Question

A ladder carried by a fire truck is 20. 0 m long. The ladder weights 3600 N and its center of gravity is at its center. The ladder is pivoted at one end (A) about a pin (Figure 1); ignore the friction torque at the pin. The ladder is raised into position by a force applied by a hydraulic piston at C. Point C is 8. 0 m from A, and the force F⃗ exerted by the piston makes an angle of 40 ∘ with the ladder

Answer 1

The magnitudes of the forces on the ladder at the top and bottom can be calculated using torque equilibrium.

Step-by-step explanation:

In this problem, we have a ladder leaning against a wall. The ladder is acted upon by four forces: normal reaction force from the floor, static friction force on the floor, weight of the ladder, and normal reaction force from the wall. These forces can be divided into horizontal and vertical components, making the solution of the problem simpler.

Since the ladder is in equilibrium, the sum of the torques about any point must be zero. Choosing the point of contact with the floor as the pivot, we can determine the magnitudes of the forces on the ladder by setting up and solving torque equilibrium equations.

The magnitudes of the forces on the ladder at the top and bottom can be calculated by applying the torque equilibrium. The force at the top is the horizontal component of the normal reaction force from the wall, and the force at the bottom is the horizontal component of the static friction force on the floor.