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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. 374 PROBLEM 12.49 A series of small packages, each with a mass of 0.5 kg, are discharged from a conveyor belt as shown. Knowing that the coefficient of static friction between each package and the conveyor belt is 0.4, determine (a) the force exerted by the belt on a package just after it has passed Point A, (b) the angle θ defining the Point B where the packages first slip relative to the belt. SOLUTION Assume package does not slip. 0,t f sa F Nμ= ≤ On the curved portion of the belt 2 2 2(1 m/s) 4 m/s 0.250 mn v a ρ = = = For any angle θ 2 : cosy y n mv F ma N mg maθ ρ Σ = − = − = − 2 cos mv N mg θ ρ = − (1) : sin 0x x f tF ma F mg maθΣ = − + = = sinfF mg θ= (2) (a) At Point A, 0θ = ° (0.5)(9.81)(1.000) (0.5)(4)N = − 2.905 NN = (b) At Point B, sin ( cos ) 4 sin cos 0.40 cos 9.81 f s s n n s F N mg mg ma a g μ θ μ θ θ μ θ θ = = − = − = −
