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.