Friction is a force that resists the movement of two contacting surfaces that slide relative to one another. This force always acts tangent to the surface at the points of contact and is directed so as to oppose the possible or existing motion between the surfaces.
We will study the effects of dry friction, which is sometimes called Coulomb friction since its characteristics were studied extensively by the French physicist Charles-Augustin de Coulomb in 1781. Dry friction occurs between the contacting surfaces of bodies when there is no lubricating fluid.*
The theory of dry friction can be explained by considering the effects caused by pulling horizontally on a block of uniform weight $\mathbf{W}$ which is resting on a rough horizontal surface that is nonrigid or deformable.
The upper portion of the block, however, can be considered rigid. As shown on the free-body diagram of the block, the floor exerts an uneven distribution of both normal force $\Delta \mathbf{N}_n$ and frictional force $\Delta \mathbf{F}_n$ along the contacting surface. For equilibrium, the normal forces must act upward to balance the block's weight $\mathbf{W}$, and the frictional forces act to the left to prevent the applied force $\mathbf{P}$ from moving the block to the right.
Close examination of the contacting surfaces between the floor and block reveals how these frictional and normal forces develop. It can be seen that many microscopic irregularities exist between the two surfaces and, as a result, reactive forces $\Delta \mathbf{R}_n$ are developed at each point of contact.
As shown, each reactive force contributes both a frictional component $\Delta \mathbf{F}_n$ and a normal component $\Delta \mathbf{N}_n$.
The effect of the distributed normal and frictional loadings is indicated by their resultants $\mathbf{N}$ and $\mathbf{F}$ on the free-body diagram.
Notice that $\mathbf{N}$ acts a distance $x$ to the right of the line of action of $\mathbf{W}$. This location, which coincides with the centroid or geometric center of the normal force distribution is necessary in order to balance the "tipping effect" caused by $\mathbf{P}$.
In cases where the surfaces of contact are rather "slippery," the frictional force $\mathbf{F}$ may not be great enough to balance $\mathbf{P}$ and consequently the block will tend to slip. In other words, as $\mathbf{P}$ is slowly increased, $\mathbf{F}$ correspondingly increases until it attains a certain maximum value $F_s$, called the limiting static frictional force.
When this value is reached, the block is in unstable equilibrium since any further increase in $\mathbf{P}$ will cause the block to move. Experimentally, it has been determined that this limiting static frictional force $F_s$ is directly proportional to the resultant normal force $N$. Expressed mathematically,
$$ F_s = \mu_s N $$
where the constant of proportionality, $μ_s$ (mu "sub" s), is called the coefficient of static friction.
Typical values for μs are given. Note that these values can vary since experimental testing was done under variable conditions of roughness and cleanliness of the contacting surfaces. For applications, therefore, it is important that both caution and judgment be exercised when selecting a coefficient of friction for a given set of conditions.
When a more accurate calculation of $F_s$ is required, the coefficient of friction should be determined directly by an experiment that involves the two materials to be used.