Question

The smooth pipe rests against the wall at the points of contact \(A, B\), and \(C\), as shown in Figure 1 of 1. Determine the magnitude of the reactions at these points needed to support.

Answer 1

To determine the magnitude of the reactions at the contact points A, B, and C, we need to consider the forces acting on the ladder in equilibrium. First, calculate the weight of the ladder and then analyze the forces acting on it, including normal forces, weight force, and friction force. Finally, solve the equations to find the magnitudes of the reaction forces.

Step-by-step explanation:

To determine the magnitude of the reactions at the contact points A, B, and C, we need to consider the forces acting on the ladder in equilibrium.

First, we can calculate the weight of the ladder using its mass and the acceleration due to gravity.

Then, we can analyze the forces acting on the ladder, including the normal forces from the floor and the wall, the weight of the ladder, and the friction force that prevents slipping. Using trigonometry, we can express these forces in terms of the reaction forces at points A, B, and C.

Finally, we can solve the equations to find the magnitudes of these reaction forces.

The magnitude of the reaction forces at points A, B, and C will depend on the specific values of the ladder's weight, the coefficient of static friction, and the angle of inclination between the ladder and the floor.