# Proton-proton collisions in an accelerator

## Homework Statement

What fraction of the energy of a rapidly moving proton is not available for inelastic interactions in proton-proton collisions when the target proton is at rest in the laboratory and the energy of the accelerator is (a) 3 GeV (b) 7 GeV (c) 25 GeV (d) 200 GeV (e) 1000 GeV?

## Homework Equations

E = mγc2
T = E - mc2 = mc2(γ - 1)
Conservation of energy

## The Attempt at a Solution

I have puzzled over this and still really have no idea how to begin. First, what does the energy of the accelerator mean for that of the moving proton? Does the proton simply have as kinetic energy the energy of the accelerator? So if that is 3 GeV, I can take the KE of the proton to be 3 GeV? Or is it more complicated than that? Second, the fraction of the energy not available for inelastic interactions would be the remainder after subtracting what is required for elastic ones. But how do I know that any energy is required for elastic interactions at all? Why shouldn't all the energy be absorbed inelastically? I feel like I have not been given enough data to do this. Any help greatly appreciated.