# Coefficient of Kinetic Friction: Definition, Formula & Examples

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• 0:00 Kinetic Friction:…
• 1:32 Friction On An Inclined Plane
• 2:23 Example 1: A Flat Surface
• 3:15 Example 2: Down An…
• 5:08 Example 2.5: Up An…
• 5:39 Lesson Summary
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Lesson Transcript
Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

The coefficient of kinetic friction can be a difficult concept. This lesson goes over what it is, when it's used, and how to work problems involving this coefficient.

## Kinetic Friction: Definition and Formula

Kinetic friction, also known as sliding friction or moving friction, is the amount of retarding force between two objects that are moving relative to each other. This is important in understanding the coefficient of kinetic friction, which is the proportion you get when you take the pulling force needed to keep an object moving and divide that by the force holding the two sliding surfaces together. This coefficient is specific to the materials involved in the contacting surfaces. A rougher surface will have a higher coefficient.

The equation that helps you to find the coefficient of kinetic friction is this:

The normal force is the amount of force perpendicular to the surfaces that are in contact, or the force holding the objects together. And the force of kinetic friction is the amount of force necessary to keep the two objects moving relative to each other. The force of kinetic friction acts in a opposite direction to the movement of the two objects.

For an object at rest on a flat surface, with no other force acting on it, the normal force would be the force of gravity on the object, or the weight of the object. This force is calculated by multiplying the object's mass by the acceleration of gravity (N=mg). Two cubes lying next to each other on a flat surface with faces touching would have a normal force of zero because there is no force holding the two surfaces together.

## Friction On An Inclined Plane

For friction on surfaces that are tilted level, the normal force is this:

In the diagram you're looking at on screen, the object is at rest, it has no outside forces acting on it. Depending on other forces, the normal force can change in magnitude or the force of friction can act in the opposite direction.

N = Normal force (this is both the force up and to the right exerted by the surface and the force down and to the left exerted by the object)

m(g) = force of gravity

## Example 1 - Flat Surface

Maggie has just completed a physics friction experiment with the following data:

Object material: rubber

Surface material: wooden board

Mass of dragged object = 2.11kg

Force required to keep object moving (average of 10 readings) = 12.6 Newtons

The object was pulled on a level surface.

The accepted acceleration of gravity in this location is 9.82m/s/s

What is the coefficient of kinetic friction? Using the formula for kinetic friction we can calculate the following:

Coefficient of kinetic friction = (12.6 N) / (2.11kg)(9.82m/s/s) = 0.608

## Example 2: Down An Inclined Plane

Maggie sets up her experiment with an angle of 30 degrees from horizontal and then measures the force necessary to keep the object moving down the wooden board. Do you expect it to be greater or less than the 12.6 Newtons in the first experiment? To calculate this, we need to think about all of the forces acting on this object, both perpendicular to the surfaces and parallel to the surfaces.

Perpendicular: the only force acting perpendicular to the surface is the normal force.

Normal force = m g cos(30) = (2.11kg)(9.82m/s/s)(0.866) = 17.9 N

Parallel: there is gravity acting down the hill, as well as the force Maggie applies to the rubber block, and the force of kinetic friction acting up the hill.

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