How to Solve an Indeterminate Cable System with Multiple Unknowns?

[Puchinita5]

Homework Statement

A weight of 200 pounds is supported by a cable system as shown. Determine all cable forces and the force in the vertical boom BC.

Homework Equations

The Attempt at a Solution

i separated the x compontents and y components:
x:CAcos60-CDcos36.86989765+DEcos15=0
y: CAsin60-CDsin36.86989765+DEsin15-200+CB=0

but this looks like i have too many unknowns?

 

[tiny-tim]

Hi Puchinita5!

i separated the x compontents and y components:
x:CAcos60-CDcos36.86989765+DEcos15=0
y: CAsin60-CDsin36.86989765+DEsin15-200+CB=0

but this looks like i have too many unknowns?

That's because you've lumped everything together.

Do equations for the three forces on D, and then equations for the forces on BC.

(btw, the question doesn't say that the force on BC is vertical)

 

[tomcue]

Your approach is correct, but you are correct in pointing out that there are more unknowns than equations. This means that the system is indeterminate and there are multiple solutions that could satisfy the given conditions. To find a unique solution, you would need additional information such as the length of the boom BC or the tension in one of the cables. Without this additional information, it is not possible to determine the cable forces and the force in the vertical boom BC.