# Relativity : Muons traveling Qns

1. Jan 19, 2007

### Delzac

1. The problem statement, all variables and given/known data
Muons move in circular orbits at a speed of 0.9994c in a storage ring which has a radius of 500m. How many trips around the storage ring do we expect the muons to make before they decay? How many trips around the storage ring do the muons think they have made? Are there any contradictions?
[ The question didn't give the by what time will muons decay, so i did a little search and took 2.2*10^-6 sec as the time before the decay.)

2. Relevant equations
$$L = L_0/\gamma$$
$$\Delta T = \gamma \Delta T_0$$

3. The attempt at a solution

(i) v = 0.9994c, r=500m, C=2*pi*500=1000*pi, $$\Delta T_0 = 2.2*10^-6$$

Therefore using $$\Delta T = \gamma \Delta T_0$$,
$$\Delta T = 6.35*10^-5$$
Distance moved = (0.9994)(3.0*10^8)(6.35*10^-5)=19,038.57m
Trips around storage ring = 19,038.57/1000pi = 6.06 times.

(ii)
Distance moved in the frame of muons = 0.9994c*2.2*10^-6 = 659.604
Trips around the ring as in frame of muons = 659.604/1000pi = 0.20996

(iii)
There are not contradiction since in the frame of muon, the ring or the distance traveled by it has been length contracted. Therefore, the muon actually traveled more than it seem to have traveled.

In the frame of an observer however the muon although should decay in 2.2micro seconds didn't due to time dilation. Thus with this apparent increase in time, the muon can cover more distance and hence have more trips around the rings.
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Can anyone check my answer for part i ii and iii. I believe i got i and ii correct. But most importantly is my explanation in iii in anyway wrong or unclear or lacking?

Any help will be greatly appreciated

Last edited: Jan 20, 2007
2. Jan 20, 2007

### Delzac

Ermm....any help?