Question

A uniform 5-m long ladder weighing 70 n leans against a frictionless vertical wall. the foot of the ladder is 4 m from the wall. what is the minimum coefficient of static friction between the ladder and the floor necessary for the ladder not to slip?

Answer 1

To prevent the ladder from slipping, the minimum coefficient of static friction between the ladder and the floor is 0.784.

Step-by-step explanation:

To find the minimum coefficient of static friction between the ladder and the floor necessary for the ladder not to slip, we need to analyze the forces acting on the ladder.

There are four forces acting on the ladder: the normal reaction force (N) from the floor, the static friction force (f) between the ladder and the floor, the weight (w) of the ladder, and the normal reaction force (F) from the wall.

The minimum coefficient of static friction (us) can be determined using the equation us = tan(ß), where ß is the angle of inclination between the ladder and the floor.

Substituting the given values, we have ß = arctan(4/5) = 38.66°.

Therefore, the minimum coefficient of static friction between the ladder and the floor necessary for the ladder not to slip is us = tan(38.66°) = 0.784.