Engineering Mechanics: Statics & Dynamics (14th Edition)

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

Chapter 3 - Equilibrium of a Particle - Section 3.3 - Coplanar Force Systems - Problems - Page 102: 28

Answer

$\begin{aligned} & F_{A B}=50 \mathrm{lb} \\ & F_{A D}=70.7 \mathrm{lb} \\ & h=23 \mathrm{ft}\end{aligned}$

Work Step by Step

At point $B$ : $ \begin{array}{ll} +\uparrow \Sigma F_y=0 ; & \frac{1}{\sqrt{2}} F_{B C}-50=0 \\ & F_{B C}=70.71=70.7 \mathrm{lb} \\ \Sigma F_X=0 ; & \frac{1}{\sqrt{2}}(70.71)-F_{A B}=0 \\ & F_{A B}=50 \mathrm{lb} \end{array} $ At point $A$ : $ \begin{array}{ll} \stackrel{ \pm}{\rightarrow} F_x=0 ; & 50-F_{A D} \cos \theta=0 \\ +\uparrow \Sigma F_y=0 ; & F_{A D} \sin \theta-50=0 \\ & \theta=45^{\circ} \\ & F_{A D}=70.7 \mathrm{lb} \\ & h=18+5=23 \mathrm{ft} \end{array} $
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