1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted