Fermilab relativity energy problem

[erisedk]

Homework Statement

This is why we build them as colliders now:

Some years ago Fermilab used to extract its high energy proton beam for use by "fixed target" experiments situated at the ends of external beamlines a mile north of the Tevatron ring. The energy available for the production of (unstable) heavy particles in collisions between a high energy proton and a stationary proton is very different from that available when two beams with the full Tevatron energy collide head on.

Calculate the energy of the most massive single particle that can be produced in a collision of a proton with total energy 1000 GeV with a stationary proton with total energy mc^2 = 0.93827 GeV. Also calculate the energy of the most massive particle that can be produced in a head on collison of two 1000GeV beams. (It's fine to use the approximation β = 1 when appropriate).

Homework Equations

Relativistic energy and momentum conservation

The Attempt at a Solution

Why do I feel like I should just be adding the two terms to get total energy of final particle in both cases? Answer is obviously wrong.

 

[kuruman]

Your relevant equations and attempt at a solution show little detail. Perhaps if you explained what you did and why it is obviously wrong, someone would be able to divine why you feel the way you do.