A uniform ladder rests against a smooth vertical wall and a rough horizontal floor. A person climbs up the ladder from the bottom to the top. Consider the following four statements regarding the forces acting on the ladder as the person ascends: I. The normal reaction from the floor increases. II. The normal reaction from the wall increases. III. The friction force exerted by the floor increases. IV. The ladder is mo

Step-by-step solution

Let the mass of the ladder be m and the mass of the person be M . Statement I is incorrect: For vertical equilibrium, the normal reaction from the floor is N_ floor = (m + M)g , which remains constant regardless of the person's position. Statement II is correct: Taking torque about the bottom of the ladder, N_ wall L = mg L 2 + Mg x , where x is the distance of the person from the bottom. As x increases, N_ wall must increase to maintain equilibrium. Statement III is correct: For horizontal equilibrium, the frictio