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h1. Kinetic Friction

{excerpt}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 [kinetic 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.{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}
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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.
Kinetic Friction as a Force
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 proportional to the normal force exerted by the surface on the object. This mathematical relationship is usually stated:
 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~.  

{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.


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], 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], 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}




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where μk is a constant of proportionalty called 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.
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 μk < μs. 
Direction
Kinetic friction is always directed opposite to the direction of the velocity. 
Kinetic Friction as Non-Conservative Work
When the Surface is at Rest
When an object is sliding on a surface that can be considered to be at rest in an inertial frame of reference, 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 special case of a friction force with constant magnitude , the definition of work can be integrated to give Wf = – Fkd where d is the distance traveled by the object along the surface.
When the Surface is Moving
Finding the work done by friction can be confusing when a reference frame is chosen in which the surface is moving. See the discussion of static friction for more details.
Example Problems involving Kinetic Friction
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