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Welcome back.

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In the last video, I showed you
or hopefully, I did show

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you that if I apply a force
of F to a stationary, an

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initially stationary object with
mass m, and I apply that

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force for distance d, that that
force times distance, the

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force times the distance that
I'm pushing the object is

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equal to 1/2 mv squared, where
m is the mass of the object,

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and v is the velocity of the
object after pushing it for a

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distance of d.

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And we defined in that
last video, we just

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said this is work.

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Force times distance by
definition, is work.

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And 1/2 mv squared, I said this
is called kinetic energy.

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And so, by definition, kinetic
energy is the amount of work--

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and I mean this is the
definition right here.

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It's the amount of work you need
to put into an object or

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apply to an object to
get it from rest

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to its current velocity.

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So its velocity over here.

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So let's just say I looked at an
object here with mass m and

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it was moving with
the velocity v.

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I would say well, this
has a kinetic

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energy of 1/2 mv squared.

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And if the numbers are confusing
you, let's say the

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mass was-- I don't know.

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Let's say this was a 5 kilogram
object and it's

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moving at 7 meters per second.

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So I would say the kinetic
energy of this object is going

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to be 5-- 1/2 times the mass
times 5 times 7 squared, times

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velocity squared.

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It's times 49.

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So let's see.

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1/2 times 49, that's
a little under 25.

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So it'll be approximately 125
Newton meters, which is

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approximately-- and Newton
meter is just

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a joule-- 125 joules.

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So this is if we actually
put numbers in.

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And so when we immediately know
this, even if we didn't

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know what happened, how did this
object get to this speed?

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Let's say we didn't know that
someone else had applied a

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force of m for a distance of
d to this object, just by

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calculating its kinetic energy
as 125 joules, we immediately

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know that that's the amount of
work that was necessary.

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And we don't know if this is
exactly how this object got to

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this velocity, but we know that
that is the amount of

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work that was necessary to
accelerate the object to this

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velocity of 7 meters
per second.

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So let's give another example.

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And instead of this time just
pushing something in a

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horizontal direction and
accelerating it, I'm going to

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show you an example we're going
to push something up,

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but its velocity really
isn't going to change.

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Invert.

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Let's say I have a different
situation, and we're on this

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planet, we're not
in deep space.

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And I have a mass of m and
I were to apply a force.

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So let's say the force that I
apply is equal to mass times

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the acceleration of gravity.

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Mass times-- let's just call
that gravity, right?

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9.8 meters per second squared.

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And I were to apply this force
for a distance of d upwards.

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Right?

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Or instead of d, let's say h.

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H for height.

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So in this case, the force times
the distance is equal

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to-- well the force is mass
times the acceleration of

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gravity, right?

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And remember, I'm pushing with
the acceleration of gravity

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upwards, while the acceleration
of gravity is

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pulling downwards.

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So the force is mass times
gravity, and I'm applying that

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for a distance of h, right?

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d is h.

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So the force is this.

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This is the force.

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And then the distance I'm
applying is going to be h.

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And what's interesting is-- I
mean if you want to think of

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an exact situation, imagine an
elevator that is already

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moving because you would
actually have to apply a force

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slightly larger than the
acceleration of gravity just

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to get the object moving.

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But let's say that
the object is

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already at constant velocity.

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Let's say it's an elevator.

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And it is just going up with
a constant velocity.

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And let's say the mass of the
elevator is-- I don't know--

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10 kilograms. And it moves up
with a constant velocity.

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It moves up 100 meters.

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So we know that the work done
by whatever was pulling on

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this elevator, it probably was
the tension in this wire that

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was pulling up on the elevator,
but we know that the

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work done is the force necessary
to pull up on it.

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Well that's just going to
be the force of gravity.

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So we're assuming that
the elevator's not

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accelerating, right?

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Because if the elevator was
accelerating upwards, then the

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force applied to it
would be more than

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the force of gravity.

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And if the elevator was
accelerating downwards, or if

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it was slowing down upwards,
then the force being applied

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would be less than the
acceleration of gravity.

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But since the elevator is at a
constant velocity moving up,

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we know that the force pulling
upwards is completely equal to

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the force pulling downwards,
right?

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No net force.

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Because gravity and this force
are at the same level, so

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there's no change in velocity.

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I think I said that two times.

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So we know that this upward
force is equal to

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the force of gravity.

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At least in magnitude in
the opposite direction.

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So this is mg.

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So what's m? m is 10 kilograms.
Times the

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acceleration of gravity.

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Let's say that's 9.8 meters
per second squared.

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I'm not writing the units here,
but we're all assuming

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kilograms and meters
per second squared.

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And we're moving that for a
distance of 100 meters.

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So how much work was put into
this elevator, or into this

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object-- it doesn't have to be
an elevator-- by whatever

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force that was essentially
pushing up on it or

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pulling up on it?

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And so, let's see.

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This would be 98 times 100.

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So it's 9,800 Newton meters
or 9,800 joules.

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After we've moved up 100 meters,
notice there's no

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change in velocity.

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So the question is, where
did all that work get

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put into the object?

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And the answer here is, is that
the work got transferred

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to something called
potential energy.

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And potential energy is
defined as-- well,

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gravitational potential
energy.

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We'll work with other types of
potential energy later with

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springs and things.

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Potential energy is defined
as mass times the force of

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gravity times the height
that the object is at.

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And why is this called
potential energy?

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Because at this point, the
energy-- work had to be put

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into the object to get it
to this-- in the case of

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gravitational potential energy,
work had to be put

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into the object to get
it to this height.

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But the object now, it's not
moving or anything, so it

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doesn't have any
kinetic energy.

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But it now has a lot of
potential to do work.

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And what do I mean by potential
to do work?

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Well after I move an object up
100 meters into the air,

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what's its potential
to do work?

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Well, I could just let go of it
and have no outside force

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other than gravity.

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The gravity will
still be there.

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And because of gravity, the
object will come down and be

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at a very, very fast velocity
when it lands.

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And maybe I could apply this to
some machine or something,

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and this thing could do work.

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And if that's a little
confusing, let

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me give you an example.

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It all works together
with our--

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So let's say I have an object
that is-- oh, I don't know-- a

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1 kilogram object and
we're on earth.

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And let's say that is 10 meters
above the ground.

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So we know that its potential
energy is equal to mass times

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gravitational acceleration
times height.

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So mass is 1.

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Let's just say gravitational
acceleration is 10 meters per

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second squared.

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Times 10 meters per
second squared.

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Times 10 meters, which
is the height.

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So it's approximately equal to
100 Newton meters, which is

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the same thing is 100 joules.

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Fair enough.

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And what do we know
about this?

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We know that it would take about
100-- or exactly-- 100

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joules of work to get this
object from the ground to this

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point up here.

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Now what we can do now is use
our traditional kinematics

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formulas to figure out, well, if
I just let this object go,

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how fast will it be when
it hits the ground?

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And we could do that, but
what I'll show you is

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even a faster way.

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And this is where all of
the work and energy

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really becomes useful.

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We have something called the law
of conservation of energy.

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It's that energy cannot be
created or destroyed, it just

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gets transferred from
one form to another.

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And there's some minor
caveats to that.

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But for our purposes, we'll
just stick with that.

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So in the situation where I just
take the object and I let

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go up here, up here it has a
ton of potential energy.

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And by the time it's down here,
it has no potential

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energy because the height
becomes 0, right?

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So here, potential energy is
equal to 100 and here,

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potential energy
is equal to 0.

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And so the natural question is--
I just told you the law

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of conservation of energy, but
if you look at this example,

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all the potential energy
just disappeared.

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And it looks like I'm running
out of time, but what I'll

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show you in the next video is
that that potential energy

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gets converted into another
type of energy.

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And I think you might be able
to guess what type that is

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because this object is going to
be moving really fast right

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before it hits the ground.

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I'll see you in the
next video.