Final answer:
The normal force exerted on the ladder by the wall has the same magnitude as the frictional force exerted by the floor, as these are the two horizontal forces in a static equilibrium. This is consistent with equilibrium conditions and Newton's third law.
Step-by-step explanation:
The student's question pertains to the forces acting on a ladder leaning against a wall at rest. Specifically, it asks which force must have the same magnitude as the frictional force exerted on the ladder by the floor. When dealing with static equilibria and forces on inclined planes, it's important to find components of the forces acting perpendicular and parallel to the contact surfaces.
The correct answer is that the normal force exerted on the ladder by the wall (Option A) must have the same magnitude as the frictional force exerted on the ladder by the floor because these are the two horizontal forces that balance each other when the ladder is at rest. This is due to Newton's third law (for every action, there is an equal and opposite reaction) and the condition for equilibrium that dictates the net force in any direction must be zero.
To understand this, we must resolve the weight of the ladder into two components - one perpendicular to the floor (which is related to the normal force exerted by the floor) and one parallel to the floor (which must be balanced by the static friction force to prevent slipping). The weight's perpendicular component is balanced by the normal force from the floor, while the parallel component must be balanced by the static friction. Particularly for an object at rest on an inclined plane, the static frictional force and the horizontal component of the ladder's weight are equal in magnitude but opposite in direction.