the rod (is this even possible?) ie. the end of the rod is travelling towards the other end faster than the pressure wave which would relocate the other end. How far could you compress the rod in this case?
     
  17. Mar 18, 2007 #16

    DaveC426913

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    Make no mistake. The compression is not an illusion - the rod really would compress and the wave of compression would travel the length of the rod.

    The rod's maximum stiffness would be manifest in that the speed of sound (speed of compression) would be very near the speed of light - but no higher.

    This is the upper limit on stiffness of any material. It is also why there is no such thing - even theoretically - as a perfectly rigid material.
     
  18. Mar 18, 2007 #17
    Well do what a lot of scientist do pretend it exist. What if this mystical magical perfectly rigid material did exist. what would happen if there was such a thing then what would happen i think thats what the guy wants to know.

    Honestly i don't know what would happen i would definitely think that it would travel almost faster than the speed of light because every action has an equal and opposite reaction its almost bending one law while it is keeping to conservation of energy.
     
  19. Mar 18, 2007 #18
    You can't build an argument from false premises. You can certainly approximate- but not if the thing you're leaving out of the model is the very thing you wish to prove.
     
  20. Mar 19, 2007 #19

    DaveC426913

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    Don't misunderstand. It's not simply that it's "impossible to build something that rigid" - the fact is, something being perfectly rigid would actually defy special relativity. It can't exist.

    To pretend a perfectly rigid material exists is to free yourself from the shackles of generally-accepted science. You may, with abandon, postulate that the rod will spontaneously turn into a ghost or a faerie.
     
    Last edited: Mar 19, 2007
  21. Mar 26, 2007 #20
    well yes but if all your trying to do is answer his question we can pretend that it exist as long as he knows that the only way his hypothesis would work is if this incompressible rod did exist. Is it stupid to say. yes. but this the way to answer the question. So we answer the question and get a little bit of fun out of it too.

    its like when you teach kids physics when they are only a junior in high school. We tell them that there is this thing that instantaneously accelerates to 45 meters per second. Now does this happen no but for the purpose of not having to use calculus we use it. Is it impossible to have instant acceleration of course but we still use it in equations and it seems to work just fine as long as the kids now that there is no such thing as it.

    ....mind you i am only a freshmen in college and i call them kids lol.....i am the child here
     
    Last edited: Mar 26, 2007
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