Need help solving tension problem.

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SUMMARY

The discussion centers on calculating the shortest length of cable ACB required to support a load without exceeding a tension of 870 N. The user derived the angle θ as 43.6 degrees using the equations of equilibrium for forces acting on point C. The final calculation determined that the minimum length of the cable must be 5.22 meters when the tension is set at 870 N. This solution is based on the relationship between the tension, angle, and height of the cable.

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Knowing that portions AC and BC of cable ACB must be equal, determine the shortest length of cable that can be used to support the load shown if the tension in the cable is not to exceed 870 N.

i attached the picture that came with the problem.

i am lost and not sure how to approach the problem.
 

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Hi X8V,

X8V said:
Knowing that portions AC and BC of cable ACB must be equal, determine the shortest length of cable that can be used to support the load shown if the tension in the cable is not to exceed 870 N.

i attached the picture that came with the problem.

i am lost and not sure how to approach the problem.

Try drawing a force diagram for the point C. What does that give you?
 
I think i figured it out. Here's what I did.

T'=1200 N
T=T

Fx = - Tcosθ + Tcosθ = 0
Fy = Tsinθ + Tsinθ - 1200N = 0

2Tsinθ = 1200N
2(870N)sinθ = 1200N
(1740N)sinθ = 1200N
sinθ = 1200N / 1740N
θ = 43.6 degrees

h = 1.8m / sin43.6
h = 2.61m

5.22m is the minimum length the cable can achieve when T=870N
 

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