Friction
Friction
            Friction is a force (measured in Newtons) acting along the surfaces of two objects in physical contact that impedes the relative motion of these objects (the motion of one with respect to the other). As such, it can be said that friction always acts opposite the motion of the object or the force applied.
 
          There are two main types of friction:
                   1. Static friction: the frictional force that opposes any attempt to move a stationary object along a surface.
                   2. Sliding friction: (sometimes called "kinetic" friction): this frictional force opposes the sliding motion of two surfaces rubbing together.
          A third type of friction, rolling friction, is a special case of static friction and will be discussed later.
         
Physically, friction arises from surface roughness and attractive forces between the surfaces of two objects in contact.
            The frictional force depends on how hard the surfaces are pushed together: usually that quantity is calculated by determining the surface ï¿½normalï¿½ force (Fn).
The harder the surfaces are pushed together, the more surface contacts are made, increasing friction.
          Interestingly, friction does not depend on the surface area of the objects in contact. This is because as the area gets larger, the force per unit area gets smaller, decreasing the number of points in physical contact. Some of the characteristics of static and kinetic friction are:
Static friction:     
ï¿½        designated as fs
ï¿½        proportional to Fn(surface normal force)
ï¿½        independent of area
ï¿½        variable to a maximum value (which depends on the surfaces)
Sliding friction:
ï¿½        designated as fk
ï¿½        proportional to Fn
ï¿½        independent of area
ï¿½        independent of speed
ï¿½        always less than static friction
                  
          Letï¿½s examine the relationship between these two forces and the applied force that creates them (they can be thought of as "reaction" forces).  If you observe the graph below, it shows the static frictional force increasing to a maximum with the application of a force ("applied force") then dropping off sharply to a lesser value (kinetic, or sliding, friction) once the object starts moving.  This diagram is typical of many contact surfaces.
            We can quantify this force in the following way: since friction is proportional to the force pressing the surfaces together (Fn), we can write,
f a Fn
which means that,
f / Fn = constant
This constant we call the coefficient of friction: m (the Greek letter ï¿½muï¿½). Thus we can write the equation as,
f = (m)(Fn)
            Since static friction and kinetic friction are different, there is a m for each:
                                ms = coefficient of static friction
                                mk = coefficient of kinetic (sliding) friction
so that we can write for each type of friction,
Static:                       fs < msFn
Kinetic:                    fk = mkFn
Note that static friction is expressed as an inequality.  This is because it varies from zero to a maximum.  At the maximum value, and only at the maximum value (just before the object moves), the static frictional force is exactly equal to msFn, or
fs max = msFn
We can find the actual values of ms and mk in the following way:
for ms: a block is placed on a variable incline that is slowly raised from the horizontal until the block just begins to slide....
This is called the "critical angle", qc.  At this angle, the static friction has reached its maximum value and we can write SFx = 0    (the max value of static friction occurs the instant before the block moves), so:
                                    SFx = 0                                  SFy = 0
                  -fs + mgsinqc = 0                 Fn - mgcosqc = 0
           -msFn + mgsinqc = 0                              Fn = mgcosqc
and using the value of Fn from the y-equation we get,
                        -(ms)mg(cosqc) +mg(sinqc) = 0
                                        ms = mgsinqc / mgcosqc
                                     ms = tanqc
And so the coefficient of static friction is simply defined as the tangent of the critical angle.
 
for mk: we perform the same experiment as above but now the block is moving down the incline at some acceleration.
Newtonï¿½s 2nd law becomes:
SFx = ma