Question

A person of mass m_{p} is standing on a rung one-third of the way up a uniform ladder of mass m_{L} and length d. The ladder is inclined at an angle θ with respect to the horizontal. Assume there is no friction between the ladder and the wall but there is friction between the base of the ladder and the floor with a coefficient of static friction μ_{s} Find the minimum coefficient of friction between the ladder and the floor so that the person and ladder do not slip?

Answer 1

The minimum coefficient of friction between the ladder and the floor can be determined using the equation μs ≥ (mg*cos(theta) + mL*g) / (mg*sin(theta) + mL*g)

Step-by-step explanation:

In order for the person and ladder not to slip, the frictional force between the ladder and the floor must be greater than or equal to the force trying to make them slip. This force is the component of the person's weight perpendicular to the ladder (mg*cos(theta)) plus the force due to the ladder's weight (mL*g).

The normal reaction force at the base of the ladder is equal to the sum of the person's weight and the ladder's weight.

The minimum coefficient of friction between the ladder and the floor is given by the equation μs ≥ (mg*cos(theta) + mL*g) / (mg*sin(theta) + mL*g)