4.8 Applications Involving Friction, Inclines
Friction
The origin of friction is electric forces between atoms of
materials in contact.
Inclines
We will be concerned with two kinds of frictional forces: forces
between stationary objects and forces between moving
objects.
Problem-Solving Approaches
Frictional forces result from surfaces in contact. Frictional
forces oppose the sliding of surfaces in contact. Static friction
forces point opposite to the direction of motion an object
would move over a surface if no friction were present. Figure
out which way an object would move without friction present.
Then Fstatic is aimed the opposite direction.
If the object is sliding down the plane,
the frictional force is “kinetic” and
directed up the plane.
Fk
v
If some force is just about to push (or
pull) the object up the plane, the
frictional force is “static” and is directed
down the plane.
If the object is stationary, then the
component of its weight down the plane
“wants” to pull it down. The frictional
force is “static” and is directed up the
plane.
P
Fs
Fs
Of course, friction acts between when a surface is horizontal or
vertical, as well as tilted.
v
If some object is pushing (or pulling)
the object up the plane, the frictional
force is “kinetic” and is directed down
the plane.
v
P
Fk
P
Fk
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Experimentally, the magnitude of frictional forces is observed
to be proportional to the normal force between objects, and
the direction is opposite to the motion, or the impending
motion.
We model the magnitudes of frictional forces using these two
official starting equations:
Fk = µk N
Fs ≤ µ s N
Static friction forces start out zero and increase up to a
maximum.
If I try to pull a lead brick across a rough surface using very
little “pull,” the friction force will be small, but sufficient to
overcome my “pull.”
The friction force will increase as I increase the “pull.”
Usually, µs > µk. What does this have to do with antilock
brakes?
Eventually, when my “pull” exceeds the maximum static
friction force, the brick starts accelerating.
Here are a couple of toys to play with:
http://physics.bu.edu/~duffy/java/SecondLaw2.html
http://physics.bu.edu/~duffy/java/SecondLaw.html
In the case of both static and kinetic friction forces, the friction
force opposes motion of one surface across the other, so it is
directed parallel to the surfaces.
The friction force is not necessarily
directed opposite to an applied force,
as in the diagram to the right.
v
Where would we be without friction?
—slip-sliding away
Friction is not a “separate” kind of force—it is a result of
electromagnetic forces between microscopic objects.
P
Fk
Friction forces oppose actual motion (kinetic friction) or motion
that would take place if no friction were present (static
friction).
Here are some notes from another class. They represent a
different way of presenting the above material. I am going to
paste them into this lecture, so you are about to get a 2nd
perspective on what I just covered.
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Friction is a force, so it is a vector. Friction forces
occur at contact points between surfaces and are
always directed parallel to the (local) surface.
Kinetic friction forces on a surface point in the
direction parallel to the surface and opposite the
velocity.
Static friction force direction: figure out which way an
object would move without friction. Then is aimed in
the opposite direction.
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Work friction examples: (a) what is the force of friction on a
block at rest on an inclined plane; (b) what is the maximum
angle for block to remain at rest on an inclined plane.
4.9 Problem Solving—A General Approach
This is what we’ve been doing all along!
There is no new material in this section.
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