Carpenter on a plank

As the carpenter moves toward the right end of the plank the upward forces due to the two supports change: that due to the left support becomes smaller and smaller.
How small can either force be ?

The answer is zero -- and it cannot be negative (a support can push up but it can't pull down). So the carpenter's limiting position occurs when the force due to the left support has just gone to zero. Then the plank is still (precariously) in equilibrium under three forces:
(1) the weight mg of the plank, acting downward at the center of the uniform plank;
(2) the weight Mg of the carpenter;
(3) the upward force F₁ due to the right support, and
(4) the force due to the left support is zero, F₂=0.

Unit 4, Question 4

Unit 4 Table of Contents

Demonstrations