sample question for you:
A non-uniform ladder AB of weight 240N and length 6m rests with its end A on smooth horizontal ground and its end B against a rough vertical wall. The coefficient of friction between the ladder and the wall is 0.3. The centre of mass of the ladder is 2m from A. The ladder lies in a vertical plane perpendicular to the wall and the ground, and is inclined at an angle x to the horizontal, where tanx = 3/2. The ladder can be prevented from sliding down the wall by applying a horizontal force of magnitude PN to the bottom of the ladder. By modelling the ladder as a non uniform rod determine the minimum value of P.
(edited)
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