World Science Scholars
18.2 Disintegrating Muons
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Sami Al-Suwailem
The numbers seem to be not accurate. Gamma = 1/sqrt(1-0.994^2) = 9.14243. Dividing 5.9 km by gamma = 0.645343 km. To obtain the speed of the muon in km/s, we divide 0.645343 km by (2.2 * 10^-6 s) = 293,338 km/s. Speed of light = 299,792 km/s. Dividing these two numbers = 293,338 / 299,792 = 0.978472. This not equal to 0.994 that we started with.
Sami Al-Suwailem
I am sorry about this mess! I wanted to edit my reply, but the system instead posted a different reply each time I make an edit. I don't know how to delete my previous comments. If anyone knows, please help!
Marius Smallegoor
This indeed is a riddle! I agree with your calculations. Also when you calculate the time that passed on earth (2,2 * 10^-6 * gamma = 2,0113346 * 10^-5 s) and use this to calculate the speed you also get v = 5,9/2,0113346 = 293,338 km/s = 0,978C I don't see where this goes wrong because the only thing we use is 5,9 km, v=0,994C and lifetime muon in rest = 2,2*10^-6. All the rest is derived using gamma.......
Marius Smallegoor
The only conclusion I can draw is that 5,9 km is wrong. When you use the time passed on Earth (2,0113346 s * 10^-5) to calculate the distance travelled according to an observer on Earth you get 2,0113346 s * 10^-5 * 299,792*0,994 = 5,9936413 km instead of 5,9 km!! Using this 5,9936413 you find 0,655585 km as the Lorentz contracted distance. And this gives you the speed v = 0,655585 / 2,2 * 10^-6 = 297,993 km/s. This is 297,993/299792 =0,994C !
Marius Smallegoor
I checked the lifetime of a muon: 2.1969811 * 10^-6. This gives you 5,9854 km (see calculations above).
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