F _ A , F _ B and F _ C are three forces acting at point P as shown in figure. The whole system is in equilibrium state. The magnitude of F _ A is

Step-by-step solution

The system is in equilibrium at point P. We resolve the forces F_A and F_B into their horizontal and vertical components. For horizontal equilibrium: F_B (45^ ) - F_A (30^ ) = 0 F_B 1 2 = F_A 3 2 F_B = F_A 3 2 = F_A 1.5 For vertical equilibrium: F_A (30^ ) + F_B (45^ ) = F_C Since F_C = 100 N, we have: F_A (30^ ) + (F_A 1.5 ) (45^ ) = 100 F_A (0.5) + F_A 1.5 ( 1 2 ) = 100 F_A (0.5) + F_A ( 3 2 ) ( 1 2 ) = 100 F_A (0.5) + F_A ( 3 2 ) = 100 F_A (0.5 + 0.866) = 100 F_A (1.366) = 100 F_A = 100 1.366 73.206 N. Answer: 7