Question

Two forces, F1= 8.0 N, 60 degrees 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

$F_x=-8\cdot\cos60°-12\cdot\cos45°=-12.5\ (N)$

$F_y=8\cdot\sin60°-12\cdot\sin45°=-1.6\ (N)$

$F=\sqrt{12.5^2+1.6^2}=12.6\ (N)$

$\tan\theta=\frac{1.6}{12.5}=0.128\to \theta=7.3°$ N of E.