lecture_5_07

lecture_5_07 - Physics 13 Fall 07 G.R Goldstein 1 Velocity...

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Unformatted text preview: 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 1 Velocity transformation • S ′ : object moving with velocity u ′ (object, not frame) • What is u in S? S ′ moves rel.t. S(V =(V x ,0,0)). u x = υ ξ + ς 1 + ς υ ξ χ 2 υ ψ = υ ψ γ 1 + ς υ ξ χ 2 ανδ σιμ ιλαρλψφορυ z 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 2 Velocity transformation - example x ′ x u ′ S S ′ V Suppose S ′ is frame of spaceship with V=0.8c. It launches a probe from its deck with u ′ =0.9c. What does Earth viewer see? u x = υ ξ + ς 1+ ςυ ξ χ 2 = 0.9χ+ 0.8χ 1+ 0.8 0.9 = 1.7χ 1.72 = 0.99χ 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 3 Momentum • Elastic collision in 2 frames S 1 2 v-v 1 v-v 2 initial p xi =0=mv-mv p yi =0 final p xf =0 p yf =0=mv-mv S ′ (2 initially at rest) V=-v initial mv 1 xi = μ ω 1 ξ- ς 1 - ς ω 1 ξ χ 2 = 2μ ω 1 + ω 2 χ 2 φιναλ μ ω 1 ξφ = μ-ς 1 = μ ω= μ ω 2 ξφ μ ω 1 ψφ = μ ω γ = -μ ω 2 ψφ x y 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 4 Momentum problems • So initially in S ′ total momentum is • p xi ′ = 2mv/(1+v 2 /c 2 ) (with no y comp.) • But finally • p xf ′ = 2mv • Momentum is not conserved in S ′ ! • Need a relativistic definition of momentum 2 m v 1 + ω 2 χ 2 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 5 Relativistic Momentum • Ansatz: particle of velocity v...
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This note was uploaded on 03/27/2008 for the course PHY 13 taught by Professor Garyr.goldstein during the Fall '04 term at Tufts.

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lecture_5_07 - Physics 13 Fall 07 G.R Goldstein 1 Velocity...

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