Question

non-self-supporting ladders are not to be used at an angle such that the horizontal distance from the top support to the foot of the ladder is approximately one-fourth of the working length of the ladder (the distance along the ladder between the foot and top support).

Answer 1

The question deals with a high school physics problem analyzing a ladder in static equilibrium. It involves finding the reaction forces at the ladder's base and ensuring that the static friction is adequate to prevent slipping, considering that a person is standing on the ladder.

Step-by-step explanation:

The question is regarding the physics of a ladder in static equilibrium, which is a topic often covered in high school physics classes. Analyzing the forces acting on the ladder requires understanding concepts such as torque, normal force, static friction, and the conditions for equilibrium. According to the problem, the ladder has a mass of 10.0 kg, and it is leaning against a wall with its base 2.00 m from the house. The ladder's center of mass is located 2 m from the bottom, and a person weighing 70.0 kg is standing 3 m from the bottom. Given the wall is frictionless, the forces acting at the top only include the normal force from the wall. At the base, both the normal reaction force from the ground and static friction must be present to prevent slipping.

To find the reaction forces at the base of the ladder, one must apply the principles of static equilibrium. These include ensuring that the sum of the forces in the horizontal and vertical directions are equal to zero and that the net torque about any point is also zero. For the vertical forces, the normal reaction at the base must balance the weight of the ladder and the person. The friction force at the base provides the necessary horizontal force to balance the horizontal component of the force at the top of the ladder. Calculating the exact values for the forces would involve applying the pivot point principle for torque balance and summing up forces for balance in the horizontal and vertical directions. It's important to note that the coefficient of static friction (­us) must be sufficient to prevent the ladder from slipping, meaning it must be high enough to produce a static friction force that can balance the net torque caused by the weights of the ladder and the person.