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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 =m N
m = coefficient of friction
mk = coefficient of kinetic friction
ms = 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.
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.
Friction and Surface Roughness
In general, the coefficients of friction for
static and kinetic friction are different.
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.
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.
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
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.
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 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.
The Accomplishments of Newton
(1642-1727)
We shall concentrate on three developments
1) Newton's Three Laws of Motion
2) The Theory of Universal Gravitation
Newton's First Law of Motion:
I. Every object in a state of uniform motion
tends to remain in that state of motion unless an
external force is applied to it.
This we recognize as essentially Galileo's concept of
inertia, and this is often termed simply the "Law of
Inertia".
Newton's Second Law of Motion:
II. The relationship between an object's mass m, its
acceleration a, and the applied force F is F = ma.
Acceleration and force are vectors (as indicated by their
symbols being displayed in slant bold font); in this law the
direction of the force vector is the same as the direction
of the acceleration vector.
Newton's Third Law of Motion:
III. For every action there is an equal and opposite reaction.
What Really Happened with the Apple?
The apple is
accelerated, since
its velocity
changes from zero
as it is hanging on
the tree and moves
toward the ground.
Thus, by Newton's
2nd Law there
must be a force
that acts on the
apple to cause this
acceleration. Let's
call this force
"gravity",
Sir Isaac's Most Excellent Idea
Now came Newton's
truly brilliant insight: if
the force of gravity
reaches to the top of
the highest tree, might
it not reach even
further; in particular,
might it not reach all
the way to the orbit of
the Moon!
If we increase the muzzle velocity of
an imaginary cannon, the projectile
will travel further and further
before returning to earth. Newton
reasoned that if the cannon
projected the cannon ball with
exactly the right velocity, the
projectile would travel completely
around the Earth, always falling in
the gravitational field but never
reaching the Earth, which is curving
away at the same rate that the
projectile falls. That is, the cannon
ball would have been put into orbit
around the Earth. Newton concluded
that the orbit of the Moon was of
exactly the same nature
the Moon continuously "fell" in its path around the Earth because of
the acceleration due to gravity, thus producing its orbit.
By such reasoning, Newton came to the conclusion that any two objects in
the Universe exert gravitational attraction on each other, with the force
having a universal form: