408_Physics ProblemsTechnical Physics

408_Physics ProblemsTechnical Physics - 410 Universal...

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Unformatted text preview: 410 Universal Gravitation ANSWERS TO EVEN PROBLEMS P13.2 2.67 × 10 −7 m s 2 P13.40 (a) 10.0 m s 2 ; (b) 21.8 km s P13.4 3.00 kg and 2.00 kg P13.42 11.8 km s P13.6 (a) 4.39 × 10 20 N toward the Sun; (b) 1.99 × 10 20 N toward the Earth; (c) 3.55 × 10 22 N toward the Sun P13.44 GM E m 12 RE P13.8 see the solution; either 1 m − 61.3 nm or 2.74 × 10 −4 m P13.46 (a) v 0 F GM IJ =G HrK (c) r f = P13.10 2 3 P13.12 (a) 1.02 km s ; (b) 1.35 mm P13.14 see the solution P13.16 1.27 P13.18 Planet Y has turned through 1.30 revolutions P13.20 1.63 × 10 4 rad s P13.22 18.2 ms P13.24 (a) 1.31 × 10 17 N toward the center; (b) 2.62 × 10 12 N kg E 12 ; (b) vi = 5 GM E 1 2 r ej 25r 7 P13.48 ; 2.26 × 10 −7 P13.50 4 2 GM 1 GM ; 3 R 3 R P13.52 (a), (b) see the solution; (c) 1.85 × 10 −5 m s 2 P13.54 492 m s P13.56 see the solution P13.58 (a) G 1 2 c − 3 2 h1 2 ; (b) ~ 10 −34 m P13.60 (a) 7.79 km s; (b) 7.85 km s;(c) −3.04 GJ ; (d) −3.08 GJ ; (e) loss = 46.9 MJ ; (f) A component of the Earth’s gravity pulls forward on the satellite in its downward banking trajectory. P13.62 (a) 29.3 km s ; (b) K p = 2.74 × 10 33 J ; P13.26 (a) −4.77 × 10 9 J ; (b) 569 N down; (c) 569 N up P13.28 2.52 × 10 7 m P13.30 2.82 × 10 9 J P13.32 (a) see the solution; (b) 340 s P13.34 (a) 42.1 km s ; (b) 2.20 × 10 11 m P13.64 119 km P13.36 1.58 × 10 10 J P13.66 (a) −36.7 MJ ; (b) 9.24 × 10 10 kg ⋅ m 2 s ; (c) 5.58 km s; 10.4 Mm; (d) 8.69 Mm; (e) 134 min P13.68 see the solution P13.70 (a) 2.77 m s 2 ; (b) 3.70 m s 2 P13.38 b U p = −5.40 × 10 33 J ;(c) K a = 2.57 × 10 33 J; U a = −5.22 × 10 33 J; yes g bGM g ; (b) bGM g b R + hg ; L R + 2 h OP − 2π R m (c) GM m M MN 2 R bR + hg PQ b86 400 sg (a) 2π RE + h E E −1 2 E −1 2 32 12 E 2 E E E 2 E 2 The satellite should be launched from the Earth’s equator toward the east. ...
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