A 3 m long ladder weighing 20 kg leans on a frictionless vertical wall. Its feet rest on the floor 1

Question

A 3 m long ladder weighing 20 kg leans on a frictionless vertical wall. Its feet rest on the floor 1 m from the wall. What is the reaction force of the wall? (Take $g = 9.8	ext{ m/s}^2$)

Professor PC Thomas Classes · Answer

The forces on the ladder are its weight W acting at its centre of gravity, reaction force $F_1$ of the wall, and $F_2$ of the floor. For rotational equilibrium, taking the moments of the forces about the foot of the ladder: $2\sqrt{2} F_1 - (0.5)W = 0$. Since $W = 20 	imes 9.8 = 196	ext{ N}$, solving for $F_1$ gives $F_1 = \frac{196 	imes 0.5}{2\sqrt{2}} \approx 34.6	ext{ N}$.