Question

What is the kinetic energy of a

proton (proper mass is m0 = 1.67 x 10^-27 kg) travelling at 40 % of the speed

of light?

Answer 1

$\gamma=\frac{1}{\sqrt{1-(v/c)^2}}=\frac{1}{\sqrt{1-(0.4c/c)^2}}=\frac{1}{\sqrt{1-0.16}}=1.091$

$E_k=(\gamma-1)mc^2=(1.091-1)\times1.67\times10^{-27}kg\times(2.998\times10^8\frac{m}{s})^2=1.37\times10^{-11}J$

Answer: $1.37\times10^{-11}J$