Question

Two forces, F₁ = 8.0 N, 60^o Northwest and F₂ = 12.0 N, Southwest, are applied to a particle at the origin. What third force is needed so that the particle will not be displaced from the origin?

Answer 1

$-F_{3x}=F_1cos 60°+F_2cos45°,\\ F_{3x}=-12.49~\text{N},$

$F_{3y}=F_2sin45°-F_1sin60°,\\ F_{3y}=1.56~\text{N}.$

$F=\sqrt{F_{3x}^2+F_{3y}^2}=12.59~\text{N},$

$\alpha=arctan|\frac{F_{3y}}{F_{3x}}|=83°~$ East of North.