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Equation verification

  1. Aug 4, 2010 #1
    so we have total energy of partical ->E


    1)E=γpmc2=E0+K=Rest energy+ kinetic energy
    the second line correct?

    2) E2-(pc)2=E0
    so P= mv or p=γpmv

    im sure that we are suppose to use p=γpmv but not sure some one verify pls
  2. jcsd
  3. Aug 5, 2010 #2


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    I can't quite understand 2).

    However for 1), if you expand p in a power series in (v/c)2, the first two terms are what you are showing. The higher order terms matter when v/c -> 1.
  4. Aug 7, 2010 #3
    Nope, the second line is not correct. mv2 is the newtonian expression for kinetic energy (KE).
    You can obtain the correct relativistic expression for KE from:


    E=γmc2=E0+KE = Rest energy+ kinetic energy

    KE = E-E0 = γmc2-mc2 = mc2(γ-1)

    You should be using p = γmv = mv(1-(v/c)2)-1/2 so that



    E2=(mc2)2+(γmvc) 2
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