- #1
RedDelicious
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Homework Statement
This problem comes from an intermediate step in the textbook's derivation of relativistic energy. It states that
E_k\:=\:\int _0^u\frac{d\left(\gamma mu\right)}{dt}dx
then leaves the following intermediate calculation as an exercise to the reader:
Show that
d\left(\gamma mu\right)=\frac{m}{\left(1-\frac{u^2}{c^2}\right)^{\frac{3}{2}}\:}du
Homework Equations
Where
\gamma \:=\:\frac{1}{\sqrt{1-\frac{u^2}{c^2}}}
The Attempt at a Solution
:[/B]
I tried using the product rule
\frac{d}{du}\left(\gamma mu\right)=m\:\frac{d}{du}\left(\gamma u\right)=\:m\left(\gamma 'u+u'\gamma \right)=\:m\left[u\:\frac{d}{du}\left(1-\frac{u^2}{c^2}\right)^{-\frac{1}{2}}+\left(1-\frac{u^2}{c^2}\right)^{-\frac{1}{2}}\right]
=m\left[\frac{u^2}{c^2}\left(1-\frac{u^2}{c^2}\right)^{-\frac{3}{2}}+\left(1+\frac{u^2}{c^2}\right)^{-\frac{1}{2}}\right]
Anyone know what I'm doing wrong?
