Final answer:
To determine the normal reaction and friction forces at the base of a ladder in static equilibrium, we analyze vertical and horizontal forces, as well as torques. We use the principles of statics, considering the ladder's weight and center of mass, and the person's location on the ladder.
Step-by-step explanation:
Forces on a Ladder in Static Equilibrium
To find the normal reaction and friction forces on a ladder at its base, we apply the principles of static equilibrium. The ladder is in a state of balance when rests against a wall, so the sum of all vertical forces and the sum of all horizontal forces must equal zero. The sum of torques around any pivot point should also be zero. In this situation, a 6.00-m aluminum ladder with a center of mass 2 m from the bottom has a person standing 3 m from the bottom.
The weight of the person and the ladder act downwards, while the normal reaction force acts upwards from the ground at the base. The friction force acts horizontally, and is static as the ladder is not sliding. For a frictionless contact at the top with the wall, the only horizontal force at the top is the normal reaction force acting on the wall. They must counteract the force due to the person's and ladder's weight for equilibrium.
By summing up the forces and torques, we can solve for the magnitudes. The lever arms in the torque calculations are the distances from the pivot point to where the forces are applied. Thus, taking moments around the base will help us to find the necessary forces at the base and the top of the ladder without friction.