Ch 12 Physics for Scientists and Engineers

# Ch 12 Physics for Scientists and Engineers - 12.1 Solve(b...

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12.1. Model: Model the sun (s), the earth (e), and the moon (m) as spherical. Solve: (a) F Gm m r sone se 22 3 0 N m kg 1.99 10 kg kg m N == ×⋅ × × × 2 11 24 11 2 22 6 67 10 5 98 10 150 10 353 10 (. / ) ( ) ) ) . (b) F GM M r mone me N m kg kg kg m N × × × 2 11 22 24 82 20 6 67 10 7 36 10 5 98 10 384 10 199 10 / ) ) ) ) . (c) The moon’s force on the earth as a percent of the sun’s force on the earth is 100 0 56 20 22 . . .% × × ×= N N

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12.2. Model: Assume the two lead balls are spherical masses. Solve: (a) FF Gm m r 1on2 2on 22 N m kg 10 kg 0.100 kg 0.10 m N == = ×⋅ 1 12 2 11 2 9 667 10 (. / ) ( ) ( ) () . (b) The ratio of the above gravitational force to the weight of the 100 g ball is 98 681 10 9 9 . ( . ) . × N 0.100 kg m/s 2 Assess: The answer in part (b) shows the smallness of the gravitational force between two lead balls separated by 10 cm compared to the weight of the 100 g ball.
12.3. Model: Model the sun (s) and the earth (e) as spherical masses. Due to the large difference between your size and mass and that of either the sun or the earth, a human body can be treated as a particle. Solve: F GM M r s on you sy se = 2 and F GM M r e on you ey e = 2 Dividing these two equations gives F F M M r r s on y e on y s e e kg kg m m = = × × × × 2 30 24 6 11 2 4 199 10 598 10 637 10 15 10 600 10 . . . . .

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12.4. Model: Model the sun (s), the moon (m), and the earth (e) as spherical masses. Solve: F GM M r s on m sm = 2 and F GM M r e on m em = 2 Dividing the two equations and using the astronomical data from Table 12.2, F F M M r r s on m e on m s e kg kg m m = = × × × × = 2 30 24 8 11 2 199 10 598 10 384 10 150 10 218 . . . . . Note that the sun-moon distance is not noticeably different from the tabulated sun-earth distance.
12.5. Solve: F GM M r sphere on particle sp = 2 and F GM M r earth on particle ep e = 2 Dividing the two equations, F F M M r r sphere on particle earth on particle s e e 24 5900 kg 5.98 10 kg m .50 m = = × × 2 6 2 7 637 10 0 160 10 . .

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12.6. Model: Model the woman (w) and the man (m) as spherical masses or particles. Solve: FF GM M r w on m m on w wm mw 22 N m kg 50 kg 70 kg 1.0 m N == = ×⋅ 2 11 2 7 667 10 23 10 (. / ) ( ) ( ) () .
12.7. Model: Model the earth (e) as a sphere. Visualize: The space shuttle or a 1.0 kg sphere (s) in the space shuttle is Rr es 6 m 0.30 10 m += × + × = 637 10 6 . 667 10 6 . × m away from the center of the earth. Solve: (a) F GM M e on s 22 N m kg kg 1.0 kg m N = + = ×⋅ × × = () ( . / )( . )( ) (. ) . 2 11 24 62 6 67 10 5 98 10 897 (b) Because the sphere and the shuttle are falling with the same acceleration, there cannot be any relative motion between them. That is why the sphere floats around inside the space shuttle.

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12.8.
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Ch 12 Physics for Scientists and Engineers - 12.1 Solve(b...

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