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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. 442 PROBLEM 12.90 A 1 kg collar can slide on a horizontal rod, which is free to rotate about a vertical shaft. The collar is initially held at A by a cord attached to the shaft. A spring of constant 30 N/m is attached to the collar and to the shaft and is undeformed when the collar is at A. As the rod rotates at the rate 16 rad/s,θ = the cord is cut and the collar moves out along the rod. Neglecting friction and the mass of the rod, determine (a) the radial and transverse components of the acceleration of the collar at A, (b) the acceleration of the collar relative to the rod at A, (c) the transverse component of the velocity of the collar at B. SOLUTION First note ( )sp AF k r r= − (a) 0 and at ,F Aθ = 0r spF F= − = ( ) 0A ra = ( ) 0Aa θ = (b) :r rF maΣ = 2( )spF m r rθ− = − Noting that collar/rod ,a r= we have at A 2 collar/rod 2 collar/rod 0 [ (150 mm)(16rad/s) ] 38400 mm/s m a a = − = or 2 collar/rod( ) 38.4 m/sAa = (c) After the cord is cut, the only horizontal force acting on the collar is due to the spring. Thus, angular momentum about the shaft is conserved. 0( ) ( ) where ( )A A B B A Ar m v r m v v rθ θ θ θ= = Then 150 mm ( ) [(150 mm)(16rad/s)] 800 mm/s 450 mmBv θ = = or ( ) 0.800 m/sBv θ =
