A uniform stationary ladder of length L and mass M leans against a smooth vertic

Question

A uniform stationary ladder of length L and mass M leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is mu. The ladder makes an angle theta with respect to the floor. A painter of weight 1/2 M stands on the ladder a distance d from its base. Find an expression for the magnitude of the normal force N exerted by the floor on the ladder. Find an expression for the magnitude of the normal force N_W exerted by the wall on the ladder. Find an expression for the largest value of d_max for which the ladder does not slip? What is the largest value for d, in centimeters, such that the ladder will not slip? Assume that ladder is 4.5 m long, the coefficient of friction is 0.54, the ladder is at an angle of 44 degree, and the ladder has a mass of 75 kg.

Explanation / Answer

Smooth wall so, it is Frictionless => wall supplies no vertical component

=> Sum of the vertical forces DOWN = Normal Force on bottom of ladder.


Weight of ladder =M kg * 9.8 m/s^2 = 9.8M NEWTONS
Weight of painter = (1/2)*M * 9.8 m/s^2 = 9.8M/2 NEWTONS

Normal Force = 9.8M+9.8M/2 =(3/2)*9.8* M NEWTONS = 1.687 M NEWTONS

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