Quick Stability / FBD question

[EricVanWyk]

I need to give a lesson on stability tonight, but it has been a while since I've done freebody diagrams.

Can you folks help idiot check me before I fill the students' heads with lies?


For BEST, they have made what is essentially a rectangle on PVC pipe casters - see beautiful figure 1. I'm going to model it as a point mass with two struts. They push it to move it, and it has a tendancy to tip over. I want to create a simple formula to determine whether a redesign will tip, before they actually design it.

To do this, I'm calculating torques about the far strut. I see 3 contributors:
F*d1 = The force imparted by pushing times the height of the push point.
N*d2 = The normal force (weight) times the horizontal distance from the strut to the center of mass.
0 = The friction force from sliding over the carpet. I'm not so sure on this one - I think it is zero because it is right at the tip point?

This gives me F*d1 < N*d2 to ensure static stability. However, F is limited by friction, so I limit it to N*u.
This gives me N*u*d1 < N*d2, which becomes d2/d1 > u

This simple formula is pretty grokable, but is it true? Or more specifically, is it true enough?

Thanks guys, and be nice... our mentors are all ECEs, marketers and psychologists.