lecture_5_07

lecture_5_07 - 05/07/09 Physics 13 - Fall 07 - G.R....

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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 = + 1 + 2 = 1 + 2 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 = + 1+ 2 = 0.9+ 0.8 1+ 0.8 0.9 = 1.7 1.72 = 0.99 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 = 1 - 1 - 1 2 = 2 1 + 2 2 1 = - 1 = = 2 1 = = - 2 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 + 2 2 05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 5 Relativistic Momentum Ansatz: particle of velocity v...
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lecture_5_07 - 05/07/09 Physics 13 - Fall 07 - G.R....

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