# Chapter12 - 12.1 Solve(b Model Model the sun(s the earth(e...

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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 s on e s e s e 2 2 30 N m kg 1.99 10 kg kg m N = = × × × × = × 2 11 24 11 2 22 6 67 10 5 98 10 1 50 10 3 53 10 ( . / )( )( . ) ( . ) . (b) F GM M r m on e m e m e 2 2 N m kg kg kg m N = = × × × × = × 2 11 22 24 8 2 20 6 67 10 7 36 10 5 98 10 3 84 10 1 99 10 ( . / )( . )( . ) ( . ) . (c) The moon’s force on the earth as a percent of the sun’s force on the earth is 1 99 10 3 53 10 100 0 56 20 22 . . . % × × × = N N

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12.2. Model: Assume the two lead balls are spherical masses. Solve: (a) F F Gm m r 1on 2 2 on 2 2 N m kg 10 kg 0.100 kg 0.10 m N = = = × = × 1 1 2 2 11 2 9 6 67 10 6 67 10 ( . / )( )( ) ( ) . (b) The ratio of the above gravitational force to the weight of the 100 g ball is 6 67 10 9 8 6 81 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 s y s e = 2 and F GM M r e on you e y e = 2 Dividing these two equations gives F F M M r r s on y e on y s e e s e kg kg m m = = × × × × = × 2 30 24 6 11 2 4 1 99 10 5 98 10 6 37 10 1 5 10 6 00 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 s m s m = 2 and F GM M r e on m e m e m = 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 e m s m kg kg m m = = × × × × = 2 30 24 8 11 2 1 99 10 5 98 10 3 84 10 1 50 10 2 18 . . . . . 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 s p s p = 2 and F GM M r earth on particle e p e = 2 Dividing the two equations, F F M M r r sphere on particle earth on particle s e e s p 24 5900 kg 5.98 10 kg m .50 m = = × × = × 2 6 2 7 6 37 10 0 1 60 10 . .

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12.6. Model: Model the woman (w) and the man (m) as spherical masses or particles. Solve: F F GM M r w on m m on w w m m w 2 2 N m kg 50 kg 70 kg 1.0 m N = = = × = × 2 11 2 7 6 67 10 2 3 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 R r e s 6 m 0.30 10 m + = × + × = 6 37 10 6 . 6 67 10 6 . × m away from the center of the earth. Solve: (a) F GM M R r e on s e s e s 2 2 N m kg kg 1.0 kg m N = + = × × × = ( ) ( . / )( . )( ) ( . ) . 2 11 24 6 2 6 67 10 5 98 10 6 67 10 8 97 (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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