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Homework Help: Kinetic energy, special relativity

  1. Aug 21, 2010 #1

    fluidistic

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

    Calculate the kinetic energy of an electron whose momentum is 2MeV/c.

    2. Relevant equations
    [tex]P=\gamma m_0 v =mv[/tex].
    [tex]E_K=(m-m_0)c^2[/tex].

    3. The attempt at a solution
    I'm told that [tex]\gamma m_0 v=\frac{2MeV}{c}[/tex].
    If only I had the mass at rest of the electron (it isn't given in the problem), I could calculate its velocity with the first formula I gave. Then I could calculate its mass (not its rest mass, its apparent mass or whatever it's called). And then I could apply the third formula and this would solve the problem. Am I right?
    So, should I look for the electron's rest mass in some book? Is there a missing data, or can I solve the problem without this info?
     
  2. jcsd
  3. Aug 21, 2010 #2
    You can do that. But you shouldn't have to look anything up. Do you know the relationship between [tex] \lambda[/tex] (the lorentz factor) and v? if so, solve for the rest mass. Similarly, you can find the relationship between [tex] m [/tex] and [tex] m_0 [/tex]. I hope that helps!
     
    Last edited: Aug 21, 2010
  4. Aug 21, 2010 #3

    fluidistic

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    I appreciate very much your help.
    What I know is [tex]\gamma =\frac{1}{\sqrt {1-\frac{v^2}{c^2}}}[/tex]. I don't know how to solve for the rest mass since v is unknown. I get [tex]m_0=\frac{P}{v}\sqrt {1-\frac{v^2}{c^2}}[/tex] where P and c are known but not v...
     
  5. Aug 21, 2010 #4
    ahh what was i thinking. you're right! you need to look up the rest mass. I'm really sorry, at a quick glance I thought this was just algebra.
     
  6. Aug 22, 2010 #5

    fluidistic

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    Ok thanks for your help. Problem solved!
     
  7. Aug 22, 2010 #6
    great!
     
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