You know that you can safely stand on the overhanging end of a heavy plank that rests on a table.How far out depends on your mass and the mass of the plank.Suppose you can stand on the end of a plank that overhangs the edge of the supporting table 1/4 its total length.Then how massive is the plank compared to your mass?
A)1/2 your mass
B)the same as your mass
C)1 1/2 times your mass
D)twice your mass
E)4 times your mass

Question

Quizplus · Accepted Answer

This problem can be solved using the principle of torques. The torque due to your weight must be balanced by the torque due to the weight of the plank. Since you can safely stand on the end of the plank that overhangs 1/4 of its total length, the center of mass of the plank must lie at a distance of at least 3/4 of its total length from the end of the table. This means that the plank must be at least 4 times as long as you are tall. Therefore, if the plank is x times more massive than you, then its center of mass is x/2 times farther from the table edge than you are, and the torque due to its weight is (x/2) times the torque due to your weight. Equating the two torques, we get x/2 = 1/4, or x = 1/2, which means that the mass of the plank is the same as your mass. Therefore, the answer is B).

You Know That You Can Safely Stand on the Overhanging