[EricH]

u, or μ as I prefer to denote it, is zero due to the roller, so you are correct that that force is zero. As for the torque part, that is also true, if I recall correctly--but a zero force has no torque application anyway.

The equations are a little trickier. The first one is correct--F*d1 < N*d2 for stability. However, making F=N*μ as a maximum probably isn't the way to go here.

Let's try this: F*d1=N*d2 for the point at which slip stops and tip starts. If N is known, and d2 is known, then F and d1 are unknown. d1 is the height of the force, which may be knowable. (For simple stuff, CG is the point of application.) That leaves F as unknown, and that means that Fmax = N*d2/d1.

[Note: The above assumes that it isn't tipping because it hits something at that foot--if that were the case, you'd add a moment at the point, and F*d1 would need to be less than N*d2+the moment.]