How Do You Calculate the Weight of Signal C in a Suspended Cable System?

[jonnyboy]

Homework Statement

Two traffic signals are temporarily suspended from a cable as shown. Knowing that the signal at B weighs 300N. Determine the weight at signal C.

Homework Equations

Red arrows show lengths of cables and their components.
Answer is : W_c = 97.7N

The Attempt at a Solution

I started by drawing two free body diagrams. One for particle B and the other for particle C. They both share the cable BC, hence, they share the same tension, T_bc, right? So, I tried to solve for T_bc with the free body diagram of particle B resulting in the sum of the forces along x: -T_ab(3.6/3.9) + T_bc(3.4/3.42) =0
(Sigma = addition of forces) SigmaF_y: T_ab(1.5/3.9) + T_bc(.4/3.42) - 300 = 0

So, solving for T_bc I get 251 N. I then follow the same steps as above for particle C.
I get Sigma F_x: T_bc(3.4/3.42) + T_cd(2.4/2.5) = 0
Sigma F_y: T_bc(.4/3.42) + T_cd(.7/2.5) - W_c = 0
so far? when I plug in what I got for T_bc to the second eqns. I get a different answer for w_c than what I'm supposed to get. please help

 

[rl.bhat]

the free body diagram of particle B resulting in the sum of the forces along x: -T_ab(3.6/3.9) + T_bc(3.4/3.42) =0
simaF_y: T_ab(1.5/3.9) + T_bc(.4/3.42) - 300 = 0
So, solving for T_bc I get 251 N. I then follow the same steps as above for particle C.
Check this calculation. I am getting differenct answer.

 

[thomate1]

I would suggest revisiting your calculations and equations to ensure accuracy. Additionally, it is important to consider all forces acting on particle C, including the weight of the signal itself and the tension in the cable BC. It may be helpful to draw a diagram and label all known and unknown forces, and then use the appropriate equations to solve for the weight at C. It is also important to double check your units and conversions to ensure consistency. If you are still having trouble, I would recommend seeking assistance from a teacher or tutor.