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Homework Help: Do I use Relativistic Energy here?

  1. Oct 13, 2008 #1
    1. The problem statement, all variables and given/known data

    What is the speed of a proton when its kinetic energy is equal to its rest energy?

    2. Relevant equations

    [tex]K = mc^2(\gamma - 1)[/tex]
    [tex]E_0 = mc^2[/tex]
    [tex]\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

    3. The attempt at a solution

    [tex]K = E_0[/tex]
    [tex]mc^2(\gamma - 1) = mc^2[/tex]
    [tex]\gamma = 2[/tex]
    [tex]\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = 2[/tex]
    [tex]0.5 = \sqrt{1 - \frac{v^2}{c^2}}[/tex]
    [tex]0.5^2 = 1 - \frac{v^2}{c^2}[/tex]
    [tex]c^2 \sqrt{1 - 0.25} = v^2[/tex]
    [tex]v = c \sqrt{0.75} = 0.866 c[/tex]

    Am I right to use relativistic energy? Have I come to the correct answer? Please advise.
  2. jcsd
  3. Oct 14, 2008 #2
    correct (for any massive particle, not just the proton)
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