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 4.4 - Principle of Moments - Problems - Page 144: 47

Answer

$$ \mathbf{M}_A=\{-16.0 \mathbf{i}-32.1 \mathbf{k}\} \mathrm{N} \cdot \mathrm{m} $$

Work Step by Step

$$ \begin{aligned} \mathbf{F} & =100\left(\frac{-0.4 \mathbf{i}+0.6 \mathbf{j}+0.2 \mathbf{k}}{0.7483}\right) \\ \mathbf{F} & =\{-53.5 \mathbf{i}+80.2 \mathbf{j}+26.7 \mathbf{k}\} \mathbf{N} \\ \mathbf{M}_A & =\mathbf{r}_B \times \mathbf{F}=\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 0 & -0.6 & 0 \\ -53.5 & 80.2 & 26.7 \end{array}\right|=\{-16.0 \mathbf{i}-32.1 \mathbf{k}\} \mathbf{N} \cdot \mathbf{m} \end{aligned} $$ $$ \mathbf{M}_A=\mathbf{r}_C \times \mathbf{F}=\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -0.4 & 0 & 0.2 \\ -53.5 & 80.2 & 26.7 \end{array}\right|=\{-16.0 \mathbf{i}-32.1 \mathbf{k}\} \mathbf{N} \cdot \mathrm{m} $$
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