1. The problem statement, all variables and given/known data LHC can accelerate proton beams to energies of 8Tev. 1. What is the centre-of-mass energy of two colliding protons? 2. What would be the beam energy needed if one wanted to reach the same centre-of-mass energy when colliding beam protons with protons in a target at rest? 2. Relevant equations E2 = (pc)2+(E0)2 KE = E - E0 3. The attempt at a solution Common sense tells me that two particles of equal mass and energy colliding head on results in all the energy of the particle transferring to "collision energy". So I assume an Etot = (8+8)TeV = 16TeV sounds reasonable unless I need to include rest mass energy, which i would have though is negligible. Does this Etot relate simply to Ecm? I am having trouble understanding the loss of collision energy in the rest target case, surely all energy supplied to the particle for momentum must be conserved/transferred to the rest proton and there is no center-of-mass energy? I guess my understanding of what Ecm (center-of-mass energy) may be throwing me off slightly?