Final answer:
This problem involves calculating the maximum distance a painter can walk on a plank before it tips using the principles of torque and static equilibrium. The plank is in equilibrium on the scaffold until the painter's weight causes a tipping torque.
Step-by-step explanation:
The student is asking a physics problem related to static equilibrium and torques. The uniform plank is in a state of static equilibrium until the moment the painter's weight causes it to tip. In order to determine how far the painter can walk on the overhanging part of the plank, we need to apply the principles of torque and rotational equilibrium around the pivot point (the edge of the scaffold closest to the overhang).
The condition for tipping is when the torque due to the painter's weight exceeds the torque due to the weight of the plank on the opposite side. Torque is calculated as the product of the force and the perpendicular distance from the pivot point. We know that the entire plank is in equilibrium, and its center of gravity (middle of the plank) is 1.65m from the pivot. First, we calculate the torque due to the plank itself, which is the weight of the plank (31.9kg * 9.8m/s²) times half the distance between the scaffold bars (1.95m). Then, we set this torque equal to the torque created by the painter (73.8kg * 9.8m/s²) times the maximum distance x he can be from the pivot before the plank tips. Solving for x gives us the maximum distance the painter can walk before the plank tips.