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Statics Equilibrium: Normal Force and Static Friction

  1. Sep 15, 2012 #1
    1. The homogeneous square body is positioned as shown. If the coefficient of static friction at B is 0.40, determine the critical value of the angle theta below which slipping will occur. Neglect friction at A.

    The image: 2d48dfbb-5752-4b3b-a834-281ddfaaf4cd.png




    2. NA is the Normal force at A, which is perpindicular to the 60° incline.
    NB is the Normal force at B, which is in the positive y direction.
    W=mg which is the weight in the negative y direction.
    ƩFx=0
    ƩFy=0
    ƩMB=0 (the moment about B eliminates the unknowns NB and Ff.




    3. I have three pages of handwritten work. I started with the Moment about B, and took the moment arm from B to the center of mass (s/2)((sin∅-cos∅)i + (sin∅+cos∅)j. W is simply -Wj. I took the moment arm for the NA force to be s(-cos∅i + sin∅j). NA=NA(cos(30)i + sin(30)j). Putting all of those together into the ƩMB= r1 x W + r2 x NA = 0.

    I took the cross products and then summed the y forces and x forces. I have not been able to find equations to set equal to each other or substitue into each other to end up with an answer of (some tangent function of ∅) = (some number)


    The answer to the problem is 20.7, but I have had no luck getting there. Thanks for the help ahead of time.
     
  2. jcsd
  3. Sep 16, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    What you have shown from your work looks correct.
    Show your further work in detail so we can see what went wrong.


    ehild
     
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