When a proton is traveling at 0.80c, what is the ratio of its kinetic energy to its rest energy?
A) 0.67
B) 1.2
C) 0.80
D) 0.60
E) 1.7

Question

Quizplus · Accepted Answer

The kinetic energy of a proton traveling at 0.80c is given by:$$K = (\gamma - 1)mc^2$$where $\gamma$ is the Lorentz factor, $m$ is the rest mass of the proton, and $c$ is the speed of light.The Lorentz factor is given by:$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$where $v$ is the velocity of the proton.Substituting the given values into these equations, we get:$$\gamma = \frac{1}{\sqrt{1 - 0.80^2}} = 1.67$$$$K = (1.67 - 1)mc^2 = 0.67mc^2$$Therefore, the ratio of the kinetic energy to the rest energy is:$$\frac{K}{mc^2} = 0.67$$

When a Proton Is Traveling at 0