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Homework Help: Special relativity (A.P. French 7.5)

  1. Mar 24, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle of rest mass m and velocity v collides elastically with a stationary particle of rest mass M. Express the recoil and scattering angels in terms of the corresponding angles in the zero-momentum system. Show that your answers reduce to the non-relativistic ones if v<<c

    2. Relevant equations

    I think I have to show that (mc^2)/(1-(v/c)^2)^1/2 reduces to .5mv^2 by using the binomial theorem when v<<c. since momentum is related to kinetic energy.

    3. The attempt at a solution

    (not clear how to do it though) Please help me!
  2. jcsd
  3. Mar 24, 2012 #2


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    That's not what the question is asking you to do. In the center-of-mass system, say the particle with mass m scatters at an angle of ##\theta'##. What happens to the other particle? Now what does this collision look like as seen in the lab frame? What angle ##\theta## in the lab frame corresponds to the angle ##\theta'## in the COM frame?

    Once you figure that out, you're supposed to show it reduces to the non-relativistic equivalents when v<<c.
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