# How to find the coefficient of friction?

Irina Fateeva

January 11, 2013

36030

Friction is a rather complicated process of work of solids in the process of relative motion or during the motion of a body in liquid or gaseous form. How to find the coefficient of friction force? It directly depends on the material of friction surfaces, the quality of processing and a huge number of other factors. Very often in problems in physics it is necessary to find out how to find the coefficient of sliding friction ?. We will try to answer this question.

- If the body moves along the horizontal part of the surface of the other body, then the support reaction is directed perpendicular to the given slip plane. According to Coulomb's law, F = kN, where N is the support reaction force, and k is the friction coefficient. Let us transform this formula into N = Fth = mg, since the reaction of the support is directed vertically.
- Also, the friction coefficient can be calculated using the following formula: k = Ftr / N = Ftr / mg. Here we should be aware of the force of sliding friction. It can be found if we know the acceleration a.Slightly transforming the formula, we get k = (F-ma) / N. From this it follows that the friction coefficient is a dimensionless quantity.
- Another way to find the friction coefficient is as follows. If the body slides along an inclined plane, for example, from a block, then the angle of inclination of the plane is assumed to be φ. N is the reaction force of the support, which is perpendicular to the specified plane. The equation of motion of the body, according to Newton's law, is written as follows: N = mg * cosφ, mg * sinφ-Ftr = mg * sinφ-kN = ma. We transform this equation and we get: g * sinφ-kg * cosφ = a. Now it becomes clear that k = (g * sinφ-a) / (g * cosφ).
- Having considered a fairly well-known special case of an object sliding down an inclined plane, in which a = 0 or, in other words, the body moves in a straight line and evenly. In this case, the equation of motion is g * sinφ-kg * cosφ = 0. We express the coefficient k = tgφ. This shows that in order to find the slip coefficient, it is enough just to know the tangent of the angle of inclination.

Now you can easily tell everyone how to find the coefficient of friction in several ways.