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About the mass-energy relation

  1. Mar 31, 2010 #1
    I see how the premises

    [tex]

    p = \gamma m v

    [/tex]

    [tex]

    F = \frac {dp}{dt}

    [/tex]

    and

    [tex]


    W= \int F dx

    [/tex]

    lead to

    [tex]

    dW = mc^2 d \gamma

    [/tex]

    and therefore

    [tex]

    W = \gamma mc^2 + k

    [/tex]

    where m is the rest mass and k is a constant of integration. But why do we conclude that k=0?
     
  2. jcsd
  3. Mar 31, 2010 #2

    Doc Al

    User Avatar

    Staff: Mentor

    That constant won't equal 0. (The work done equals the KE, not the total energy.) Assume you start from rest and integrate to speed v.
     
  4. Mar 31, 2010 #3
    I get

    [tex]

    W = \gamma mc^2 - mc ^2 = ( \gamma - 1 ) mc^2


    [/tex]

    so

    [tex]

    k = -mc^2 \neq 0

    [/tex]

    Since W(v=0) = 0 this is indeed the kinetic energy and not the total energy. Thanks, Doc Al.
     
  5. Apr 1, 2010 #4
    Follow-up: Am I to conclude that the constant of integration here represents the (negative) "rest energy" of the object, or is there a better way to arrive at that relationship?
     
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