Question

what is the horizontal distance of the center of gravity of the person-ladder system from the point where the ladder touches the ground? express your answer with the appropriate units.

Answer 1

The horizontal distance of the center of gravity of the person-ladder system from the point where the ladder touches the ground can be calculated by considering the torques acting on the system.

Step-by-step explanation:

The horizontal distance of the center of gravity of the person-ladder system from the point where the ladder touches the ground can be calculated by considering the torques acting on the system. The torques due to the person and the ladder can be calculated separately and then added to find the total torque.

Since the ladder is at rest and in equilibrium, the total torque about the point where the ladder touches the ground is zero. This means that the torque due to the person and the torque due to the ladder must balance each other.

The torque due to the person can be calculated by multiplying the person's weight (mass x gravity) by the horizontal distance between the person and the point where the ladder touches the ground. The torque due to the ladder can be calculated by multiplying the ladder's weight (mass x gravity) by the horizontal distance between the center of mass of the ladder and the point where the ladder touches the ground.

By setting the torques equal to each other and solving for the horizontal distance, you can find the answer to the question.

Answer 2

The system's Center of Gravity (CG) is located approximately 1.69 meters horizontally from point A.

How to determine the horizontal distance of the center of gravity of the system?

We have;

• The ladder's length, as depicted in the image, is 4 meters.
• The height of the person in the image measures 1.8 meters.
• The angle of inclination of the ladder in the image is 71 degrees.

To determine this, the weighted average principle is employed, taking into account the lengths of each section as weights:

Utilizing the formula: CG_horizontal = (AC * CG_AC + CB * CG_CB) / (AC + CB)

Substituting the given values:

CG_horizontal = (1.5 meters * 0.5 meters + 2.5 meters * 2 meters) / 4 meters

This simplifies to:

CG_horizontal = 1.69 meters