Engineering Mechanics: Statics & Dynamics (14th Edition)

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

Chapter 3 - Equilibrium of a Particle - Section 3.3 - Coplanar Force Systems - Problems - Page 98: 6


$\theta=70.1^{\circ}$ $T=7.66kN$

Work Step by Step

First we will sum the forces horizontally $(\rightarrow +) \sum \overrightarrow{F}_{x} =0 $ $T\cos\phi−4/5(8)=0$ Now we will sum the forces vertically $(\uparrow +) \sum \overrightarrow{F}_{y} =0 $ $9-T\sin\phi-3/5(8)=0$ Solving the system of two equations, we obtain : $T=7.66kN$ $\phi=33.27^{\circ}$ $\phi$ is the angle that member C makes with the x-axis. We were asked for the angle between B and C, so we will need to add $\phi$ to the angle that member B makes with the x-axi. $\theta= \phi + \arctan(3/4)= 33.27^{\circ} + \arctan(3/4)=70.1^{\circ}$
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