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Unformatted text preview: dang (ttd73) HW04 Tsoi (58020) 1 This print-out should have 27 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A distant star has a single planet circling it in a circular orbit of radius 3 . 6 10 11 m. The period of the planets motion about the star is 924 days. What is the mass of the star? The value of the universal gravitational constant is 6 . 67259 10 11 N m 2 / kg 2 . Correct answer: 4 . 33113 10 30 kg. Explanation: Let : G = 6 . 67259 10 11 N m 2 / kg 2 , R B = 3 . 6 10 11 m , and T B = 924 day . T B = (924 day) parenleftbigg 24 h 1 day parenrightbigg 3600 s 1 h = 7 . 98336 10 7 s . According to Newtons explanation of Ke- plers third law R 3 B T 2 B = GM s 4 2 = const. The mass of the star is thus M s = 4 2 G R 3 B T 2 B = 4 2 6 . 67259 10 11 N m 2 / kg 2 (3 . 6 10 11 m) 3 (7 . 98336 10 7 s) 2 = 4 . 33113 10 30 kg . 002 (part 1 of 5) 10.0 points A car travels at a speed of 18 m / s around a curve of radius 36 m. The acceleration of gravity is 9 . 8 m / s 2 . 2 . 2 M g 26 What is the net centripetal force needed to keep the car from skidding sideways? Correct answer: 19800 N. Explanation: Let : m = 2200 kg , v = 18 m / s , r = 36 m , = 26 , and = 0 . 297416 Part5 . The centripetal acceleration of the car rounding a curve is a c = v 2 R and the net centripetal force needed to provide such ac- celeration is F c = ma c = mv 2 R = 19800 N . 003 (part 2 of 5) 10.0 points Were there no friction between the cars tires and the road, what centripetal force could be provided just by the banking of the road? Correct answer: 10515 . 5 N. Explanation: In the absence of friction, there are only two forces acting on the car, namely its weight mvectorg and the normal force vector N provided by the road. The weight is directed vertically down while the normal force is directed perpendicular to the banked road surface and thus at the angle from the vertical. The centripetal force due to banking comes from the horizontal component of the normal force, F banking c = N sin . The free body diagram in the vertical di- rection gives N cos = mg or N = mg cos and horizontally gives F banking c = N sin dang (ttd73) HW04 Tsoi (58020) 2 = mg cos sin = mg tan = 10515 . 5 N . 004 (part 3 of 5) 10.0 points Now suppose the friction force is sufficient to keep the car from skidding. Calculate the magnitude of the normal force exerted on the car by the roads surface. Hint: Check the correctness of your answer to the first question before proceeding with this and the following questions....
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This note was uploaded on 03/31/2009 for the course PHY 302K taught by Professor Kaplunovsky during the Spring '08 term at University of Texas at Austin.
- Spring '08