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{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 proportional to the [normal force] exerted by the surface on the object.  This mathematical relationship is usually stated:

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 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.
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}

where μ~k~ 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 
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 &mu;~k~ < &mu;~s~.  

h4. Direction

Kinetic friction is always directed opposite to the direction of the [velocity].  

h3. Kinetic Friction as Non-Conservative Work

h4. 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|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 special case of a friction force with _constant magnitude_ , the definition of [work] can be integrated to give {_}W{~}f{~}{_} = -- {_}F{~}k{~}d{_} where _d_ is the [distance] traveled by the object along the surface.

h4. 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.

h3. Example Problems involving Kinetic Friction

h4. {toggle-cloak:id=dyn} Examples from Dynamics involving Kinetic Friction

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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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h4. {toggle-cloak:id=nc} Examples from Energy and Work involving Kinetic Friction

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h4. {toggle-cloak:id=rot} Examples from Rotation and Torque inolving Kinetic Friction

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h4. {toggle-cloak:id=all} All Example Problems inolving Kinetic Friction

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