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 4.5 - Moment of a Force about a Specified Axis - Problems - Page 153: 63

Answer

$$M_{C A}=226 \mathrm{~N} \cdot \mathrm{m} $$

Work Step by Step

$$ \begin{aligned} &\mathbf{u}_{C A}=\frac{|-2 \mathbf{i}+2 \mathbf{j}|}{\sqrt{(-2)^2+(2)^2}}\\ &\mathbf{u}_{C A}=\{-0.707 \mathbf{i}+0.707 \mathbf{j}\}\\ &M_{C A}=\mathbf{u}_{C A} \cdot\left(\mathbf{r}_{A D} \times \mathbf{F}\right)=\left|\begin{array}{ccc} -0.707 & 0.707 & 0 \\ 2.5 & 0 & 4 \\ 50 & -20 & -80 \end{array}\right|\\ &M_{C A}=226 \mathrm{~N} \cdot \mathrm{m} \end{aligned} $$
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