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Finding relativistic force in terms of acceleration

  1. Oct 21, 2015 #1
    1. The problem statement, all variables and given/known data
    The instantaneous force F acting on a particle, as measured in frame S, is png.latex?F%20%3D%20%5Cfrac%7Bd%5Cvec%7Bp%7D%7D%7Bdt%7D.png
    Use the formula for the linear momentum ( D%3D%5Cfrac%7Bm%20%5Cvec%7Bu%7D%7D%7B%5Csqrt%7B1-%5Cfrac%7Bu%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%7D%7D.png ) in and the definition of the acceleration a to show that
    D%7D%7Bc%5E%7B2%7D%7Da_%7By%7D+%5Cfrac%7Bu_%7Bx%7Du_%7Bz%7D%7D%7Bc%5E%7B2%7D%7Da_%7Bz%7D%5D.png
    D%7Bc%5E%7B2%7D%7D%29a_%7By%7D+%5Cfrac%7Bu_%7By%7Du_%7Bz%7D%7D%7Bc%5E%7B2%7D%7Da_%7Bz%7D%5D.png
    s;%281-%5Cfrac%7Bu_%7Bz%7D%5E%7B2%7D+u_%7Bx%7D%5E%7B2%7D%7D%7Bc%5E%7B2%7D%7D%29a_%7Bz%7D%5D.png

    3. The attempt at a solution
    The professor said that this required use of programs such as mathematica in order ot solve, however, I can't figure out a way to solve this, I can derive the force transformation in to another inertial reference frame, but the equation needs to be in terms of acceleration in the S frame, not the S' frame. I just need to know where to start with this.
     
  2. jcsd
  3. Oct 21, 2015 #2

    Geofleur

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    It looks like you will need to treat ## \mathbf{u} ## and its magnitude as functions of ## t ## and take the time derivative of the expression given for ## \mathbf{p} ##.
     
  4. Oct 21, 2015 #3
    Is there anyway to do this without expressing u in terms of t? In the prevoud question I found the velocity transformation as follows:
    c%5E%7B2%7D%7D.gif
     
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