To find the coefficients of friction in a given system, an experiment needs to be performed. Finding the coefficient of static friction is the natural first step.
Once this coefficient is found, the more complicated problem of finding the coefficient of kinetic friction is not so cumbersome. In this experiment, the force of static friction will be found and used to determine the corresponding coefficient of static friction. Coefficient of Static Friction: The orthodox convention for solving this problem involves trigonometric functions, but here only algebra and our good friend "the Pythagorean Theorem" will be used. To find this coefficient experimentally, place a block on a board; both of which are covered with known materials.
Tilt the board by raising one end. Nothing will visibly occur for a while, though forces are changing to a point where the block will begin sliding down the board. In this experiment, the interesting mathematics occur the moment motion begins. As the board is being tilted, the normal and hence the frictional force decrease.
As stated on the background page, this is due to less and less of the block's weight acting in the normal direction. The remaining component of the weight, in a trigonometric sense, acts in a direction parallel to the plane of the board. This force will be denoted as Fp; representing the parallel force. As the incline is increased, Fp will increase.
The moment Fp becomes larger than Ff, the block will begin to slide down the board. It is convenient to note that the triangles formed by the apparatus and the force vectors are similar at all times. This enables us to find the coefficient of friction without using trigonometry.