1. The problem statement, all variables and given/known data
An electron of energy 10 GeV strikes a proton at rest. What is the velocity of the electron-proton CM system? What energy is available to produce new particles?
2. Relevant equations
Conservation of momentum and energy,
E2=p2c2+m2c4
3. The attempt at a solution
I'm really not sure where to start - solving for the velocity in classical mechanics is simple but the equations here would be really messy so I think there must be a simple way I'm missing. If the two particles were identical it would be easy... Then once I've got that velocity, then would the sum of the energies in the CM frame before the collision be the energy available to produce new particles in the lab frame - i.e the extra energy in the lab frame goes toward conserving momentum? Any clues would be appreciated, thanks.
An electron of energy 10 GeV strikes a proton at rest. What is the velocity of the electron-proton CM system? What energy is available to produce new particles?
2. Relevant equations
Conservation of momentum and energy,
E2=p2c2+m2c4
3. The attempt at a solution
I'm really not sure where to start - solving for the velocity in classical mechanics is simple but the equations here would be really messy so I think there must be a simple way I'm missing. If the two particles were identical it would be easy... Then once I've got that velocity, then would the sum of the energies in the CM frame before the collision be the energy available to produce new particles in the lab frame - i.e the extra energy in the lab frame goes toward conserving momentum? Any clues would be appreciated, thanks.
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