Finding the Coefficient of Friction for a Homogeneous Cube in Static Equilibrium

[matematikuvol]

Homework Statement

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 \frac{\pi}{6}.What is the value to the coefficient of friction between the cube and the floor to cube remain in balance.

Homework Equations

\sum F=0
\sum M=0
M=rF
M is momentum of force.

The Attempt at a Solution

In static case

\sum F=0
\sum M=0
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 r is size of cube so a. Do you have any idea? I think this goes in one line but it is hard for me.

 

[matematikuvol]

Any help?

I think that this is picture

 

[matematikuvol]

Here is a picture

 

[matematikuvol]

How to define \sum M=0?

 

[Whovian]

Um ... momentum of force ... ?

If \displaystyle M=r\cdot F, then \displaystyle\sum\left(M\right)=r\cdot\sum\left(F \right), and so, as r≠0, \displaystyle\sum\left(F\right)=0, which we already knew. That's the equivalent of just no net force being applied.

 

[matematikuvol]

I mean in this case.