Coefficient of friction

The coefficients of friction or coefficients of friction link the opposition to sliding offered by the surfaces of two bodies in contact according to the intensity of the mutual support they experience. It is a dimensionless coefficient. It is usually represented by the Greek letter μ (mi).

The value of the coefficient of friction is characteristic of each pair of materials in contact; it is not an intrinsic property of a material. It also depends on many factors such as temperature, surface finish, relative speed between surfaces, etc. The nature of this type of force is linked to the interactions of the microscopic particles of the two surfaces involved.

For example, ice on a sheet of polished steel has a low coefficient; while rubber on pavement has a high coefficient. The coefficient of friction can take values from almost zero and normally does not exceed unity.

Static friction and dynamic friction

Most surfaces, even those considered polished, are extremely rough on a microscopic scale. When two surfaces are put in contact, the movement of one with respect to the other generates tangential forces called friction forces, which have the opposite direction to the movement, the magnitude of this force depends on the coefficient of dynamic friction.

There is another form of friction related to the previous one, in which two rigid surfaces at rest do not move relative to each other as long as the force parallel to the tangent plane is small enough, in this case the relevant coefficient is the coefficient of static friction. The condition for there to be no slippage is that:

F F ≤ ≤ μ μ e{displaystyle {frac {F_{associated}}{F_{bot }}}{leq mu _{e}

Where:

F {displaystyle F_{associated}}, it is the force parallel to the plane of tangence that tries to slide the surfaces.

F {displaystyle F_{bot }}, it is the normal or perpendicular force to the tangence plane.

μ μ e{displaystyle mu _{e},}It's the static friction coefficient.

For deformable surfaces it is convenient to state the above relationship in terms of normal and tangential stresses at a point, there will be relative slip if at any point:

日本語Δ Δ 日本語日本語σ σ 日本語=日本語n× × T(n)日本語日本語n⋅ ⋅ T(n)日本語≤ ≤ μ μ e{displaystyle {frac {intance}{intau occupancy}{int}{sigma cult}}}={{frac {intmathbf {n} times mathbf {T} (mathbf {n}}{n}}{mathbf {t}{T}{mathbf {nleq}}}}}}}}{n}}}}}}}{

Where:

n{displaystyle mathbf {n} } is the normal unitary vector to the tangent surface contact plane.

T(⋅ ⋅ ){displaystyle mathbf {T} (cdot)} is the tension tensor in one of the two solids in contact.

Angle of friction

The sand adopts a cone shape with the inclination of its inner thread angle.

When considering the sliding of a body on an inclined plane, it is observed that by varying the inclination of said plane, the object begins to move when a critical angle of inclination is reached. This is because as the inclination increases, the perpendicular component of the weight, the force N, which is proportional to the cosine of the inclination angle, is gradually reduced. Regardless of the weight of the body, since the greater the weight, both the force that pulls the object downhill and the normal force that generates friction increase. In this way, a given coefficient of friction between two bodies is equivalent to a certain angle, which is known as the angle of friction.

Using this angle, μ_e can be calculated, observing up to what angle of inclination the two surfaces can remain static with respect to each other:

So... α α =μ μ e{displaystyle tan alpha =mu _{e},}

Certain granular materials, such as sand, gravel, soil and bulk in general, have a certain coefficient of friction between the grains that make them up. The associated angle is precisely the angle that a stable pile of said material would form, which is why this property is known as the angle of internal friction.