A uniform ladder is leaning against a smooth wall on a rough ground. The ladder has a mass of 10 kilograms and is 4 metres long. If the ladder is in equilibrium, state an equation for the coefficient of friction of the ground

Uniform means that the centre of mass is half way up the ladder. Smooth wall means no friction is felt on the wall and rough ground means that there is friction felt there. First, draw a diagram and take moments from the ground to find a way to express the reaction force on the wall: 5gcot(theta), where theta is the angle made between the ladder and the ground.Then, since the ladder is in equillibrium, equate the reaction force from the ground to the weight of the ladder to get an expression for the reaction force. Then, assuming friction is maximum, use the equation for friction (F=muR) and equate that to the reaction force on the wall to get a final answer of mu=0.5cot(theta)