A uniform ladder of length and mass rests in a vertical plane against a smooth…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A uniform ladder of length L=4.0m and mass 18kg rests in a vertical plane against a smooth (frictionless) wall. The bottom end is on a rough horizontal floor. The ladder makes an angle θ=53∘ with the floor. A painter of mass 65kg stands on the ladder a distance d=2.5m measured along the ladder from the bottom. The system is at rest.
(1) Part 1: (a) Draw a free-body diagram for the ladder, indicating all forces acting on it.
(2) Part 2: (b) Write the two independent algebraic equations that express the translational equilibrium of the ladder.
(3) Part 3: (c) Taking torques about the point where the ladder contacts the floor, derive an expression for the minimum static coefficient of friction μs between the ladder and the floor that will keep the ladder from slipping.
(4) Part 4: (d) Discuss qualitatively how the required value of μs changes as the painter climbs higher toward the top of the ladder. Provide reasoning based on your expressions from part (c).