Torque: Why does tension = Friction

[anirzehc]

Homework Statement

A 10.0 kg sphere is attached to the incline by a horizontal string. Whats the tension in the string.

Homework Equations

sum of all horizontal forces = 0
sum of all vertical forces = 0
sum of all torques = 0

The Attempt at a Solution

The sum of the horizontal forces[/B] is -Tsin55 degrees - F + mgsin35 degrees = 0
Why does F= T?
I know F= T because when I substitute F=T and solve for T I get the right answer (30 .9 N) but why is this?

 

[haruspex]

I know F= T because when I substitute F=T and solve for T I get the right answer (30 .9 N) but why is this?

If you want a quick way to get a relationship between F and T, the trick is to take moments about a point where only those two forces have a moment. What other forces are present? What point do none of those have a moment about?