Friction is an essential concept in physics, engineering, and everyday life. It is the force that opposes the relative motion or tendency of such motion between two surfaces in contact. One of the most common types of friction encountered in various applications is dry friction. Dry friction problems can be broadly categorized into three types, each with unique characteristics and challenges.

The first type of dry friction problem involves situations where there is no apparent impending motion. A prime example of this is when a force is applied to a crate but remains stationary. The frictional forces developed between the floor and the crate oppose the applied force and keep the crate stationary.

To solve this type of problem, one must consider the three unknowns involved: the normal force, the frictional force, and the applied force. These unknowns can be evaluated using the three equilibrium equations that govern the system. Once these unknowns are determined, the developed frictional force can be calculated, providing insight into the factors affecting the crate's stability.

The second type of dry friction problem involves situations where impending motion occurs at all contact points. An example of this problem is a ladder placed against a smooth wall. In this scenario, the ladder is on the verge of slipping, and one must determine the smallest angle at which the ladder can be placed without slipping.

To solve this problem, one must first identify the four unknowns present: the normal forces at both contact points, the frictional force at the base of the ladder, and the angle. These unknowns can be determined using the three equilibrium equations and one static friction equation that apply at the contact points. Once these values are calculated, the smallest angle at which the ladder can be placed without slipping can be evaluated.

The third type of dry friction problem involves situations where impending motion occurs at some, but not all, points of contact. An example of this type of problem is a two-member frame subject to an unknown horizontal force. In this case, the frame may experience slipping at one end while remaining stationary at the other.

To solve this problem, one must identify the seven unknowns involved: the normal forces at both contact points, the frictional forces at both ends, the applied horizontal force, and the reaction forces at the supports. Six equilibrium equations and one of the two possible static friction equations can be used to determine these unknowns. Solving these equations can determine the horizontal force required to cause movement in the frame.

As the force applied to the frame increases, two possibilities may occur: slipping at the left end while the right end remains stationary or vice versa. By analyzing these possibilities, one can better understand the factors influencing the motion of the frame and the conditions under which it will slip.