Download Static Friction

Friction
Frictional resistance to the relative motion of two solid objects is usually proportional to
the force which presses the surfaces together as well as the roughness of the surfaces.
Since it is the force perpendicular or "normal" to the surfaces which affects the frictional
resistance, this force is typically called the "normal force" and designated by N. The
frictional resistance force may then be written:
ffriction = &mu N
&mu = coefficient of friction
Standard model
&muk = coefficient of kinetic friction
of friction
&mus = coefficient of static friction
The frictional force is also presumed to be proportional to the coefficient of friction.
However, the amount of force required to move an object starting from rest is usually
greater than the force required to keep it moving at constant velocity once it is started.
Therefore two coefficients of friction are sometimes quoted for a given pair of surfaces a coefficient of static friction and a coefficent of kinetic friction. The force expression
above can be called the standard model of surface friction and is dependent upon several
assumptions about friction.
While this general description of friction (which I will refer to as the standard model) has
practical utility, it is by no means a precise description of friction. Friction is in fact a
very complex phenomenon which cannot be represented by a simple model. Almost
every simple statement you make about friction can be countered with specific examples
to the contrary. Saying that rougher surfaces experience more friction sounds safe enough
- two pieces of coarse sandpaper will obviously be harder to move relative to each other
than two pieces of fine sandpaper. But if two pieces of flat metal are made progressively
smoother, you will reach a point where the resistance to relative movement increases. If
you make them very flat and smooth, and remove all surface contaminants in a vacuum,
the smooth flat surfaces will actually adhere to each other, making what is called a "cold
weld".
Kinetic Friction
When two surfaces are moving with respect to one another, the frictional resistance is
almost constant over a wide range of low speeds, and in the standard model of friction the
frictional force is described by the relationship below. The coefficient is typically less
than the coefficient of static friction, reflecting the common experience that it is easier to
keep something in motion across a horizontal surface than to start it in motion from rest.
Static Friction
Static frictional forces from the interlocking of the irregularities of two surfaces will
increase to prevent any relative motion up until some limit where motion occurs. It is that
threshold of motion which is characterized by the coefficient of static friction. The
coefficient of static friction is typically larger than the coefficient of kinetic friction.
In making a distinction between static and kinetic coefficients of friction, we are dealing
with an aspect of "real world" common experience with a phenomenon which cannot be
simply characterized. The difference between static and kinetic coefficients obtained in
simple experiments like wooden blocks sliding on wooden inclines roughly follows the
model depicted in the friction plot from which the illustration above is taken. This
difference may arise from irregularities, surface contaminants, etc. which defy precise
description. When such experiments are carried out with smooth metal blocks which are
carefully cleaned, the difference between static and kinetic coefficients tends to
disappear. When coefficients of friction are quoted for specific surface combinations are
quoted, it is the kinetic coefficient which is generally quoted since it is the more reliable
number.
Coefficients of Friction
Friction is typically characterized by a coefficient of friction which is the ratio of the
frictional resistance force to the normal force which presses the surfaces together. In this
case the normal force is the weight of the block. Typically there is a significant difference
between the coefficients of static friction and kinetic friction.
Note that the static friction coefficient does not characterize static friction in general, but
represents the conditions at the threshold of motion only.
Friction and Automobile Tires
The friction between the tires of your automobile and
the road determine your maximum acceleration, and
more importantly your minimum stopping distance. So
the nature of that friction could actually be a matter of
life and death. But like all applications of friction, it
has frustrating ambiguities.
Many years of research and practice have led to tread
designs for automobile tires which offer good traction
in a wide variety of conditions. The tread designs
channel water away from the bearing surfaces on wet
roads to combat the tendency to hydroplane - a
condition which allows your car to "ski' on the road
surface because you have a layer of water lubricant
under all parts of your tire.
Jones and Childers report coefficients of friction of about 0.7 for dry roads and 0.4 for
wet roads. The tread design represents an "all weather" compromise. If you were an
Indianapolis race driver, you would use "slick" racing tires with no tread. On dry surfaces
you might get as high as 0.9 as a coefficient of friction, but driving them on wet roads
would be dangerous since the wet road coefficient might be as low as 0.1 .
Sooner or later, most people have to deal with the tricky judgment of how hard to put on
the brakes in an emergency stop. It is a difficult issue, and no final answers are given
here. But the illustration below may point out some of the relevant physical principles
involved. In the best case scenario, you should keep your wheels rolling while braking
because the bottom point of the tire is instantaneously at rest with respect to the roadway
(not slipping), and if there is a significant difference between static and kinetic friction,
you will get more braking force that way. But you generally don't have the luxury of time
to make a delicate judgment about how hard to put on the brakes. For good tires on dry
surfaces, there is not much difference between rolling and sliding friction, and if you
back off the braking force very much, you will get less braking than if you just locked
them down. The other issue is that in an extreme emergency, the braking is instinctive
and you tend to hit the brakes as hard as you can before you can even think about it.
Maybe locking the brakes is not so bad in good conditions on the dry road, and you may
not be able to keep from doing so in an extreme emergency. But if you lock the wheels
on a wet road, the results could be disastrous! I don't have anything like reliable estimates
of the effective coefficient of friction, but I am guessing that it could easily drop to less
than half of the "wheels rolling" braking because you are sliding on a surface which is
lubricated by water. It may be that even with wheels rolling you might have in the
neighborhood of 0.4 as a coefficient compared to 0.7 on the dry road, and it might drop
down to the 0.1 of the slick tire. Those scary scenarios are depicted below in a qualitative
way - I don't have reliable numbers.
Normal Force
Frictional resistance forces are typically proportional to the force which presses the
surfaces together. This force which will affect frictional resistance is the component of
applied force which acts perpendicular or "normal" to the surfaces which are in contact
and is typically referred to as the normal force. In many common situations, the normal
force is just the weight of the object which is sitting on some surface, but if an object is
on an incline or has components of applied force perpendicular to the surface, then it is
not equal to the weight.
The above cases are the commonly encountered situations for objects at rest or in straight
line motion. For curved motion, there are cases like a car on a banked curve where the
normal force is determined by the dynamics of the situation. In that case, the normal
force depends upon the speed of the car as well as the angle of the bank.
Friction Assumptions
In the standard model for friction between surfaces, there are certain inherent
assumptions:
1. The frictional force is independent of area of contact
Exceptions
2. The frictional force is independent of the velocity of motion
Exceptions
3. The frictional force is proportional to the normal force.
Exceptions
One can readily find circumstances where any or all of these assumptions are invalid, but
they provide a straightforward framework for a beginning treatment of friction that
satisfactorily describes many phenomena.
Friction and Area of Contact
Part of the standard model of surface friction is the assumption that the frictional
resistance force between two surfaces is independent of the area of contact.
While exceptions exist, the assumption has enough validity to be useful in many
circumstances. For example, it implies that wide tires will not in general give better
traction than narrow tires, and will not change the normal braking distance for a car.
Better traction can be obtained with wide tires, or tires with lower pressure, if the
pressure changes the coefficient of friction, as on a surface of snow.
Friction and Velocity
Part of the standard model of surface friction is the assumption that the frictional
resistance force between two surfaces is independent of the velocity of relative
movement. While this is approximately true for a wide range of low speeds, as the speed
increases and air friction is encountered, it is found that the friction not only depends on
the speed, but upon the square and sometimes higher powers of the speed. If there are
fluid lubricants involved, then viscous resistance is encountered, and it is speed
dependent.
Like the other standard assumptions, exceptions are easy to find, but the assumption is
nevertheless useful for modeling a wide variety of circumstances where two solid
materials move relative to each other.
Friction and Normal Force
Part of the standard model of surface friction is the assumption that the frictional
resistance force between two surfaces is proportional to the normal force pressing them
together. A common exception occurs in snow where greater traction occurs by having
wider tires with lower pressure. The same normal force is exerted, but the traction
(friction) is greater with the wider tire since it doesn't pack the snow as much. The
packing of the snow tends to depend on the pressure exerted on the snow, and supporting
the same weight on a smaller area implies that more pressure is exerted. This example is
also an exception to the assumption of independence of area of contact. With a given area
of contact, increasing the normal force will pack the snow, decreasing the effective
coefficient of friction.
While exceptions such as this are easily found, the assumption that friction is
proportional to the normal force is still reasonably valid in many cases and forms a useful
model for many circumstances.
A valid question is why does the frictional resistance increase proportionally with normal
force? Jones and Childers have a thoughtful discussion of this. They point out that the
area of coverage for a sliding block is actually much larger than the area of contact.
Because of microscopic irregularities in the surface, the block is actually riding on a
small fraction of the coverage area. Because such points of contact are deformable, an
increase in normal force will actually increase the area of actual contact and increase the
resistance to movement.
Friction Plot
Static friction resistance will match the applied force up until the threshold of motion.
Then the kinetic frictional resistance stays about constant. This plot illustrates the
standard model of friction.
The above plot, though representing a simplistic view of friction, agrees fairly well with
the results of simple experiments with wooden blocks on wooden inclines. The
experimental procedure described below equates the vector component of the weight
down the incline to the coefficient of friction times the normal force produced by the
weight on the incline.
Having taken a large number of students through this experiment, I can report that the
coefficient of static friction obtained is almost always greater than the coefficient of
kinetic friction. Typical results for the woods I have used are 0.4 for the static coefficient
and 0.3 for the kinetic coefficient.
When carefully standardized surfaces are used to measure the friction coefficients, the
difference between static and kinetic coefficients tends to disappear, indicating that the
difference may have to do with irregular surfaces, impurities, or other factors which can
be frustratingly non-reproducible. To quote a view counter to the above model of friction:
"Many people believe that the friction to be overcome to get something started (static
friction) exceeds the force required to keep it sliding (sliding friction), but with dry
metals it is very hard to show any difference. The opinion probably arises from
experiences where small bits of oil or lubricant are present, or where blocks, for example,
are supported by springs or other flexible supports so that they appear to bind." R. P.
Feynman, R. P. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. I, p. 125, Addison-Wesley, 1964.
Standard Newton's Laws Problems
Some examples of standard "building block" problems which help build understanding of
the principles of mechanics. Click on any of them for further details.