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Unformatted text preview: alexander (jra2623) homework 12 Turner (92510) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 3) 10.0 points A student builds and calibrates an accelerom- eter, which she uses to determine the speed of her car around a certain highway curve. The accelerometer is a plumb bob with a protrac- tor that she attaches to the roof of her car. A friend riding in the car with her observes that the plumb bob hangs at an angle of 20 from the vertical when the car has a speed of 27 . 3 m / s. The acceleration of gravity is 9 . 8 m / s 2 . At this instant, what is the centripetal ac- celeration of the car rounding the curve? Correct answer: 3 . 56691 m / s 2 . Explanation: For the plumb bob, along the vertical direc- tion we have T cos = m g along the horizontal direction we have T sin = m v 2 r From these two equations the centripetal ac- celeration is a c = v 2 r = g tan , the radius of the curve is r = v 2 g tan , and the speed of the car v = radicalbig g r tan . The deflection angle is 1 = 20 , so a c = g tan 1 = ( 9 . 8 m / s 2 ) tan20 = 3 . 56691 m / s 2 . 002 (part 2 of 3) 10.0 points What is the radius of the curve? Correct answer: 208 . 946 m. Explanation: The radius is r = v 2 g tan 1 = (27 . 3 m / s) 2 (9 . 8 m / s 2 ) tan20 = 208 . 946 m . 003 (part 3 of 3) 10.0 points What is the speed of the car if the plumb bobs deflection is 8 . 5 while rounding the same curve? Correct answer: 17 . 4936 m / s. Explanation: Here the deflection angle is 2 = 8 . 5 so v 2 = radicalbig g r tan 2 = radicalBig (9 . 8 m / s 2 ) (208 . 946 m) tan8 . 5 = 17 . 4936 m / s . 004 10.0 points A highway curves to the left with radius of curvature R = 44 m. The highways surface is banked at = 16 so that the cars can take this curve at higher speeds. Consider a car of mass 1900 kg whose tires have static friction coefficient = 0 . 67 against the pavement. The acceleration of gravity is 9 . 8 m / s 2 . alexander (jra2623) homework 12 Turner (92510) 2 top view R = 44 m 16 rear view = . 6 7 How fast can the car take this curve without skidding to the outside of the curve? Correct answer: 22 . 5977 m / s....
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This note was uploaded on 10/20/2011 for the course PHY 302K taught by Professor Kaplunovsky during the Summer '08 term at University of Texas at Austin.
- Summer '08