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Relativistic Momentum and Energy

  1. Aug 18, 2012 #1
    Hello guys,

    The question is: What is the momentum, in conventional SI units, of a proton of momentum 685 MeVc-1?

    So, I tried two methods which yielded slightly different answers, both proximate to the actual answer (3.66 x 10-19)


    What I first tried to do was to rearrange: ρ=γm0v

    To find the particles velocity and then multiply it by the proton's rest mass in kg. I got 2.995 x 10-19 kgms-1

    The second method, which gave me the result 3.45 x 10-19 kgms-1 was the following:

    From: E2 = (m0)2c4 + p2c2 I got a value for total energy. I then subtracted the rest energy from that and I got a value for KE.

    I equalled that to p2/2m and solved for p (using m in kg and the energy converted from MeV to J)

    Are my answers wrong? The book says 3.66 x 10-19 and I simply can't get that!

    Thanks in advance!
     
  2. jcsd
  3. Aug 18, 2012 #2
    the book answer is correct.

    a question for you : What does MeVc-1 mean?

    can you do a dimension analysis on MeVc-1
     
  4. Aug 18, 2012 #3
    Oh, got it! Thanks! I got the number!
     
    Last edited: Aug 18, 2012
  5. Aug 18, 2012 #4
    Oh, and, if you don't mind, could you (or anyone else) help me with the following problem please?

    A proton initially at rest finds itself in a region of uniform electric field of magnitude 5.0 x 106 Vm-1. The electric field accelerates the proton for a distance of 1 km.

    Find the kinetic energy of the proton.

    So, what I did was the following:

    KE = q * E * s

    I then converted the result from J to MeV. I, however, get 5000 MeV and the book gets 500 MeV. Is my line of thought incorrect?

    Thanks once again!
     
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