Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 11 - Virtual Work - Section 11.3 - Principle of Virtual Work for a System of Connected Rigid Bodies - Problems - Page 596: 22



Work Step by Step

The required angle can be determined as follows: $F_s=k(2sin\theta-2sin0)$ $\implies F_s=50(2sin\theta-0)=100sin\theta$ The virtual displacements are given as $\delta_{yC}=\frac{d(4sin\theta)}{d\theta}=4cos\theta$ and $\delta_{yD/2}=\frac{d(2sin\theta)}{d\theta}=2cos\theta$ Now, according to the virtual-work equation $\delta U=0$ $\implies P\delta_{yC}F_s\delta_{yD/2}=0$ We plug in the known values to obtain: $8(4)cos\theta-100sin\theta(2)cos\theta=0$ This simplifies to: $\theta=9.21^{\circ}$
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