A muon has rest energy 105 MeV. What is a muon's kinetic energy when its speed is 0.95c?

Question

Quizplus · Accepted Answer

The kinetic energy of a particle is given by 
K = (gamma - 1)mc^2 
where gamma is the Lorentz factor and m is the rest mass of the particle. 
Gamma can be calculated as 
gamma = 1/sqrt(1-(v/c)^2) 
where v is the velocity of the particle and c is the speed of light. 
Substituting the given values, we get 
gamma = 1/sqrt(1-(0.95)^2) = 3.2 
K = (gamma - 1)mc^2 = (3.2-1) * 105 MeV = 231 MeV 
Therefore, the answer is (C) 231 MeV.

A Muon Has Rest Energy 105 MeV