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S=vt in special relativity

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=45796&stc=1&d=1333329309.jpg


    2. Relevant equations



    3. The attempt at a solution
    Can I do it like this:
    [itex]F=γma[/itex]
    [itex]F=γm\frac{dv}{dt}[/itex]
    [itex]F=γm\frac{dv}{ds}\frac{ds}{dt}[/itex]
    [itex]v\frac{dv}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{F ds}{m}[/itex]

    The finial answer will becom
    v=[itex]\frac{\sqrt{2c^2mFx-Fx}}{mc}[/itex]

    What's wrong?
     

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    Last edited: Apr 1, 2012
  2. jcsd
  3. Apr 1, 2012 #2

    K^2

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    [tex]F=\frac{dp}{dt}[/tex]
    [tex]F=\frac{d}{dt}(\gamma mv)[/tex]
    [tex]F=\gamma m \frac{dv}{dt} + mv\frac{d\gamma}{dt}[/tex]

    Because gamma is a function of v and varies with time, you run into problems. You should still be able to solve it this way if you take the extra term into account, but it's a lot more work than energy conservation method.
     
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