Find the applied force to cause a body to tip over

[preet]

Homework Statement

Assuming I have a simple body, like a box, with known center of mass, how do I find the applied force, through its center of mass that will cause the object to tip over? The object is at rest on a flat surface.

Known elements:
weight of object, static friction between surface and object, position of center of mass.

Homework Equations

$$(\vec{F}_{net})_x = \Sigma F_x = 0$$

$$(\vec{F}_{net})_y = \Sigma F_y = 0$$

$$(\vec{M}_{net})_G = \Sigma M_G = 0$$

The Attempt at a Solution

Drew a free body diagram, and my forces {Weight, Applied Force, Friction and Normal Force). Showed the normal force located at the corner opposite the applied force. The applied force is only present in the X direction. I'm guessing I need to solve for Friction to solve for the Applied Force. I'm a little lost as to how to do this.

Thanks
Preet

 

[Dick]

If you are thinking of a box, then to tip over the box has to pivot around one of the corners. Find the torque associated with the weight of the box acting at the center of mass around that pivot point and equate that to the torque created by the applied force. I would just assume that there is enough static friction to keep the pivot point fixed.

 

[preet]

That makes a lot of sense... thanks for clarifying.
I have one quick follow up question. The scope of the initial problem I'm trying to solve is a little bigger -- the box is on a platform that accelerates in the X direction. I reduced this to have a pretend inertial force (my Applied Force) acting on the mass. Is this acceptable?

 

[Dick]

Sounds fine to me, you should be able to treat the acceleration as a 'pretend' gravitational type force.