Text Material Preview
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. 378 PROBLEM 12.51 A carnival ride is designed to allow the general public to experience high acceleration motion. The ride rotates about Point O in a horizontal circle such that the rider has a speed v0. The rider reclines on a platform A which rides on rollers such that friction is negligible. A mechanical stop prevents the platform from rolling down the incline. Determine (a) the speed v0 at which the platform A begins to roll upwards, (b) the normal force experienced by an 80-kg rider at this speed. SOLUTION Radius of circle: 5 1.5cos70 5.513 m : R m = + ° = Σ =F a Components up the incline, 70°: 2 0cos 20 sin 20A mv m g R − ° = − ° (a) 0Speed :v 1 1 2 2 0 (9.81 m/s) (5.513 m 12.1898 m/s tan 20 tan 20 g R v = = = ° ° 0 12.19 m/sv = Components normal to the incline, 20°. 2 0sin 20 cos 20 . mv N mg R − ° = ° (b) Normal force: 280(12.1898) (80)(9.81)sin 20 cos 20 2294 N 5.513 N = ° + ° = 2290 NN =
