How to Calculate the Coefficient of Friction

By Ariel Balter

There are two basic types of friction: kinetic and static. Kinetic friction acts when objects are in relative motion, whereas static friction acts when there is a force on an object, but the object remains immobile. A simple but effective model for friction is that the force of friction, f, is equal to the product of the normal force, N, and a number called the coefficient of friction, μ, that is different for every pair of materials. This includes a material interacting with itself. The normal force is the force perpendicular to the interface between two sliding surfaces -- in other words, how hard they push against each other. The formula to calculate the coefficient of friction is f = μN. The friction force always acts in the opposite direction of the intended or actual motion, but only parallel to the surface.

Measure μ for Kinetic Friction and Static Friction

Start the block as far from the pulley as possible, release the block, and record the time, t, it takes to move a distance, L, along the track. When the hanging mass is small, you may need to nudge the block very slightly to get it moving. Repeat with different hanging masses.

Calculate the friction force. The formula for the net force on the block is Fnet = 2ML/t^2, where M is the mass of the block in grams.

Calculate Fnet. The applied force on the block, Fapplied, is the pull from the string cause by the weight of the hanging mass, m. The formula is Fapplied=mg where g = 9.81 meters per second squared is the gravitational acceleration constant.

Calculate Fapplied. The normal force is the weight of the block, N = Mg.

Calculate N. The friction force is the difference between the applied force and the net force: f = Fapplied - Fnet.

Calculate f.

Graph the friction force, f, on the y-axis against the normal force, N, on the x-axis. The slope will give you the kinetic friction coefficient.

Place the object on the track at one end and slowly lift that end to make a ramp. Record the angle, θ, at which the block just begins to slide. At this angle, the effective force of gravity acting down the ramp is just barely greater than the friction force preventing the block from beginning to slide. Incorporating the physics of friction with the geometry of the inclined plane gives a simple formula for the coefficient of static friction: μ = tan(θ), where μ is the coefficient of friction and θ is the angle.

About the Author

Ariel Balter started out writing, editing and typesetting, changed gears for a stint in the building trades, then returned to school and earned a PhD in physics. Since that time, Balter has been a professional scientist and teacher. He has a vast area of expertise including cooking, organic gardening, green living, green building trades and many areas of science and technology.