Question - Determination of Resultant Force Magnitude and Direction

\(R_{x} = 6 \cos(45^\circ)N - 2N\)

\(R_{x} = 4.2426N - 2N\)

\(R_{x} = 2.2426N\)

\(R_{y} = 6 \sin(45^\circ)N\)

\(R_{y} = 4.2426N\)

\(R = \sqrt{R_{x}^2 + R_{y}^2}\)

\(R = \sqrt{2.2426^2 + 4.2426^2}N\)

\(R = \sqrt{5.0291 + 18.0000}N\)

\(R = \sqrt{23.0291}N\)

\(R \approx 4.8001N\)

\(\theta = \arctan\left(\frac{R_{y}}{R_{x}}\right)\)

\(\theta = \arctan\left(\frac{4.2426}{2.2426}\right)\)

\(\theta \approx 62.1021^\circ\) clockwise from the +x-axis

\(R_{x} = 800 \cos(30^\circ)N - 600 \cos(45^\circ)N\)

\(R_{x} = 692.82N - 424.26N\)

\(R_{x} = 268.56N\)

\(R_{y} = 800 \sin(30^\circ)N + 600 \sin(45^\circ)N\)

\(R_{y} = 400N + 424.26N\)

\(R_{y} = 824.26N\)

\(R = \sqrt{R_{x}^2 + R_{y}^2}\)

\(R = \sqrt{268.56^2 + 824.26^2}N\)

\(R = \sqrt{72105.59 + 679186.67}N\)

\(R = \sqrt{751292.27}N\)

\(R \approx 866.77N\)

\(\theta = \arctan\left(\frac{R_{y}}{R_{x}}\right)\)

\(\theta = \arctan\left(\frac{824.26}{268.56}\right)\)

\(\theta \approx 71.5651^\circ\) counterclockwise from the +x-axis