inelastic_relativistic_collision_sol_1

inelastic_relativistic_collision_sol_1 - inelastic...

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inelastic relativistic collision A particle of mass m , moving at speed v = 4 c /5, collides inelastically with a similar particle at rest. (a) What is the speed v C of the composite particle? (b) What is its mass m C ? Solution by Rudy Arthur: Call the moving particle ‘M’, and the particle at rest ‘R’ (the composite particle is defined to be ‘C’). The momentum of the moving particle is M 2 2 4 3 1 mv p v c == m c M 2 . ( 1 ) And, the square of its energy is M 22 2 () E mc p c =+ . ( 2 ) The energy of the particle at rest is R 2 E mc = . ( 3 ) The square of the energy of the composite particle is CC C 2 ( 2 ) E mc pc . ( 4 ) By conservation of energy: , or squaring and rearranging, MR EEE += C 2 C M R 2 E EEEE =−− ( 5 ) Substituting (2) and (4) into (5): ( ) C C M 2 2 2( ) ( ) 2 ( ) ( ) E Em c p c m c p c −+ By conservation of momentum, CM p p = , so this reduces to C ) 2 ( ) E c m c =− Squaring again: ( C 2 2 2 4( ) 2 ( EE m c ) ) ( 6 ) Substituting from (2) and (3) into (6) and expanding on the right,
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inelastic_relativistic_collision_sol_1 - inelastic...

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