Question 2.57: If F2 = 150 and θ = 55°, determine the magnitude and directi...
If F_{2} = 150 and θ = 55°, determine the magnitude and direction, measured clockwise from the positive x axis, of the resultant force of the three forces acting on the bracket.
Scalar Notation: Summing the force components algebraically, we have
\overset{+}{\longrightarrow } F_{R_{x} } = \sum{F_{x}; F_{R_{x}}=80+52\left(\frac{15}{3} \right) } +150 cos 80^{°}= 126.05 lb →
+\uparrow F_{R_{y} } = \sum{F_{y}; F_{R_{y} }=52\left(\frac{12}{13} \right) } -150 sin 80^{°}= -99.72 lb = 99.72 lb ↓
The magnitude of the resultant force F_{R} is:
F_{R} = \sqrt{F^{2}_{R_{x} } + F^{2}_{R_{y} }} =\sqrt{126.05^{2}+99.72^{2} } =161 lb
The direction angle θ measured clockwise from positive x axis is
θ = tan^{-1} \frac{F_{R_{y} }}{F_{R_{x} }} =tan^{-1}\left(\frac{99.72}{126.05} \right) =38.3°
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