Final answer:
To find the magnitudes of the forces on the ladder at the top and bottom, we need to consider the weight of the ladder and the person, the normal force exerted by the wall, and the force applied by the person. By applying the principles of equilibrium, we can determine that the force at the top of the ladder is approximately 784 N, while the force at the bottom is approximately 336 N.
Step-by-step explanation:
In this problem, we have a ladder placed against a wall and a person standing on the ladder. To find the forces on the ladder, we need to consider the forces acting on it. The weight of the ladder acts downward at the center of mass, and the normal force exerted by the wall acts perpendicular to the wall. The force applied by the person exerted at the bottom of the ladder acts upward at an angle, due to the person's weight.
To find the magnitudes of these forces, we can use the principles of equilibrium. Since the ladder is not accelerating, the sum of the forces in the vertical direction must be zero. The vertical component of the force applied by the person must balance the weight of the ladder and the person. Similarly, the horizontal component of the force applied by the person must be balanced by the normal force exerted by the wall.
Therefore, the magnitudes of the forces on the ladder at the top and bottom are:
Force at the top: equal to the weight of the ladder and the person, which is approximately 784 N.
Force at the bottom: equal to the horizontal component of the force applied by the person, which is approximately 336 N.