Coefficient of friction in sliding and rolling

Under terrestrial conditions, any moving bodies (or coming into motion) come into contact with the environment or with other bodies. In this case, there are forces that resist their movement. These forces are called frictional forces, they translate a part of the mechanical energy of motion into internal energy, which is accompanied by heating of bodies and the environment.

Friction is external and internal. The internal (otherwise called viscosity) consists in the appearance of a tangential force between the moving layers of liquid or gas, which interferes with this displacement.

In contrast to this, external friction arises at the places of contact of solids in the form of a force tangential to their surface and hindering their mutual displacement. It, in turn, is divided into static (friction of rest) and kinematic. Static friction is manifested when trying to move one fixed body relative to the other. The kinematic exists between moving bodies in contact with each other. External friction can be divided into friction sliding and rolling.

What is the physical meaning of friction? Is it useful or harmful? At first glance, friction only hinders us: the details of the mechanisms, the tires of cars wear out, the soles of shoes are being erased, etc. And the creation of a perpetual motion machine is impossible only for this reason. But look closely. Disappearing friction - we can not walk or flip the book, nor move the car, nor stop moving. A huge number of physical phenomena in the world is based on friction. The two main achievements of mankind, which determined the development of civilization - the mining of fire and the invention of a wheel - would have been impossible without it.

This phenomenon is based on the unevenness of any bodies: at the contact of the notch one always clings to the roughness of the other. For perfectly smooth (for example, carefully ground) surfaces, close to each other, the laws of molecular friction, based on the mutual attraction of molecules, act.

The science of tribology studies friction. In 1781 the French physicist S. Coulomb formulated the basic laws of dry friction. Experimentally, the scientist established that the frictional force F, which occurs during sliding, is directly proportional to the force N acting on the body of normal pressure. This relationship is as follows:

N: F = k ∙ N;

Where k is the coefficient of friction (proportionality coefficient). Its value was calculated as follows: the body was placed on an inclined plane and its uniform motion was achieved by changing the angle of inclination . In this case, the frictional force F was equal to the driving force P:

F = P ∙ sin a;

The force N (the force of normal pressure) is P ∙ cos a; Therefore, k = tan a. The coefficient of friction is hence the tangent of the angle of inclination of the surface along which the body slides uniformly, ie, at a constant speed.

In practice, its value can only be calculated approximately. The surfaces of the bodies, as a rule, are more or less contaminated, have oxides, rust and other inclusions. The coefficient of friction, determined in pairs for combinations of different materials by experiments, is included in special reference tables.

When rolling, friction arises because the moving wheel is slightly pressed into the road surface, i.e., forced to overcome a small bump. The harder the road, the smaller this bump and the less the frictional force. Its value is calculated in this case by the formula: F = k ∙ N / r, in which r is the radius of the wheel. Consequently, the rolling friction coefficient has a dimension of length. Usually it is expressed in centimeters in contrast to the coefficient of sliding friction, which is a dimensionless quantity.

As mentioned above, the coefficient of internal friction exists not only for solids, but also for liquids. In hydraulics, it is often necessary to calculate the loss of specific energy of hydraulic systems that arise in pipelines. They can be of two types: length losses occurring in straight pipes with uniform flow, and local losses, the cause of which is the deformation of the flow due to changes in the shape of the channel (constriction, expansion, turns). Hydraulic losses are calculated using a similar value, which is called the "hydraulic friction coefficient".