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>> Look at that view.
We're here at the scenic
Morgan Falls hydroelectric dam,
located along the
Chattahoochee River
in Sandy Springs.
The gravity type dam
and powerhouse built
in the early 20th century
was one of the first
hydroelectric power projects
in Georgia, and it's still
in operation today
as part of Georgia Power's
network of electricity-producing
plants throughout the state.
This is a great place
to tell you about the law
of conservation of energy--
not to be confused with
energy conservation.
Energy conservation
is what you do when you
insulate your home
and try to save energy
by heating and air conditioning.
This is different.
The law of conservation
of energy is all about
where energy comes from
and where it goes.
The law states that energy
cannot be created or destroyed.
It can just be converted
from one form to another.
So let's follow the energy.
I'm in the powerhouse
of the plant that uses
the stored energy of water
in the reservoir
to create electricity.
A large pipe carries water
from the reservoir
to turbines in the powerhouse.
The flowing water
turns a propeller-like
water wheel,
or turbine,
which is connected by
a shaft to the generator,
which spins and produces
electricity.
This turbine
is normally underwater,
but we've been given a look
inside the penstock
that houses the turbine.
After the water spins
in the turbine,
it is discharged through a tube
and returns unaltered
to the river below the dam.
The electricity produced
by the spinning generator
is conducted through
the power transformer,
where the voltage is increased.
The high voltage electricity
is fed into Georgia Power's
transmission lines
and distributed
throughout the region.
So how does this illustrate
the law of conservation
of energy?
Water flowing through
this plant is turning
gravitational potential energy
into kinetic energy,
and eventually into electricity.
Remember the relationship
between gravitational
potential energy
and kinetic energy
when you have a falling object.
Gravitational energy
is transformed into an
equal amount of kinetic energy.
Here, however,
it's not quite the case.
Here, you end with
less kinetic energy
than the amount of
gravitational potential energy
you started with.
Why is that?
Where did that extra energy go?
When water hits rocks,
water scatters into a spray,
and some of that energy
is used to vaporize water
into the atmosphere.
The water also bumps into itself
and the walls of the pipes,
creating friction,
which produces heat
and sound energy as it flows.
There's also friction
within the generators,
as the electromagnets turn.
The energy isn't lost--
it's still there,
but it's difficult
to measure all of it,
and it's not available
for useful work.
Non-conservative forces
cause energy to be converted
into forms that cannot be
easily regained.
Forces like friction,
air resistance,
and water resistance
are non-conservative forces.
They're more difficult
to harness, making it hard
to get them back in the form
of usable work.
Work done by non-conservative
forces depends on
the path taken.
On the other hand,
conservative forces
cause energy to be converted
into forms that can be regained.
Examples are forces like
gravity, spring force,
and the electrostatic force.
They do the same amount of work
on an object being moved
no matter the path taken.
For example,
gravity does the same amount
of work on the water
moving through the dam
whether the spillway
taking the water from the top
to the bottom is a steep,
straight shot, or a shallow,
curving flow before the water
gets to the bottom,
since the total vertical drop
the water has traveled
is the same.
A long, curving path
produces more friction,
which is a non-conservative
force, and thus produces
wasted energy.
Okay, so let's see
why it's worth knowing
about all of this.
Let's say I want to know
the velocity of this ball
right before it hits
the ground--
the ball's maximum velocity
before it comes to a stop.
We could solve this problem
using the kinematic equations
we learned in other segments,
but now, let's explore
another option
to determine velocity.
This time, we'll look at
the energy relationship.
Let's say I have
a 1 kilogram ball in my hands
standing at the top of this dam.
We're on Earth,
where the acceleration
due to gravity is 9.8 meters
per second squared.
I'm holding the ball
17.0 meters above the Earth--
the height of the dam.
We know that gravitational
potential energy is mass
times the acceleration
due to gravity times height.
So the mass is 1 kilogram,
times the acceleration
of gravity, 9.8 meters
per second squared,
times the height,
which is 17.0 meters.
The answer is 166.6 joules,
and using significant digits,
it's 167 joules.
When I let go of the ball,
the ball will start falling
and accelerating.
Now, a split second
before the ball hits the bottom
of the dam,
how much potential energy
is left?
Well, the height now is 0,
so put that in the equation.
And the potential energy is 0.
We know from the law
of conservation of energy,
energy can't be destroyed.
So where did the energy go?
Well, from another segment,
you learned how gravitational
potential energy can change
into kinetic energy.
So in this ideal world,
all of the gravitational
potential energy is converted
to kinetic energy.
We can use this to figure out
the velocity of the ball
right before it hit the ground.
Let's assume we're only dealing
with conservative forces--
gravitational potential energy
being converted
into kinetic energy,
with no work being done
by friction.
Using the law
of conservation of energy,
we can see that the total energy
of the ball at its initial,
highest point is equal
to the total energy
at its final, lowest point.
Or, the initial
gravitational potential energy
plus initial kinetic energy
equals the ball's final
gravitational potential energy
plus its final kinetic energy.
So now, let's plug in
the numbers we know so far.
The ball's initial
gravitational potential energy
was calculated
to be 167 joules.
Remember the formula
for kinetic energy.
It's 1/2 times mass
times velocity squared.
Right before the ball
is dropped,
its kinetic energy is 0.
It's 0 because
its initial velocity is 0.
Right before
it hits the ground,
the ball has a gravitational
potential energy of 0,
and has maximum
kinetic energy.
So, right before
it hits the ground,
the ball has a kinetic energy
of 167 joules.
To find the final
velocity of the ball,
we can plug in
our equation
for kinetic energy,
setting that equal
to 167 joules.
The mass of the ball
is 1 kilogram,
and when you multiply it
by 1/2,
you get 167 joules
equals 0.5 kilograms
times the velocity squared.
After dividing both sides
by 0.5 kilograms,
we can see that 334 joules
per kilogram
equals the final
velocity squared.
We then take the square root
of both sides
and we see that
the final velocity of the ball
is 18.3 meters
per second.
You'll find in physics
there are many approaches
to the same problem.
You're going to find
that sometimes it's easier
to use conservation of energy
equations to figure out
motion problems,
especially if a ball
doesn't fall straight down
and instead zig-zags
to the ground.
Using energy rather than
tracking the path of the ball
will make it that much easier.
You have to love physics
for that.
For more practice problems
on the conservation of energy,
check out our Closer Look.
That's it for this segment
of "Physics in Motion".
We'll see you next time.
>> For more practice problems,
lab activities,
and note-taking guides,
check out the
"Physics in Motion" toolkit.