Question

Ladders must extend how far above a landing?

Answer 1

The magnitudes of the forces on the ladder at the top and bottom are determined using the principles of statics. The normal reaction force at the bottom is equal to the sum of the weights of the ladder and the person. The frictional force at the bottom is zero. At the top of the ladder, the normal reaction force from the wall is equal to the weight of the ladder.

Step-by-step explanation:

In this scenario, we can use the principles of statics to determine the magnitudes of the forces on the ladder at the top and bottom. The forces acting on the ladder are the normal reaction force and the frictional force. Let's break it down step by step:

1. First, we need to find the weight of the ladder. The weight of an object can be calculated using the formula: weight = mass x acceleration due to gravity. In this case, the ladder weighs 400.0 N.
2. The normal reaction force on the ladder at the bottom can be calculated using the formula: normal reaction force = weight of ladder + weight of person. The normal reaction force at the bottom is equal to the sum of the weights of the ladder and the person, which results in a value of 470.0 N (400.0 N + 70.0 N).
3. The frictional force on the ladder at the bottom can be calculated using the formula: frictional force = coefficient of friction x normal reaction force. However, since the ladder rests against a frictionless surface as mentioned in the question, the frictional force is zero.
4. At the top of the ladder, the forces acting on the ladder are the normal reaction force from the wall and the weight of the ladder. Since the ladder is in equilibrium, the magnitudes of these forces must be equal. Therefore, the normal reaction force at the top is also 400.0 N.