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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. Static Friction as a Force

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}

h3. Static Friction as 
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, 
 or whatever else is sitting on a moving surface.  
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
|rigid body]
). 
  
 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.
{info}

h3. {
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:
id
=
examples
} 
 Example 
 
 Problems 
 
 involving 
 
 Static 
 
 Friction


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