일반물리학 2 — Relativity: Problem 6

6 (a) If m is a particle's mass, p is its momentum magnitude, and K is its kinetic energy, show that \[ m = \frac{(pc)^2 - K^2}{2Kc^2} \] (b) For low particle speeds, show that the right side of the equation reduces to m. (c) If a particle has \( K = 55.0 \text{ MeV} \) when \( p = 140 \text{ MeV/c} \), what is the ratio \( m/m_e \) of its mass to the electron mass?