Question

a proton with rest mass of 1.6 x10^-27 kg moving in accelerator with a speed of 0.6c . its total energy is

Answer 1

Energy can be calculated using the mass-energy formula: $E=mc^2$.

However, we need to use the relativistic formula, because the speed is relative to that of light. Therefore, the formula is: $E = \alpha mc^2$. Where $\alpha$ is the Lorentz factor of the relativistic formula.

$\alpha =\frac{1}{\sqrt{1-\frac{v^2}{c^2} } }$.

Here, the velocity is 0.6c. Therefore, $\alpha =\frac{1}{\sqrt{1-\frac{(0.6c)^2}{c^2} } }$.

$\alpha =\frac{1}{\sqrt{1-\frac{0.36c^2}{c^2} } }$.

$\alpha =\frac{1}{\sqrt{1-0.36} } \\\alpha =\frac{1}{\sqrt{0.64} } \\\alpha =1.25$.

Therefore, $E=1.25*1.6*10^{-27}*(3*10^8)^2=1.876151435613099938*10^{-10}J$