Stick-Slip Friction and Velocity Dependence

In any case where the coefficient of kinetic friction is less than the coefficient of static friction there will exist a tendency for the motion to be intermittent
rather than smooth.  The two contact surfaces will stick until the sliding force reaches the value of the static friction.  The surfaces will then slip over one
another with a small-valued kinetic frcition until the two surfaces stick again.  The most simple model for explaining this mechanism of friction, known as
'stick-slip,' is the case of a spring with a mass attatched. In this setup there is a mass attatched to a coiled spring being pulled by a tension force so that
the spring moves at a constant velocity.  The surface upon which this setup rests has a coefficient of kinetic friction that is much less than the coefficient of
static friction.

When the spring is pulled one unit of distance, the tension is enough to overcome the force of static friction, and the block begins to move.
Because the kinetic friction is far less than the static friction the block moves at a velocity faster than that of thespring, rapidly restoring the spring to its unstretched
length causing the block to once again come to rest to start the entire process over again.  The body will again remain at rest until the tension exceeds the
static friction causing the block to move forward another unit of distance until the mass stops because of the compression of the spring back to its unstretched length.
By performing this run at numerous spring velocities and making plots of position versus time, the trend we begin to see is that the faster the spring velocity,
the motion of the mass becomes less jerky.  Also, the motion of the mass becomes less jerky if the two coefficients of friction approach the same value.

Now the case of the mass and spring may seem like a very localized case of 'stick-slip' friction, but the fact is that even a stiff rod has some amount of elasticity
and will stretch when it is pulled.  Although the 'stick-slip' mechanism may not be as visible to the eye, it will still occur on a reduced microscopic level.
Furthermore, elastic deformation occurs in all driving mechanisms, such as the transmission of an automobile, the chain on a bicycle, or in various cutting tools.
All of these examples are cases wher the static friction is higher than the kinetic friction and may be prone to intermittent 'stick-slip' motion.
Finally, what about the velocity dependence of this and other types of friction?  In the case of 'stick-slip' friction the velocity dependence is easily seen in
the case of the mass and spring.  This same type idea applies to kinetic friction in general.  The coefficient of kinetic friction for all materials shows some
dependece on velocity to a marked degree.  At very slow speeds mu for kinetic friction increases with speed until it reaches some localized maximum,
at which point mu begins to decrease with increasing velocity.  In fact very low values of mu are found for metals moving at very high speeds (several hundred
meters per second).  Thus, kinetic friction and 'stick-slip' friction are, for the most part, velocity dependent forces.