What is Energy?

1. Introduction.

Energy. We all use it. We all talk about it. We all pay for it. Governments formulate energy policy and have huge departments to administer energy policy. We worry about our natural sources of energy "running out". Some days we have low energy, and take pills to boost it. We observe children at play and say, "I wish you could bottle all that energy."

Yet if asked "Just what is energy?", most persons are unable to give a coherent answer. A freshman physics student may answer by giving various "kinds" or "forms" of energy: kinetic energy, potential energy, heat energy, chemical energy, nuclear energy, and electrical energy. But that's not an answer; it's a shopping list.


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We speak of energy in language that suggests energy is "something contained in material things". We speak of "extracting" energy from coal and oil. We say energy can be "converted from one form to another". Such language suggests that we are thinking of energy as a "substance". But the notion of bottling pure energy is absurd. Has anyone ever touched or seen pure energy?

Science education has convinced most people that the energy available from earth's natural resources is finite, but realizing the finiteness of a resource doesn't stop us from wasting it carelessly and unnecessarily. Still, if the average person were asked whether it's possible that we might someday build machines that produce more energy than they consume, they would dismiss the idea as absurd, saying, "You can't get something from nothing," or, "There's no free lunch."

In the early history of technology even this superficial understanding of energy was not known. The very idea of energy is a recently developed concept. The history of physics can be divided into several periods: (1) Antiquity to the 17th century, when the concept of force had not yet been precisely formulated. (2) 17th century to 18th century, when force and torque were quite well understood and classical Newtonian mechanics evolved into a very successful model. (3) 19th century, when work, energy and momentum became quite well-understood (at least by physicists and engineers), and the laws of thermodynamics were formulated. (4) 1900 to the present, when atomic theory and quantum mechanics achieved tremendous success.

But for all of these advances, the physics student today must still progress through the physics concepts of each of these periods, but at an accelerated pace. This process generally begins with Aristotelian concepts, which must be replaced: first by understanding acceleration, then appreciating the concept of force as a vector quantity, learning the work-energy theorem, struggling with the simultaneous application of the laws of conservation of momentum and conservation of energy, and then on to the subtleties of the laws of thermodynamics. For those who do not fall by the wayside, the holy grails of quantum mechanics and relativity loom menacingly as the final hurdle toward becoming a physicist.

Mathematics teachers say that many students "lose it" in math instruction when fractions are introduced, usually in the 4th grade. Physics teachers know that many students "lose it" when vectors and forces are introduced. Those who progress beyond these hurdles often succeed (barely) by cramming, cribbing, and a "plug-and-chug" approach to problem solving, but without genuine understanding. They achieve only a fragile and superficial grasp of the subject, often just enough for low-level functionality in a technical field. They may not fully realize what they have missed.

A reverse look at classical physics.

1. Energy.

Modern textbooks sweep aside the tortuous history of our struggle to understand energy, momentum and force, and present these subjects in a neatly organized logical exposition of formulae and procedures for solving physics problems. Usually Newton's laws and the concept of force are introduced first, then kinetic and potential energy, work, and momentum. Students, however, often fail to grasp the underlying concepts and logical connections. Let's approach the subject a bit differently—not that there's anything wrong with the usual presentation. Consider this just a "review from a different perspective" for the person who has gone through the usual presentation and still has lingering questions. I will avoid mathematical derivations, for these can be found in standard textbooks. But, make no mistake, the math is essential for understanding. Words alone can only give a suggestion of the strength of the logical connections.

How many kinds of energy are there? It depends on how you define "kinds". My answer would be "Two—kinetic and potential." Kinetic energy is energy due to a body's motion, expressed as mv2/2. Potential energy is energy due to a system's configuration in space in situations where the components of the system can exert force on one another.

Already I hear some readers object. "What about heat? Nuclear energy? Psychic energy?" Let's take these one by one. Psychic energy is nothing but pseudoscientific moonshine, unworthy of further comment here. There's no evidence of its existence. "Heat" is a colloquial term for what physicists call "thermal energy". It is nothing more than the total disordered kinetic energy of the particles in a body, of molecules and atoms. Nuclear energy is a form of potential energy of the elementary particles that are scrunched into nuclei. And so it goes. Any energy you can name is either kinetic or potential energy, or a mixture of both.

We have long studied how bodies exchange energy one with another. Already we must be careful with language. The word "exchange" suggests transfering something material from one body to the other, like merchants exchanging money. That's misleading, for energy isn't a material substance. What we are talking about are situations where two bodies interact with one another in some way and one gains the same amount of energy as the other loses. We are avoiding being explicit about how that happens. The conventional view is that the intermediary of the process is force exerted by one body on the other. That force is responsible for an exchange of energy we call work. But are forces "real"? Is energy "real"? What we observe is that the behavior of each body is changed by the transaction. One or both bodies may be caused to change its velocity (a change in kinetic energy), or one or both bodies may be moved to somewhere else where their potential energy is different than it was before.

Observe the common feature of changes in energy. Whether you change the kinetic or potential energies of a body, in either case you move the body. When you use the language of force, you conclude that in order to change the energy of a body, the force that acts to make that change must move the body.

Kinetic energy is a good starting point, for the kinetic energy of a body can be easily determined by measuring the mass and speed of a body. Early on in ths history of machines the spring-scale was invented, which is a convenient way to measure force. When we crunch the numbers by calculating the amount the body's energy changes due to a force acting on it, we find that the change is the size of the force multiplied by the distance the body has been moved. We call this "the work done by the force on the body". There's a refinement that must be made in this when the direction of the force and the distance the body moves aren't parallel. The work must then be defined as the product of the force and distance multiplied by the cosine of the angle between the force and distance vectors. When the direction of a distance is important physically, we call it a displacement and treat it by vector mathematics.

Now that we have defined work in a useful way, we conclude that if the force and the body's displacement are at right angles to each other, that force does no work on the body. If the force acting on a body is zero, no work is done on or by it. And if the forces acting on a body produce no displacement, then no work has been done by those forces. Finally, if no net work is done on a body, its energy does not change. These are confirmed by experiment.

Let's return to some everyday examples that everyone can experience.

  • Suppose you push with all your strength on the rigid stone wall of a building. No matter how great a force you exert on it, you do no work on the wall, for the wall does not move. You may feel fatigue from the effort, you may "work up a sweat", and you may say, "That was work!" You have indeed expended energy, but that has been almost entirely within your body. It is work done by the force of muscular contraction and relaxation, and the result is internal heating of your muscles and surrounding tissues. Some work has also been expended in the accompanying chemical changes in your muscles. And a very small amount may have been wasted in slight compression and flexing of the object you are trying to push.

  • Stretch an ordinary rubber band. The force of your fingers moves the ends of the rubber farther apart, making the band temporarily longer. You have done work on the rubber, and in its stretched state it has potential energy due to the spatial re-configuration of its material components. Some of the work you did also caused the rubber to "warm up", which you can confirm by doing this repeatedly, then quickly pressing the rubber to your lips. The rubber feels warmer after repeated stretching. (The lips are more sensitive to small temperature changes than other parts of the body.) So in this experiment, the work you did changes both the potential energy and the kinetic energy (of molecular motion) of the rubber band.

  • Let go of one end of the stetched band. It snaps back (the motion having kinetic energy), probably with an audible sound. That sound wave carries away some of the band's stored energy, the rest increases its thermal energy, increasing its temperature.

  • Lift a book from the floor and place it on a table. The work you did on the book is the product of the weight of the book multiplied by the vertical distance from floor to table. You also did some additional work within your body, due to muscular action (as noted above). So it isn't correct to say that the total work you did was only the work done on the book. Your body acts as a machine, and machines always waste some of the energy they consume. By "waste" we mean that not all the energy of the machine goes toward the task the machine is designed to do; it is not what we call "useful work".

  • Nudge the book, so it falls from the table. On the way down its potential energy decreases, while its kinetic energy increases as its speed increases. As it falls, the sum of its kinetic and potential energies is constant. When the book lands on the floor its potential energy has decreased to the same value it had before you lifted it. At that instant before landing, its kinetic energy is equal to the work you did on it when you lifted it to the table top. After collision it is at rest, and its kinetic energy of motion is zero. But its internal energy of motion has increased (thermal energy), but that is a chaotic motion of zillions of particles moving in all possible directions. This disorganized motion does not contribute to any motion of the book as a whole.

It is time to make another distinction. Thermal energy is different from the energy due to a body's motion as a whole, even though both are kinetic energies. A book, stone, baseball, planet or any other solid object maintains its structural identity as it moves. All of its particles have the same velocity as that we observe of the body as a whole. But in addition to this, its particles also have chaoatic motions of vibration within the solid body. These constitute the thermal energy that all bodies have if they are above absolute zero temperature.

Finally, we have noted that interacting bodies can result in changes in the energy of both bodies due to the forces they exert on each other. But material bodies can also interact in other ways, and one of the most important ways is by thermal interaction. When two bodies are in contact, those chaotically moving particles in each body interact where the bodies are in contact. These are force interactions, but this is a microscopic version of what we described above, so small that it has no observable effect on the motion of the bodies as a whole. But in this way one body can gain thermal energy and the other loses the same amount. The amount of energy exchanged is called "heat". So, in physics we recognize two ways bodies exchange energy, through work or through heat. We avoid using the term "heat" as something "in" or "posessed by" a body. Likewise we never speak of "work in a body". Both "heat" and "work" are measures of energy changes that result from force interactions.

For the sake of discussion we should distinguish two realms: microscopic and macroscopic phenomena. Microscopic physical phenomena are those at the size of molecules and smaller. Thermal energy is a microscopic phenomenon. Bulk motion of solid objects like machinery or planets is macroscopic.

There is a fundamental assymetry in all this. Because thermal energy is chaotic (disorganized) kinetic energy, it cannot be completely converted to macroscopic work. Some work must be done when converting thermal energy to work, and there are limits to how much can be converted. However, in the other direction, work may be entirely converted to thermal energy. This is quite reasonable when you consider that to convert thermal energy of a body at rest into motion of the body as a whole we must do work to redirect the chaotic motion of many particles with velocities in all possible directions so they move in the same direction.

How can energy be stored? The question is misleading, since energy isn't a material substance. Of course, we can collect and store materials that have energy, such as storing gasoline, which has chemical potential energy in its molecular structure. We can store thermal energy, say of heated water, part of which can be extracated by heat engines (subject to the limitations of thermodynamic laws). Matter itself represents stored energy, and in some cases some of that can be transfered to other forms through nuclear reactions.

But it is a mistake to assume, as some do, that anything that can exert a force represents a "source" of energy. We were cautious above to avoid treating "force" as anything more than a convenient way to express and quantify energy interactions between material bodies. I get questions about the possibility of "extracting energy from gravity". To a physicist, this is an absurd idea, but it's not easy to explain why to someone who doesn't deal with physics everyday.

Re-examine the examples above. In the book and table example, the potential energy of the book on the table was due to the fact that we did work on the book to increase its distance from the earth. The book's weight was due to the earth's gravitational force on the book. So when the book fell from the table, its kinetic energy increased and was finally converted to thermal energy. Where did that energy come from? Not from gravity, it came from the work someone did when lifting the book from the floor. The whole sequence of processes did not extract anything from gravity, and did not diminish the earth's gravitational field. It came from the person or machine doing the lifting.

No machine ever made, nor any natural process, has ever extracted any energy from gravity.

I have had people tell me that there's infinite energy in a magnetic field. As "proof" they cite the refrigerator magnet clinging to the vertical wall of the refrigerator and supporting its own weight against the pull of gravity, presumably forever. Some add that it will only fall when the "stored energy" in the magnet is exhausted. So, they say, the magnet must have an unlimmited amount of energy stored in it. These people are slow learners. The magnet, at rest on the refrigerator wall, is doing no work, and is expending no energy, for its force of attraction causes no motion of the magnet or the refrigerator. The magnet does have a small amount of stored energy (from the work required to magnetize it), but it isn't using up any of that. Nor is it stealing any energy from gravity. It simply isn't expending energy in any form. Consider a similar situation. Use glue to fasten a block of wood to the the refrigerator wall. No magnetism is involved. The block will stay there, supporting its own weight, indefinitely. Would the person who used the magnet example now claim that the glue has unlimited energy stored in it? What about a nail driven in the wall to hang a picture? Or a closet coat-hook? Folks who still use the refrigerator magnet argument as an argument for extracting unlimited energy from magnets are committing not only an error of physics, but an error of critical thought and a singular lack of common-sense.

No machine ever made, nor any natural process, has ever extracted more energy from a magnet than the small amount used to magnetise the magnet.

One reason we hear such outrageous misrepresentations of physics is that many people do not do the mathematics, not even the simple calculations of the amounts of work done in processes and the amounts of energy exchanged. A magnet in a permanent magnet motor can last for years of constant operation, and the slight reduction in its magnetic properties represents a tiny change in energy, miniscule compared to the amount of work done by the motor during its operation.

2. Potential energy.

Let's look more carefully at the potential energy we mentioned. How do we measure it. We have, so far, assumed that we can measure mass (with any of several ancient measuring instruments) and force (with spring-scales or force sensors). Velocity is measured with measuring sticks and stop-watches. (It was the difficulty of measuring short time intervals that delayed our understanding of motion in the early history of physics.) So we have the tools for measuring kinetic energies, and also for measuring work. With these we can do experiments to study how bodies exchange energies through force interactions.

The potential energy of a system is equal to the work required to assemble the system's componenets, working against the interactive forces of its components and any external forces acting on them. There are complications to measuring that, due to energy wasted in dissipative processes, producing thermal energy, sound, etc. but we needn't let that distract us from the important issues.

Suppose we stretch or compress the spring of a spring-scale. We must do work to accomplish that. After the string is compressed, we latch it in the compressed position. Where is the energy equal to the work we did? We say it is "potential energy, stored in the spring". We can verify that by unlatching the spring and letting it do work on something else as it expands. The potential energy of the compressed spring is just equal to the work we did against the elastic force of the spring as we compressed it.

When we lifted the book from floor to table, we say the book on the table had been given potential energy, and we can calculate that energy to be mgh where m is its mass, g is a constant and h is the vertical distance it was lifted. We can verify that by letting it fall and measuring its kinetic energy just before it hits the floor. The potential energy of the book on the table is just equal to the work we did against the gravitational force as we lifted the book from floor to table.

3. Gravity.

We call this "gravitational potential energy". But the name can miselead us if we don't examine what it represents. So let's look more carefully at gravity.

Isaac Newton puzzled about the question, "Why do bodies fall." The story has been told many times, but the bottom line is that he postulated that the earth exerts a force on bodies near it, and not only near, but this gravitational force extends even to the moon and beyond, though it diminishes in strength with distance from the earth, varying as 1/R2 where R is the distance from the earth's center. This was an idea that had been suspected by a number of other people at the time, but it was Newton who did the necessary mathematics to confirm that it did indeed agree with what we knew about falling bodies, and with the orbit of the moon. Yet the idea shocked many, for it proposed that there's a force "influence" that can act on bodies even at a distance, with no other evidence than the fact that it is affecting their observed motion. Gravity is not "observed", it is "inferred" from observations of motion of bodies. And gravity is not just a result of the earth, but, Newton said that any body with mass influences every other body with mass, in amount proportional to the product of their masses. The final equation stated that the force each body exerts on the other is of size F = GmM/R2 where m and M are the masses, G is the universal gravitational constant and R is the distance of the separation of the bodies.

We are saying that gravity is responsible for altering the observed motion of bodies in the same manner as when a two bodies are affected by forces due to bodies being in contact. Contact isn't necessary with gravity. While we easily accepted contact forces, being something we "feel" when we push or lift an object, we cannot feel the force that the earth and moon exert on each other. Yet in both cases we do not directly measure the force. The force is assumed, inferred, from the change of motion we observe. In one sense niether force is "real". In another sense, both are equally "real". We leave discussion of "what is really real" to another document. Real or not, we can measure the motion and calculate the sizes and directions of forces, and it all forms a consistent picture.

4. Force.

One experimental fact emerges when we start measuring things precisely and accurately. When two bodies interact, and the process results in one of them gaining energy, the other one loses the same amount of energy. Such facts led physicists to the law of conservation of energy. Now this law applies whether the interaction is one where one body does work on the other, and also when one body heats the other. Both are exchanges due to force(s) acting through distance, whether at the macroscopic level, or the microscopic level (heat).

When a force and displacement are in the same direction, we say that force does positive work on the body it acts upon. When a force and displacement are in opposite directions, we say that force does negative work on the body it acts upon. In other words, if body A exerts a force F on B, and the force and displacement are in the same direction, then A does positive work on B. If body A exerts a force F on B, and the force and displacement are in the opposite direction, then A does negative work on B. This is the same as saying that if body A does work on body B then B does an equal sized and oppositely signed work on A. From this one can work back to Newton's third law: "If body A exerts a force on body B then body B exerts an equal and oppositely directed force on A."

So, by working backwards from the concept of energy, and energy conservation, we arrive at Newton's laws. Historically the order of discovery of these concepts was the opposite sequence. But whichever direction you follow the logic, the conservation of energy and Newton's laws are inextricably linked. If one is true, so is the other. And if either were untrue, both would be untrue. We have absolutely no evidence that either of these are faulty at the macroscopic level of classical physics.

Latest revision Dec, 2017.