Answer
The rest energy is $9.0\times 10^{13}~J$
The kinetic energy is $6.0\times 10^{13}~J$
The total energy is $1.50\times 10^{14}~J$
Work Step by Step
We can find the rest energy:
$E = mc^2$
$E = (1.0\times 10^{-3}~kg)(3.0\times 10^8~m/s)^2$
$E = 9.0\times 10^{13}~J$
The rest energy is $9.0\times 10^{13}~J$
We can find $\gamma$:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{1-\frac{(0.80~c)^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{1-0.64}}$
$\gamma = \frac{1}{\sqrt{0.36}}$
$\gamma = 1.67$
We can find the kinetic energy:
$K = (\gamma -1)~mc^2$
$K = (1.67 -1) (9.0\times 10^{13}~J)$
$K = 6.0\times 10^{13}~J$
The kinetic energy is $6.0\times 10^{13}~J$
We can find the total energy:
$E_{total} = 9.0\times 10^{13}~J+6.0\times 10^{13}~J$
$E_{total} = 1.50\times 10^{14}~J$
The total energy is $1.50\times 10^{14}~J$
