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.