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Just a quick question on the derivation of energy

  1. Sep 25, 2011 #1
    I've been reading through a book on relativity and I came across this

    [itex]\mathcal{E}=p . v - L[/itex]
    [itex]\mathcal{E} =\frac{m v}{\sqrt{1-\frac{v^2}{c^2}}}.v + m c^2\sqrt{1-\frac{v^2}{c^2}}[/itex]

    I know this part well enough but then the book arrives at

    [itex]\mathcal{E}=\frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]

    How did that happen?
    All I can get is this

    [itex]\mathcal{E} =\frac{m v^2}{\sqrt{1-\frac{v^2}{c^2}}} + m c^2\sqrt{1-\frac{v^2}{c^2}}\neq \frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]

    What am I doing wrong here?

    Thanks in advance
     
  2. jcsd
  3. Sep 25, 2011 #2
    Multiply the second term by
    [tex]\frac{\sqrt{1-\frac{v^2}{c^2}}}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]
    and I think you'll find that it works.
     
  4. Sep 25, 2011 #3
    Ah, thanks Parlyne
    I feel like a tool now :L
     
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