Engineering Mechanics: Statics & Dynamics (14th Edition)

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

Chapter 4 - Force System Resultants - Section 4.7 - Simplification of a Force and Couple System - Problems - Page 174: 97

Answer

$$ \begin{aligned} & F_R=365 \mathrm{~N} \\ & \theta=70.8^{\circ} \text {. } \\ & \left(M_R\right)_o=2364 \mathrm{~N} \cdot \mathrm{m} \text { (counterclockwise) } \end{aligned} $$

Work Step by Step

$$ \begin{aligned} & \stackrel{+}{\rightarrow}\left(F_R\right)_x=\Sigma F_x ; \quad\left(F_R\right)_x=600 \cos 60^{\circ}-455\left(\frac{12}{13}\right)=-120 \mathrm{~N}=120 \mathrm{~N} \leftarrow \\ & +\uparrow\left(F_R\right)_y=\Sigma F_y ; \quad\left(F_R\right)_y=455\left(\frac{5}{13}\right)-600 \sin 60^{\circ}=-344.62 \mathrm{~N}=344.62 \mathrm{~N} \downarrow \end{aligned} $$ $$ F_R=\sqrt{\left(F_R\right)_x^2+\left(F_R\right)_y^2}=\sqrt{120^2+344.62^2}=364.91 \mathrm{~N}=365 \mathrm{~N} \quad \text { Ans. } $$ And $$ \theta=\tan ^{-1}\left[\frac{\left(F_R\right)_y}{\left(F_R\right)_x}\right]=\tan ^{-1}\left(\frac{344.62}{120}\right)=70.80^{\circ}=70.8^{\circ} \text { マ } $$ Also, $$ \begin{aligned} ↺+\left(M_R\right)_O=\Sigma M_O ;\left(M_R\right)_O & \\=455\left(\frac{12}{13}\right)(2)+600 \cos 60^{\circ}(0.75)+600 \sin 60^{\circ} \\ =2364 \mathrm{~N} \cdot \mathrm{m}(\text { counterclockwise }) \end{aligned} $$
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