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Unformatted text preview: Patel (ppp285) 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 6 kg masses are located at points in the xy plane as shown. 37 cm 53 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: 1 . 95196 10 8 N. Explanation: Let : m = 6 kg , x = 37 cm = 0 . 37 m , y = 53 cm = 0 . 53 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 ) (6 kg) 2 (0 . 37 m) 2 = 1 . 75466 10 8 N . The other force points in the y direction and has magnitude F 2 = (6 . 6726 10 11 N m 2 / kg 2 ) (6 kg) 2 (0 . 53 m) 2 = 8 . 55157 10 9 N . F 2 F 1 F The magnitude of the resultant force is F = radicalBig F 2 1 + F 2 2 = bracketleftBig (1 . 75466 10 8 N) 2 + (8 . 55157 10 9 N) 2 bracketrightBig 1 / 2 = 1 . 95196 10 8 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: 25 . 9828 . Explanation: The angle shown is = arctan parenleftbigg f 2 f 1 parenrightbigg = arctan parenleftbigg 8 . 55157 10 9 N 1 . 75466 10 8 N parenrightbigg = 25 . 9828 . 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 = 289 kg and radius R 2 = 1 . 22 m is inside and concen- tric with a spherical shell of mass m 1 = 207 kg and radius R 1 = 2 . 38 m (see the figure). Patel (ppp285) 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 2 kg located at a dis- tance 0 . 52 m from the center of the sphere and spherical shell. Correct answer: 1 . 10445 10 8 N. Explanation: In this case the distance a = 0 . 52 m from the particle of mass m = 2 kg to the center of the sphere (whose mass is m 2 = 289 kg) is smaller than the radius R 2 = 1 . 22 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 = (289 kg) (2 kg) (1 . 22 m) 3 (0 . 52 m) 6 . 67259 10 11 N m 2 / kg 2 = 1 . 10445 10 8 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 2 kg located at a distance 1 . 84 m from the center of the sphere and spherical shell....
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solution_pdf hw 6 - Patel (ppp285) HW06 TSOI (58160) 1 This...

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