p38_045 - 10 − 5 s , and the distance it travels is d ≈...

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45. The distance traveled by the pion in the frame of Earth is (using Eq. 38-12) d = v t . The proper lifetime t 0 is related to ∆ t by the time-dilation formula: ∆ t = γ t 0 . To use this equation, we must Frst Fnd the Lorentz factor γ (using Eq. 38-45). Since the total energy of the pion is given by E =1 . 35 × 10 5 MeV and its mc 2 value is 139 . 6MeV, then γ = E mc 2 = 1 . 35 × 10 5 MeV 139 . 6MeV = 967 . 05 . Therefore, the lifetime of the moving pion as measured by Earth observers is t = γ t 0 = (967 . 1)(35 . 0 × 10 9 s) = 3 . 385 ×
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Unformatted text preview: 10 − 5 s , and the distance it travels is d ≈ c ∆ t = (2 . 998 × 10 8 m / s)(3 . 385 × 10 − 5 s) = 1 . 015 × 10 4 m = 10 . 15 km where we have approximated its speed as c (note: its speed can be found by solving Eq. 38-8, which gives v = 0 . 9999995 c ; this more precise value for v would not signiFcantly alter our Fnal result). Thus, the altitude at which the pion decays is 120 km − 10 . 15 km = 110 km....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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