Determine the concurrent forces:

Four coplanar concurrent forces act at point and keep it at rest. These are mention in Figure. Determine the forces P and Q.

Solution

Let us assume that forces P and Q act away from the point O. As the point O remains at rest, we may apply equations of equilibrium

∑ F_x  = 0

∴ 310 + P cos 60^o - 1260 cos 60^o = 0

∴ 310 + 0.5 P - 1260 × 0.5 = 0

∴ P = (630 - 310) /0.5 = 640 N

As P works out to be positive, its assumed direction is correct. Thus, P acts away from O.

Also, ∑ F_y  = 0

∴ P sin 60^o + 1260 sin 60^o - Q = 0

∴ Q = (640 + 1260) sin 60^o

∴ Q = 1645.4 N

As Q is also positive, the assumed direction of Q is correct. Therefore, Q acts away from O.