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27_InstSolManual_PDF_Part5

# 27_InstSolManual_PDF_Part5 - 2 2 5 0.140 c v 5 c" 1 2 1...

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27.20. Set Up: Let S be the laboratory frame and let be the frame of one of the particles, as shown in Fig- ure 27.20. Let the positive x direction for both frames be the direction from particle 1 to particle 2. Then and is the velocity of particle 2 as measured in the lab frame. Figure 27.20 Solve: The speed measured in the laboratory for the second particle is 0.784 c . and since in the laboratory the two particles move in opposite directions. 27.21. Set Up: Equation 27.10 says and Let Solve: and and The resulting equations are related to Equations 27.10 by and 27.22. Set Up: The momentum of a particle has magnitude Solve: means 27.23. Set Up: The momentum of a particle has magnitude is less than 1, so Solve: (a) The problem specifies that (b) the relativistic value is greater than the nonrelativistic value. 27.24. Set Up: If is 1.0% greater than 1 then if is 10% greater than 1 then and if is 100% greater than 1 then Solve: (a) (b) (c) v 5 c " 1 2 1 / 1 2.00 2 2 5 0.866 c v 5 c " 1 2 1 / 1 1.10 2 2 5 0.417 c v 5 c " 1 2 1 / 1 1.010 2 2
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Unformatted text preview: 2 2 5 0.140 c v 5 c " 1 2 1 / g 2 g 5 2.00. g g 5 1.10 g g 5 1.010, g g 5 1 " 1 2 v 2 / c 2 . p . m v ; v 5 c " 1 2 1 1 / 1.010 2 2 5 0.140 c 5 4.20 3 10 7 m / s. 1.010 5 1 " 1 2 v 2 / c 2 . p 5 1.010 m v . p . m v . " 1 2 v 2 / c 2 p 5 m v " 1 2 v 2 / c 2 . v 5 c " 1 2 1 1 / 3 2 2 5 0.943 c . 1 " 1 2 v 2 / c 2 5 3. p 5 3 m v p 5 m v " 1 2 v 2 / c 2 . u S 2 u . t 4 t r x 4 x r , t 5 a t r 1 u c 2 1 x r 1 ut r a 2 5 t r 1 a 2 1 u 2 / c 2 2 1 ux r / c 2 a 5 t r 1 ux r / c 2 " 1 2 u 2 / c 2 . x 5 a 1 x r 1 ut r 2 1 2 u 2 / c 2 5 x r 1 ut r " 1 2 u 2 / c 2 . x 2 1 u 2 x c 2 1 a ut r 2 5 a x r t 2 ux c 2 5 a t r . x 2 ut 5 a x r a 5 " 1 2 u 2 / c 2 . t r 5 t 2 ux / c 2 " 1 2 u 2 / c 2 . x r 5 x 2 ut " 1 2 u 2 / c 2 u , v . v 5 v r 1 u 1 1 u v r / c 2 5 1 0.950 c 1 1 2 0.650 c 2 1 1 1 2 0.650 c 21 1 0.950 c 2 / c 2 5 1 0.784 c . x r y r x y S S r 2 1 v v r 5 1 0.950 c . 2 0.650 c u 5 S r Relativity 27-5...
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