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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 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. 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.




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