A proton in a certain particle accelerator has a kinetic ene

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 Times 10^8 m/s. mproton = 1.67 Times 10^27 kg)

Solution

Kinetic energy measured by physicist working with the acclerator K= rest energy of proton

Since both particle and physicist are in same reference frame.

So, K = mc ²

Where m = rest mass of proton = 1.67 x10 ^-27 kg

Therefore K = (1.67 x10 ^-27 ) (3 x10 ⁸ ) ²

                 = 1.50 x10 ^-10 J

Total energy E = kinetic energy + rest energy

                      = K + mc ²

                      = (1.503 x10 ^-10 J)+(1.503 x10 ^-10 J)

                      = 3.01 x10 ^-10 J