In the laboratory frame an electron of mass moves along the axis with total energy MeV

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime · Relativistic dynamics and fields in flat spacetime

Relativity and Gravitation, Ch Relativistic momentum, energy and collisions

Problem

In the laboratory frame SS an electron of mass me=0.511 MeV/c2m_e = 0.511\ \mathrm{MeV}/c^2 moves along the +x+x axis with total energy E=2.000E = 2.000 MeV. It is a free particle: no fields act on it. The frame S′S' is in standard configuration with SS, moving at v=0.600cv = 0.600c along the common +x+x axis. ((a)) Find the magnitude of the electron's momentum in SS, in MeV/c\mathrm{MeV}/c. ((b)) The four-momentum P=(E/c, p⃗)\mathbf{P} = (E/c,\ \vec p) transforms exactly as any four-vector does. Find the electron's energy and xx-momentum in S′S'. ((c)) From your answer to (b) obtain the electron's speed in S′S' as a multiple of cc, and confirm it with the velocity transformation of Chapter 1.

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