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.