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Unformatted text preview: Muraj, Hamza Homework 30 Due: Apr 14 2006, 4:00 am Inst: Florin 1 This printout should have 11 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 2) 10 points Given: G = 6 . 67259 10 11 Nm 2 / kg 2 . A 1550 kg geosynchronous satellite orbits a planet similar to Earth at a radius 193000 km from the planets center. Its angular speed at this radius is the same as the rotational speed of the Earth, and so they appear stationary in the sky. That is, the period of the satellite is 24 h . What is the force acting on this satellite? Correct answer: 1582 . 05 N. Explanation: Let : G = 6 . 67259 10 11 Nm 2 / kg 2 , M satellite = 1550 kg , and T = 86400 s . Solution: v = 2 r T F = M satellite v 2 r = M satellite 4 2 r T 2 (1) = (1550 kg) 4 2 (1 . 93 10 8 m) (86400 s) 2 = 1582 . 05 N . 002 (part 2 of 2) 10 points What is the mass of this planet? Correct answer: 5 . 69783 10 26 kg. Explanation: Using the general gravitation law and Eq. 1, we have F = G M satellite M planet r 2 = M satellite 4 2 r T 2 G M satellite M planet r 2 = M satellite 4 2 r T 2 , so M planet = 4 2 G T 2 r 3 = 4 2 (6 . 67259 10 11 Nm 2 / kg 2 ) (86400 s) 2 (1 . 93 10 8 m) 3 = 5 . 69783 10 26 kg . 003 (part 1 of 3) 10 points The density of a sphere is given by ( r ) = C r . The sphere has a radius of 4 . 21 m and a mass of 1011 kg. Find the constant C . Correct answer: 9 . 07835 kg / m 2 . Explanation: r = 4 . 21 m and M = 1011 kg . The mass of a differential element of the sphere is dm = dV = C r (4 r 2 dr ) . M = Z dm = 4 C Z r R dR , = 4 C 1 2 R 2 fl fl fl fl r = 2 C r 2 = (35 . 4482 m 2 ) C C = M (35 . 4482 m 2 ) = 1011 kg (35 . 4482 m 2 ) = 9 . 07835 kg / m 2 ....
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This note was uploaded on 04/12/2010 for the course PHY 58195 taught by Professor Turner during the Spring '09 term at University of Texas at Austin.
 Spring '09
 Turner

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