The discussion revolves around determining the maximum angle a ladder can make with the vertical while leaning against a frictionless wall, given a specific coefficient of static friction between the ladder and the floor. The focus is on the theoretical aspects of forces and moments acting on the ladder.
Participants generally agree on the approach to the problem and the calculations involved, but there is no consensus on the final answer or the implications of the results presented.
The discussion includes repeated statements of the same mathematical relationships without introducing new variables or assumptions, which may limit the exploration of alternative models or solutions.
This discussion may be useful for individuals interested in mechanics, particularly those studying forces and moments in static equilibrium scenarios involving friction and angles.
haruspex said:Let ladder be at angle θ to vertical.
Let (horizontal) force from wall be H.
By moments about foot of ladder, 2H.cos(θ) = M.sin(θ).
Force from floor has horizontal component H, vertical component M.
If coefft friction is λ, max H = λ.M, at which point tan(θ) = 2.λ.
ramly said:what did you get as an answer?
_______________________________haruspex said:Let ladder be at angle θ to vertical.
Let (horizontal) force from wall be H.
By moments about foot of ladder, 2H.cos(θ) = M.sin(θ).
Force from floor has horizontal component H, vertical component M.
If coefft friction is λ, max H = λ.M, at which point tan(θ) = 2.λ.