Question

A uniform ladder of weight w leans without slipping against a wall making an angle with the floor. What is the magnitude of the normal force exerted by the floor on the ladder?

A) w cos
B) w sin
C) w tan
D) w cot

Answer 1

The magnitude of the normal force exerted by the floor on the ladder is w cos(θ), which is the component of the ladder's weight perpendicular to the floor.

Step-by-step explanation:

The question asks about the magnitude of the normal force exerted by the floor on a ladder leaning against a wall at an angle. In this scenario, when a ladder is leaning against the wall, the weight of the ladder acts downwards and the normal force by the floor opposes this weight. The normal force can be found by resolving the weight of the ladder into components that are perpendicular and parallel to the floor.

Considering the equilibrium conditions for the ladder, the vertical components of the forces must balance out. The weight w has a component w cos(θ) perpendicular to the incline, which is balanced by the normal force N exerted by the floor. Hence, the magnitude of the normal force exerted by the floor is equal to the component of the ladder's weight perpendicular to the floor, which is w cos(θ).