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I Invariance of elastic potential energy

  1. Jun 21, 2017 #1
    At non-relativistic speeds is the elastic potential energy of a compressed spring frame-invariant? That is, would all reference frames agree on how much elastic potential energy is stored in the spring?
     
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  3. Jun 21, 2017 #2

    dextercioby

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    Rather than asking this question and waiting for an answer, can you state your opinion first? And what mathematical formulas would you use to support it?
     
    Last edited: Jun 21, 2017
  4. Jun 21, 2017 #3
    It is my opinion that at non-relativistic speeds, all reference frames would agree on the elastic potential energy of the spring. I assert this because the elastic potential energy is given by: 1/2 k (delta l) squared, where k is the spring constant and delta I is the change in length of the spring. Since k is a constant, all reference frames will agree on this value, and all reference frames would agree on delta l or the change in the length of the spring. But am I missing something?
     
  5. Jun 21, 2017 #4

    dextercioby

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    No, you are not missing anything. Since time is absolute, the length between two points is an invariant when hypothetically measured, thus this purely potential energy k delta l^2 should be invariant under Galilean relativity.
     
  6. Jun 21, 2017 #5

    pervect

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    I'd agree with this, though as it stands it's a statement about non-relativistic physics in the relativity forum. Are you interested in a discussion of the relativistic case at all? My thoughts on this would be that in the relativistic case, we represent the compressed spring by its stress energy tensor ##T^{ab}##. We generally don't try to separate out "potential energy" from "kinetic energy", in the relativistic case we concentrate on how ##T^{ab}## transforms via the tensor transformation rules.

    There is a lot more that could be said and maybe should be said, but it's not clear that you're interested in the relativistic case - or what your background knowledge of tensors might be. I will say that I don't think there is a good way to treat the issue of a relativistic compressed spring without tensors (in particular the stress-energy tensor).

    [add]I'll add that I believe Rindler has a treatment of the relativistically moving compressed spring (I think the text uses a rod, which is makes no difference to the analysis) which uses the stress-energy tensor in "Essential Relativity".
     
  7. Jun 21, 2017 #6
    Thank you for your responses. Maybe I should have posted this in the general physics forum because I am not interested in the relativistic case.
     
  8. Jun 21, 2017 #7

    Nugatory

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    Note: this thread has been moved to General Physics.
     
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