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h1. Kinetic Friction

{excerpt}The specific manifestation of [friction] that is directly opposed to an object's sliding motion along a surface.  The force of kinetic friction has a size independent of the speed of the object, and proportional to the [normal force] exerted on the object by the surface.{excerpt}

h3. Kinetic Friction as a Force

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.  In contrast to the case of
[static friction], there is no upper limit in the expression.  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~.  

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.


h3. Kinetic Friction as Non-Conservative Work

When an object is sliding on a surface that can be considered to be at rest in an [inertial frame of reference|inertial reference frame], kinetic friction is the prototypical [non-conservative force].  When the motion of an object sliding on a surface is viewed from a frame at rest with respect to the surface, the force of friction always opposes the object's motion, and so always does negative [work].  For the case of a constant friction force, the definition of [work] can be integrated to give:
{panel:title=Work done by a Constant Friction Force}{latex}\begin{large}\[W_{f} = -F_{k}d\]\end{large}{latex}{panel}
where _d_ is the *distance* traveled by the object along the surface.

{info}Contrast this with a conservative force like [gravity (near-earth)], which does negative [work] on an object that is rising, and then returns energy by doing positive [work] on the object as it falls.{info}
{warning}The [work] done by [friction] becomes very confusing when a reference frame is chosen in which the surface is _moving_.  See the discussion of [static friction] for more details.{warning}

h3. {toggle-cloak:id=examples}Example Problems involving Kinetic Friction

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{contentbylabel:kinetic_friction,example_problem|operator=AND|maxResults=50|showSpace=false|excerpt=true}

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