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In Sample Problem 9-7, if the wall were not frictionless, would the empirical laws of friction supply us with the extra condition needed to determine the extra (vertical) force exerted by the wall on the ladder?
The figure below shows the forces acting on the ladder held against the wall.If there is friction between the wall and the ladder, the vertical equilibrium of the ladder can be represented as:Here f1 is the frictional force between the wall and the ladder, M is the mass of the firefighter, m is the mass of the ladder, g is the acceleration due to gravity and N is the normal force on ladder from ground.Therefore one can see that the normal force exerted by the ground on the ladder reduces by the amount equal to the magnitude of frictional force between the wall and the ladder.Also the empirical law for the friction is
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