Question

A wooden plank with length L = 7.5 m and mass M = 104 kg is centered on a granite cube with side S = 2.0 m. A person of mass m = 64 kg begins walking from the center of the plank outward, as shown in the figure. How far from the center of the plank does the person get before the plank starts tipping?

The answer is 2.62 m, but I'm not sure as how to go about this problem. I've tried drawing a free-body diagram, but it hasn't really helped me. Any help is greatly appreciated.

Answer 1

The fulcrum will be at the edge of the marble, or 1 m from the center. So when tipping, all downward force will be a this point.

sum of moments about the center( clockwise moments +), and measurements from the center

0=-force upward at edge(1)+64g*L
0=-(104+64)g*1+64g*L

L=168/64

Remember, at tipping, the granite is pushing upward a force equal to the weight of the man and the plank.

Answer 2

How did you go from -(104+64)g*1 + 64gL to L=168/64?

When I sum the forces of -(104+64)g*1 + 64gL, I get 3060.72.