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Unformatted text preview: Nguyen, Thanh Homework 18 Due: Nov 9 2007, 7:00 pm Inst: D Weathers 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Three 2 kg masses are located at points in the xy plane as shown. 42 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: 1 . 70847 10 9 N. Explanation: Let : m = 2 kg , x = 42 cm = 0 . 42 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 m m x 2 = G m 2 x 2 = (6 . 6726 10 11 N m 2 / kg 2 )(2 kg) 2 (0 . 42 m) 2 = 1 . 51306 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 )(2 kg) 2 (0 . 58 m) 2 = 7 . 93413 10 10 N . F 2 F 1 F The magnitude of the resultant force is F = q F 2 1 + F 2 2 = h (1 . 51306 10 9 N) 2 + (7 . 93413 10 10 N) 2 i 1 / 2 = 1 . 70847 10 9 N . keywords: 002 (part 1 of 1) 10 points A m = 75 . 9 kg object is released from rest at a distance h = 1 . 03794 R above the Earths surface. The acceleration of gravity is 9 . 8 m / s 2 . For the Earth, R E = 6 . 38 10 6 m, M = 5 . 98 10 24 kg. The gravitational acceleration at the surface of the earth is g = 9 . 8 m / s 2 . Find the speed of the object when it strikes the Earths surface. Neglect any atmospheric friction. Caution: You must take into account that the gravitational acceleration depends on dis tance between the object and the center of the earth. Correct answer: 7980 . 48 m / s. Explanation: Let : h R E = 1 . 03794 , or h = (1 . 03794) R E , where R E = 6 . 38 10 6 m , M E = 5 . 98 10 24 kg , g = 9 . 8 m / s 2 , and m = 75 . 9 kg , not required . Nguyen, Thanh Homework 18 Due: Nov 9 2007, 7:00 pm Inst: D Weathers 2 Basic Concepts: U = G M m r and g = G M R 2 E ....
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