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# hw30 - Muraj Hamza Homework 30 Due 4:00 am Inst Florin This...

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Muraj, Hamza – Homework 30 – Due: Apr 14 2006, 4:00 am – Inst: Florin 1 This print-out should have 11 questions. Multiple-choice 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 N m 2 / kg 2 . A 1550 kg geosynchronous satellite orbits a planet similar to Earth at a radius 193000 km from the planet’s 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 N m 2 / kg 2 , M satellite = 1550 kg , and T = 86400 s . Solution: v = 2 π r T F = M satellite v 2 r = M satellite 4 π 2 r T 2 (1) = (1550 kg) 4 π 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 π 2 r T 2 G M satellite M planet r 2 = M satellite 4 π 2 r T 2 , so M planet = 4 π 2 G T 2 r 3 = 4 π 2 (6 . 67259 × 10 - 11 N m 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 ρ ( 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 = ρ dV = C r (4 π r 2 dr ) . M = Z dm = 4 π C Z r 0 R dR , = 4 π C 1 2 R 2 ¶ fl fl fl fl r 0 = 2 π C r 2 = (35 . 4482 m 2 ) π C C = M (35 . 4482 m 2 ) π = 1011 kg (35 . 4482 m 2 ) π = 9 . 07835 kg / m 2 . 004 (part 2 of 3) 10 points Find the gravitational field 5 . 25 m from the center of the sphere. Correct answer: 2 . 44753 × 10 - 9 N / kg.

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hw30 - Muraj Hamza Homework 30 Due 4:00 am Inst Florin This...

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