Engineering Mechanics: Statics & Dynamics (14th Edition)

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

Chapter 2 - Force Vectors - Section 2.4 - Addition of a System of Coplanar Forces - Problems - Page 41: 45

Answer

$F_{R}$ = $\sqrt {F_{1}^{2}+F_{2}^{2}+2F_{1}F_{2}CosU}$ Angle X= $tan^{-1}[\frac{F_{1}sin U}{F_{2} + F_{1}CosU}]$

Work Step by Step

By using $Cosine Law:$ $F_{R}$ = $\sqrt {F_{1}^{2}+F_{2}^{2}-2F_{1}F_{2}Cos(180-U)}$ "U" is the angle between $F_{1}$ and $F_{2}$ since $Cos(180-U) = -CosU$ $F_{R}$ = $\sqrt {F_{1}^{2}+F_{2}^{2}-2F_{1}F_{2}(-CosU)}$ $F_{R}$ = $\sqrt {F_{1}^{2}+F_{2}^{2}+2F_{1}F_{2}CosU}$ Ans $X$ is the direction angle made by $F_{R}$ tan$X$= $[\frac{F_{1}sin U}{F_{2} + F_{1}CosU}]$ Angle $X$= $tan^{-1}[\frac{F_{1}sin U}{F_{2} + F_{1}CosU}] Ans$
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