Types of Friction Problems

Dry friction problems can be categorized into three types.

The first type is the no apparent impending motion. Consider a force applied to a crate.

There are three unknowns, which can be evaluated from the three equilibrium equations. So, the developed frictional force can be determined.

The second type is the impending motion at all contact points, for example, a  ladder placed against a smooth wall.

The four unknowns can be determined from the three equilibrium equations and one static frictional equation that apply at the contact point.

Then, the smallest angle at which the ladder can be placed without slipping is evaluated.

The third type is the impending motion at some points of contact. Consider a two-member frame subject to unknown horizontal force.

There are seven unknowns, six equilibrium equations and one of the two possible static frictional equations. Upon solving them, the horizontal force required to cause movement can be determined.

As we increase the force, two possibilities occur, slipping at the left end and not on the right end, or vice versa.