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Special Relativity GRE question (Where is my method flawed?)

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data
    http://grephysics.net/ans/9277/70

    I'm not interested in how you get the right answer, I'm really just curious if somebody could show me where my thought process was flawed.

    Total Energy = E = 100mc^2
    Rest Energy = Mc^2
    Total Energy = Kinetic Energy + Rest Energy
    100mc^2 = p^2/2m + mc^2
    99mc^2 = p^2/2m
    198(mc)^2 = p^2
    sqrt(198)mc = P
    and yet the correct answer is
    10^4(mc)

    where is my method flawed?
     
  2. jcsd
  3. Sep 5, 2013 #2

    phyzguy

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    The formula KE = p^2/(2m) and TE = p^2/(2m) + mc^2 are non-relativistic approximations, and are only valid when pc << mc^2. They come about from taking the full relativistic equation and expanding the square root, keeping only the leading term, as follows:
    [tex] E^2 = p^2 c^2 + m^2 c^4[/tex]
    [tex] E = \sqrt{p^2 c^2 + m^2 c^4} = mc^2 \sqrt{1+\frac{p^2 c^2}{m^2 c^4}}[/tex]
    [tex] E \approx mc^2 (1+\frac{p^2 c^2}{2m^2 c^4}) = mc^2 + \frac{p^2}{2m}[/tex]
     
  4. Sep 5, 2013 #3
     
  5. Sep 5, 2013 #4
     
  6. Sep 6, 2013 #5

    phyzguy

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    Science Advisor

     
    Last edited: Sep 6, 2013
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