In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder

Question

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $θ$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $μ_{1}$ and that between the floor and the ladder is $μ_{2}$ . The normal reaction of the wall on the ladder is $N_{1}$ and that of the floor is $N_{2}$ If the ladder is about to slip, then

TestHub · Accepted Answer

Condition of translational equilibrium N 1 = μ 2 N 2 N 2 + μ 1 N 1 = M g Solving N 2 = m g 1 + μ 1 μ 2 N 1 = μ 2 m g 1 + μ 1 μ 2 Applying torque equation about corner (left) point on the floor m g l 2 cos ⁡ θ = N 1 l sin ⁡ θ + μ 1 N 1 l cos ⁡ θ Solving tan ⁡ θ = 2 - μ 1 μ 2 2 μ 2

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