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.