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{excerpt}A force applied by a surface to any object sliding along that surface or subject to forces that would cause it to slide in the absence of friction.  The force of friction will always resist the existing or intended sliding motion.{excerpt}

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h2. Motivation for Concept

It takes effort to get an object sliding along a surface, and sustained effort to keep the object moving once started.  The effort required will depend on the surface characteristics and the object's characteristics.  Sliding a wooden block along a tiled floor is much easier than sliding it along a rubber mat.  The effort required will also depend upon the contact force between the object and the surface.  Brushing sandpaper lightly across wood is easy, but when the sandpaper is pressed hard against the wood, movement requires substantial effort.

h2. Static Versus Kinetic Friction
 
Friction has two basic manifestations that are qualitatively different.  

h4. Definition of Static Friction

If an object is at rest with respect to a surface, friction will attempt to resist efforts to start the object sliding along the surface.  Friction has the goal of keeping the object *static* _with respect to the surface_.  This *static friction* is a response force.  It provides just enough force to keep the object stationary, and no more.  Static friction is characterized by a limiting value.  When the net force attempting to create sliding motion exceeds a certain value, static friction will be unable to prevent motion.  

h4. Defintion of Kinetic Friction

Whenever sliding motion is occuring, friction will apply a force that is directly opposed to the sliding motion.  This force will have essentially constant size independent of the speed of the object for a given object sliding on a given surface.  The size of the friction force _will_ depend, however, on the contact force existing between the object and the surface and also on the material characteristics of the surface and the object.

h2. Quantitative Model of Static Friction

h4. The Limiting Size of Static Friction

The basic characteristics of static friction are well approximated by the limit expression:

{latex}\begin{large}\[ F_{s} \le \mu_{s} N\]\end{large}{latex}

where μ~s~ is the *coefficient of static friction*.  The coefficient of static friction is a dimensionless number, usually less than 1.0 (but _not_ required to be less than 1.0).  Rough or sticky surfaces will yield larger coefficients of friction than smooth surfaces.  _N_ is the [normal force] exerted on the object _by the surface which is creating the friction_, which is a measure of the strength of the contact between the object and the surface.

h4. Determining the Force of Static Friction

To determine the force of static friction on an object, calculate the net force _in the absence of any friction_ and compare it to the limiting value of the friction force.  If the maximum static friction force is larger than the net force in the absence of friction, then friction will provide the force necessary to make the total net force equal zero *assuming* that the net force has no component perpendicular to the surface.  If, however, the maximum static friction force is _less_ than the net force in the absence of friction, static friction will *not apply* (it will not provide a force).  Instead, kinetic friction will apply.

{note}It is very important to remember that for an object at rest on a surface and subject to *no* forces that would act to cause sliding, the static friction force will be *zero*!  (The object will not move without friction, so friction "has no job to do".){note}

h4. Examples

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h2. Quantitative Model of Kinetic Friction

h4. Magnitude

For an object that is already sliding along a surface or is accelerating from rest on a surface, the size of the friction force will be given by:

{latex}\begin{large}\[ F_{k} = \mu_{k} N\]\end{large}{latex}

{note}Note that the size of the kinetic friction is fixed by the normal force and the coefficient.  There is no limit expression as there was for static friction.  Thus, it is not necessary to consider the complete net force to find the friction force for the kinetic case.{note}

where μ~k~ is the *coefficient of kinetic friction*.  The coefficient of kinetic friction is a dimensionless number, usually less than 1.0 (but _not_ required to be less than 1.0).  Rough or sticky surfaces will yield larger coefficients of friction than smooth surfaces.  _N_ is the [normal force] exerted on the object _by the surface which is creating the friction_, which is a measure of the strength of the contact between the object and the surface.

The coefficient of kinetic friction for a given object on a given surface will usually be *different* than the corresponding coefficient of static friction.  It is usually the case that &mu;~k~ < &mu;~s~.  

{info}The fact that &mu;~k~ is generally less than &mu;~s~ has important consequences for cars.  Antilock brakes are specifically designed to prevent skids, which change the tire-road friction from static to kinetic.  Changing braking friction to kinetic by skidding reduces the force of friction and so the effectiveness of the braking.{info}

h4. Direction

There are two possibilities to consider when determining the direction of kinetic friction:

# For a sliding object, the direction of the kinetic friction must be opposite to the direction of the velocity.  
# For an object just beginning to slide (the object still has zero velocity) then the friction must oppose the acceleration.