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Relativistic kinetic energy and momentum

  1. Jan 28, 2017 #1
    1. The problem statement, all variables and given/known data
    A proton has a speed of 0.2c. Find the speed of an electron that has (a) the same kinetic energy as the proton, and (b) the same momentum as the proton.

    2. Relevant equations
    K=ϒmc^2-mc^2

    3. The attempt at a solution
    upload_2017-1-28_14-48-6.png

    This is what I did for the same kinetic energy part, but I would end up with a negative under my square root. I found the formula in my notes, I'm not really sure what to do but I tried something. Can anyone offer me some guidance? I have not attempted the momentum part yet
     
  2. jcsd
  3. Jan 28, 2017 #2

    TSny

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    You are OK all the way up to your final expression for v. You made a minor mistake in solving for v. Check your work to see if you can find the mistake.

    Also, you can rearrange ##\frac{1}{\frac{K+mc^2}{mc^2}}## to a simpler fraction.
     
  4. Jan 28, 2017 #3
    It will be multiplied by a negative c ?
     
  5. Jan 28, 2017 #4

    TSny

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    Sorry, but I'm not sure what you are saying here.
     
  6. Jan 28, 2017 #5
    My mistake was that when I solved for v I forgot the negative sign
     
  7. Jan 28, 2017 #6

    TSny

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    Yes. Good.
     
  8. Jan 28, 2017 #7
    This is what I did for when they have the same momentum
    upload_2017-1-28_18-1-41.png
    It just seems weird that it gives me the speed of light I feel like that's probably wrong.
     
  9. Jan 28, 2017 #8

    TSny

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    Looks good, but if your calculator is accurate enough, you should find that the answer for v is slightly less than c.
     
  10. Jan 28, 2017 #9
    Ok, it was a bit less but I rounded it. I could right the exact answer
     
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