1.) problem statement(adsbygoogle = window.adsbygoogle || []).push({});

Relativistic protons that have a certain speed "v" are selected by measuring the time it takes the proton to travel between two detectors separated by a distance "L". Each detector produces an electronic pulse of very short duration (LaTeX Code: \\Delta t << L/v) when a proton passes through it. A coincidence circuit is made by delaying the pulse from the first detector by an amount L/v. The signals from the two detectors are fed into a logic circuit that produces an output pulse if the pulses arrive at the same time. For input pulses that arrive at the same time as measured in the laboratory frame, calculate the time difference between arrival of the input pulses as measured in the rest frame of the proton.

2. Relevant equations

LaTeX Code: \\Delta t = LaTeX Code: \\Delta t'/ (1-v^2/c^2)^1/2 where LaTeX Code: \\Delta t' is the time elapsed in reference frame of moving particle.

3. The attempt at a solution

I take the LaTeX Code: \\Delta t elapsed in the reference frame of the lab to = L/v

So my question is, when I switch to the frame of the proton - the length of the path it travels is now moving towards it - do I have to do a length contraction ?? Or will my time dilation equation take this into account?

I got:

(delta) t (proton) = 1/(1-v^2/c^2)^1/2 L/v

just solving the time dilation equation in the reference frame of the proton seeing the apparatus moving towards it. (Thus the time in the lab is ticking slower relative to the proton's frame.)

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# Homework Help: Lorentz transformation: time dilation

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