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Force in different frames

  1. May 9, 2012 #1
    A point mass has a force on it in its rest frame (F). Now go to a frame moving in the +x direction (F'). EM book claims the forces can be related like this:
    [tex]
    f'_{x'}=f_{x}\\f'_{y'}=\frac{f_{y}}{\gamma}\\f'_{z'}=\frac{f_{z}}{\gamma}
    [/tex]
    I would like to be able to see this with four vectors, but am having trouble. Four vectors have arrows. Tau is proper time.
    [tex]
    \vec{f}=\frac{dp}{d\tau}=\Gamma(\frac{dp_{x}}{dt},\frac{dp_{y}}{dt},\frac{dp_{z}}{dx},\frac{dE}{dt} \frac{1}{c})=(f_{x},f_{y},f_{z},\frac{dE}{dt} \frac{1}{c})\\
    \vec{f'}=\frac{dp'}{d\tau}=\gamma(f'_{x'},f'_{y'},f'_{z'},\frac{dE}{dt'} \frac{1}{c})
    [/tex]
    In this case, big gamma=1 because there is no velocity in the rest frame at the time of interest.
    Transform
    [tex]
    \vec{f'}=(\gamma f_{x} - \gamma \beta \frac{dE}{dt} \frac{1}{c},f_{y},f_{z},...)
    [/tex]
    I can see for y and z, but not for x.
     
  2. jcsd
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