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Welcome back.

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I'm now going to introduce
you to the

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concepts of work and energy.

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And these are two words that
are-- I'm sure you use in your

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everyday life already and
you have some notion

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of what they mean.

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But maybe just not in the
physics context, although

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they're not completely
unrelated.

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So work, you know
what work is.

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Work is when you do something.

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You go to work, you
make a living.

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In physics, work is-- and I'm
going to use a lot of words

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and they actually end up being
kind of circular in their

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definitions.

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But I think when we start doing
the math, you'll start

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to get at least a slightly more
intuitive notion of what

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they all are.

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So work is energy transferred
by a force.

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So I'll write that down, energy
transferred-- and I got

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this from Wikipedia because
I wanted a good, I guess,

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relatively intuitive
definition.

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Energy transferred by a force.

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And that makes reasonable
sense to me.

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But then you're wondering, well,
I know what a force is,

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you know, force is mass
times acceleration.

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But what is energy?

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And then I looked up energy on
Wikipedia and I found this,

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well, entertaining.

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But it also I think tells you
something that these are just

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concepts that we use to, I
guess, work with what we

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perceive as motion and force
and work and all of these

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types of things.

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But they really aren't
independent notions.

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They're related.

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So Wikipedia defines energy
as the ability to do work.

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So they kind of use each other
to define each other.

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Ability to do work.

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Which is frankly, as good of a
definition as I could find.

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And so, with just the words,
these kind of don't give you

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much information.

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So what I'm going to do is move
onto the equations, and

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this'll give you a more
quantitative feel of what

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these words mean.

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So the definition of work in
mechanics, work is equal to

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force times distance.

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So let's say that I have a block
and-- let me do it in a

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different color just
because this yellow

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might be getting tedious.

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And I apply a force of--
let's say I apply

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a force of 10 Newtons.

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And I move that block
by applying

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a force of 10 Newtons.

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I move that block, let's
say I move it-- I

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don't know-- 7 meters.

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So the work that I applied to
that block, or the energy that

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I've transferred to that block,
the work is equal to

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the force, which is 10 Newtons,
times the distance,

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times 7 meters.

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And that would equal 70-- 10
times 7-- Newton meters.

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So Newton meters is one, I
guess, way of describing work.

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And this is also defined
as one joule.

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And I'll do another presentation
on all of the

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things that soon.

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Joule did.

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But joule is the unit
of work and it's

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also the unit of energy.

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And they're kind of
transferrable.

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Because if you look at the
definitions that Wikipedia

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gave us, work is energy
transferred by a force and

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energy is the ability to work.

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So I'll leave this relatively
circular definition alone now.

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But we'll use this definition,
which I think helps us a

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little bit more to understand
the types of work we can do.

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And then, what kind of energy
we actually are transferring

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to an object when we do
that type of work.

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So let me do some examples.

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Let's say I have a block.

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I have a block of mass m.

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I have a block of mass m and it
starts at rest. And then I

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apply force.

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Let's say I apply a force, F,
for a distance of, I think,

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you can guess what the distance
I'm going to apply it

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is, for a distance of d.

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So I'm pushing on this block
with a force of F for a

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distance of d.

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And what I want to figure
out is-- well, we know

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what the work is.

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I mean, by definition, work is
equal to this force times this

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distance that I'm applying
the block-- that

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I'm pushing the block.

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But what is the velocity going
to be of this block over here?

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Right?

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It's going to be something
somewhat faster.

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Because force isn't-- and I'm
assuming that this is

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frictionless on here.

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So force isn't just moving
the block with a constant

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velocity, force is equal to
mass times acceleration.

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So I'm actually going to be
accelerating the block.

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So even though it's stationary
here, by the time we get to

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this point over here,
that block is going

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to have some velocity.

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We don't know what it is
because we're using all

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variables, we're not
using numbers.

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But let's figure out what
it is in terms of v.

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So if you remember your
kinematics equations, and if

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you don't, you might
want to go back.

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Or if you've never seen the
videos, there's a whole set of

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videos on projectile motion
and kinematics.

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But we figured out that when
we're accelerating an object

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over a distance, that the final
velocity-- let me change

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colors just for variety-- the
final velocity squared is

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equal to the initial velocity
squared plus 2 times the

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acceleration times
the distance.

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And we proved this back then,
so I won't redo it now.

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But in this situation, what's
the initial velocity?

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Well the initial
velocity was 0.

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Right?

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So the equation becomes vf
squared is equal to 2 times

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the acceleration times
the distance.

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And then, we could rewrite
the acceleration

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in terms of, what?

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The force and the mass, right?

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So what is the acceleration?

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Well F equals ma.

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Or, acceleration is equal to
force divided by you mass.

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So we get vf squared is equal
to 2 times the force divided

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by the mass times
the distance.

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And then we could take the
square root of both sides if

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we want, and we get the final
velocity of this block, at

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this point, is going to be equal
to the square root of 2

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times force times distance
divided by mass.

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And so that's how we could
figure it out.

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And there's something
interesting going on here.

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There's something interesting
in what we did just now.

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Do you see something that looks
a little bit like work?

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Well sure.

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You have this force
times distance

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expression right here.

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Force times distance
right here.

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So let's write another
equation.

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If we know the given amount of
velocity something has, if we

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can figure out how much work
needed to be put into the

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system to get to
that velocity.

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Well we can just replace force
times distance with work.

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Right?

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Because work is equal to
force times distance.

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So let's go straight from this
equation because we don't have

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to re-square it.

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So we get vf squared
is equal to 2

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times force times distance.

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That's work.

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Took that definition
right here.

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2 times work divided
by the mass.

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Let's multiply both sides of
this equation times the mass.

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So you get mass times
the velocity.

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And we don't have to write-- I'm
going to get rid of this f

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because we know that we started
at rest and that the

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velocity is going to be--
let's just call it v.

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So m times V squared is equal
to 2 times the work.

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Divide both sides by 2.

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Or that the work is equal
to mv squared over 2.

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Just divided both sides by 2.

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And of course, the unit
here is joules.

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So this is interesting.

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Now if I know the velocity of
an object, I can figure out,

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using this formula, which
hopefully wasn't too

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complicated to derive.

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I can figure out how much work
was imputed into that object

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to get it to that velocity.

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And this, by definition, is
called kinetic energy.

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This is kinetic energy.

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And once again, the definition
that Wikipedia gives us is the

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energy due to motion, or the
work needed to accelerate from

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an object from being stationary

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to its current velocity.

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And I'm actually almost out of
time, but what I will do is I

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will leave you with this
formula, that kinetic energy

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is mass times velocity
squared divided by

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2, or 1/2 mv squared.

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It's a very common formula.

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And I'll leave you with
that and that

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is one form of energy.

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And I'll leave you
with that idea.

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And in the next video,
I will show you

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another form of energy.

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And then, I will introduce
you to the law of

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conservation of energy.

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And that's where things become
useful, because you can see

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how one form of energy can be
converted to another to figure

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out what happens to an object.

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I'll see

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