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Unformatted text preview: Version One Homework 5 Heinz 81204 Sep 23, 2004 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. Horizontal Circle 05 06:01, trigonometry, numeric, > 1 min, nor- mal. 001 (part 1 of 1) 10 points A 22 g ball is fastened to one end of a string 20 cm long and the other end is held fixed at point O so that the string makes an angle of 20 with the vertical, as in the figure. This angle remains constant as the ball rotates in a horizontal circle. The angle would remain constant only for a particular speed of the ball in its circular path. The acceleration of gravity is 9 . 8 m / s 2 . v r 9 . 8 m / s 2 2 c m 22 g 20 Find this speed v . Correct answer: 0 . 493955 m / s. Explanation: The centripetal acceleration of the rotating ball has magnitude a c = v 2 r = v 2 sin (1) and is directed horizontally towards the rota- tion axis. Substituting this acceleration into Newtons Second Law, we have m~a c = ~ T + m~g , or ma c = T sin , and 0 = T cos - mg . T mg Consequently, a c = g tan = (9 . 8 m / s 2 )tan20 = 3 . 56691 m / s 2 . and using Eq. 1, we have v = p a c sin = p g tan sin = s g sin 2 cos = s (9 . 8 m / s 2 )(20 cm)sin 2 20 cos20 = 0 . 493955 m / s . Inclined Curve 06:01, trigonometry, numeric, > 1 min, nor- mal. 002 (part 1 of 1) 10 points A high-speed test track for cars has a curved section an arc of a circle of radius R = 952 m. The curved section is banked at angle = 15 from the horizontal to help the cars to stay in the road while moving at high speeds. The acceleration of gravity is 9 . 8 m / s 2 . r SIDE VIEW TOP VIEW One day, oil spills on the track making a few meters of the curved section frictionless....
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