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h1. Static Friction

{excerpt}
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|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.  
{excerpt}

h3. 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}
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 Excerpt
The specific manifestation of friction which attempts to resist efforts to move an object that is currently at rest with respect to a surface. If possible, static friction provides just enough force to keep the object stationary, and no more. When the net force attempting to create sliding motion exceeds a certain limiting value proportional to the normal force exerted by the surface on the object, static friction will be unable to prevent motion. 
Static Friction as a Force
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 
where μs 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}





do".)
Static Friction as Non-Conservative Work
The work done by static friction would seem to be obviously zero, since an object subject to static friction is required to be stationary. There is an important loophole, however, in the fact that the object is only required to be stationary with respect to the surface in order for static friction to apply. Thus, if the surface itself is moving, the object is moving as well! This loophole is relevant in problems where one object sits on another, e.g. a box on a truck bed or a block on a second block, etc. In these examples, static friction can be the sole force responsible for changing the horizontal motion of the box, the top block, etc. Thus, it must be the case that the friction can do work.
 Info
There is at least one other major loophole that allows static friction to do work. Real objects like people and cars are actually deformable (they are not perfectly modeled as rigid bodies). Thus, a person can cause their center of mass to translate without moving their feet, and a car can move forward without translating the point of contact between the tires and the ground. In this way (when viewing the person or car as a single object) the force of static friction on the person's feet or the car's tires can be made to do work.
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 Example Problems involving Static Friction
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