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Equilibrium problem

  1. Mar 27, 2016 #1
    1. The problem statement, all variables and given/known data

    il9g09.jpg

    The system is on static equilibrium. Determine tan θ !

    2. Relevant equations
    ΣF = 0
    Στ = 0

    3. 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..
     
  2. jcsd
  3. Mar 27, 2016 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    OK so far.

    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.
     
  4. Mar 27, 2016 #3
    Okay, this is my sketch of free body diagram
    o6fst5.jpg



    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
    tan θ = Tb / W = (3/4) W / W = 3/4

    Is it correct ???
     
  5. Mar 27, 2016 #4

    TSny

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    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.
     
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