Display, in a raised position, a 100 mL
beaker of water, and ask, “What does this have in common with
the Hoover Dam?”
The answer is that both the beaker of water
and the dam represent potential energy. Both contain liquid raised to
an elevated position. Released from that position, the liquid could
do work. Specifically:
Hoover Dam stops the natural flow of the Colorado River on
the Nevada-Arizona border about 30 miles southeast of Las Vegas,
creating Lake Meade. The lake is 180 kilometers long and contains a
little more than 35 cubic kilometers of water. (That’s 35 billion
metric tons of water.) From the surface of the lake on one side of
the dam to the bottom of the dry canyon on the other is a drop of
about 210 meters.
The beaker of water here in the classroom has been raised
about two meters (or whatever) in that frame of reference. It
contains 340 grams, or a trifle more than a third of a kilogram of
Potential energy can be converted to other
forms of energy, especially kinetic energy.
Next, pose this question: “What does a
car going down a highway and a thrown baseball on its way to the
plate have in common?”
Both possess kinetic energy, from the fact
that they are in motion. Kinetic, in fact, comes from the
Greek word for motion. The water in our first example will have
kinetic energy if set in motion because of gravity.
Distribute copies of the Kinetic vs.
Potential Energy Worksheet (S-8-7-2_Kinetic vs. Potential Energy Worksheet and KEY.doc) to students, and have them
silently fill in the answers.
Lead a discussion of each item:
water sitting in an uphill reservoir—potential
car moving down a highway—kinetic
car parked on a slope—potential, since it could roll down
wrecking ball hitting a wall—kinetic
gallon of gasoline—potential as it can fuel a car
water flowing out of a reservoir—kinetic
coal in a mine—potential as it can be used as fuel
debris in a road as seen by an approaching car—kinetic
The last item is a trick question intended
to introduce the concept of frame of reference. Make the
Both potential and kinetic energy require a frame of
reference—things are relative, in other words. For potential
energy this is obvious. The water behind Hoover Dam has potential
energy in the frame of reference of the generator turbines below the
dam. Above the dam, the water represents no potential energy.
Likewise, a moving object has kinetic energy only in the frame of
reference of an observer who does not share the object’s velocity.
To a car going down a highway, a crate that has fallen off a truck
and is now lying in the road possesses kinetic energy. Since motion
is relative, the car may as well be at rest with the crate (and
road) rushing at it. But to someone standing off the side of the
road, the crate has no kinetic energy at all.
“Once a frame of reference is
established, potential and kinetic energy are measured much the same
way. Various ways of measuring energy have been in use since humanity
began harnessing energy at the start of the Industrial Revolution.
The first and still most popular is the horsepower, dating to 1783.
It was based on the observation that a horse harnessed to a treadmill
could raise 33,000 pounds to a height of one foot in one minute.
“But this is a rather large quantity,
and was based on obsolete English measure (feet and pounds.) Today we
use a much smaller measure of energy, called the joule
(pronounced jewel, as in diamond or ruby) named for English physicist
James Prescott Joule (1818-1889).
“A joule is the energy needed to move
one kilogram for a distance of one meter at an acceleration of one
meter per second squared. In other words, it measures energy in terms
of mass times distance moved times the force of the acceleration
behind the movement.
“The contents of our water glass,
meanwhile, represents potential energy because it has been placed in
a position where the liquid could fall downward and perhaps do some
work while falling.
“Figuring the amount of potential
energy in our glass of water would seem like rocket science. Actually
it’s rather straightforward. Remember, the joule represents mass
times distance times acceleration. In this situation we have the
three data points we need:
Mass is a measure of the amount of H20
in the beaker.
The distance moved is the distance
it’s going to fall, which is the height we chose to raise it. In
this case we will raise it about a foot, or about a third of a
The acceleration is the acceleration
of gravity, since the mass is going to be falling. Here on the
surface of the Earth that’s 9.8 meters per second squared (9.8
m/s2). If you’re stuck in an elevator and
have to calculate using it, just use 10.
“So joules of potential energy equals
mass times height times gravity.” Write the equation on the
Have a student (presumably with a calculator
or spreadsheet) actually perform the calculation for the glass of
water, assuming it will be poured from 0.3 meters, weighs 0.34
kilograms, with an acceleration of 9.81.
The answer is 1 joule.
“How did it come to acquire this
potential energy? In the case of our glass of water, we invested the
muscle energy needed to raise it to that height. With Hoover Dam, the
climate provided the energy needed to deposit snow on the slopes of
the Rocky Mountains, which later melted, ran downstream, collected
behind Hoover Dam, and formed Lake Mead.
“What does 1 joule look like?”
Have one student carefully pour the contents
of the glass into another glass, while a second student holds a one
meter stick so that the first glass is at approximately the proper
distance (30 centimeters) above the second one. They should try to
complete the act in one second.
“And that is a joule of energy.
“If we had put a pinwheel in the stream
of water, so that it turned, we could say that it did work.
“And that is how Hoover Dam works,
except that instead of a pinwheel it has 17 huge turbines with water
hitting them at 137 kilometers per hour. The overall capacity is
about 2 billon watts.
“A simpler definition is that one joule
is equal to one watt of electricity for one second. In other words, a
100-watt light bulb shining for one second consumes 100 joules. Other
The metabolism of an average person is also about
equivalent to a 100-watt light bulb, or 100 joules per second.
The storage capacity of one AA alkaline (nonrechargeable)
battery is usually rated (brand new) at about 2.5 watt-hours of
power. That is the same as about 9,000 watt-seconds, or 9,000
One standard horsepower exerted for one second is 746
joules. Modern tests show that is actually a little more than the
average horse can maintain. A person can maintain a sustained effort
of about one-tenth horsepower.
The solar radiation reaching the Earth amounts to 1,366
joules per square meter per second. But the efficiency of typical
solar power generators is only about 10 percent.
The combustion energy in one liter of 87-octane gasoline
is 32 million joules per liter or 44.4 million joules per kilogram
(or 121.1 million joules per gallon).
“But when we poured out the water, we
converted its potential energy to kinetic energy, which is the form
of energy of a moving object.
“Using kilograms (m
for mass) and meters per second (v for velocity)
produces joules.” Write this equation on the blackboard:
JOULES = (1/2)mv²
“So let’s look at our beaker of water
example again. Pouring it from a height of 30 centimeters happens to
produce a velocity of 2.42611 meters per second. (The formula to
derive the velocity of an object after it has fallen a certain
distance is the square root of twice the acceleration of gravity
times the distance fallen.) Again, the mass was 340 grams.”
Distribute an appropriate number of copies
of the Energy Comparisons Worksheet (S-8-7-2_Energy Comparisons Worksheet and KEY.doc).
After reviewing the students’ work and
going over the answers, make these points:
The battery power sources are shown for comparison. They
cannot release all their energy quickly short of exploding.
You’ll note that gasoline offers 68 times more energy per
gram than lithium ion batteries, and 244 times more than car
batteries. This may help explain why electric cars have been slow to
catch on, and why researchers are constantly seeking batteries with
more energy density.
The lithium ion and car batteries are
rechargeable, unlike gasoline, which is combustible.
Assume you have built a reservoir on a hill 100 meters above
a river. It is exactly the size of a football field (6,232 square
meters) and is ten meters deep. Given that a cubic meter of water
weighs about 1,000 kilograms (one metric ton, or tonne), what is the
potential energy of the contents of the reservoir, if the water is
piped down to a generator turbine at the banks of the river? (61.136
Assume you can sell your resulting power for the national
average of 12 cents per kilowatt hour. (A joule is the same as a
watt-second.) Assuming 100 percent efficiency, what would be your