Relativistic particles travelling at near light speed, past a detector

1. Mar 4, 2012

bruce123

1. The problem statement, all variables and given/known data
Part a - A set of particles are travelling at a constant speed close to the speed of light, past a detector. From the detector's point of view, it takes a set period of time (t seconds) for the entire set of particles to pass by a set point on the detector. Write an expression to link the time t, with the constant speed v and the length of the set of particles, l.

Part b - Looking at the problem from the particle's point of view, write an expression to link the length l with the length of the set of particles from the particle's point of view, l'. Then, write a final expression to link t and v to l'.

2. Relevant equations
L=L0 $\sqrt{1-v2/c2}$

3. The attempt at a solution
Part a - I'm thinking that because it's all in one frame, you could simply use a modified form of the distance = speed x time. In other words, L = v x t.

Part b - As L=L0 $\sqrt{1-v2/c2}$, this can be altered so L'=L $\sqrt{1-v2/c2}$. Therefore we can alter the original L = v x t to form L' = L $\sqrt{1-v2/c2}$ = v x t.

I'm not too confident with this area of physics and am struggling with most of these equations! Any help would be much appreciated! :)