Question

The kinetic energy of a particle is 42MeV. If the momentum is 110MeV/c, what is the particle's mass? (mass units are MeV/c^2)

Answer 1

The only way I could think to do this was to solve for the velocity it was traveling at, then plug that back into its other equations. So


\[ K=E-E_0 =\gamma mc^2-mc^2 = mc^2(\gamma-1)\]
\[p=\gamma mv \quad \longrightarrow m=\frac{p}{\gamma v}\]
\[ K= \big( \frac{p}{\gamma v} \big)c^2(\gamma -1)\]
\[ \frac{K}{pc^2}=\frac{(\gamma-1)}{\gamma v}\]
and I ended up with (for checking work)

\[v=\frac{2Kpc^2}{K^2+p^2c^2}\]

You have all those things - so if you keep c as c, you get the velocity as some fraction of c. Then you can plug that back into either the kinetic energy or the momentum and solve for the mass, which I found to be 123 MeV/c^2 (which is in the range of subatomic particles... :P)