Finding Tension in a String Holding a Meter Stick Against a Wall

[proace360]

Homework Statement

A 0.13 kg meter stick is held perpendicular to a wall by a 2.7 m string going from the wall to the far end of the stick.
(a) Find the tension in the string.
(b) If a shorter string is used, will its tension be greater than, less than, or the same as that found in part (a)?
(c) Find the tension in a 2.0 m string.

Homework Equations

Torque=Nr?

The Attempt at a Solution

I discovered the angle to be 68.38 degrees, and I thought that, since the y-component of the force cancels out mg, T=mg/sin(theta). Why is it wrong?

 

[Doc Al]

The string tension is not the only force (besides the weight) acting on the stick.

 

[proace360]

I know that the wall exerts a horizontal force, but that doesn't matter in the Fy equation.

 

[Doc Al]

But the vertical force it exerts does.

 

[proace360]

wait... how does it exert a vertical force? Is there a friction force?

 

[Doc Al]

wait... how does it exert a vertical force? Is there a friction force?

There better be. But you need not worry about the wall force to solve this problem.