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Nail and cylinder problem in SR

  1. Oct 13, 2006 #1

    This may look like a homework, but it is rather a refresher for my hobby-time.
    I just found a nice collection of exercices: Test problems in mechanics and special relativity.

    The exercise 2.2 is funny:

    Sure this is no flaw of SR !!
    What's the explanation?
    What are the interresting lessons from this exercice?

    Last edited: Nov 22, 2011
  2. jcsd
  3. Oct 13, 2006 #2

    Doc Al

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    It wouldn't be much of a refresher if we didn't let you solve it for yourself, right? Hint: Do all parts of the nail stop instantly when the hat hits the cylinder?
  4. Oct 13, 2006 #3
    Doc Al,

    For me, the easy side of the question is after the nail head and the cylinder get in contact.
    It is clear that the compression wave cannot speed faster than light and causality therefore makes the answer easy.

    What is less clear is the precise time when the nail and the cylinder just get into contact.:wink:

    Lets assume the cylinder is equipped with a detector at both ends.
    One detects the contact of the head of the nail with the cylinder.
    The other detects the perforation at the other end.
    These detectors send a signal to an "AND gate" or "coïncidence gate" at the middle of the cylinder.
    Will the "coïncidence gate" trigger?

    Last edited: Oct 13, 2006
  5. Oct 13, 2006 #4

    Doc Al

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    According to the nail frame, the tip hits the paper before the head hits the cylinder.
    According to the cylinder frame, the head hits first.

    Either way, no coincidence gate triggers.
  6. Oct 13, 2006 #5
    Doc Al,

    I was not sure either. That's why I put the winking smile besides.
    That's why I equipped the cylinder with two detectors.

    Is this not surprising?

  7. Oct 13, 2006 #6
    What is a compression wave? :confused:
  8. Oct 13, 2006 #7

    Doc Al

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    Not to me. What would be surprising is if one frame said coincidence occurs while the other didn't! :wink:
  9. Oct 13, 2006 #8

    Just like sound: The initial compression propagates through the medium.

  10. Oct 13, 2006 #9


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    There can't be any truly rigid objects in relativity--when the nail head hits the cylinder and rapidly accelerates to a state of rest relative to the cylinder, the rest of the nail keeps moving inertially as if nothing had happened until a compression wave travelling through the nail at the speed of sound reaches each part and accelerates it to a state of rest relative to the head. That's why the point of the nail will still be predicted to reach the end of the cylinder in the frame where the nail's length appears less than the cylinder, because the compression wave from the head won't reach the tip in time to stop it from hitting the back.
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