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PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. 379 PROBLEM 12.52 A curve in a speed track has a radius of 1000 ft and a rated speed of 120 mi/h. (See Sample Problem 12.6 for the definition of rated speed). Knowing that a racing car starts skidding on the curve when traveling at a speed of 180 mi/h, determine (a) the banking angle θ , (b) the coefficient of static friction between the tires and the track under the prevailing conditions, (c) the minimum speed at which the same car could negotiate that curve. SOLUTION Weight W mg= Acceleration 2v a ρ = : sin cosx xF ma F W maθ θΣ = + = 2 cos sin mv F mgθ θ ρ = − (1) : cos siny yF ma N W maθ θΣ = − = 2 sin cos mv N mgθ θ ρ = + (2) (a) Banking angle. Rated speed 120 mi/h 176 ft/s.v = = 0F = at rated speed. 2 2 2 0 cos sin (176) tan 0.96199 (1000) (32.2) 43.89 mv mg v g θ θ ρ θ ρ θ = − = = = = ° 43.9θ = ° (b) Slipping outward. 180 mi/h 264 ft/sv = = 2 2 2 2 cos sin sin cos (264) cos 43.89 (1000) (32.2)sin 43.89 (264) sin 43.89 (1000) (32.2)cos 43.89 0.39009 F v g F N N v g θ ρ θμ μ θ ρ θ μ −= = = + ° − °= ° + ° = 0.390μ =
