How can I find the tension in a rope at equilibrium point on a high wire?

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SUMMARY

The discussion focuses on calculating the tension in a rope at the equilibrium point while Arlene walks across a high wire. Given her mass of 52.0 kg and a sag angle of 10.0 degrees, the gravitational force acting on her is 509.6 N. The tension in the rope can be determined using the formula Ft = (m*g)/(2sinθ), which accounts for the equilibrium of forces acting on her. The derivation of this formula is essential for understanding how the components of tension relate to the gravitational force.

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  • Study the derivation of the tension formula Ft = (m*g)/(2sinθ)
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Homework Statement


Arlene is to walk across a "high wire" strung horizontally between two buildings 14.0m apart. The sag in the rope when she is at the midpoint is 10.0 degrees. If her mass is 52.0kg , what is the tension in the rope at this point?

Homework Equations


Fnet=ma
a=0 so fnet=0

The Attempt at a Solution


So I know that Fg=9.8*52=509.6 N, and I broke down Ft into Ftx and Fty. sin10=Fty/Ft but I have no idea how to use Fg in that formula to find Ft.
In my notes I have "Ft=(m*g)/(2sinθ) which gives the correct answer, but I don't understand how I got that formula. Can someone explain where it came from/give me some guidance. Why 2sin?
 
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Since she is in equilibrium, ƩF = 0. In particular, the y-component of the net force must equal zero.

What forces act on her? What are their y-components?
 

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