# Coefficient of Friction: Definition, Formula & Examples

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Lesson Transcript
Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

The concept of coefficient of friction may be confusing, but don't fret. Come inside to discover what the coefficient of friction is, how it is calculated, and to see some examples of this coefficient for a few common surfaces.

## Definition & Calculation

What is the coefficient of friction? That's the question Francine's teacher, Mr. Campo, asked in physics class. Mr. Campo starts off explaining which coefficient of friction he's talking about because there are many types of friction: static, sliding or kinetic, air resistance, and the internal friction of a deformable body, among others. Each of these situations has a different way to measure the coefficient of friction. The friction Francine and her classmates are being asked about in this lesson is static friction. Static friction is the force that resists movement of an object pressed against a surface.

The coefficient of static friction is the minimum force required to get an object to slide on a surface, divided by the forces pressing them together. There are no units associated with coefficients of friction. In more precise mathematical terms:

Francine asks what the number means in everyday language, and Mr. Campo responds, 'The coefficient of static friction is just a number that indicates how difficult it is to get surfaces to slide past each other. A coefficient of 1 would mean that it takes just as much force to lift an object as it does to slide it on a level surface. For most everyday objects and materials, the coefficient is a number between 0 and 1.'

Mr. Campo explains that this doesn't apply to all situations. There are many cases where the coefficient of friction can be greater than 1, with Velcro being one obvious example. There has even been one published report of a negative coefficient of friction. However, this was on a microscopic scale with some very exotic materials.

The coefficient of static friction is determined experimentally by measuring how much an object weighs and how large a force is required to get it to just start sliding on a flat surface with great precision. The coefficient depends only on the two materials in question.

## Examples

After the explanation, Mr. Campo writes a problem up on the board and works it through for Francine and her classmates. 'Let's take a look at an example to see if you're following along. It takes exactly 67.3 Newtons to just move an object weighing 12.41 kg. What is the coefficient of static friction for these two materials? Use the acceleration of gravity of 9.81 m/s/s in your calculations.'

'The first thing we do is, what?' asks Mr. Campo.

Francine and several of her classmates respond with one of his often repeated phrases, 'Substitute what we know into the equation.'

'Right!' he exclaims, and continues writing on the board.

Coefficient of static friction = 67.3 Newtons / (9.81 m/s/s)(12.41 kg) = 0.553

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