Problem 314 | Equilibrium of Concurrent Force System

$\Sigma F_y = 0$

$F \sin 30^\circ + 40 \cos 15^\circ = 30 \sin 30^\circ + 20 \sin 60^\circ$

$0.5F = -6.3165$

$F = -12.63 \, \text{ kN}$           answer
 

 

$\Sigma F_x = 0$

$P + 20 \cos 60^\circ + 40 \sin 15^\circ = 30 \cos 30^\circ + F \cos 30^\circ$

$P + 10 + 10.35 = 25.98 + (-12.63)(0.8660)$

$P = -5.31 \, \text{ kN}$           answer