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There's even a little
bit more that we can

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learn about our energy diagram.

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And I'd like to just clean this
diagram up for a little second,

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because I want to
work in this area.

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Suppose our system, because
the work non-conservative is 0,

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tells us that the mechanical
energy is constant.

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Now we don't know how much
mechanical energy our system

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is.

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That's a constant of the system.

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But let's just suppose
that our mechanical energy

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is written like that.

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And we'll just
clean up a little,

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give ourselves a little space.

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So here is the mechanical
energy of the system,

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and that's a constant.

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And now we can talk about
two more special points.

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A point over here,
and at this point,

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let's just think about what
our mechanical energy tells us.

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This is a special point,
but let's begin with one

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right here.

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If our particle is
at this location,

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then this represents
the potential energy

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and the difference between the
energy and the potential energy

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is the kinetic energy.

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So this here represents
the kinetic energy.

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And now we can
ask ourselves what

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would happen to the energies
as our particle is moving?

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So if we start right here,
the kinetic energy is 0.

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Because all the
potential energy,

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all the energy is potential.

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And as a particle
starts to move,

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let's say it has a
little bit of energy.

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It starts to move
in this direction.

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Then the kinetic energy
starts to increase

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until we get to this point,
where the kinetic energy is

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maximum at the
stable equilibrium

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point where the force is 0.

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Now the kinetic energy
decreases because remember,

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it's now going
against the force.

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The side the force was
pointing in that direction.

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Here it was in the
other direction.

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And until we finally
get to this point

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where, again, the
energy of system

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is equal to all
potential energy,

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and so there is
no kinetic energy.

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So I'll call this
point A, and I'll

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refer to this point
over here, diagram

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is getting a little
crowded, as B.

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And those points
A and B are what

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we call the turnaround points.

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And they represent the places
where the kinetic energy at XA

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is equal to the kinetic
energy at XB, which is 0.

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Now the last thing
that we like--

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there's a lot of
information, as you can see,

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contained in these
energy diagrams.

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And the last bit of information
that we'd like to ask ourselves

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is what would happen if
instead of having-- confining

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our system to this area, we
increased our mechanical energy

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so we're up here.

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And let's just
follow qualitatively

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the motion of a
particle that begins

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say, over here, with a
little bit of kinetic energy

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and potential energy.

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And if the particle starts
off with the velocity

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in the positive x
direction, then it's

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going to move in this direction.

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And you can see the kinetic
energy is increasing.

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Here we have a maximum
amount of kinetic energy.

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But notice that over
here the particle still

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has some positive
kinetic energy,

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and so it can get
over this hill.

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And when it gets
to the other side,

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the force was in the
positive direction.

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It increases its kinetic
energy, and it goes off

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to what we're referring
to as infinity.

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So one analogy that
people like to make

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is to understand the motion,
think of a marble that's

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rolling down a hill.

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And this is just a metaphor for
this potential energy function.

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As the marble rolls down the
hill, it gains kinetic energy.

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It loses potential energy.

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It comes maximum at
the bottom of the hill.

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As it goes up the hill, it
still has enough kinetic energy

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to get over the top of
the hill and to start

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to come down the other side.

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And of course, our
particle can never

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get to the speed of light.

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So our model has to
break off at one point.