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Special Relativity Forces and Energy

  1. Oct 22, 2016 #1
    1. The problem statement, all variables and given/known data
    Hi, I have this problem:

    For motion under a pure (rest mass preserving) inverse square law force f = −αr/r3 , where α is a constant, derive the energy equation γmc2 − α/r = constant.

    2. Relevant equations
    E = γmc2
    dE/dt = f.u for a pure force

    3. The attempt at a solution
    I start by saying:

    dE/dt = f.u = f.dr/dt

    Next, I know f is independent of time, so I can just integrate this to get:

    E = f.r +constant

    So then you get:

    γmc2 = -α/r + constant

    Which is painfully close to the result I'm meant to get but out by a minus sign. I don't know if I've made an error here or if the question is erroneous.

    Thanks for any help.
     
  2. jcsd
  3. Oct 24, 2016 #2
    Looks like there's some symbol-related confusion here.
    You have 2 different variables both named "E".
     
  4. Oct 24, 2016 #3
    Really? I don't understand how that's the case, they're both the particle's energy.

    edit - I actually get something viable by considering dE/dt = grad(E) dot dr/dt, since r is a function of time and I forgot to chain rule it.
     
    Last edited: Oct 24, 2016
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