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Mechanics statics problem

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Homogeneous cube with one edge lying on the floor and the other on a smooth vertical wall. The underside of cube with a horizontal surface makes angle of [tex]\frac{\pi}{6}[/tex].What is the value to the coefficient of friction between the cube and the floor to cube remain in balance.


    2. Relevant equations
    [tex]\sum F=0[/tex]
    [tex]\sum M=0[/tex]
    [tex]M=rF[/tex]
    M is momentum of force.


    3. The attempt at a solution
    In static case

    [tex]\sum F=0[/tex]
    [tex]\sum M=0[/tex]
    I need help to write this equation from the problem statement. I don't have idea.
    Because cube is homogenuous the forces are equal from all parts I suppose.

    My assymption is that [tex]r[/tex] is size of cube so [tex]a[/tex]. Do you have any idea? I think this goes in one line but it is hard for me.
     
    Last edited: Apr 22, 2012
  2. jcsd
  3. Apr 22, 2012 #2
    Any help?

    I think that this is picture
     
    Last edited: Apr 22, 2012
  4. Apr 22, 2012 #3
    Here is a picture
     

    Attached Files:

  5. Apr 23, 2012 #4
    How to define [tex]\sum M=0[/tex]?
     
  6. Apr 23, 2012 #5
    Um ... momentum of force ... ?

    If [itex]\displaystyle M=r\cdot F[/itex], then [itex]\displaystyle\sum\left(M\right)=r\cdot\sum\left(F \right)[/itex], and so, as r≠0, [itex]\displaystyle\sum\left(F\right)=0[/itex], which we already knew. That's the equivalent of just no net force being applied.
     
  7. Apr 23, 2012 #6
    I mean in this case.
     
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