What happens to the kinetic energy of a speedy proton when its relativistic mass doubles?
A) It must increase, but it is impossible to say by how much.
B) It less than doubles.
C) It more than doubles.
D) It doubles.

Question

Quizplus · Accepted Answer

The kinetic energy of a relativistic particle, such as a proton moving at a significant fraction of the speed of light, increases more than proportionally to its relativistic mass due to the relativistic formula for kinetic energy, $KE = (\gamma - 1)mc^2$, where $\gamma$ is the Lorentz factor, $m$ is the rest mass, and $c$ is the speed of light. As the relativistic mass (which includes the rest mass and the mass equivalent of the kinetic energy) doubles, the increase in kinetic energy is more than double due to the nonlinear relationship introduced by the Lorentz factor $\gamma$.

What Happens to the Kinetic Energy of a Speedy Proton