The tension in the 5.0 m supporting cable is determined as 1,633.3 N.
What is the angle between the cable and the beam?
The angle between the cable and the beam is calculated by applying trigonometry ratio as follows;
sinθ = opposite side / hypotenuse side
sinθ = 3 m / 5 m
sinθ = 0.6
To calculate the tension in the cable, take a moment about the pivot of the beam as shown below;
let the distance from the pivot to the 5.0 m cable = d
let the tension in the 5.0 m cable = T
sinθ = d/4
d = 4 x sinθ
∑M = 0
T(4 x sinθ) = W x 4
where;
- T is the tension is the rope
- W is weight of the sign supported
Recall, sinθ = 0.6
T(4 x 0.6) = 980 x 4
2.4T = 3920
T = 3920/2.4
T = 1,633.33 N
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