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Let's consider what we call
the window washer problem.

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What we have is suspended
from some ceiling.

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We have a pulley.

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And the pulley is suspended
by a rope, which we're

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going to call this string 3.

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And we have a rope that is
wrapping around this pulley.

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And then it wraps
around another pulley.

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So this rope is going
around another pulley.

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And it's fixed to the ceiling.

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And this is what we're
going to call string 1.

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And then this string,
there's another string

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that comes down to a platform.

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And this one we're
going to call string 2.

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And sitting on the
platform is a person.

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So we have a person
sitting on the platform.

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And that person is
pulling the rope down.

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Now this is a very
complicated problem.

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And it's a classic
example of how

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do we choose systems so that we
can apply Newton's second law.

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Now, one of the important
things we're going to do

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is learn to see when we
choose a system what forces

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are internal and external.

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And that will enable us to
pick a very nice system, which

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will make the analysis easy.

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The way we'll do this is
will approach it in stages.

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We'll first focus on the person,
the platform, and this pulley.

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By the way, this is pulley
A. And this one is pulley B.

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And let's use a symbol
P for the platform.

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And we'll call this
a washer person.

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And we're going to use the
symbol W for the person.

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So what makes this
problem complicated

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is all these different elements.

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Now the first stage is
that what we're going to do

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is we're going to
separately look

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at the person, the
platform, and then

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combine them into a system
of person and platform.

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But notice, the rope is
connected to the platform.

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So the next stages
will also consider

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a system consisting of pulley
A, person, and the platform,

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and the washer.

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Now let's draw the
free body diagram.

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Let's begin by drawing the free
body diagram on the washer.

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So what do we have
on the washer?

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The first thing to think
about is the string.

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The washer is pulling
the string down.

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So the string is
pulling the washer up.

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So that's a force of
string 1 on the washer.

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Now, there's also the
gravitational force m washer g.

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And what we also have
to consider the fact

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is that the person is
sitting on the platform.

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So the platform is
pushing the person up.

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And we'll call that a
normal force on the washer

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due to the platform.

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And those are the free body
diagram for the body diagram

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on the washer.

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Now let's focus on the platform.

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So here, we'll
draw the platform.

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And now let's look at the
forces on the platform.

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Let's begin by looking for the
internal forces, the Newton's

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third law pairs.

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The platform is
pushing the person up.

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The person is pushing
the platform down.

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So we'll write that force
as N on the platform

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due to the washer.

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And immediately, let's just
circle this third law pair.

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Now, string 2 is
pulling the platform up.

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So let's draw that force.

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We'll call that a tension
force in the string.

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It's on the platform
due to string 2.

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And finally, we have
the gravitational force

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on the platform.

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And that's our free body
diagram on the platform.

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Now, you may have said, well,
why should I separate these

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out?

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Why didn't I just use the
person and the platform?

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So let's draw that picture.

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So now imagine underneath
this is a system consisting

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of the person and the platform.

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And I'll just draw
that system like that.

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So what we're doing
is we're taking

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these two separate
free body diagrams

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and we're going to
combine them here.

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And by Newton's third
law, all internal forces

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should cancel in pairs.

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So now let's separately
think about the forces

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and see that that's the case.

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Well, we have the
gravitational force

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on the system, which is
the mass of the platform

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plus the mass of
the washer times g.

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We still have the string
pulling the person up

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because the person is
pulling the string down.

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So we still have the
force F1 on the washer.

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That's string 1 on the washer.

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And we still have the pulley,
the tension in string 2,

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pulling it up.

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So we still have the
force T2 on the platform.

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Now, when you look at
this, what we're doing is

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we're adding these two free
body diagrams together.

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The internal forces now
are the normal force.

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They're equal in magnitude,
opposite in direction.

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So when you add them
together, they cancel.

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And we're just left with
that, with that, with that,

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and with that.

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And so this is now
the combined system.

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Now you might ask, why did
we not include the pulley?

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Well, let's take a look at that.

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So I'm going to draw the free
body diagram just on pulley

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A. So let's draw pulley A.

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Now what we have here is
the string on both sides

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is pulling pulley A up.

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And that's the
tension in string 1.

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So what we have is-- I'm going
to call that tension in string

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1, tension in string 1.

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And just to alert you that keep
in mind that this force here

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is the force of the
string on the person

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and this too is also
tension in the string,

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because this is our assumption
of a massless string.

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So notice that everywhere in the
string, the tension is uniform.

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So I'm just going to simplify
that by calling it T1.

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What are the other
forces on the pulley?

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Well, we're assuming that
these pulleys are massless.

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And so there's no gravitational
force on the pulley.

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And the only thing we have
is the string pulling--

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is the tension in the string.

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So now this is a
little bit different.

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This is a force
on the pulley too.

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So at the moment, let's
do something a little bit

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different.

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Let's consider our
system to be the string.

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So it's pulley A. We
call that string 2.

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That's our system.

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So I modified that a little bit.

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I just didn't consider
the pulley separately.

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I considered the pulley and
the string as the system.

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Then here the string is
pulling the platform up.

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The platform therefore is
pulling the string down.

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And once again, we
have a third law pair.

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And so if I added
these two together,

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then what I now have-- and this
is why this problem is kind

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of complex-- we have pulley
A, string 2, platform P

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and washer person.

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And if we now add these
two systems together,

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we have this complicated system.

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But what are the
forces in this system?

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Well, the rope is pulling it up.

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The person was-- remember
we had this force, W1,

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was the force of
string 1 on the washer.

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That also was the tension
everywhere in the string.

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So we have another T1 up.

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These two forces
now cancel in pairs,

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the internal forces there.

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And so down, we just have
mass platform plus mass

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of a washer times g.

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And so you see in
this problem, if we

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tried to treat
everything separate--

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and I could have
even had the string

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separate-- I have a lot
of free body diagram.

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But when I think about what's
internal and what's external,

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I can take these two
pieces, combine them here,

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internal forces cancel in pairs.

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I can draw these two separate
systems, again, combine them.

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Internal forces cancel in pair.

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And now I have this pulley A.

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Now I can write down
Newton's second law.

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So what I'll do next
is I'll introduce--

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I still have to consider pulley
B. I'll use this as my system.

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And I'll write down
Newton's second law.

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And we'll be able to
solve this problem.