Solving Equilibrium Problem: Determine tan θ

[terryds]

Homework Statement

The system is on static equilibrium. Determine tan θ !

Homework Equations

ΣF = 0
Στ = 0

The Attempt at a Solution

∑Fx = 0
Ta sin θ = Tb

ΣFy = 0
Ta cos θ = mg

Then, I got stuck..
I want to continue to Στ = 0 but I don't know which one to pick as fulcrum, the perpendicular forces acting on the block. It's hard to imagine where is actually the θ in the block section.

Please help me..

 

[TSny]

The Attempt at a Solution

∑Fx = 0
Ta sin θ = Tb

ΣFy = 0
Ta cos θ = mg

OK so far.

Then, I got stuck..
I want to continue to Στ = 0 but I don't know which one to pick as fulcrum, the perpendicular forces acting on the block.

For static equilibrium Στ = 0 about any point. So, you can pick any convenient point for setting up Στ = 0.

It's hard to imagine where is actually the θ in the block section.Please help me..

I'm not sure what you mean here.
Be sure to draw a good free body. Pick a convenient point for the origin and set up Στ = 0.

 

[terryds]

Okay, this is my sketch of free body diagram

I pick the bottom of the block as the fulcrum (so Tb is eliminated)

∑τ = 0
W * 15 cm - Ta cos θ * 30 cm = 0

Then, I pick the top of the block as the fulcrum (so Ta is eliminated)
∑τ = 0
W * 15 cm - Tb * 20 cm = 0
Tb = (3/4) W

From

∑Fx = 0
Ta sin θ = Tb

ΣFy = 0
Ta cos θ = W

tan θ = Tb / W = (3/4) W / W = 3/4

Is it correct ?

 

[TSny]

Correct. Good. You might try picking the origin (fulcrum) at the upper left end of the rod and see if you get the same answer.