Problem involving Forces, torque,friction and object tipping

[lingoo]

Homework Statement

A refrigerator of mass 120 kg, as shown in the picture, has a plastic feet resting on a stone floor and is being pushed with a force F.
The coefficient of static friction is equal to 0.2 and the dynamic friction coefficient is equal to 0.15.

Homework Equations

A)
Check if:
(1) The refrigerator will fall before sliding, OR
(2) slide before tipping;
And,for the case (1) or (2), What is the value of the force F at the time of occurrence

B)
Considering the case of slipping of the refrigerator (1) or (2)
calculate the value of the maximum force F that can be applied without having the fall of the refrigerator. For the calculated force, what would be the acceleration of the refrigerator?

The answers are:

A)-Case (2) and the force is 235 N

B)-Force is 638N and acceleration of 3,85(m/s²)

The Attempt at a Solution

At first, I have tried to calculate the torque of the force F and the friction force, but I can't reach anywhere. The force is being applied over the center of mass, I suppose it's going to fall, but I don't know if it's going to slide before or after. Anyway, I would really appreciate a help from anyone here.
Best Regards

 

[LawrenceC]

Hint:

For part A, sum moments (torques) about point B.

For part B, sum moments about point B. The equation will contain two unknowns, namely the force F and the acceleration. Come up with another equation that relates acceleration to force F and solve simultaneously.

 

[lingoo]

I tried to sum all forces in x and y
In x, I think there will be friction force in foot A and friction force in foot B,and sure, the Force F that is being applied. F - Fa - Fb = ma

In y, Normal forces cancel with gravitational force, so Na+Nb-W=0

But to calculate the torque, is being really a problem, because when I calculated the torque in B, I will have the force F, Na and the acceleration "a" as unknowns.
If I calculate the torque around A, we will have F,Nb, and acceleration" a" as unknowns.
In the point of application of point F, the forces Fa,Fb,Nb and again the acceleration will be the unknowns...

I have tried everything, but I think I am missing something...

 

[LawrenceC]

Calculate the torque about B, not A. It does not rotate about A, it rotates about B. Also here is a copy of what I previously said.

The equation will contain two unknowns, namely the force F and the acceleration. Come up with another equation that relates acceleration to force F and solve simultaneously.

 

[lingoo]

Can I assume that Na is equal to zero ? Because the rotation is around B, so all the weight would be concentrated at B, leaving A without weight applicated...

 

[LawrenceC]

Yes, that's what happens when tipping is incipient.

 

[LawrenceC]

You should have one moment equation and a Newton's Second Law equation for the second equation. Make sense?