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This week, we will examine
some more advanced topics

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in the application of
Newton's laws of motion.

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First, we will look at more
examples of constrained motion,

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where the motion
is forced to obey

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some particular
condition in addition

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to Newton's laws of motion.

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These conditions usually specify
some particular relationship

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between coordinates of objects
and the system we are studying.

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Specifically, we will
re-examine the case

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of objects suspended
with pulleys and ropes,

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but with more complex
systems than we

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have discussed previously.

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The fact that the
ropes have fixed length

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will provide a
constraint condition

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relating the coordinates
of our various masses.

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Second, we will examine
the case of forces

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acting on a continuous, extended
mass distribution as opposed

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to acting on discrete
point masses.

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This will allow us to introduce
a powerful differential

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analysis technique from calculus
where we model continuous mass

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distributions as made up of
lots of small, discrete mass

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elements and then
examine the limiting case

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of infinitesimally
small elements

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to obtain the
continuous behavior.

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This is a technique
that you will

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see applied over and over again
in physics and engineering.

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And in fact, we will return to
it again later in this course.

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Our specific example will
be to study how tension

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varies in a long, massive rope.

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This is in contrast
to the light,

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effectively massless ropes
that we discussed previously.

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Finally, we will discuss
velocity-dependent forces--

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that is, forces whose strength
depends on the velocity

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or some function of the velocity
of the mass being acted on.

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The most common example of this
is resistive forces or drag

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forces, which are caused
by motion of a solid object

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through a fluid,
like air or water.

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That is the example we
will discuss this week.

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Another example
you may be aware of

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is the magnetic force that acts
on a charged particle, which

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depends upon the velocity
of the charged particle.

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In all three of these
cases, we will simply

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be applying Newton's
three laws of motion,

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but the situations will require
a more sophisticated treatment

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to what has come before.