Two engineering concepts governed the design of the friction apparatus.   They are static friction and kinetic friction.  Using a test block of known weight and geometry, it is possible to determine both coefficients via a simple experiment.

Static friction, Fs, is defined as the frictional force that prevents the block from going into motion.  It is defined as the product of the coefficient of static friction, ms, and the normal force, N.  When on an inclined plane, the normal force is dependent on the angle of inclination, q, and the weight, W, of the block.  Through summation of forces, it can be determined that the following equation holds, given the figure:

Kinetic friction, F,  is defined as the frictional force that retards motion once it has started.  It can be determined using the law of conservation of energy.  When a block travels between two points along an inclined slope, we can set the bottom point as having kinetic energy (KE) and no gravitational potential energy (PE).  The top point can be defined as having PE and no KE.  The values of the total energy possessed by the block at these two points are not equal.  The difference in this energy is due to friction.  The following variables need to be determined before applying the formula for the coefficient of kinetic friction, mk: the distance, d, of the test specimen; the time, Dt, the block takes to pass through the photo gate timer (thus producing the velocity, V); and the angle, q, of inclination.  Additionally, gravity, g, must be considered.  Using algebra, it can be determined that the following equation holds, given the figure and variables: