27_InstSolManual_PDF_Part10

27_InstSolManual_PDF_Part10 - Figure 27.44 Solve: (a) with...

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Solve: (a) The speed of each proton relative to the other is (b) In nonrelativistic mechanics the speeds just add and the speed of each relative to the other is c . (c) (i) Relative to the lab frame each proton has speed The total kinetic energy of each proton is (ii) In its rest frame one proton has zero speed and zero kinetic energy and the other has speed In this frame the kinetic energy of the moving proton is (d) (i) Each proton has speed and kinetic energy (ii) One proton has speed and the other has speed c . The kinetic energy of the moving proton is Reflect: The relativistic expression for K gives a larger value than the nonrelativistic expression. The kinetic energy of the system is different in different frames. 27.44. Set Up: Let S be the lab frame and let the frame of the proton that is moving in the direction in the lab frame, as shown in Figure 27.44. In the other proton moves in the direction with speed so In the lab frame each proton has speed where is a constant that we need to solve for.
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Unformatted text preview: Figure 27.44 Solve: (a) with and gives and and or Cant have so only is physi-cally allowed. The speed measured by the observer in the lab is 0.268 c . (b) (i) (ii) K 5 1 g 2 1 2 mc 2 5 145 MeV. g 5 1.1547. v 5 0.500 c . K 5 1 g 2 1 2 mc 2 5 35.6 MeV. g 5 1.0380. v 5 0.269 c . a 5 0.268 v . c , a 5 3.73. a 5 0.268 a 2 2 4 a 1 1 5 2a 5 2 0.50 1 a 1 2 0.50 a . 2a c 5 2 0.50 c 1 a c 1 1 1 a c 21 2 0.50 c 2 / c 2 v r 5 2 0.50 c u 5 1a c v 5 2a c , v 5 v r 1 u 1 1 u v r / c 2 x r y r x y S S r u 5 1 xc v 5 2 xc a a c , v r 5 2 c / 2. c / 2, 2 x r S r 1 x S r K 5 1 2 mc 2 5 938 MeV 2 5 469 MeV v 5 K 5 1 2 m v 2 5 A 1 2 m B1 c / 2 2 2 5 mc 2 8 5 938 MeV 8 5 117 MeV v 5 c / 2 K 5 938 MeV 1 2 A 4 5 B 2 2 1 938 MeV 2 5 625 MeV 4 5 c . K 5 938 MeV 1 2 A 1 2 B 2 2 1 938 MeV 2 5 145 MeV. v 5 c / 2. K 5 mc 2 " 1 2 v 2 / c 2 2 mc 2 4 5 c . v r 5 v 2 u 1 2 u v / c 2 5 2 c / 2 2 c / 2 1 2 1 c / 2 21 2 c / 2 2 / c 2 5 2 4 c 5 27-10 Chapter 27...
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