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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. 373 PROBLEM 12.48 A 250-g block fits inside a small cavity cut in arm OA, which rotates in the vertical plane at a constant rate such that 3=v m/s. Knowing that the spring exerts on block B a force of magnitude P 1.5 N= and neglecting the effect of friction, determine the range of values of θ for which block B is in contact with the face of the cavity closest to the axis of rotation O. SOLUTION 2 : sinn n v F ma P mg Q mθ ρ Σ = + − = To have contact with the specified surface, we need 0,Q ≥ or 2 sin 0 mv Q P mg θ ρ = + − > 21 sin v P g m θ ρ > − (1) Data: 0.250 kg, 3 m/s, 1.5 N, 0.9 mm v P ρ= = = = Substituting into (1): 21 (3) 1.5 sin 9.81 0.9 0.25 sin 0.40775 θ θ > − > 24.1 155.9θ° < < °
