# Relativistic accelerator

1. Jan 12, 2009

### Rory9

1. The problem statement, all variables and given/known data

In a conventional accelerator, the energy of the particles bombarding the target at rest is connected to their velocity by the relativistic formula where the relevant velocity of the bombarding particles v1 is the velocity relative to the target at rest, v1 = v1_rel. In an accelerator using two counter-propagating colliding beams of particles of equal energy, the energy of each beam is given by the same relativistic formula but the relevant velocity v2 $$\neq$$ v2_rel. Determine v2_rel, stating the reference frame you are using.

3. The attempt at a solution

I'm just not seeing something here. If I'm interpreting the question correctly, by 'relevant velocity' I presume it just means the velocity that was used to calculate the energy, which in the case of the first beam was the velocity of the beam relative to the target, but in the case of the second was not (?). So am I to take it that the energies have been calculated in different frames of ref, and happened to be equal on comparison? If so, not knowing what frame of reference was used to determine the second energy, I don't see that I can connect v2 and v2_rel, at the moment...

This is irritating me, as I'm sure the answer is simple, but I may not be interpreting the question correctly! Thanks in advance for any help.

2. Jan 12, 2009

### turin

I don't understand the question. I don't think you are given enough information. What is the definition of v2? What is the definition of v2_rel?