27_InstSolManual_PDF_Part11

27_InstSolManual_PDF_Part11 - p 2 2 m 5 E rest 1 K nr , K...

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27.45. Set Up: The energy that enters the ice is The mass increase is the mass equivalent of this amount of energy, Solve: 27.46. Set Up: Let S be the lab frame and let be the frame of the nucleus. Let the direction be the direction the nucleus is moving. Solve: (a) (b) (c) emitted in same direction: (i) (ii) (d) emitted in opposite direction: (i) (ii) 27.47. Set Up: Equation 27.24 says and the classical (nonrelativistic) kinetic energy is Solve: as was to be shown. 27.48. Set Up: The proper distance to the star is 500 light years. The energy needed is the kinetic energy of the rocket at its final speed. Solve: (a) The proper time is measured by the astronauts. This is 14% of the U.S. yearly use of energy. (b) This is 5.5 times the U.S. yearly use. K 5 1 9.00 3 10 19 J 2 1 1 " 1 2 1 0.99 2 2 2 1 2 5 5.5 3 10 20 J D t 0 5 71 yr D t 5 d u 5 4.73 3 10 18 m 1 0.99 21 3.00 3 10 8 m / s 2 5 1.6 3 10 10 s 5 505 yr, u 5 0.99 c . K 5 mc 2 " 1 2 v 2 / c 2 2 mc 2 5 1 1000 kg 21 3.00 3 10 8 m / s 2 2 1 1 " 1 2 1 0.500 2 2 2 1 2 5 1.4 3 10 19 J D t 0 5D t " 1 2 u 2 / c 2 5 866 yr D t 5 d u 5 4.73 3 10 18 m 1 0.50 21 3.00 3 10 8 m / s 2 5 3.2 3 10 10 s 5 1000 yr u 5 0.50 c . l 0 500 light years 5 4.73 3 10 18 m. E 5 mc 2 Å 1 1 1 pc 2 2 1 mc 2 2 2 < mc 2 1 1 1 1 2 1 pc 2 2 1 mc 2 2 2 2 5 mc 2 1 1 2 p 2 c 2 mc 2 5 mc 2 1
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Unformatted text preview: p 2 2 m 5 E rest 1 K nr , K nr 5 1 2 m v 2 5 p 2 2 m . E rest 5 mc 2 E 5 &quot;1 mc 2 2 2 1 1 pc 2 2 . K r 5 1 1 &quot; 1 2 v 2 / c 2 2 1 2 mc 2 5 1 0.511 MeV 2 1 1 &quot; 1 2 1 0.9995 2 2 2 1 2 5 15.7 MeV K 5 1 1 &quot; 1 2 v 2 / c 2 2 1 2 mc 2 5 1 0.511 MeV 2 1 1 &quot; 1 2 1 0.9965 2 2 2 1 2 5 5.60 MeV K r 5 1 1 &quot; 1 2 v 2 / c 2 2 1 2 mc 2 5 1 0.511 MeV 2 1 1 &quot; 1 2 1 0.9995 2 2 2 1 2 5 15.7 MeV K 5 1 1 &quot; 1 2 v 2 / c 2 2 1 2 mc 2 5 1 0.511 MeV 2 1 1 &quot; 1 2 1 0.999929 2 2 2 1 2 5 42.4 MeV v 5 2 0.9995 c 1 0.7500 c 1 1 1 0.7500 21 2 0.9995 2 5 2 0.9965 c v r 5 2 0.9995 c . v 5 v r 1 u 1 1 u v r / c 2 5 0.9995 c 1 0.7500 c 1 1 1 0.7500 21 0.9995 2 5 0.999929 c v r 5 1 0.9995 c . u 5 0.7500 c . 1 x S r m 5 E c 2 5 mL f c 2 5 1 4.00 kg 21 3.34 3 10 5 J / kg 2 1 3.00 3 10 8 m / s 2 2 5 1.48 3 10 2 11 kg m 5 E c 2 . E 5 Q 5 mL f . Relativity 27-11...
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