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solniwko [45]
3 years ago
6

A circus tightrope walker weighing 800 N is standing in the middle of a 15 meter long cable stretched between two posts. The cab

le was originally horizontal. The lowest point of the cable is now at his feet and is 30 cm below the horizontal. Assume the cable is massless. What is the tension in the cable
Physics
1 answer:
Lorico [155]3 years ago
4 0

Answer:

T = 10010 N

Explanation:

To solve this problem we must use the translational equilibrium relation, let's set a reference frame

X axis

       Fₓ-Fₓ = 0

       Fₓ = Fₓ

whereby the horizontal components of the tension in the cable cancel

Y Axis  

        F_{y} + F_{y} - W =0

        2F_{y} = W

let's use trigonometry to find the angles

        tan θ = y / x

        θ = tan⁻¹ (0.30 / 0.50 L)

        θ = tan⁻¹ (0.30 / 0.50 15)

        θ = 2.29º

the components of stress are

         F_{y} = T sin θ

we substitute

       2 T sin θ = W

       T = W / 2sin θ

        T = \frac{ 800}{ 2sin 2.29}

        T = 10010 N

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