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 138: 7

Answer

$$ \begin{aligned} & \left(M_{F_1}\right)_A=433 \mathrm{~N} \cdot \mathrm{m}↻ \\ & \left(M_{F_2}\right)_A=1.30 \mathrm{kN} \cdot \mathrm{m}↻ \\ & \left(M_{F_3}\right)_A=800 \mathrm{~N} \cdot \mathrm{m} ↻ \end{aligned} $$

Work Step by Step

The moment arm measured perpendicular to each force from point $A$ is $$ \begin{aligned} & d_1=2 \sin 60^{\circ}=1.732 \mathrm{~m} \\ & d_2=5 \sin 60^{\circ}=4.330 \mathrm{~m} \\ & d_3=2 \sin 53.13^{\circ}=1.60 \mathrm{~m} \end{aligned} $$ Using each force where $M_A=F d$, we have $$ \begin{aligned} ↺+\left(M_{F_1}\right)_A & =-250(1.732) \\ & =-433 \mathrm{~N} \cdot \mathrm{m}=433 \mathrm{~N} \cdot \mathrm{m}(\text { Clockwise }) \\ ↺+\left(M_{F_2}\right)_A & =-300(4.330) \\ & =-1299 \mathrm{~N} \cdot \mathrm{m}=1.30 \mathrm{kN} \cdot \mathrm{m}(\text { Clockwise }) \\ ↺+\left(M_{F_3}\right)_A & =-500(1.60) \\ & =-800 \mathrm{~N} \cdot \mathrm{m}=800 \mathrm{~N} \cdot \mathrm{m}(\text { Clockwise }) \end{aligned} $$
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