A ladder of mass M and length L stays at rest against a smooth wall. The coefficient of friction between the ground and the ladder is `mu`
(a) Let `F_("wall")`, W and `F_(g)` be the force applied by wall, weight of the ladder and force applied by ground on the ladder. Argue to show that the line of action of these three forces must intersect.
(b) Using the result obtained in (a) show that line of action of Fg makes an angle `tan^(-1) (2 tan theta)` with the horizontal ground where `theta` is the angle made by the ladder with the ground.
(c) Find the smallest angle that the ladder can make with the ground and not slip.
(d) You climb up the ladder, your presence makes the ladder more likely to slip. Where are you at A or B? C is the centre of mass of the ladder.

Answer

(a) `alpha = tan^(-1) (2 tan theta)`
(c) `theta_("min") = tan^(-1) ((1)/(2 mu))`
(d) Slippage is more likely when at A