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Retrospective
Yesterday we thought a bit about how science works.
We defined position, velocity, acceleration. We found
that if we know acceleration, calculus gives us position
and velocity at all times.
Who cares? Anybody whose job or life involves moving
things.
Then we discussed Newton’s laws.
These laws are really postulates about how nature works.
You cannot prove them in a mathematical sense. We
believe them because they work.
Who cares? Anybody whose job or life involves objects
that exert forces on each other.
Friction
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.
Friction forces oppose actual motion (kinetic friction)
or motion that would take place if no friction were
present (static friction).
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 f is aimed in
the opposite direction.
s
Digression: have you ever heard of an “empirical
parameter?” It’s a number that goes into an equation to
make the equation match reality.
Do you know the real name for an empirical parameter?
Fudge factor.
“Models” for nature are much less desirable than theories.
Nevertheless, fs  s N and f k  k N work well enough for
us to use them, without needing to grapple with the very
complex physics and mathematics that they represent.
Example: a block of mass m rests on a slope inclined by
an angle , with coefficient of static friction s between
the block and plane. What is the magnitude of fs?
Physics 23, lecture 7, page 10.
I will work this on the board in class. You can compare
my solution with that on the web. I may choose different
axes. The single correct answer should be the same!
Insight: for the object to remain at rest, the static
friction force must “balance” the weight component
directed down the incline.
The mathematics, which is really inseparable from the
diagram and therefore the physics, has provided insight.
Can we generalize this insight? We’ll see.
Example: what is the greatest angle  for which the block
in the previous example won’t slide?
Physics 23 lecture 7 page 11.
Insight: the friction force is maximum ( fs  s N ) and
barely balances the weight component along the incline.