06_InstSolManual_PDF_Part11

06_InstSolManual_PDF_Part11 - w r 5 G mm E 1 R E 2 2 2 5 4...

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6.26. Set Up: The earth has radius Let the earth’s mass be and your mass be m . Solve: At the surface of the earth your weight is At height h above the earth’s surface, so and 6.27. Set Up: The circumference c is related to the radius of the planet by Take downward and use the measured motion to find the acceleration due to gravity at the surface of the planet. Solve: (a) gives so (b) Reflect: and so which checks. 6.28. Set Up: Let and be the revised values of the mass and radius of the earth and let be the revised weight of the object. Solve: (a) (b) (c) (d) 6.29. Set Up: The mass of the probe on earth is The radius of Titan is Solve: Reflect: The mass of the probe is independent of its location. 6.30. Set Up: where the subscript m refers to the moon. For the earth, and Solve: g m 5 G 1 m E / 81 2 1 R E / 4 2 4 5 16 81 Gm E R E 2 5 16 81 g E 5 16 81 1 9.80 m / s 2 2 5 1.9 m / s 2 R m 5 R E / 4. m m 5 m E / 81 g E 5 Gm E R E 2 . g m 5 Gm m R m 2 , w 5 G mm T R T 2 5 1 6.673 3 10 2 11 N # m 2 / kg 2 21 318.4 kg 21 1.35 3 10 23 kg 2 1 2.575 3 10 6 m 2 2 5 433 N R T 5 1 2 1 5150 km 2 5 2.575 3 10 6 m. m 5 w E g E 5 3120 N 9.80 m / s 2 5 318.4 kg. w r 5 G m 1 2 m E 2 1 2 R E 2 2 5 W / 2 m r 5 2 m E . R r 5 2 R E , w r 5 G m 1 m E / 2 2 1 R E / 2 2 2 5 2 W m r 5 m E / 2. R r 5 R E / 2, w r 5 G
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Unformatted text preview: w r 5 G mm E 1 R E / 2 2 2 5 4 W R r 5 R E / 2. w r 5 G m 1 2 m E 2 R E 2 5 2 W m r 5 2 m E . w r 5 G mm r 1 R r 2 2 W 5 G mm E R E 2 ; w r R r m r g p 5 3.76 1 1.56 2 2 g E 5 15.2 m / s 2 , m p 5 3.76 m E R p 5 1.56 R E m p 5 3.76 m E m p 5 gR p 2 G 5 1 15.2 m / s 2 21 9.93 3 10 6 m 2 2 6.673 3 10 2 11 N # m 2 / kg 2 5 2.25 3 10 25 kg g 5 Gm p R p 2 R p 5 c 2 p 5 6.24 3 10 7 m 2 p 5 9.93 3 10 6 m a y 5 2 1 y 2 y 2 t 2 5 2 1 5.00 m 2 1 0.811 s 2 2 5 15.2 m / s 2 y 5 y 1 v y t 1 1 2 a y t 2 y 2 y 5 5.00 m t 5 0.811 s, v y 5 0, m E 5 5.97 3 10 24 kg a y 5 g , 1 y c 5 2 p R p . R p h 5 A" 2 2 1 B R E 5 0.414 R E 5 2.64 3 10 3 km " 2 R E 5 h 1 R E 1 2 R E 2 5 1 1 h 1 R E 2 2 . w 2 5 w 1 / 2 w 2 5 G mm E 1 h 1 R E 2 2 , w 1 5 G mm E R E 2 . m E R E 5 6.38 3 10 6 m. Circular Motion and Gravitation 6-11...
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