HW6 Solution - salazar (ggs332) HW06 TSOI (58160) 1 This...

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Unformatted text preview: salazar (ggs332) HW06 TSOI (58160) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points Three 4 kg masses are located at points in the xy plane as shown. 50 cm 58 cm What is the magnitude of the resultant force (caused by the other two masses) on the mass at the origin? The universal gravita- tional constant is 6 . 6726 10 11 N m 2 / kg 2 . Correct answer: 5 . 32061 10 9 N. Explanation: Let : m = 4 kg , x = 50 cm = 0 . 5 m , y = 58 cm = 0 . 58 m , and G = 6 . 6726 10 11 N m 2 / kg 2 . The force from the mass on the right points in the x direction and has magnitude F 1 = G mm x 2 = Gm 2 x 2 = (6 . 6726 10 11 N m 2 / kg 2 ) (4 kg) 2 (0 . 5 m) 2 = 4 . 27046 10 9 N . The other force points in the y direction and has magnitude F 2 = (6 . 6726 10 11 N m 2 / kg 2 ) (4 kg) 2 (0 . 58 m) 2 = 3 . 17365 10 9 N . F 2 F 1 F The magnitude of the resultant force is F = radicalBig F 2 1 + F 2 2 = bracketleftBig (4 . 27046 10 9 N) 2 + (3 . 17365 10 9 N) 2 bracketrightBig 1 / 2 = 5 . 32061 10 9 N . 002 (part 2 of 2) 10.0 points At what angle from the positive x-axis will the resultant force point? Let counterclockwise be positive, within the limits 180 to 180 . Correct answer: 36 . 6184 . Explanation: The angle shown is = arctan parenleftbigg f 2 f 1 parenrightbigg = arctan parenleftbigg 3 . 17365 10 9 N 4 . 27046 10 9 N parenrightbigg = 36 . 6184 . 003 (part 1 of 3) 10.0 points Given: G = 6 . 67259 10 11 N m 2 / kg 2 A uniform solid sphere of mass m 2 = 108 kg and radius R 2 = 1 . 26 m is inside and concen- tric with a spherical shell of mass m 1 = 233 kg and radius R 1 = 2 . 39 m (see the figure). salazar (ggs332) HW06 TSOI (58160) 2 R R a b c m m 1 1 2 2 Find the magnitude of the gravitational force exerted by the sphere and spherical shell on a particle of mass 1 kg located at a dis- tance 0 . 58 m from the center of the sphere and spherical shell. Correct answer: 2 . 08946 10 9 N. Explanation: In this case the distance a = 0 . 58 m from the particle of mass m = 1 kg to the center of the sphere (whose mass is m 2 = 108 kg) is smaller than the radius R 2 = 1 . 26 m of the sphere. Thus, the particle is inside the sphere and the gravitational force F a exerted on it increases linearly with the distance from the particle to the center of the sphere F a = G m 2 m R 3 2 a = (108 kg) (1 kg) (1 . 26 m) 3 (0 . 58 m) 6 . 67259 10 11 N m 2 / kg 2 = 2 . 08946 10 9 N . 004 (part 2 of 3) 10.0 points Find the magnitude of the gravitational force exerted by the sphere and spherical shell on a particle of mass 1 kg located at a distance 1 . 86 m from the center of the sphere and spherical shell....
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HW6 Solution - salazar (ggs332) HW06 TSOI (58160) 1 This...

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