Energy - a Basic Physics Concept and a Social Value
John L. Roeder
The Calhoun School
433 West End Avenue
New York, NY 10024
Abstract:Though it emerged relatively recently as a physics concept, energy has become the most transcendent concept in physics and a pervasive entity in our lives. Thirty years ago the Arab Oil Embargo caused us to stop taking gasoline for granted and caused me to start teaching students about the importance of energy and give special emphasis to the physics underlying it. Most recently my appreciation of energy was enhanced by developing a workshop manual on this topic for the Physics Teaching Resource Agent program of the American Association of Physics Teachers. I would like to share with you some of the key insights I gained from that experience.
Thirty years ago I began teaching at The Calhoun School in New York City. Soon after I arrived, the Arab Oil Embargo meant that the availability of gasoline at the corner service station could no longer be taken for granted, and before year's end I would pay in excess of a dollar for a gallon of it for the first time. The term "energy crisis" entered our vocabulary, and at Calhoun we decided to start a seminar about it.
That seminar later led to more organized and systematic teaching about energy, first in a course on "Critical Social Issues" and later in a physical science course called "Energy for the Future." I got involved with the educational work of the National Energy Foundation, then headquartered in New York City, spent two summers working on NSTA's "Project for an Energy Enriched Curriculum," and became a Resource Agent for the New York Energy Education Project.
Although my energy-focused physical science course gave way to Conceptual Physics and later Active Physics, after Paul Hewitt convinced me in 1989 that physics could and should be taught to ninth graders, only last year did I return to my earlier "life" as an energy educator and develop an Active Physics-formatted chapter on energy issues, in which the challenge was the same as the final exam of my former course: for students to plan their energy future without
I reported on this chapter at last summer's meeting1 at one of the Physics and Society's sessions, and I fell into telling Jim Nelson about it during the weeklong PTRA institute that preceded the meeting. Before week's end I heard him ask me, "How would you like to develop a workshop manual on energy for us?"
As you know, it's hard to say "no" to Jim Nelson; and, besides, I looked at this as a new opportunity to address a topic that had always seemed to hold out a dual appeal to me: energy was at once the vital essence we needed to make things happen in our lives and also the most elusive concept I had ever encountered, yet one which made its presence felt in every nook and cranny of physics. I had long rejected the textbook definition that "energy is the ability to do work," yet never felt comfortable with any pat alternative.
I asked Jim whether I should include stuff about energy issues that I used to include in my energy-focused physical science course and also included in my Active-Physics formatted chapter, and he said "yes." But I knew, from the format of the many PTRA workshop manuals I had seen over the years, that he wanted the basic stuff in there, too, and that this would mean motivating the basic concept of energy.
I ended up liking this activity so well that I had my students do it last year. One group obtained the data for force vs. distance along the slope shown in Fig. 1, which you can see looks like an inverse type of relationship. Borrowing from what I have learned about the Modeling approach to linearize graphs, I then asked them to plot force vs. the reciprocal of distance, and they got the linear relationship shown in Fig. 2.
The consequence of this relationship between force and distance along the slope is that, regardless of the slope, the product of the force and distance is an invariant. Now invariance is an indication that something is special in science. This told me that this product of force and distance had some special significance, which in turn could merit giving it a special name, which, for want of further originality, we could call "work."
But I felt that more than just the concept of work was motivated by this invariance of force x distance. All the expressions for work done were equal to the work required to lift the cart up directly, and this further motivates the concept of potential energy as something that is gained by an object when it is lifted, with the potential energy gain equal to the work done.
If potential energy is gained when a roller coaster is lifted to the top of the first hill, it is lost when the coaster goes down the hill. But when it rolls down the hill, the coaster starts to move, and it moves faster the farther it rolls down the hill. Is there a correspondence between the increase in motion and the decrease in potential energy? If so, can we say that the potential energy is not "lost" but rather "transformed" into something related to the cart's motion as it rolls down the hill?
The advent of photogates to use with CBLs and LabPros meant we could try that one too -- in fact, one book I will never write is "Physics Without Photogates." The results from one of my groups of students are shown in Fig. 3. That a graph of velocity vs. PE lost veers off to the right of a straight line suggests linearizing by plotting the square of velocity vs. PE lost (Fig. 4).
Here I went a step further, one that I learned last summer in the PTRA "Graphical Analysis" workshop conducted by Modelers Rex and Debbie Rice. They taught me to determine the equation for the straight line by measuring the slope and identifying its units, which in this case turn out to be the reciprocal of mass in kg. I then sought to express the slope as a number divided by the only mass in this experiment, the mass of the cart. The whole number closest to
my numerator was "2," and I was experimentally led to the conventional expression for kinetic energy.
I was really starting to enjoy this odyssey, in which I could not only motivate but also determine the conventional expressions for energy experimentally. This part was, in fact, a continuation of my realization at last summer's PTRA workshop at the Harrisonburg, VA, "rural center" at James Madison University that we were able to derive the equations of motion experimentally in the "Kinematics" workshop there.
But would it work for elastic energy? I mulled this one around for some time, because I knew that there were added complications -- the presence of kinetic and gravitational potential as well as elastic energy. I settled on a vertical oscillating spring, because I had previously been able to make good measurements of its position with a motion sensor (Fig. 5). Just as I had
determined the expression for kinetic energy by finding out what function of velocity corresponded to gravitational potential energy lost by a cart rolling down an incline, I how used kinetic energy lost as a way to measure the potential energy of the oscillating spring. A graph of displacement vs. PE for my 48 data points (Fig. 6) looks absolutely cacophonous, but when I squared the displacement, a linear pattern started to emerge (Fig. 7). Furthermore, the units of the slope turn out to be the reciprocal of those for the spring constant. The slope obtained from doing a linear regression on my TI-83 turned out to be remarkably close to 2 divided by the spring constant.
Thus began a new odyssey for me. I started by searching for a way to motivate the concept of energy that would be interesting and relevant to students' lives -- and came up with the idea of designing a roller coaster. The Physics Day at the Amusement Park worksheets ask students why roller coasters use a gentle slope to the top of the first hill, and I recast this into having students measure the force needed to pull a cart up an incline to a given height (the height of the first hill) -- and the corresponding distance required for different slopes of the incline.
But I wasn't off the hook so easily on this one. My reviewers protested that I hadn't included the gravitational potential energy, which I was embarrassed to find was not negligible. But the fact that the data were so good kept gnawing at me. Then I realized the answer. Gravitational potential energy adds a linear term in the displacement, and adding a linear term to a quadratic term still gives a parabola, only with a shifted vertex. I was able to show that
the quadratic dependence on displacement was really about the equilibrium point y = -mg/k and that
(1/2)k(y + mg/k)2 = (1/2)ky2 + mgy + (1/2)m2g2/2k,
with the first term being elastic potential energy for displacement of a spring with no weight suspended from it, the second term being the weight's gravitational energy, and the third term just a constant (of no significance in defining potential energy).
I next wanted to show the transformation of gravitational potential or kinetic energy into other forms, such as electrical and thermal. I knew I could show transformation from electric to thermal by the "electrical equivalent of heat" experiment, which I had done for years -- except that I used to use it as a way to measure the correspondence between number of calories (or Calories) of thermal energy output vs. number of joules electrical energy input. Now, though, that calories are "out," I was finding embarrassment in having more joules of thermal energy output than electrical energy input. If I was going to put this in a PTRA manual, I'd have to get this bug out.
I'm telling you about this, in case you have had a similar problem. What I did one afternoon was to set up four electrical equivalent of heat experiments, with four different models of DC power supply, and I found that one gave me reasonable results, while the other three gave me the excess thermal energy output described above. Rotations among the electric meters caused no change, and I was led to conclude that it was the DC power supplies that underlay the
problem. My belief in this was strengthened when an oscilloscope showed that the power supplies yielding excess thermal energy output produced only doubly rectified DC power, while the power supply that had given reasonable results provided DC current that had been further "smoothed out."
I would welcome an explanation from any listener of why the DC power supplies
furnishing doubly rectified DC would give meter readings leading me to the appearance of excess thermal energy output, but I decided that these power supplies presented a complication I didn't want to deal with, and I scurried off to buy me some immersion coils.
But, to keep a continuous chain of energy transformations, I needed to show the transformation from gravitational potential or kinetic energy to electric. The one activity that I came up with to measure all the necessary quantities for both was to energize a motor with D-cells to lift a known mass. I could measure the electrical energy used from the voltage, current, and time, and the gravitational potential energy gained from the mass and the distance through which it was lifted. But, alas, the largest percentage of the electrical energy I could convert to gravitational potential energy was 11%. It made me wonder how energy ever became considered to be a conserved quantity, anyway -- to the extent that we were willing to wait a quarter century between the hypothesis and discovery of a particle which would preserve its conservation!
This taught me something else, too -- that the presence of the Second Law of Thermodynamics is as with us just as much as the First. Only when the energy transformation is to thermal energy can we be assured of 100% transformation efficiency -- and even then what we are left with is a measurement of specific heat. The electrical equivalent of heat experiment really leads us to a measurement of the specific heat of water, and the alternative I had to resort to to complete the chain connecting mechanical, electrical, and thermal energy -- the conventional experiment of measuring temperature increase in metal shot after hundreds of inversions in a container (made possible in smaller containers by temperature probes measuring to the hundredths of a degree) -- ends up with measurements of specific heats of metals. The conservation of energy among its many forms outside the mechanical realm seems to rest upon the fact that all of our experiments transforming energy to thermal form have led to a
self-consistent set of measured values for specific heats.
It is the Second Law of Thermodynamics, too, that makes energy an important concept in society as well as in physics. After all, if we had only the First Law to worry about, we wouldn't have to worry: energy might not be created, but it isn't destroyed either. All the energy in the world today would continue to be available to us.
But for energy to meet our needs, it must be transformed -- e.g., we need to increase the thermal energy in our homes in winter, and we need a lot of energy brought to our appliances by electrons in electric current if they are to operate. The Second Law of Thermodynamics tells us that when energy is transformed, some of it gets transformed to a form that is less useful (the most typical example of this is "waste heat"). Energy "sources" are more useful forms of energy that can be transformed to meet our needs. When we "produce" energy, what we are really doing is to transform useful energy from these energy "sources" to a form that meets our needs. When we "use" these energy "sources,” energy in a form that met our needs is transformed to a less useful form. When we "conserve" energy, we "use" the smallest amount of an energy "source" to accomplish a particular task.
An important plan for any energy future is to "conserve" as much as we can, but "conserve" as much as it might, an industrial society still needs to "use" new "sources" of energy – to heat and cool its buildings, to run its appliances, to move its people, and to manufacture its goods. Because of their convenience, the "sources" of choice for more than a hundred years have been fossil fuels, the fuels I ask my students to plan their future without.
Why? Not just because a shortage of fossil fuels got us into trouble in 1973 – and again in 1979. Not just because burning fossil fuels produces carbon dioxide which leads to global warming. More fundamentally, we're eventually going to run out of them. Their continued use to support an ever-increasing population is not "sustainable" -- in the sense that our use of them denies future generations the benefits of their use (and as a manufacturing material as well as an energy "source").
Twenty years after the 1973 Arab Oil Embargo I took a retrospective look at what our actions showed we had learned from it. I learned that US total energy "use" had declined the years immediately following the energy crises of 1973 and 1979, that US energy use through 1990 had fallen below a host of predictions, but that most of the reduction was due to the industrial sector. But little had been done to wean us from our diet of fossil fuels.
The Solar Energy Research Institute was charged at its founding in 1977 to meet 20% of US energy needs from renewable sources by 2000. It was renamed the National Renewable Energy Laboratory (NREL) in 1991. I thought that this 30-year anniversary of the Arab Oil Embargo might be a good time to find out whether this goal had been met.
Data for US fossil fuel and total energy use are plotted on Figures 8 and 10. Both graphs show a decline following the energy crisis years of 1973 and 1979 and that both fossil fuel and total energy use had climbed back to their peak 1979 values a decade later and continue to climb. But, while fossil fuel use doubled from 1949 to 1968, it has not increased even 50% more than the 1968 usage since then. And not until 2000 did petroleum use climb back to its
But the fact that we have put the brakes on increasing our petroleum use more than for other fossil fuels since the energy crises of the 1970s is no overt cause for rejoicing. For while imports still comprise only a small fraction of the coal (1.5%) and natural gas (20%) that we use, the fraction of petroleum imported passed 50% in 1990. M. King Hubbert, whose ability to forecast future fossil fuel production in terms of past data was legendary, wrote in the September 1971 Scientific American2 that "In the case of oil the period of peak production appears to be the present," and he was right.
We've decreased the rate at which our use of energy in general and fossil fuels in particular has increased, but these uses are still increasing. Moreover, the time since the energy crises of the 1970s have seen a decline in US production of petroleum and continually increasing imports.
How're we doing on renewables? Did NREL achieve the goal of 20% of US energy from renewable sources by 2000? Fig. 9 plots energy from conventional hydroelectricity, biomass, geothermal, and solar, and only since 1988 has solar gotten up off the t-axis on the graph. Most of our renewable energy continues to come from the two sources that have played the leading role even before renewable energy was fashionable: hydroelectricity and biomass. Geothermal has also started to make a more significant contribution since the energy crisis