Question

The resultant of the three concurrent forces acting on the eyebolt is the force R = 800j lb. Determine the magnitude of the force P and the angle θ that specifies the direction of the 900-lb force.

Answer 1

Assume the body diagram below

For equilibrium condition in y-direction

$\Sigma F_y=0$

$900sin\theta+500sin\alpha=800$

$900sin\theta+500(3/5)=800$

$sin\theta=500/900=5/9$

$\theta=33.74^o$

for the horizontal force, x-direction

$\Sigma F_x=0$

$-900cos\theta+500cos\alpha+P=0$

$-P=-900cos(33.74^o)+500(4/5)$

$P=348.40N$