FRICTION

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FRICTION
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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 frictionmk coefficient of
kinetic frictionms coefficient of static
friction
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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.
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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.
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Friction and Surface Roughness
In general, the coefficients of friction for
static and kinetic friction are different.
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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.
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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.
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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
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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.
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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.
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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.
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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
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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".
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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.
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Newton's Third Law of Motion
III. For every action there is an equal and
opposite reaction.
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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",
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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!
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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
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the Moon continuously "fell" in its path around
the Earth because of the acceleration due to
gravity, thus producing its orbit.
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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