Max Angle for Ladder Leaning on Wall

[ramly]

There is a ladder with mass M that is leaning against a frictionless wall. The coefficient of static friction between the floor and the ladder is say 0.4. What is the max angle that the ladder can make with the vertical before it starts to slide? *the axis of rotation is at the ladder's contact with the floor*

 

[haruspex]

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]

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.

what did you get as an answer?

 

[Khashishi]

is this homework?

 

[ramly]

no its not

 

[haruspex]

what did you get as an answer?

You're asking me to compute atan(2*0.4) for you? OK: 0.67 radians, or 38.7 degrees.
(Note: that's the angle to the vertical.)

 

[kingsly]

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.

_______________________________

Very detailed info.You made some good points there.thank for give us a good answer.