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Modern Physics Question

  1. Feb 10, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that [tex]d(\gamma mu)=m(1- \frac{u^2}{c^2})^{-3/2} du[/tex]

    2. Relevant equations

    It is known that is
    [tex]\gamma=\frac{1}{\sqrt{{1- \frac{u^2}{c^2}}}}[/tex]

    3. The attempt at a solution

    The question stated in part 1 is the precise question given in the textbook.

    I'm not sure how to proceed here. I believe it's asking you to take the derivative using the product rule. I even wondered if it was a type and du was supposed to be on the left hand side.
     
  2. jcsd
  3. Feb 10, 2008 #2

    CompuChip

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    Science Advisor
    Homework Helper

    It's not a typo,
    [tex]d(\gamma mu)=m(1- \frac{u^2}{c^2})^{-3/2} du[/tex]
    is just physicists' notation for
    [tex]\frac{d}{du} (\gamma mu)=m(1- \frac{u^2}{c^2})^{-3/2} [/tex]
    (if you want, consider du as an infinitesimal quantity, dividing by it gives you a differential quotient aka derivative on the left hand side).
    So indeed, you just plug in the expression for [itex]\gamma[/itex] you gave and differentiate w.r.t. u; then simplify to get the requested result
     
  4. Feb 10, 2008 #3

    pam

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    What text are you using?
    [tex]u^2[/tex] stands for [tex]\vec u}\cdot{\vec u}[/tex].
    This leads to an additional term in the derivative.
     
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