Friction depends partly on the smoothness of the contacting surfaces, a greater force being needed to move two surfaces past one another if they are rough than if they are smooth. However, friction decreases with smoothness only to a degree; friction actually increases between two extremely smooth surfaces because of increased attractive electrostatic forces between their atoms. Friction does not depend on the amount of surface area in contact between the moving bodies or (within certain limits) on the relative speed of the bodies. It does, however, depend on the magnitude of the forces holding the bodies together. When a body is moving over a horizontal surface, it presses down against the surface with a force equal to its weight, i.e., to the pull of gravity upon it; an increase in the weight of the body causes an increase in the amount of resistance offered to the relative motion of the surfaces in contact.
The coefficient of friction is the quotient obtained by dividing the value of the force necessary to move one body over another at a constant speed by the weight of the body. For example, if a force of 20 newtons is needed to move a body weighing 100 newtons over another horizontal body at a constant speed, the coefficient of friction between these two materials is 20/100 or 0.2. Different materials in contact yield different results; e.g., different resistances are felt if one pushes a block of wood over surfaces of wood, steel, and plastic. A different coefficient of friction must be calculated for each different pair of materials.
There is more than one coefficient of friction for a given pair of materials. More force is needed to start a body moving across a surface than is needed to keep it in motion once started. Thus the coefficient of static friction (describing the former case) for a pair of substances is greater than the coefficient of kinetic friction (describing the latter case) for the substances. Similarly, sliding friction is greater than rolling friction. The force of friction between two materials can be calculated by multiplying the coefficient of friction between these materials (determined experimentally and listed in engineering handbooks) by the force holding them together (e.g., the weight of the moving body).
Fluid friction is observed in the flow of liquids and gases. Its causes are similar to those responsible for friction between solid surfaces, for it also depends on the chemical nature of the fluid and the nature of the surface over which the fluid is flowing. The tendency of the liquid to resist flow, i.e., its degree of viscosity, is another important factor. Fluid friction is affected by increased velocities, and the modern streamline design of airplanes and automobiles is the result of engineers' efforts to minimize fluid friction while retaining speed and protecting structure.
For surfaces at rest relative to each other , where is the coefficient of static friction. This is usually larger than its kinetic counterpart. The Coulomb friction may take any value from zero up to , and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence.
For surfaces in relative motion , where is the coefficient of kinetic friction. The Coulomb friction is equal to , and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface.
This approximation mathematically follows from the assumptions that surfaces are in atomically close contact only over a small fraction of their overall area, that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact), and that frictional force is proportional to the applied normal force, independently of the contact area (you can see the experiments on friction from Leonardo Da Vinci). Such reasoning aside, however, the approximation is fundamentally an empirical construction. It is a rule of thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility – though in general the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems.
The coefficient of friction (also known as the frictional coefficient) is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction (the two materials slide past each other easily), while rubber on pavement has a high coefficient of friction (the materials do not slide past each other easily). Coefficients of friction range from near zero to greater than one – under good conditions, a tire on concrete may have a coefficient of friction of 1.7.
When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, Scotch tape resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive in this way.
The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road.
The coefficient of friction is an empirical measurement – it has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but Teflon, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property – even Magnetic levitation vehicles have drag. Rubber in contact with other surfaces can yield friction coefficients from 1.0 to 2.
Another important example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction.
The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction, although this term is not used universally. The value is given by the product of the normal force and coefficient of static friction.
Examples of kinetic friction:
Superlubricity, a recently-discovered effect, has been observed in graphite: it is the substantial decrease of friction between two sliding objects, approaching zero levels. A very small amount of frictional energy would still be dissipated.
Another way to reduce friction between two parts is to superimpose micro-scale vibration to one of the parts. This can be sinusoidal vibration as used in ultrasound-assisted cutting or vibration noise, known as dither.
When an object is pushed along a surface, the energy converted to heat is given by:
The work done by friction can translate into deformation, wear, and heat that can affect the contact surface's material properties (and even the coefficient of friction itself). The work done by friction can also be used to mix materials such as in the technique of friction welding.