How to Calculate the Coefficient of Friction

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Friction occurs in two ways: kinetic and static. Kinetic friction acts on an object that slides on a surface, whereas static friction occurs when friction prevents the object from moving. 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. The coefficient is different for every pair of materials that contact each other, including a material that interacts 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.

TL;DR (Too Long; Didn't Read)

The formula to calculate the coefficient of friction is μ = f÷N. The friction force, f, always acts in the opposite direction of the intended or actual motion, but only parallel to the surface.

Measure the Time of Movement

To measure the force of friction, set up an experiment in which a block, pulled by a string that runs over a pulley and is attached to a hanging mass, slides across a track. 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 this measurement with different hanging masses.

Calculate Friction Force

Calculate the friction force. To begin, first calculate Fnet, the net force on the block. The equation is


where M is the mass of the block in grams.

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

Calculate N, the normal force is the weight of the block.


Now, calculate the friction force, f, the difference between the applied force and the net force. The equation is:


Graph the Friction Force

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.

Record Ramp Data

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.