1. The problem statement, all variables and given/known data When a beam if high-energy protons collides with protons at rest in the laboratory, pions are produced by the reaction p + p --> p + p + ∏. Compute the threshold energy of the protons in the beam for this reaction to occur. 2. Relevant equations (mc^2)^2 = E^2 - (pc)^2 Einitial = Efinal 3. The attempt at a solution I tried to do an energy balance but can't seem to get it right. I don't understand how to account for the momentum of the proton if I'm not given its velocity. How can the momentum of the first stage be equal to the momentum of the second stage if none of the particles are moving? I think: 2x(rest energies of protons) + (Kinetic Energy of proton) = 2x(rest energies of protons) + (rest energy of pion) Is the threshold energy the total energy (i.e. the rest energy and kinetic energy) of the proton that is moving, or is it just its kinetic energy? My professor went over this very quickly and wrote down that zero is equal to something which makes no sense to me. I'm pretty confused and the book isn't helping either. Can anyone clarify this?