It's professor date, let's learn about friction.
In examining Newton's laws of motion, we have to
understand that the kinds of motion we
observe on earth don't always appear to obey
these laws, because there are extraneous
variables acting upon earthbound objects,
and most of these involve some kind of
frictional force. Friction is an
important concept to understand so let's
go over it in some detail. Whenever an
object is in motion along a surface
the surface exerts a force upon the
object. One component of this force is
the normal force, which is perpendicular
to the surface. There is also a component
of this force that is parallel to the
surface, and this is called the
frictional force, or simply friction. This
is the force that will resist the motion
of the object along the surface. Every
surface has some frictional coefficient
that will vary depending on its
composition. To see this demonstrated, try
to push a small block across some ice
and then try to push it across some
sandpaper. These materials differ in
their resistance to motion for reasons
that relate to their composition. The
smoother a surface is the less friction
it will provide, but even surfaces that
appear perfectly smooth will have
imperfections on the microscopic level
that provide some friction. As the object
moves across the surface there are
select points of contact where atoms in
the objects interact with atoms in the
surface, and this attractive interaction
hinders motion to some measurable degree
no matter how small.
Let's define two main types of friction:
static and kinetic. Static friction is
the friction that resists the initiation
of motion. If you place a block on a
table and try to very lightly push it
into motion it will first resist that
motion because of the frictional force
operating in the direction opposite the
applied force of your push. You can push
harder and it will still remain still
because the frictional force will always
precisely oppose the applied force.
Static friction will increase until the
magnitude of the applied force exceeds
the maximum static frictional force the
table can exert, then the force of the
push can
no longer be cancelled out and the block
will begin to accelerate. This frictional
force is proportional to the normal
force so the heavier the object, the
greater the normal force, and the greater
the frictional force. This is because as
the weight of the object increases, the
harder it presses down on the surface
which will increase the number of
contact points between the object and
the surface. The static frictional force
will be anywhere from zero to the
maximum possible value, depending on the
forces operating on the object, since the
static frictional force will be equal
to the applied force until the maximum
is reached. The magnitude of this maximum
can be calculated this way: F max is
equal to the coefficient of static
friction times the magnitude of the
normal force. This coefficient,
represented by the Greek letter mu, is
unitless and unique to the surface in
question, and we have tabulated these
coefficients for a variety of common
surfaces like glass, steel, wood, and
rubber, and the various combinations
thereof. As we said, once the applied
force exceeds the maximum static
friction, the object will begin to move.
Bear in mind that this equation involves
scalar quantities, not vectors, and
therefore implies nothing about
direction. As we said, static friction
opposes the initiation of motion, but
once an object is in motion
it is now moving against kinetic
friction. This is the force that opposes
relative sliding motion. Kinetic friction
is always lesser than static friction,
which you will notice if you try to push
any object across the surface, like a
heavy box across the floor. It will be
more difficult to get the box going than
it is to keep it moving once you've
started. There are coefficients of kinetic
friction as well, and these will be
different from the coefficient of static
friction for the same materials. These
values allow us to calculate the
magnitude of the kinetic frictional
force acting on a sliding object.
Friction isn't always a nuisance,
it can also be used to our advantage.
When we walk, the static friction between
our feet and the ground allows us to
propel ourselves forward, rather than our
feet simply sliding back.
Car tires take advantage of friction to
move the car forward, and they are
designed with grooves to divert water away
so that it does not interfere with the
contact between the tire and the ground.
This allows it to maintain traction
rather than skidding. We should note that
air resistance is another type of fluid
friction. When a car or a plane moves
through the atmosphere, the particles in
the air hinder its motion, offering some
kinetic friction.
This is true of motion through any fluid
in a way that depends on the viscosity
of the fluid, which represents the fluid's
resistance to flow. So by now we are
familiar with a few of the vectors we
will commonly use in physics. An object
at rest on a flat surface on earth will
experience a downward force due to its
weight, as well as an upward normal force
that is equal in magnitude. If some
horizontal force is applied there will
also be an opposing frictional force. If
the applied force is less than the
maximum static frictional force of that
surface, the horizontal vectors will
cancel each other out, just like the
vertical ones and the object will remain
at rest. If the applied force exceeds the
maximum friction, the object will
accelerate in the direction of the push
and the kinetic frictional force will
oppose its forward motion. So we can
expect to see these four vectors in lots
of the free body diagrams from this
point forward.
A common example is the inclined plane.
In this scenario, we can examine a block
sliding down a ramp. Gravity, represented
by mg, will pull straight down, and this
vector can be divided into components
that are perpendicular and parallel to
the incline. Those will be mg cosine
theta and mg sine theta. The force
opposite the perpendicular component
will be the normal force, equal in
magnitude and opposite in direction. We
can then include a vector for the force
of friction, which opposes the other
component of gravity. If we calculate the
net force acting on the block this will
allow us to predict the acceleration on
the block as it slides down the incline,
and since the two perpendicular forces
cancel each other out,
we just add the parallel ones together
to find the net force. To try this more
quantitatively, let's check comprehension.
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