Chapter 9, Problem 7Q

A ladder, leaning against a wall, makes a 60° angle with the ground. When is it more likely to slip: when a person stands on the ladder near the top or near the bottom? Explain.

To determine

When is it more likely to slip: when a person stands on the ladder near the top or near the bottom?

Answer to Problem 7Q

Solution:

The ladder is more likely to slip when the person stands near the top of the ladder.

Explanation of Solution

Given info:

A ladder, leaning against a wall, makes a 60 degrees angle with the ground.

Assume that the pivot point is at the base of the ladder in contact with the ground. Then, the forces acting on the ladder with a person stand on the ladder near the top are: The weight of the ladder ( ${\overrightarrow{W}}_l$ ), the weight of the person ( ${\overrightarrow{W}}_p$ ), the reaction force ( ${\overrightarrow{F}}_G$ )that the ground makes with the ladder, the force that the wall ( ${\overrightarrow{F}}_{wall}$ )exerts on the ladder. As the person goes up the ladder the torque ( ${\tau }_{W_p}$ )made by their weight also increases. The torque made by weight’s ladder is constant. Now, the ladder is in equilibrium; but when the person goes up the ladder he does torque in a clockwise direction as well as the weight of the stairs increases. If the person’s weight is much greater than the force that the wall ( ${\overrightarrow{F}}_{wall}$ )exerts on the ladder, then the ladder slides. If the person is standing at the base of the ladder then, the lever arm is zero because it goes through the pivot point, therefore there is no torque different from zero and the ladder does not slide.