Friction Equation:  magnitude of friction force is equal to or less than the coefficient of friction times the magnitude of the frictional force.

Overview of the Friction Equation

The friction equation allows you to determine the friction when you know the characteristics of the surface and the normal force (contact force) between the object and the surface it is touching.

An example would be when you are investigating an object sliding across a floor.  You might use this equation to find the frictional force, then use that force to help determine the acceleration of the object.

Variables in the Friction Equation

This equation relates the frictional force, the coefficient of friction, and the normal (or contact) force.  Note that this equation has absolute values around the force vectors.  This is because the frictional force is generally not in the same direction as the normal force.  In fact, they are often perpendicular to each other.

The equation also has a “less than or equal to” symbol rather than an equals sign.  This is because the static frictional force only provides enough friction to stop the object from moving. 

Ff represents the frictional force.

μ represents the coefficient of friction.

FN represents the normal force.

The coefficient of friction is a unitless number that describes how rough a surface is.  This number usually has a value between 0 and 1, but in some high-friction cases, it may be larger than 1.  The larger the coefficient, the more friction you will experience.  Except when you are specifically calculating this value, you will usually be given a value or be able to find the value in a coefficient of friction table.

The normal force is the force of contact between the object and the surface it is touching.  This might be the weight of the object, but isn’t always, especially if the object is on an incline.  If you push down on an object on a level surface, you need to add the weight of the object and the force of the push.  If a person is holding an object against a wall, this force is how hard they are pushing.

Units in the Equation

Usually we use the following combination of units.

Ff has units of newtons

μ is unitless, as it is the ratio of two forces..

FN has units of newtons.

Things to Watch Out for in the Friction Equation

The coefficient of friction between two surfaces depends upon whether the object is moving or not.  In fact, we call these two coefficients the coefficient of static friction or the coefficient of kinetic friction.  Be sure that you read the description of the situation carefully to know which one to use.  The coefficient of kinetic friction almost always has a smaller value than the coefficient of static friction.  Once an object starts to slide, it takes less force to keep it sliding.

The other thing to be aware of is the “less than or equal to” symbol.  For static friction, the value of the frictional force increases as you push on a stationary object.  This force peaks just before the object starts to move and kinetic friction begins.  

When just given a description of the object, using the normal force and the coefficient give you the maximum value of the kinetic friction.  If you apply a force less than this to start an object moving, there will only be sufficient friction to keep the object from moving.