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Unformatted text preview: Muraj, Hamza – Homework 12 – Due: Feb 20 2006, 4:00 am – Inst: Florin 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A civil engineer is to design a road curved at a 120 m radius to carry racing cars traveling at 21 m / s. The acceleration of gravity is 9 . 8 m / s 2 . 2 . 1 M g μ = . 1 8 θ At what angle θ should it be banked for maximum control of the racing car? Correct answer: 20 . 5561 ◦ . Explanation: Let : m = 2100 kg , v = 21 m / s , r = 120 m , μ = 0 . 18 . Consider the free body diagram for the car m g s i n θ N = m g c o s θ μ N  W k m a k  mg W k = mg sin θ a k = v 2 r cos θ . Basic Concepts: F r = ma r = mv 2 r Solution: The car will have optimum con trol when the frictional is zero. Then only two forces act on the vehicle: weight acting straight down and the normal force acting perpendicular to the surface of the track. The resultant force is an inwardly directed force, and is the centripetal force. Thus tan θ = F c mg = mv 2 r mg = v 2 r g , so θ = arctan • v 2 r g ‚ = arctan • (21 m / s) 2 (120 m)(9 . 8 m / s 2 ) ‚ = 20 . 5561 ◦ . 002 (part 1 of 1) 10 points A car is moving at 19 m / s along a curve on a horizontal plane with radius of curvature 44 m . The acceleration of gravity is 9 . 8 . What is the required minimum coefficient of static friction between the road and the car’s tires to keep the car from skidding? Correct answer: 0 . 837199 ....
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This note was uploaded on 04/12/2010 for the course PHY 58195 taught by Professor Turner during the Spring '09 term at University of Texas at Austin.
 Spring '09
 Turner

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