This topic stresses mechanical energy, potential and kinetic, and also describes conversion between types of energy (while conserving the total amount), units, and the special position of heat.
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "Energy," section #15 http://www.phy6.org/stargaze/Senergy.htm |
Goals: The student will learn about|
Terms: Energy (potential, kinetic, conservation of), pendulum, joule, calorie, second law of thermodynamics. (kilojoule, kilocalories)
Stories and extras: The energy content of a candy bar. And of TNT
Starting the lesson:
Today we will study energy,so we might just as well start by asking--"What is energy?"
If someone gives the formal definition "ability to do work" ask:
We could redefine it as "overcoming resistance over a distance"--for instance, lifting a brick (against gravity) from the floor to the table, or dragging it along the floor (against friction), and then work equals resistance times distance.
Any of these could also be done by a machine, so for a start we will simply say "energy is anything that can run a machine."
--Light--that was what the electricity in the lightbulb was converted to
--Sound--that was what the electricity in the radio was converted to
--Chemical energy--when you ate breakfast, it gave you strength.
--Heat--if you cooked your food, or heated the house.
--Nuclear energy--if you enjoyed sunlight, because the Sun gets its energy by combining atomic nuclei of hydrogen to helium, deep inside it.
That energy becomes heat, and heat causes light to come out.
And you know you can trade one kind against the other: rolling down a hill, you lose height as you gain speed, and that speed helps you get up the next hill (the same in a roller coaster).
Guiding questions and additional tidbits with suggested answers.
-- When an object falls down from a height h meters, what is the relation between h and its final velocity v, in meters per second?
--What is interesting about this relation?
[The teacher may note that while the final speed is the same, the time taken to reach bottom isn't.
-- Is something kept constant in this motion?
-- Is this the energy? (No) Why?
E = mgh + (1/2)mv2
We have not yet defined mass; for the time it is understood to be "the amount of matter in motion," which we can measure by weighing.
In all our calculations involving Newtonian mechanics (unless explicitely stated otherwise) the so-called MKS units are used--distances in Meters, masses in Kilograms, time in Seconds, and all derived units based on these three. In those units g = 9.81 and energy comes out in joules. Whenever other units are given, be sure to convert them to MKS! One spacecraft sent towards Mars was lost, because engineers giving the command for a final crucial rocket burn got their units confused.
--How does a pendulum or a swing demonstrate the conservation of total energy?
--How does a roller-coaster demonstrate it?
--What is work W? How much work is performed in lifting a mass m by a height h?
W = mgh
--If m is in kilograms, h in meters, g = 9.81 meter/sec2, in what units is W, as given by the above formula?
--You have climbed to the second floor, raising yourself by 9 feet, (1 ft=30.5 cm = 0.305 meter). You weigh 150 pounds (1 pound = 0.454 kg). How much work did you perform?
h = 9*0.305 = 2.745 meters, m = 150*0.454 = 68.1 kg. If g = 9.81 m/s2, then
W = mgh = 1833.8 joule
--Into what form of energy did this work go?
--From what form of energy did it come?
Suppose you have eaten one square of chocolate weighing 4 grams (1/8 of a bar weighing one ounce). The chocolate contains 2 grams cocoa fat, providing 9 calories per gram (typical for fats), and 2 grams sugar, a carbohydrate with 4 calories per gram, for a total of 18 + 8 = 26 calories. These are "kilocalories" of 4180 joule each, so that piece of chocolate has given you the equivalent of 108,680 joules. If your body can convert it to muscle power with an efficiency of 10% = 0.1, you get 10,868 joules of usable work from that piece of candy, enough to climb 10,868/1833.8 or about 6 floors.
--You jump down from the height of one floor. With what speed v do you hit the ground?
In miles-per hour (1 mile = 1609 meters).
v = 7.3387*3600 = 26,419 meters/hour = 16.4 miles/hour.
--Even a hospital patient lying in bed all day needs to eat. Why?
On the table of energy conversions, which form is converted into which:
-- In an electric fan?
--In an elevator winch?
--Can we convert it back when the elevator descends?
--In a light emitting diode?
--Why did we say "light emitting diode" and not "electric lightbulb"?
--In a car battery?
-- Can it be converted back to chemical energy?
-- In a rocket nozzle?
Heat to kinetic energy. We will later see that the converging-diverging design of the rocket nozzle is very efficient in converting heat to kinetic energy.
Has anyone here read "October Sky", or seen the film? It is a true story of high school boys building and flying rockets, and after they discovered the proper design of the nozzle, their rockets flew much higher. The conversion is never complete--heat can never be completely converted to mechanical energy--but the nozzle comes fairly close to the theoretical limit.
--In quicklime? What happens there?
[This question may not be meaningful enough to students living in a big city.]
For making mortar, builders slake the quicklime with water. It heats up, returning its chemical energy to heat.
-- How do spacecraft get their electric energy?
Around the outer planets, sunlight is too dim to provide enough energy in this way. Spacecraft that fly there, e.g. Voyagers 1-2 and Pioneers 10-11, use radioactive sources which generate heat, and thermocouples (special junctions of different metals) convert it to electricity.
The Russians experimented with small nuclear reactors on spacecraft. One crashed into a lake in Canada, contaminating it with radioactivity and creating great resentment. No such reactors are being flown any more.
-- How is mechanical power defined? What are its units?
-- Your electric bill charges you a certain price per kilowatt-hour (kwh). What do kilowatt-hours measure?
--Food energy is measured in calories. How many calories does a gram of sugar contain?
A "small" calorie contains 4.18 joule, a "kilocalorie" has 4180 joule, and a gram of sugar--as in a piece of candy--has 16720 joule.
--How about other foods?
Fats have about 9 cal/gr., alcohol about 7
--Any materials contain more energy?
--How does TNT (tri-nitro-toluene) compare?
-- Seward, the port at the end of the Alaska Railroad, has steep Mt. Marathon towering just behind it, to a height of about 900 meters. Every 4th of July a footrace is held, from the town to the top of Mt. Marathon and (with a lot of sliding!) back. The current record is 43 minutes and a fraction.
-- Why do we often say "energy is lost as heat"?
--Assune the food a person consumes in one day delivers 2200 Kcal ("calories"), the amount contained in 550 grams (19.4 ounces) of carbohydrates or proteins. Ultimately, of course, almost all of it ends up as heat, even if in the process it powers muscles, nourishes the brain etc.
Suppose the day is hot. What heats a room more--an extra person inside it or lighting a 100W lightbulb? Assume 1 Kcal = 4180 joule.
100 × 86400 = 8,640,00 joule
The extra person generates more heat, but not by much. The energy produced by the food is
2200 × 4180 = 9,196,00 joule
--What does the second law of thermodynamics say?
[Optional: The fraction of heat energy which can be converted to other forms depends on the temperature at which the heat is provided.
The unrecovered heat is changed to a lower temperature, and the fraction we recover depends on these two temperatures--the one at which the heat is received, and the one at which the remainder can be dumped.
A power station needs not only a supply of hot steam, but also a way of dumping the heat left at the end of the cycle. Steam locomotives dumped their spent steam into the air, and therefore needed a great amount of of water, carried in their tenders. Electric power stations (of any kind) recycle their steam and cool it with air in cooling towers, like those of 3-mile island which (for some reason) became a symbol of nuclear energy. Other power stations use nearby lakes and rivers to cool and condense their steam, and steamships (of course!) do so with seawater.]
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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 10-8-2004