Einstein's Special Theory of Relativity Quesion

Quote:

Originally Posted by killasnake

I have no idea how to start this problem, We barely learned alittle part of this in class today but the teacher just said read the book and it is easy to undertand. :rolleyes: I read the book over and over but I don't know.... :confused:

$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$

I'm going to rewrite this as:

$m = m_0 \left ( 1 - \frac{v^2}{c^2} \right ) ^{-1/2}$

Now:

$dm = m_0 \cdot \frac{-1}{2} \left ( 1 - \frac{v^2}{c^2} \right ) ^{-3/2} \cdot \frac{-2v}{c^2} dv$

$dm = m_0 \frac{v}{c^2} \left ( 1 - \frac{v^2}{c^2} \right ) ^{-3/2} dv$

We have v = 0.8c and dv = 0.02c, so

$dm = m_0 \frac{0.8c}{c^2} \left ( 1 - \frac{(0.8c)^2}{c^2} \right ) ^{-3/2} \cdot 0.02c$

$dm = m_0(0.016) (1 - 0.64)^{-3/2}$

$dm = 0.074074m_0$

Now, we need this as a percentage increase in mass:

$\frac{dm}{m_0} \times 100$ %

= $\frac{0.074074m_0}{m_0} \times 100$ %

= $(0.074074) \times 100$ %

= 7.4074 %

-Dan