Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 2 - Force Vectors - Section 2.3 - Vector Addition of Forces - Problems: 21

Answer

$F_R=257N$ $\phi=163^{\circ}$

Work Step by Step

$c=\sqrt{a^2+b^2}$ $F'=\sqrt{200^2+400^2}$ $F'=447.21N$ $\theta' = \arctan(200/400)=26.57^{\circ}$ $\phi=90^{\circ}-30^{\circ}-26.57^{\circ}=33.43^{\circ}$ $c=\sqrt{a^2+b^2-2*a*b*\cos(C)}$ $F_R=\sqrt{300^2+447.21^2-2*300*447.21*\cos(33.43^{\circ})}$ $F_R=257N$ $\sin33.43^{\circ} / 257.05 = \sin \theta/ 300$ $\theta= 40.02^{\circ}$ $\phi=90^{\circ}+40.02^{\circ}+33.43^{\circ}=163^{\circ}$
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