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Unformatted text preview: Version One Homework 5 Heinz 81204 Sep 23, 2004 1 This printout should have 13 questions. Multiplechoice 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 highspeed 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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 Fall '09
 WOODAHL
 Physics, Work

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