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Unformatted text preview: bello (rtb473) hw10 Demkov (59910) 1 This print-out should have 41 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points The planet Mars has a mass of 6 . 1 10 23 kg and radius of 3 . 4 10 6 m. What is the acceleration of an object in free fall near the surface of Mars? The value of the gravitational constant is 6 . 67259 10 11 N m 2 / kg 2 . Correct answer: 3 . 521 m / s 2 . Explanation: Let : M = 6 . 1 10 23 kg , R = 3 . 4 10 6 m , and G = 6 . 67259 10 11 N m 2 / kg 2 . Near the surface of Mars, the gravitation force on an object of mass m is F = G M m R 2 , so the acceleration of an object in free fall is a = F m = G M R 2 = (6 . 67259 10 11 N m 2 / kg 2 ) 6 . 1 10 23 kg (3 . 4 10 6 m) 2 = 3 . 521 m / s 2 . 002 10.0 points Two planets with the same diameter are close to each other, as shown. One planet has twice the mass as the other planet. A m B C 2 m D At which locations would both planets gravitational force pull on you in the same direction? From among these four locations, where would you stand so that the force of gravity on you is a maximum; i.e. , at which point would you weigh the most? 1. C; A 2. B; D 3. A and D; D correct 4. A and D; A 5. A and B; D 6. D; D 7. B and C; D 8. None of these 9. B and C; C Explanation: At A and D, the planets are on the same side of you, so they pull you in the same direction, causing you to weigh more. At B and C, you would weigh less because the planets pull on you in opposite directions. The closer you stand to the more massive one, the more you weigh, so you would feel a maximum weight at D. 003 10.0 points An object of mass m moves in a smooth, straight tunnel dug between two points on a planets surface. Assume the planets den- sity is uniform throughout its volume and the gravitational force acts toward the planets center. x y F m x bello (rtb473) hw10 Demkov (59910) 2 Find the period of this simple har- monic motion. The mass of the planet is 4 . 07 10 24 kg and its radius 8 10 6 m, and the value of the gravitational constant is 6 . 67259 10 11 Ncdotm 2 / kg 2 . Correct answer: 143 . 787 min. Explanation: Let : M = 4 . 07 10 24 kg , R = 8 10 6 m , and G = 6 . 67259 10 11 Ncdotm 2 / kg 2 . The gravitational force depends on the dis- tance r from the center of the planet: vector F r = GmM r r 2 r . Since the spherical shell whose inside radius is r and outside radius is R does not contribute to the gravitational force, the force on the object is determined only by the mass inside a sphere of radius r . x y r m The density of the planet is = M V = M 4 3 R 3 = 3 M 4 R 3 ....
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