To find the coefficient of friction between two surfaces, divide the maximum frictional force that can occur when one body is moving or has reached equilibrium and cannot move by the normal reaction force. The quotient represents the friction the two surfaces have with one another.
- Use the parameters of the situation to set up the equation
Consider a situation in which an object with a mass of 20 kilograms has reached limiting equilibrium on a rough plane; limiting equilibrium means that the friction has caused the object has come to a stop. Add to the problem that the plane sits at an angle of 20 degrees to the horizontal. Set up the equation in this way: F = (mu)(R), in which F is the maximum frictional force and R is the normal reaction force, while (mu) is the coefficient of friction.
- Insert values into the equation
Remember that F - (mass)(sine of the angle) = 0; in this case, F - (20)(sin 20) = 0. Remember that R = (mass)(cosine of the angle); in this case, R = 20(sin 20). Add these values into the formula of the coefficient of fraction in limiting equilibrium: 20(sin 20) = (mu)(20)(cos 20).
- Solve for the coefficient of friction
Divide both sides of the equation by 20(cos 20) to yield the end result of mu = sin 20 / cos 20, or 0.364, taken to three significant figures.