Problem 3. The following may help, if either the formula or the phenomenon
is forgotten. One may solve it for $\gamma$, $\gamma - 1$, $1 - v/c$, or whatever else one
chooses.
$\gamma^2 - 1 = \frac{\gamma^2 v^2}{c^2}$
The proton's mass is 940 MeV/c², and the Large Hadron Collider accelerates
protons to energy of (say) five million MeV. What are the speed and mo-
mentum (magnitude) of such a proton? (Use c and MeV/c as your units; it
simplifies your calculations.)
