The Relativistic Particle Collider Ring · AI Generator #GEN-7083CB7E
Physics
Problem
A future particle accelerator consists of a circular ring where two identical particle beams travel in opposite directions. Each beam contains particles of rest mass m0=5.0×10−27kg moving at speed v=0.80c relative to the laboratory frame. When the beams collide head-on, the particles annihilate and produce a single photon.
During a test run, one of the particle beams suddenly stops due to a magnetic field failure, while the other beam continues circulating. A moving particle from the active beam now collides with a stationary particle from the failed beam.
(a) Find the speed of the center of mass of the two-particle system in the collision between the moving and stationary particles.
(b) Calculate the energy of the photon produced when two particles from the original head-on collision (both moving at 0.80c in opposite directions) annihilate.
(c) Calculate the energy of the photon produced when a moving particle collides and annihilates with the stationary particle.
(d) Explain physically why the photon energies in parts (b) and (c) are different.