Example Problem # $6$: The $225-lb$ weight is

supported by five cables, one of which contains a

spring stretched by $2$ inches. Cable $OD$ lies in the

$x-y$ plane. Disregard the weights of the cables and

spring. It is desired to determine the magnitudes of

the tension forces in the five cables needed to

maintain equilibrium.

$($a$)$ Draw two FBDs: one for the knot at $O,$ and one

for the hanging weight.

$($b$)$ Write the vector equilibrium equation$($s$)$ for the

free bodies under consideration.

$($c$)$ Write all forces using vectors.

$($d$)$ Solve for the magnitude of the tension force in

each of the cables.