Friction is a process of interaction of solid bodies at their relative movement, or at the movement of a body in the gaseous or liquid environment. The coefficient of friction depends on material of the rubbing surfaces, quality of their processing and other factors. In physical tasks the sliding friction coefficient as friction force of swing is much less most often is defined.
It is required to you
- Friction force, acceleration of a body, plane tilt angle
Instruction
1. Let's consider for a start a case when one body slides on a horizontal surface of another. Let's assume that it slides on a motionless surface. In this case force of reaction of a support operating on the sliding body is directed perpendicular to the sliding plane. On mechanical Coulomb's law friction force of sliding is equal to F = to kN where k - friction coefficient, and N - force of reaction of a support. As force of reaction of a support is directed strictly vertically, N = by Ftyazh = mg where m is the mass of the sliding body, g is acceleration of gravity. This condition follows from immovability of a body of rather vertical direction.
2. Thus, the coefficient of friction can be found on formula k = Ftr/N = Ftr/mg. For this purpose it is necessary to know sliding friction force. If the body moves uniformly accelerated, then friction force can be found, knowing acceleration of a. Let the body be affected by the driving force of F and Ftr friction force directed opposite to it. Then under the second law of Newton (F-Ftr)/m = a. Expressing to Ftr from here and substituting in a formula for friction coefficient, we will receive: k = (F-ma)/N.Iz of these formulas is visible that the coefficient of friction is dimensionless size.
3. Let's consider more general case when the body slides off the inclined plane, for example, from the fixed block. Such tasks very often occur in a school course of physics in the section "Mechanics". Let the tilt angle of the plane be equal φ. Force of reaction of support N will be directed perpendicular to the inclined plane. The body will also be affected by the gravity and friction force. We will send to an axis along and perpendicular to the inclined plane. According to the second law of Newton it is possible to write down the equations of the movement of a body: N = mg*cosφ, mg*sinφ-Fтр = mg*sinφ-kN = ma. Having substituted the first equation in the second and having reduced the mass of m, we will receive: g*sinφ-kg*cosφ = a. From here, k = (g*sinφ-a)/(g*cosφ).
4. Let's consider important private a sliding case on the inclined plane when a = 0, that is the body moves evenly. Then the equation of the movement has g*sinφ-kg*cosφ appearance = 0. From here, k = tgφ, that is for determination of coefficient of sliding is enough to know a plane inclination tangent of angle.