Two charged pions

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Particle Physics & Quantum Fields · Particles, interactions and experiment

Relativity and Gravitation, Ch Relativistic momentum, energy and collisions

Problem

Two charged pions, each of mass

m_\pi = 139.6\ \mathrm{MeV}/c^2

, move along the

x

axis of the laboratory frame

S

. Pion A has speed

0.800c

in the

+x

direction as measured in

S

. Pion B is observed from the frame

S'

, which is in standard configuration with

S

and moves at

v = 0.500c

along the common

+x

axis; in

S'

pion B has speed

0.600c

in the

+x'

direction. The pions are far apart and do not interact. ((a)) Find the speed of pion B in the laboratory frame

S

, as a multiple of

c

. ((b)) Hence find the invariant mass of the two-pion system, in

\mathrm{MeV}/c^2

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