# Equilibrium problem

## Homework Statement The system is on static equilibrium. Determine tan θ !

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.

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TSny
Homework Helper
Gold Member

## 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.

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.

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
Homework Helper
Gold Member
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.

• terryds