State the rest energy formula.

State the total relativistic energy formula for a massive particle.

State the relativistic kinetic energy formula.

A particle has rest energy \(2.00\,\mathrm{MeV}\) and \(\gamma=3.00\). Find its total energy.

A particle has rest energy \(2.00\,\mathrm{MeV}\) and \(\gamma=3.00\). Find its kinetic energy.

An electron has rest energy \(0.511\,\mathrm{MeV}\). Find its rest energy in joules using \(1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm J\).

A proton with rest energy \(938\,\mathrm{MeV}\) moves at \(0.800c\). Find its total energy.

For the proton in the previous question, find its kinetic energy.

State the invariant energy-momentum relation.

A particle has \(pc=4.00\,\mathrm{GeV}\) and rest energy \(3.00\,\mathrm{GeV}\). Find its total energy.

A particle has kinetic energy equal to its rest energy. Find \(\gamma\) and the speed.

A photon has energy \(2.50\,\mathrm{eV}\). Find its momentum in \(\mathrm{eV}\,c^{-1}\).

A mass \(1.00\,\mathrm g\) is fully converted to energy. Find the energy released.

An electron has kinetic energy \(0.511\,\mathrm{MeV}\). Find \(\gamma\) and speed.

Explain why adding work to a particle near \(c\) does not make it exceed \(c\).

Derive \(K=(\gamma-1)mc^2\) from total and rest energy.

Show that \(E=pc\) for a massless particle follows from the energy-momentum relation.

Show that the energy-momentum relation gives \(E=mc^2\) for a particle at rest.

Why must energy and momentum both be conserved in relativistic collisions?

Use the low-speed expansion of \(\gamma\) to recover \(K\approx\frac12mv^2\).