What Is the Tension in the Rope for a High Wire Walker?

[Damie904]

1.Homework Statement

Arlene is to walk across a high wire strung horizontally between two buildings 13.0 m apart. The sag in the rope when she is at the midpoint is 10.0°. If her mass is 50.0 kg, what is the tension in the rope at this point?
So I know:
Mass=50kg
Acceleration=0 m/s²

Homework Equations

This is the part I need help with because I'm not exactly sure what formula to use to find tension motion. Since F=ma would just give me 0 which would be incorrect.
The only other Formula I can think of is 2cos(theta)T_y=mg, but I'm not too sure if that's correct. Plus, I don't know what T_y is.

The Attempt at a Solution

 

[Pi-Bond]

Resolving the tension along the vertical axis should not give $2cos(\theta)T_{y}=mg$. What do you think it should?

 

[Fewmet]

You are sort of correct that the F=ma=0. Really, it is that ∑F=0, where ∑F is the sum of all the forces acting on Arlene. I think you see that is her weight pulling down, but what is pushing her up? Something has to be if ∑F=0.

Consider that the point under her feet is being pulled left by one part of the rope and right by the other part of the rope. Those forces are ±T_x.

Each of the two parts of the rope are also pulling her up. The upward force of one part would be T_y.

Do you see why there would be 2T_y? And why that would equal mg?

(Check your notes or your text: I think you'll see that you've mistranscribed 2cos(theta)T_y=mg)