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 142: 32

Answer

$$ \mathbf{M}_A=\{-110 \mathbf{i}+70 \mathbf{j}-20 \mathbf{k}\} \mathrm{N} \cdot \mathrm{m} $$

Work Step by Step

The coordinates of point $C$ are $C(0.5,0.7,-0.3) \mathrm{m}$. $$ \mathbf{r}_{A C}=\{0.5 \mathbf{i}+0.7 \mathbf{j}-0.3 \mathbf{k}\} \mathrm{m} $$ Moment of Force $\boldsymbol{F}$ About Point $\boldsymbol{A}$. $$ \begin{aligned} \mathbf{M}_A & =\mathbf{r}_{A C} \times \mathbf{F} \\ & =\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 0.5 & 0.7 & -0.3 \\ 600 & 800 & -500 \end{array}\right| \\ & =\{-110 \mathbf{i}+70 \mathbf{j}-20 \mathbf{k}\} \mathbf{N} \cdot \mathrm{m} \end{aligned} $$
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