Length L = 6m
Angle with horiontal, θ = 50°
Friction with wall = 0
Coefficient between ladder and floor, μ = 0.5
Mass of ladder = M
Mass of man, m = 11M
Let the man climbs up X m. from the bottom,
Vertical reaction of floor, R = M+11M=12M
(because wall is smooth)
Maximum static friction force to resist movement, F = μR = horizontal reaction on wall
Take moments about the base of the ladder, and for equilibrium, must equal zero:
M*Lcos50+11M*Xcos50-μ*R*Lsin50=0
Solve for X. (between 3 and 4 m.)
A ladder of mass M and length 6 m rests against a frictionless wall at an angle of 50 degrees to the horizontal. The coefficient of static friction between the ladder and the floor is 0.5. What is the maximum distance along the ladder a person of mass 11M can climb before the ladder starts to slip?
1 answer
1 answer