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**Unformatted text preview: **Lorentz Transformation Equations Δx = γ (Δ x ′ + v Δ t ′ ) Δ t = γ parenleftbiggΔ t ′+ v c 2 Δ x′ parenrightbigg are equivalent to the principle of Invariance of the Interval in Special Relativity: (Δ s )2 = c 2 (Δ t ) 2- (Δ x )2 = c 2 (Δ t′ ) 2-(Δ x ′ ) 2 Assume that the origins of systems O and O ′ coincide at t= t ′= 0.5. Consider the decay, at rest, of the π− meson into a μ −particle (“muon”) and a neutrinoν . The rest mass of the π− is 140 MeV/c 2 , the rest mass of the μ − is 105.7 MeV/c2 ,and we may regard the neutrino as massless. The average proper lifetime of the muon is 2 .20 ×10 − 6 seconds. (a) Calculate the momentum of the μ −and ν . (b) Calculate the kinetic energy of the μ − and ν . (c) Calculate the speed of the muon. (d) How far in the lab, on average, will theμ − travel before decaying?...

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- Fall '09
- Special Relativity, Lorentz Transformation Equations