How Far Can a Man Walk on a Plank Before It Tips Over?

[einstein18]

Homework Statement

A man, of m = 70 kg, walks along a thin rigid plank, of M = 210 kg. The plank sits on the roof of a 10 story building and is placed so that its center of mass sits directly on the edge of the roof.

Where, along the plank, can the man move before the plank tips over the edge? Assume that friction is strong enough to keep the plank from moving horizontally.

Homework Equations

Statics:
Y: (M+m)g=N(due to floor)
X: Not applicable
Torque=mgd=0

Rotational:
Torque=mgd=I*alpha

The Attempt at a Solution

I am confused on how to relate the statics to the rotational part. I understand that as long as the plank doesn't fall the equilibrium equations remain true, however as soon as it does it is no longer true and the ratational torque becomes the reality. Now I don't understand how to create and equation that relates the change from one to the other as a function of how far the man walks. Can someone please help me out?

 

[Doc Al]

In order to tip, you just need an unbalanced torque about the pivot point (the edge of the roof, in this case).

This problem is a bit odd since the plank's center is right at the edge of the roof. Where does the weight of the plank act? Will it exert any torque about the pivot point?