Consider a ladder with a painter climbing up it (Fig. 9-94). The mass of the uniform ladder is 12.0 kg, and the mass of the painter is 55.0 kg. If the ladder begins to slip at its base when the painter's feet are 70% of the way up the length of the ladder, what is the coefficient of static friction between the ladder and the floor? Assume the wall is frictionless.

Step-by-step solution

When the painter is at 70% of the way up to the lade r, the ladder is start to slip. We will find the coefficient of friction between the ground and ladder. The wall is frictionless.

Step 1 of 5</p>

First we draw the free body diagram.

F: the reaction force from the wall.

N: the reaction force from the ground

Ff; the friction force on the ground keeping the ladder from sliding

W; the weight of the ladder directed downward from the center of mass of the ladder.

P: the weight of the painter.

dW; the perpendicular distance from weight of ladder to point O.

dp; the perpendicular distance from weight of painter to point O.

dF; the perpendicular distance from reaction force of the wall to point O.

Step 2 of 5</p>

We are going to write the first condition of equilibrium for y axis to find the reaction force from the ground.

The reaction force from the ground.

Step 3 of 5</p>

We are going to write the first condition of equilibrium for x.

The reaction force of the wall is equal to friction force from the ground.