A uniform ladder of length 5.0 m and mass 20 kg leans against a smooth vertical wall
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform ladder of length 5.0 m and mass 20 kg leans against a smooth vertical wall, making an angle of 60∘ with the horizontal rough floor. The wall exerts only a normal force that is horizontal, while the floor exerts both a normal force Nf and a static friction force fs. The ladder remains at rest and does not slip.
(a) Draw a free-body diagram for the ladder, labeling all forces and their lines of action.
(b) Using the bottom of the ladder as the axis, derive an expression for the magnitude of the horizontal normal force Nw exerted by the wall in terms of known quantities. Show all steps.
(c) Determine the minimum value of the coefficient of static friction μs between the ladder and the floor that will prevent slipping. Provide numerical results with units.
(d) Discuss how your choice of pivot in part (b) simplifies the algebra compared with summing torques about the ladder’s center of mass.