# Question on special relativity

1. Sep 7, 2011

### gaobo9109

1. The problem statement, all variables and given/known data
In colliding beam accelerator, two proton beams of the same energy are made to collide with each other from opposite direction. To improve the chances of collision, the protons are concentrated within the beam into bunches. In the laboratory frame of reference, each bunch is about 16.0 μm long with an interval of 7.00m between each bunch
(i) What is the length of a bunch as seen by a proton from another beam?
(ii) How long does it take for protons from one beam to pass by a bunch of protons from the opposite beam?

I have found that the velocity of the proton is 0.492c from previous part of the question.

2. Relevant equations

3. The attempt at a solution
(i) By using the length contraction formula, i can find the proper length of the bunch measured from the frame of reference of a proton in a bunch. I thought length of the bunch measured from the frame of reference of another proton beam should be same as the proper length since all proton beams travel at the same velocity. But this question is worth five mark, so i thought it might not be as easy as that

(ii) I feel that this question does not provide enough information. The question does not specify from whose frame of reference is the time measured. If the time is measured from the stationary frame, then t = 7/2v where v is the velocity of the proton. I am not sure whether i am correct about this.

2. Sep 7, 2011

### Pi-Bond

The speed of the two photons is the same, but they are moving in opposite directions; so the velocity is not the same. You need to use the relativistic velocity addition formula to find the relative velocity of the two bunches, and use it in the length contraction formula.

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