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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 θ 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 Earth’s 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 Earth’s 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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This note was uploaded on 10/24/2011 for the course PHYS 1710 taught by Professor Weathers during the Winter '08 term at North Texas.
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