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Questions regarding relativistic momentum

  1. Dec 11, 2011 #1

    nos

    User Avatar

    Hi everyone,

    I found a derivation for relativistic momentum on this page:
    http://en.wikibooks.org/wiki/Special_Relativity/Dynamics

    I understand it all the way through, except the point where they have come to this equation.

    m[itex]_{red} = [/itex][itex]\frac{m_{blue}}{\sqrt{1-(\frac{u(x,r)}{c})^{2}}}[/itex]

    Where(as I understand correctly) mblue is the mass according to the frame moving at the same x-velocity as the blue ball and where mred is the mass of the red ball according to the frame moving with the same x-velocity as the blue ball.

    Then they go to:

    M =[itex]\frac{m_{0}}{\sqrt{1-(\frac{u}{c})^{2}}}[/itex]

    Where u is now the relative velocity of the red ball for the moving frame.
    But that is what I don't understand. How can they suddenly ignore the relativistic effects of the y-velocities? The first equation gives the mass of red ball in terms of the relative x-velocity of the red ball. Then how do they get to relativistic mass in terms of the relative velocity u? Because ux,red is only the x component velocity and ured has both a x-component and y-component.

    This is my hypothesis:

    They let both uy,red and uy, blue approach zero. So that the mass of the blue ball will correspond to the rest mass and that the relativistic effects of the y-velocities will cancel.

    Thank you.
     
    Last edited: Dec 11, 2011
  2. jcsd
  3. Dec 11, 2011 #2

    Dale

    Staff: Mentor

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