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Fridge about to tip, statics

  1. Feb 29, 2016 #1
    1. The problem statement, all variables and given/known data
    say a fridge of width "w" and height "L" is being pushed on by a force F at an angle θ to the horizontal. This force is applied at a height of "h" above the ground.

    I want to know what the max value of h can be such that the fridge doesn't tip and the coefficient of static friction is μ.


    2. Relevant equations
    ΣF = 0
    Στ = 0

    3. The attempt at a solution
    The force can be found:

    ΣFx = 0
    Fcosθ - f = 0, where f(max) = μN

    And

    ΣFy = 0
    N - mg - Fsinθ = 0

    So

    Fcosθ - μ(mg + Fsinθ) = 0
    F = μmg/(cosθ - μsinθ)

    This is my reasoning for the height, since only the horizontal component of F affects the perpendicular distance "h" to F, then:

    Στ = 0 (about axis where the fridge is about to tip)
    hFcosθ - mg(w/2) = 0
    h = ½mgw/(Fcosθ)

    Does that make sense? I'm skeptical about this.
     
  2. jcsd
  3. Feb 29, 2016 #2
    How you are pushing? F acting below the horizontal at theta angle or above the horizontal?
     
  4. Feb 29, 2016 #3
    Oups forgot to mention, the force is pushing above the horizontal, the vertical force is downward though
     
  5. Feb 29, 2016 #4
    If you are pushing in a direction above the horizontal then sin component will point up -in the direction of N

    so the sign of of F sin(theta) should change, if i am correctly following you!
     
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