p201f04-homework05-sol

# p201f04-homework05-sol - Version One – Homework 5 –...

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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 θ 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 θ (1) and is directed horizontally towards the rota- tion axis. Substituting this acceleration into Newton’s Second Law, we have m~a c = ~ T + m~g , or ma c = T sin θ , and 0 = T cos θ- mg . T mg θ Consequently, a c = g tan θ = (9 . 8 m / s 2 )tan20 ◦ = 3 . 56691 m / s 2 . and using Eq. 1, we have v = p a c ‘ sin θ = p g tan θ ‘ sin θ = s g ‘ sin 2 θ cos θ = 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 θ = 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 θ One day, oil spills on the track making a few meters of the curved section frictionless....
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p201f04-homework05-sol - Version One – Homework 5 –...

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