inelastic relativistic collision A particle of mass m, moving at speed v= 4c/5, collides inelastically with a similar particle at rest. (a) What is the speed vCof the composite particle? (b) What is its mass mC? 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 M22431mvpvc==−mcM2. (1) And, the square of its energy is M222()()Emcp c=+. (2) The energy of the particle at rest is R2()Emc=. (3) The square of the energy of the composite particle is CCC222()(2)Em cp c=+. (4) By conservation of energy: , or squaring and rearranging, MREEE+=C2MRCMR222E EEEE=−−(5) Substituting (2) and (4) into (5): ()()MRCCM2222222()()2()()E Em cp cmcp c=+−+By conservation of momentum, CMpp=, so this reduces to MRC22222()2()E Em cmc=−Squaring again: (MRC22222
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