Final answer:
The question involves using principles of statics in physics to determine the forces on a ladder. It requires calculating torques and forces, assuming static equilibrium, to find the normal forces at the top and bottom points of the ladder where it contacts the wall and the ground.
Step-by-step explanation:
The question is related to the applications of statics in physics, which involves calculating balance under a static (non-moving) condition. In this case, we are to find the magnitudes of the forces on an aluminum ladder resting against a wall and supporting a person's weight.
To solve this problem, we consider the torques about the base of the ladder and use the fact that the ladder is in static equilibrium, which means that the net force and the net torque on the ladder must be zero. We have four forces acting on the ladder: the weight of the ladder, the weight of the person, the normal force at the base, and the normal force at the wall (since the wall is frictionless, there is no friction force there).
Forces are calculated using the following steps:
- Calculate the torque due to the person's weight.
- Calculate the torque due to the ladder's weight.
- Equating these torques with the normal force exerted by the wall will allow us to find that normal force.
- The normal force at the base can then be found by considering the sum of vertical forces and setting it to zero.
The problem is a practical application of lever arm principles and Newton's first law of motion (law of inertia) within a real-world context.