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Welcome back.

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At the end of the last
video, I left you

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with a bit of a question.

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We had a situation where we
had a 1 kilogram object.

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This is the 1 kilogram object,
which I've drawn neater in

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this video.

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That is 1 kilogram.

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And we're on earth, and I need
to mention that because

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gravity is different from
planet to planet.

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But as I mentioned,
I'm holding it.

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Let's say I'm holding it 10
meters above the ground.

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So this distance or this
height is 10 meters.

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And we're assuming the
acceleration of gravity, which

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we also write as just g, let's
assume it's just 10 meters per

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second squared just for the
simplicity of the math instead

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of the 9.8.

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So what we learned in the last
video is that the potential

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energy in this situation, the
potential energy, which equals

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m times g times h is equal to
the mass is 1 kilogram times

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the acceleration of gravity,
which is 10

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meters per second squared.

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I'm not going to write the units
down just to save space,

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although you should do this when
you do it on your test.

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And then the height
is 10 meters.

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And the units, if you work them
all out, it's in newton

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meters or joules and so it's
equal to 100 joules.

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That's the potential energy when
I'm holding it up there.

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And I asked you, well when
I let go, what happens?

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Well the block obviously
will start falling.

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And not only falling, it will
start accelerating to the

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ground at 10 meters per second
squared roughly.

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And right before it hits the
ground-- let me draw that in

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brown for ground-- right before
the object hits the

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ground or actually right when it
hits the ground, what will

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be the potential energy
of the object?

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Well it has no height, right?

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Potential energy is mgh.

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The mass and the acceleration of
gravity stay the same, but

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the height is 0.

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So they're all multiplied
by each other.

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So down here, the potential
energy is going

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to be equal to 0.

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And I told you in the last video
that we have the law of

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conservation of energy.

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That energy is conserved.

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It cannot be created
or destroyed.

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It can just be converted from
one form to another.

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But I'm just showing you, this
object had 100 joules of

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energy or, in this case,

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gravitational potential energy.

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And down here, it
has no energy.

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Or at least it has no
gravitational potential

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energy, and that's the key.

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That gravitational potential
energy was converted into

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something else.

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And that something else
it was converted

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into is kinetic energy.

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And in this case, since it has
no potential energy, all of

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that previous potential energy,
all of this 100 joules

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that it has up here is now going
to be converted into

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kinetic energy.

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And we can use that information
to figure out its

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velocity right before
it hits the ground.

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So how do we do that?

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Well what's the formula
for kinetic energy?

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And we solved it two videos
ago, and hopefully it

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shouldn't be too much
of a mystery to you.

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It's something good to memorize,
but it's also good

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to know how we got it and go
back two videos if you forgot.

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So first we know that all the
potential energy was converted

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into kinetic energy.

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We had 100 joules of potential
energy, so we're still going

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to have 100 joules, but now
all of it's going to be

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kinetic energy.

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And kinetic energy is
1/2 mv squared.

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So we know that 1/2 mv squared,
or the kinetic

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energy, is now going to
equal 100 joules.

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What's the mass?

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The mass is 1.

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And we can solve for v now.

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1/2 v squared equals
100 joules, and v

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squared is equal to 200.

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And then we get v is equal to
square root of 200, which is

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something over 14.

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We can get the exact number.

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Let's see, 200 square
root, 14.1 roughly.

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The velocity is going to
be 14.1 meters per

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second squared downwards.

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Right before the object
touches the ground.

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Right before it touches
the ground.

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And you might say, well Sal
that's nice and everything.

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We learned a little
bit about energy.

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I could have solved that or
hopefully you could have

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solved that problem just using
your kinematics formula.

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So what's the whole point
of introducing

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these concepts of energy?

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And I will now show you.

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So let's say they have the same
1 kilogram object up here

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and it's 10 meters in the air,
but I'm going to change things

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a little bit.

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Let me see if I can competently
erase all of this.

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Nope, that's not what
I wanted to do.

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OK, there you go.

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I'm trying my best to erase
this, all of this stuff.

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OK.

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So I have the same object.

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It's still 10 meters
in the air and I'll

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write that in a second.

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And I'm just holding it there
and I'm still going to drop

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it, but something interesting
is going to happen.

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Instead of it going straight
down, it's actually going to

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drop on this ramp of ice.

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The ice has lumps on it.

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And then this is the bottom.

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This is the ground down here.

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This is the ground.

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So what's going to
happen this time?

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I'm still 10 meters in the
air, so let me draw that.

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That's still 10 meters.

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I should switch colors just
so not everything is ice.

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So that's still 10 meters, but
instead of the object going

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straight down now, it's going to
go down here and then start

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sliding, right?

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It's going to go sliding
along this hill.

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And then at this point it's
going to be going really fast

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in the horizontal direction.

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And right now we don't
know how fast.

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And just using our kinematics
formula, this would have been

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a really tough formula.

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This would have been
difficult.

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I mean you could have attempted
it and it actually

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would have taken calculus
because the angle of the slope

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changes continuously.

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We don't even know the formula
for the angle of the slope.

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You would have had to break
it out into vectors.

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You would have to do all sorts
of complicated things.

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This would have been a nearly
impossible problem.

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But using energy, we can
actually figure out what the

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velocity of this object
is at this point.

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And we use the same idea.

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Here we have 100 joules
of potential energy.

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We just figured that out.

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Down here, what's the height
above the ground?

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Well the height is 0.

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So all the potential energy
has disappeared.

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And just like in the previous
situation, all of the

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potential energy is now
converted into kinetic energy.

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And so what is that kinetic
energy going to equal?

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It's going to be equal to the
initial potential energy.

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So here the kinetic energy
is equal to 100 joules.

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And that equals 1/2
mv squared, just

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like we just solved.

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And if you solve for v, the
mass is 1 kilogram.

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So the velocity in the
horizontal direction will be,

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if you solve for it, 14.1
meters per second.

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Instead of going straight down,
now it's going to be

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going in the horizontal
to the right.

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And the reason why I said it
was ice is because I wanted

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this to be frictionless and I
didn't want any energy lost to

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heat or anything like that.

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And you might say OK Sal, that's
kind of interesting.

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And you kind of got the same
number for the velocity than

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if I just dropped the object
straight down.

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And that's interesting.

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But what else can
this do for me?

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And this is where it's
really cool.

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Not only can I figure out the
velocity when all of the

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potential energy has
disappeared, but I can figure

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out the velocity of any
point-- and this is

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fascinating-- along
this slide.

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So let's say when the box is
sliding down here, so let's

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say the box is at this point.

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It changes colors
too as it falls.

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So this is the 1 kilogram
box, right?

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It falls and it slides
down here.

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And let's say at this point it's
height above the ground

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is 5 meters.

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So what's its potential
energy here?

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So let's just write something.

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All of the energy is
conserved, right?

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So the initial potential
energy plus the initial

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kinetic energy is equal to the
final potential energy plus

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the final kinetic energy.

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I'm just saying energy
is conserved here.

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Up here, what's the initial
total energy in the system?

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Well the potential energy is 100
and the kinetic energy is

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0 because it's stationary.

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I haven't dropped it.

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I haven't let go of it yet.

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It's just stationary.

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So the initial energy is going
to be equal to 100 joules.

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That's cause this is
0 and this is 100.

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So the initial energy
is 100 joules.

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At this point right here, what's
the potential energy?

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Well we're 5 meters
up, so mass times

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gravity times height.

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Mass is 1, times gravity, 10
meters per second squared.

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Times height, times 5.

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So it's 50 joules.

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That's our potential energy
at this point.

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And then we must have some
kinetic energy with the

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velocity going roughly
in that direction.

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Plus our kinetic energy
at this point.

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And we know that no energy
was destroyed.

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It's just converted.

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So we know the total energy
still has to be 100 joules.

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So essentially what happened,
and if we solve for this--

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it's very easy, subtract 50 from
both sides-- we know that

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00:09:03,430 --> 00:09:06,120
the kinetic energy is
now also going to

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be equal to 50 joules.

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So what happened?

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Halfway down, essentially half
of the potential energy got

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00:09:12,370 --> 00:09:14,120
converted to kinetic energy.

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00:09:14,120 --> 00:09:16,120
And we can use this information
that the kinetic

221
00:09:16,120 --> 00:09:18,230
energy is 50 joules
to figure out the

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velocity at this point.

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1/2 mv squared is equal to 50.

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The mass is 1.

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Multiply both sides by 2.

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You get v squared
is equal to 100.

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The velocity is 10 meters
per second along

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this crazy, icy slide.

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And that is something that I
would have challenged you to

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solve using traditional
kinematics formulas,

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especially considering that we
don't know really much about

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the surface of this slide.

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And even if we did, that would
have been a million times

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harder than just using the law
of conservation of energy and

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realizing that at this point,
half the potential energy is

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now kinetic energy and
it's going along the

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direction of the slide.

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00:10:02,620 --> 00:10:03,870
I will see you in
the next video.

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