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 176: 111

Answer

$$ \begin{aligned} & \mathbf{F}_R=\{-40 \mathbf{j}-40 \mathbf{k}\} \mathbf{N} \\ & \mathbf{M}_{R A}=\{-12 \mathbf{j}+12 \mathbf{k}\} \mathrm{N} \cdot \mathrm{m} \end{aligned} $$

Work Step by Step

$$ \begin{aligned} \mathbf{F}_R & =\mathbf{F}_1+\mathbf{F}_2 \\ \mathbf{F}_R & =\{-40 \mathbf{j}-40 \mathbf{k}\} \mathbf{N} \\ \mathbf{M}_{R A} & =\Sigma(\mathbf{r} \times \mathbf{F}) \\ & =\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -0.3 & 0 & 0.08 \\ 0 & -40 & 0 \end{array}\right|+\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -0.3 & 0.08 & 0 \\ 0 & 0 & -40 \end{array}\right| \\ \mathbf{M}_{R A} & =\{-12 \mathbf{j}+12 \mathbf{k}\} \mathbf{N} \cdot \mathrm{m} \end{aligned} $$
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