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Relativistic energy/momentum

  1. Sep 11, 2012 #1

    ElijahRockers

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    Gold Member

    1. The problem statement, all variables and given/known data

    An electron has a speed of .75c. Find the speed of a proton that has:

    a) The same kinetic energy as the electron

    b) The same momentum as the electron

    2. Relevant equations

    γmc2 = K + mc2

    P = γmv

    3. The attempt at a solution

    PART A:

    me (electron mass) = .511MeV/c2
    Ve (electron velocity) = .75c

    Ke (KE of electron) = (γ-1)mec2
    Ke = 1.286(.511) = .657MeV

    mp (proton mass) = 938.27MeV/c2
    Vp (proton velocity) = ?

    So to find Vp:

    .657MeV = (γ-1)(938.27MeV) and after simplification, vp = .0374c

    Answer is not in the back, so I can't be sure if I did this correctly.

    PART B: (I used the kg representation of mass for this part, because I am confused by the eV units.)

    me (electron mass) = 9.1E-31 kg
    ve = .75c

    Pe (electron momentum) = γmeve
    Pe = 4.68E-22 kg*m/s

    4.68E-22 kg*m/s = γmpvp

    I simplified it down to:

    2.8E5 = Vp - Vp3/c2

    but this looks like a cubic function. I get the feeling that I am doing something wrong.

    EDIT: Ok I went back and tried it, this time without plugging any values in, and I arrived at

    [itex] V_p = \sqrt{P_{e}^{2} (m_{p}^{2} + \frac{P_{e}^{2}}{c^2})^{-1}} [/itex] and I think that is right. I came up with V_p = 280,239.5 m/s
     
    Last edited: Sep 11, 2012
  2. jcsd
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