The Physics 7A Course Materials
Fall 1996
Block 1 Notes

About these Notes
This is the first of five sets of notes you will receive this quarter. The quarter is divided into five two-week blocks. At the end of each block there will be a quiz on the material you have worked with during the block. (The last block's quiz will be incorporated into the final.)

Each set of Block Notes is organized the same way.
A Block Overview provides a quick glance of the main ideas treated in the block. This is followed by a Conversation about the content of the block. As implied, this is in a conversational tone and provides some of the reasons why things are done a particular way, how the block content fits into the larger context, perhaps some historical background. These first two sections are meant to be read as you begin working with the content of a block. The next section, the largest, called Block Content, is a concise, logical presentation of the content of the block. This section is not meant to be read the way you read the Block Overview and the Block Conversation. You are not expected to learn physics by reading the Content section. Rather, you will be engaged in activities in DL that will help you to make sense of the material in the Content section. The weekly lectures provide emphasis and direction. Your understanding increases as you answer the questions and work the problems in the assignment. By the end of the two weeks during which time you will have engaged in much serious mental effort, both in DL and outside of class, you should find that the Content section provides a useful, logically organized summary. The next section is Block Definitions and Relationships, that will provide concise definitions/examples of particularly troublesome words and relationships. The final section is the Block Assignment, 30 or so questions/problems (QPs) that pertain to the material treated in the block.

Our Views About Learning

"I think, however, that there isn't any solution to this problem of education other than to realize that the best teaching can be done only when there is a direct individual relationship between a student and a good teacher--a situation in which the student discusses the ideas, thinks about the things, and talks about the things. It's impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned. But in our modern times we have so many students to teach that we have to try to find some substitute for the ideal. ..."
Richard P. Feynman in Preface to The Feynman Lectures on Physics, 1963

We have been greatly influenced by the results of research on learning and teaching conducted over the past 15 to 20 years by educational psychologists, science education researchers, physicists, and cognitive scientists. One central and universal result that is now widely accepted by those active in science education reform efforts at all levels is that learning that goes beyond memorization (including the memorization of algorithmic problem solving approaches) requires learners to actively construct meaning for themselves. Understanding must be developed by you, the learner, individually. This kind of learning is a very active process. You must mentally struggle as they try to make sense of new sensory input in terms of what they already "know." What they "know" gets modified during this process. Learning is not a process of dumping information into a student's blank mind. Rather, it is a process of learners creating their own knowledge, of using the understandings they already have to create new understandings.

The kind of knowledge we are talking about here is not forgotten at the end of the course. It is not the instructor's, nor the TA's, nor the textbook's knowledge. Rather, it is the students' own knowledge, the "gut understandings" that students use to make sense of their experiences. This kind of understanding is not compartmentalized by the student as "physics", or "chemistry", or "biology." It is what students know, not what they remember from a science course.

If we want learners - you, our students - to develop this kind of understanding of physics, then the issue for us as instructors of introductory physics courses is how to design courses that enable learners to construct their own understandings. What can we do as instructors to make this process as efficient as possible? Research, as well as our own observations of student learning­or the lack of learning when we are honest­has repeatedly shown that traditionally-taught introductory science courses do not promote the kind of learning we are talking about for a large majority of students. Rather, for these students, traditional introductory course practices encourage students to develop strategies that actively work against their constructing their own understandings.

We have structured Physics 7 to take into account what we know about which instructional strategies promote active learning and which act against it. Our focus is on what students are actually learning, not on what we think they can or should learn. We will continue to modify what we do as we learn better what instructional strategies work best for which students, and how to best facilitate the greatest number of students' learning within the constraints of our campus setting. Thus, in some sense, Physics 7 will never be a finished product. At any given time, it will simply be where it is at that point in its development. You, the student, are an important part of this process. There are several structured opportunities for you to provide feedback to us; we also welcome your comments and suggestions at any time throughout the course.

One of the clearest implications of our own and others' work in devising instructional strategies that facilitate students' construction of understanding is that it is not realistic to expect the majority of students to develop in a one-year course an understanding of all the material we have traditionally presented. It is just too much material! That is, it is too much if we expect more than simple memorization and skill at being able to find a formula with the appropriate variables. To help alleviate this problem, we have changed to a non-traditional thematic, spiraling approach, that both reduces the emphasis on some topics and allows a more efficient approach to others. We also place a greater emphasis on the connections among the individual concepts.

Organization of Course Content
In place of the organization of traditional physics textbooks that is based on a semi-historical, logical development of topics, we group content and course activities by how we approach physics, Results of Interactions, Agents of Interactions, Details of Interactions, Models of Matter, Basic Skills, and Related Topics. We won't dwell on the meanings of these groupings for now; their meanings will become much more concrete as we get further along in the course. These are not section headings, rather, these approaches will be revisited over and over again throughout the course. Nevertheless, at any given time, it will be clear that we are taking one or another approach, or perhaps a combination of approaches.

During the first quarter we focus primarily on two approaches:
(1) Results of Interactions and (2)Models of Matter. We develop some very powerful and universally applicable ways of understanding physical phenomena using the fundamental concept of energy, both as it appears in thermodynamics and in mechanical systems, and what we call the particle model of matter. With these two approaches we develop a much more unified understanding of a large class of phenomena that are typically treated as separate, unrelated topics in introductory physics and chemistry courses. In the following quarters, the focus tends to be more on the Details of Interactions and the Agents of Interactions: forces and fields. Throughout, we will periodically step back and briefly turn our attention to important related topics, and to the acquisition and practice of certain basic skills, important to success in this course as well as in your future career in science. As we go along in the course, we will provide "road signs" to help keep us conscious of where we are and where we are going.

Block 1 Overview

This block introduces the ideas of systems, interactions among systems, and the energy exchanges that take place as systems interact. We don't concern ourselves with the details of what takes place during interactions at this time, but focus instead on the changes that occur within systems. Initially we focus on transfers of energy in the form of heat. As we move into Block 2, we include non-heat transfers of energy.

We gain more insight into the very powerful notion of energy conservation; the idea that if we keep accurate track of this abstract notion we call energy, the sum of the increases always exactly equals the sum of the decreases . We will begin to sense the generality and usefulness of this concept and will continue to develop it throughout this quarter.

In order to make progress with the notion of energy conservation, we need to develop some precise language and ways to represent energy transfers and changes in systems. We will devote some effort to representing interactions with what we call an Energy Interaction Diagram.

You probably have seen much of what we do in this first block in prior chemistry, physics, or physical science courses. One of our aims in this block is to put this material into a larger framework -- an approach to thinking about phenomena, getting answers to questions, making predictions -- that doesn't depend on many of the details and is extremely universal. We also begin reviewing what you know about the particle model of matter; that is, how, for ordinary matter, the fundamental building blocks are atoms, and how these 100 or so atoms are put together into countless numbers of molecules that constitute the stuff we interact with. We will continue to extend this model through-out the quarter.

Block 1 Conversation

Science is the systematic study of matter and its interactions with other matter. The distinguishing feature of physics which sets it apart from the other sciences is that it tends to focus on the more fundamental and universal features of interactions. Chemistry tends to concentrate on matter at the molecular level. Biological sciences deal with living matter. Geology focuses on the processes that shape the features of our planet. Physics, on the other hand, has as its focus the study of the universal and fundamental interactions of all matter, from the atomic and sub-atomic scale to the interactions of matter across the expanse of our universe. And, as far as we know, all of the laws and principles which govern the interactions of matter are indeed universal. Whether it is the matter participating in the formation of some distant galaxy, the matter making up the living cells of our bodies, or the churning matter that makes up the outer core of our planet earth, the basic interactions of all of this, and indeed all matter in the universe, are the same. In fact, as physicists generally describe them, there are only four fundamental interactions, and three of these are related, according to our current models. Whether the fourth, gravity, with which we are all familiar, is also related to the other three is yet to be known.

A major goal of this course is to help you develop a useful understanding of some of the models, theories, and approaches to understanding matter and its interactions that physicists have found so useful. Many of these models and approaches are directly applicable to your studies in other sciences, and frequently, to your everyday life as well. Another goal is to help you become accustomed to constructing scientific models yourself. We explicitly structure the course to encourage this.

The word model in the previous paragraph deserves special attention. While we use this word in everyday language in several different ways. We need to agree on what we mean by the word model in a scientific context.

Another word that we frequently use in everyday language is energy. The scientific meaning of energy is rather tricky to convey in a sentence or two. There is a good reason for this: energy is an abstract concept that scientists finally figured out about 150 years ago. Although the concept of energy is truly universal, in that energy changes occur in nearly all phenomena, energy is not closely related to a specific property of matter. For example, we all have an intuitive sense of "hotness" and we associate the concept of temperature with this property of matter. We associate the concept of force with the intuitive ideas of push and pull. Energy, on the other hand is associated with many different properties or conditions including temperature, force, motion, atomic level, mass, charge, and on and on. Partly, it is the fact that energy is so universal that makes it so difficult to get a hold of. Historically, several different quantities arose independently, along with their own units of measurement, that were later seen to all be the same thing: energy. Indeed, most introductory physics texts still separately present the concept of mechanical energy and heat, following the historical development.

Another reason energy is difficult to pin down, is that the value of energy itself is seldom of importance; rather it is only the changes in the value of energy that count for anything. In fact, we will see that change in energy is directly related to "how much" interaction occurred.

The third word that we introduce in this block that has many everyday uses, as well as many scientific uses is "system." As is frequently the case in both everyday and scientific language, the particular meaning of a word must be obtained from the context in which it is used. We will, for example, talk about physical systems, energy systems, or particle systems and will sometimes not include the modifier, but simple refer to "the system." Make sure you understand how the word system is being used in particular discussions.

As you will discover, if you haven't already, you are familiar with much if not all of the material we are discussing in this first block. You probably had much of it in your high school chemistry course, and for most of you, in your college chemistry course. You also discussed these same ideas in physical science courses further back in high school and middle school. You need to connect what you are doing now with what you have studied previously, especially in any recent chemistry classes. The concept of energy and the particle model of matter are the same, whether we talk about them in physics or in chemistry. At times, we might put a slightly different spin on some things. You need to build on and enlarge your prior understandings, sometimes modifying them in the process. The worst thing you can do is pigeon hole your knowledge into, for example, "chemistry energy" and "physics energy." How much of the material that we will talk about in these next several weeks can you connect to what you already know? Be ready­it may be necessary to make some adjustments in what you "know." Let's start connecting!

Block 1 Content

We humans have a strong drive to explain things. We invent stories­or models­to help us make sense of our experiences and to know what to expect will happen in the future. A particular culture passes on its stories from one generation to the next. Humans have done this throughout time. Likewise, scientists invent conceptual models in an attempt to understand¬to make sense of¬the natural world and to make predictions that can be tested against the real world. There are several differences between the models of science and the models that we invent or accept from our culture to make sense of our interactions with our environment. These personal or cultural models are often limited in their applicability, are often not logically consistent with other models used by the same individual, and the predictions of these models usually are not rigorously tested against reality. The models of science however, must be (1) logically consistent, (2) the predictions that follow from the models are rigorously tested against reality, and (3) the more generally applicable, the more useful scientific models are. There is one trait, however, that both kinds of models share: generally the simpler they are, the more useful they are.

Because the interactions of the natural world are so complicated, it is very difficult to invent models that are both simple and which satisfy the three criteria mentioned in the preceding paragraph: be logically consistent, be applicable to a large class of phenomena, and have predictions that are rigorously tested against reality. This is the real task of science: to construct conceptual models that are as simple as possible, but yet satisfy the three criteria.

It is sometimes easy to forget that scientists deal with models of reality, and that the models are not reality or even descriptions of reality. It is the assumptions, principles, and predictions of the models that are subject to experimental verification. All of us, including most scientists, get sloppy with our wording and easily slip into using expressions such as, "There are four fundamental forces in nature." What we really should be saying is something like, "In the current model of matter, there are four fundamental forces." Or we might say, "We live in a universe of three spatial dimensions and an independent dimension of time." More precisely we should say, "We model the universe we live in as having three spatial dimensions and an independent time dimension." This model, frequently referred to as a Galilean model of space and time, turns out to be very useful and has a large range of applicability. It certainly is consistent with our daily experience and with experiment, provided we avoid situations in which things move relative to each other at speeds approaching 3 x 108 m/s, the speed of light. Then we must turn to the model (or theory as it is usually called) of special relativity, which is applicable at all relative speeds. In special relativity, space and time get all mixed up together. The "screwy" model of space and time in special relativity is not as simple as our familiar model, but it is applicable to all situations. Does this mean our familiar model is "wrong"? No, definitely not! Models aren't "right" or "wrong", but rather more or less useful and have a greater or lesser range of applicability. In our ordinary experience, and in most typical laboratory situations as well, the predictions made using our familiar model of space and time agree with those of special relativity and with experiment. But if special relativity is "closer to reality," why don't we just forget about the Galilean model and work within the special theory of relativity all the time? Because it is not as useful or as convenient, depending on the situation. As long as we don't confuse models with reality or think they are descriptions of reality, we are free to choose¬or invent¬as simple and useful a model as we can.

The Particle Model of Matter
Let's think for a moment about a very important model: the particle model of matter. When we make a statement such as, "We 'know' that matter is composed of atoms." we really mean that we have a very useful model of ordinary matter, that considers atoms as the appropriate building block. The atomic, or particle model for the small-scale structure of matter was developed over the past few hundred years and goes something like this:

All ordinary matter­solid, liquid, or gas­is made up of tiny particles called atoms. Atoms in turn are made up of tinier particles called protons, electrons and neutrons. The protons and neutrons are massive compared to the electrons, and are stuck together as a nucleus, while the less massive electrons, in some sense, whiz around the nucleus. Why the whole thing doesn't fall apart is a very difficult and important question which was worked out during the first third of this century, and represents one of the greatest intellectual achievements in human history. The ideas and concepts behind this achievement eventually led to a microscopic model of matter we know today as quantum mechanics.

Another important element of our model of matter is that the atoms are in continuous motion­speeding to and fro if in the gaseous state and if in the liquid or solid state, bouncing back and forth against each other. The degree of motion increases with the temperature: the higher the temperature, the greater the motion. One characteristic of this motion is that it is random or disordered. That is, the exact motion of any particular atom is randomly related to the motions of all the other atoms. Our model allows us to make statements only about the average motions of the atoms, not about the detailed motion of any one atom. One very powerful statement is that for a substance in equilibrium, on average, all atoms will have the same energy. We will pursue the consequences of this much further in a couple of weeks.

According to our particle model of matter, as the temperature is lowered, the random jiggling of the atoms should decrease sufficiently so that the bonds between the atoms can lock them into fixed positions relative to each other. We say the substance freezes at this temperature; it becomes a solid. Indeed, at temperatures very close to zero kelvin, all matter, except the element helium, is in the solid state. (Helium remains a liquid unless the pressure is increased 20 or so times above atmospheric. The reason has to do with an interesting feature of quantum mechanics called "zero-point motion") As matter is warmed, the atoms tend to move more and more violently. The stronger the bonds between the atoms, the higher the temperature must be before some of the bonds break and the substance goes into the liquid state. At still higher temperatures, all of the bonds break and the substance goes into the gaseous state.

We will spend time throughout this quarter further developing the particle model of matter described above. We will make much more exact and quantitative the qualitative notions so far described. We will see that we can understand and explain many properties of matter using our particle model of matter.

Systems and Interactions
We are all familiar with phraseology such as the human "circulatory system." We are using the word "system" to designate those organs and parts of the body that are directly involved in continuously circulating blood throughout the body. In this sense, "system" indicates parts that work together to perform a task, but are not necessarily physically close to each other. At other times, we might refer to our solar system. Here, "system" refers to those objects, the sun, the planets and their moons, that are mutually attracted to each other by the gravitational force. You can probably think of many other common examples of the use of the word "system." In all cases, there is something that relates the parts. It might be the purpose they serve. It might be that they interact in a certain way. The "parts" might be actual physical entities, as in "highway system" or much less concrete, as in "legal system."

We will now get rather precise about two ways we use the word "system:" One is very physical and one much more abstract. By "physical system," we mean a group of material objects that are in close proximity. We choose the boundaries of our system to clarify the interactions that the system experiences with the rest of the universe. A physical system is a piece of the universe, some matter, which is thought of as separate from the rest of the universe. In fact, it is the interactions of the system with the rest of the universe that are critical. We specifically choose our systems so that we can focus on the changes that occur to a system as a result of its interactions with the rest of the universe.

An example of a physical system is a bowling ball hanging from a cable in the physics lecture hall: the "bowling ball system". We can focus on the changes that occur in the bowling ball system as it interacts with the rest of the universe. Often it is convenient to divide the rest of the universe up into one or more systems as well. The lecturer might interact with the bowling ball, by, for example, giving it a push. The bowling ball is also interacting with the Earth through the pull of the Earth and with the air in the lecture hall. Thus we might decide to focus on two systems, the bowling ball and lecturer system and lump everything else into the environment system.

We can diagram interacting physical systems by putting circles around pictures or names of the physical objects. The example discussed at the end of the preceding paragraph might be diagrammed as shown in the figure.

Diagram of a physics lecturer interacting with a hanging bowling ball. Two specific physical systems have been defined.

The arrows in this diagram represent interactions: the lecturer pushing the ball, the lecturer standing on the floor and pushing against it, the Earth pulling on the ball, and the air friction between the moving ball and the air in the room.

How do you know what to include in the system? Why couldn't we choose the lecturer and the ball as one system? Answer: We could. We choose system boundaries to study the interactions we are interested in pursuing. If we choose the lecturer and ball as one system, then we would not be focusing on the interactions between the ball and the lecturer. What we include in a system depends on what we are interested in at that time.

What is the purpose of all this attention to systems? It is to give us some help in thinking about interactions between identified chunks of matter. Let's pursue this line of reasoning a little further. In our example, what happens when the lecturer pushes on a motionless bowling ball hanging from the ceiling? The bowling ball changes. The ball starts to move. It begins swinging back and forth. The interaction between the bowling ball system and the lecturer system has caused a change to occur in the bowling ball system. What about the lecturer system? Did a change occur in that system as well. It is not so obvious. But consider what would happen if the lecturer pushed the bowling ball for a long period of time. Her muscles would become tired. That is a change, even if it is of an entirely different nature from the very visible change of the bowling ball.
It is not at all obvious to us, and certainly was not to the early physicists who figured this out initially. There is something about the change in the lecturer that is directly related to the change of the bowling ball. That something is change of energy. Let's simplify the situation for a moment. (We could say we are making a simpler model.) Suppose the only interaction of significance is between the bowling ball and the lecturer. (It turns out that this simpler model is OK, as long as we focus only on the time before the push and immediately after, before the ball has traveled very far.) Then the diagram would appear like this.

Diagram of a physics lecturer interacting with a hanging bowling ball with the assumption that the interactions of each system with the rest of the universe are negligibly small.

In this simplified model we can say that the amount of change that occurs in the lecturer system is exactly the same as the amount of change in the bowling ball system, but in the opposite direction. What is this construct we have just called "amount of change?" It is change of energy. So the statement becomes, "The change in energy of the lecturer system is exactly equal in magnitude and opposite in sign to the change in the bowling ball system." Why should this be? Why should there be something that we invent in our minds that has this property? There is in fact a profound reason for such a conserved quantity. It has to do with time being uniform. Clocks won't run faster tomorrow than they did yesterday. But this is not why scientists "believe" there is such a thing as energy and that it has this property. Rather, it is because we have always been able to find an appropriate energy function and are able to calculate energy changes for any systems that interact. And we always finds that "it works!"

Let's consider another example. If a hot object is placed in contact with a cold object, the temperature of the cold object rises while the temperature of the hot object falls. If the two objects were separated and wrapped with insulating material so that they did not interact with each other or with the surrounding environment, they would maintain constant temperature. Now, when the objects interacted, some energy passed from one to the other. When they were isolated from each other, no energy was transferred. The evidence of an interaction having taken place was the observable change in temperature of each object. So one useful way to think about energy is the following:

The change in energy of a system is a measure of the strength of its interactions with other systems.

Energy is an abstract mental construct that we use to describe interactions. It is not "real" in the sense that matter seems "real" to us. We cannot pick up a piece of energy like we can pick up a piece of matter. When we observe a physical event we model it in terms of interacting systems, and we characterize the interactions by a quantity called energy.

However, when we talk about the interactions of systems we often refer to energy as something tangible. We say that energy is transferred from one system to another. We use the phrases "adding energy to a system," or "energy leaves the system" as if energy were a person walking through a doorway. We say that a system "has a lot of energy", when really what we mean is that the system could greatly affect the behavior of another if they were to interact. So long as we do not forget that energy is an abstraction which describes interactions there is no harm in speaking of it as a tangible thing, and as we all become more comfortable with the concepts of systems, interactions and energy we will take greater liberties with our language.

Not only is energy not tangible, but we can detect only changes in the energy of a system. For instance, the effect of adding energy to a pot of water is to raise its temperature, or perhaps cause the water to boil. We know that the energy of the system changed because observable changes occurred in the system: the temperature changed or the water boiled. The change in energy of the system is determined by the change in temperature or state of the matter.

Energy takes many forms.
Consider a baseball. Think of all the ways to add energy to it. Heat it in an oven. Throw it. Spin it on the table top. When adding energy to the baseball in each of these ways, we change it. It was cold, now hot. It was motionless, now moving through the air. It was motionless, now spinning. Humans have an urge to name things. So, we give different names to the energy that was transferred to the ball in these three examples. Because energy tends to manifest itself in different ways, we have historically given different names to these different manifestations. In our three examples, we would say we increased the ball's thermal energy, its translational kinetic energy, and its rotational kinetic energy. We are familiar with many other manifestations of energy: chemical, nuclear, electrical, gravitational, etc.

A useful way to think about this is that the "form of energy" acts as a label for the particular kind of interaction between systems. In this way we say that there are thermal interactions, chemical interactions, electrical interactions, mechanical interactions and so forth. We will find that these various forms of energy and the associated interactions are actually manifestations of a few fundamental interactions -- namely, electrical, gravitational, and nuclear.

As we discussed previously, we divide the universe into systems and think about the transfer of energy between parts of the universe as an exchange of energy between systems. In this case "exchange" doesn't necessarily mean "fair trade." A system can give up some of its energy to another without getting anything in return. So when we say "systems exchange energy," some systems might increase, some decrease, and some stay the same.

Clarification of Some Specific Energy Terms
To help in communication among ourselves, we make a couple of technical definitions regarding the familiar and common word "heat". In everyday use, we use the word "heat" several different ways. We might say, "If we heat (1) water on the stove, we've increased its heat (2), or heat content or heat energy." Use (1) is close to how we will use the word "heat". We will use the term "thermal energy" for the meaning (2). Thus we would say, the thermal energy of the water was increased as energy was transferred to it in the form of heat from the hot burner.

Heat is the transfer of energy from one thermal energy system to another thermal system due to a temperature difference. On a macroscopic scale, heat is one way of transferring energy between systems. (The other way, that we will discuss shortly, is called work, which, is every transfer that is not heat.)

Thermal energy is the energy associated with the random jiggling of particles that make up matter. Thermal energy increases with temperature and the number of particles in the system. We will make this much more precise shortly.

A Very Important Notion about Energy

Energy Can Be Transferred or Transformed, But It Does Not Disappear

We should be comfortable now with the idea that energy is a measure of interactions, and so we can begin to use the conventional language that describes energy as a thing.

When a moving billiard ball collides with a stationary billiard ball, the moving ball slows down (perhaps even stops), while the still one begins moving. We say that some of the energy from the moving ball is transferred to the stationary one.

When I throw a baseball straight up into the air, at the top of its trajectory it slows down, comes to a brief stop, and then picks up speed on its way back down to earth. We say that, while the baseball is slowing down, its energy which characterizes its motion relative to the earth decreases, while the energy which characterizes its gravitational interaction with the earth increases. In less careful language, the ball's kinetic energy is transformed into gravitational energy. On the return trip the opposite occurs.

When I drive a nail into a piece of wood, the energy of motion of the hammer disappears and is used to heat up and deform the nail and wood. The energy is still there, somewhere, in the motion and electrical interactions of the particles which make up the nail and wood.

Regardless of the language used, the point is clear: Energy does not disappear. If we see that the energy characterizing some aspect of a system has decreased, we can be sure that some other aspect of the same system has increased in energy, or that some energy has left the system and entered another system.

Energy cannot leave one system without appearing in another system.

This is often referred to as the principle of conservation of energy.

Energy Systems We previously defined physical system and indicated how we could diagram interactions among the physical systems. It is useful to distinguish between a physical system and an energy system. An example will help to clarify what we mean by energy system and the distinction between energy and physical system.

Let's consider the bowling ball hanging in lecture. What kinds of energy changes can occur involving the ball? Assuming it is not changed chemically and is left intact, there are three possibilities. Associated with each kind of energy change is a physical change, so another way to think about the question is what kinds of physical changes can happen. The ball can be warmed by holding something hot against it. This would cause a change in its thermal energy, or thermal energy system. If pushed, the ball will gain a certain velocity, a change in its kinetic energy system. As the ball swings, it gradually comes to a stop as its height is raised slightly relative to the floor. The ball now has more gravitational energy. As the ball starts to swing back, gravitational energy is transformed into kinetic energy.

Let's consider each of the kinds of energy the bowling ball can have as separate energy systems. It is then helpful to make an energy-interaction diagram that explicitly shows the transfers of energy among the various energy systems. In our example we identified three systems directly involving the bowling ball. Are there other systems that the ball interacts with that we should include. If the lecturer pushes the ball, we should include that as a separate system. We mentioned previously that the swinging ball eventually comes to rest because there is some air friction. Let's make an energy-interaction diagram for each part of the process, from pushing the ball to get start it moving to its eventual coming to rest.

Consider first the interaction between the lecturer and the ball as she cups her hands around the ball, warming it with her hands. Which systems will be involved in energy transfers? The lecturer and the thermal system of the ball. Perhaps a small amount of energy will move from the thermal system of the ball to the environment. The temperature of the ball change as a result of the interaction. An arrow labeled with a Q, for heat, shows the transfer of energy. The change in the thermal system is indicated on the diagram.

Thermal interaction only

Next consider the lecturer pushing the ball.

Transfer of energy as work as lecturer pushes ball

Now the energy transfer from the lecturer is to the kinetic energy system as the push of the lecturer increases the speed and kinetic energy of the ball.

After the ball has been set in motion, it swings to and fro, gradually "losing" energy to the environment.

As ball swings back and forth, energy is transferred back and forth between kinetic and gravitational energy systems. Energy is slowly transferred to the environment.

(We might have also included in our model a transfer of a small amount of energy from the kinetic energy system to the thermal energy of the ball.)

We can make some general observations about drawing energy-interaction diagrams from these three.

Drawing Energy-Interaction Diagrams

Relation to Conservation of Energy
How do the previous energy-interaction diagrams indicate conservation of energy? The diagrams depict our model of the systems form an interactions and energy viewpoint. When we compare the predictions of the model with actual measurements, we might find that we left out an energy system, or that some energy transfer we thought was negligible is significant. Then we would have to improve the model. But within the models as we construct them, conservation of energy means that decreases in one system, must equal increases in energy in another system(s). So, in the first example, the lecturer system must have lost the exactly the same amount of energy as appears as an increase in the thermal system of the bowling ball. In the second example, the decrease in energy of the lecturer as she pushes the ball, must exactly equal the increase of the kinetic energy system of the bowling ball. In the last example, decreases in one system equal increases in the other, but gradually these increases and decreases diminish as energy is transferred to the environment.

The advantage of having an energy-interaction diagram in mind when thinking of energy conservation is that it helps to see explicitly what energy transformations and or transfers are taking place. With a diagram in front of you, it becomes very easy to write down appropriate algebraic equations to actually solve for unknown quantities.

Some Macroscopic Properties of Matter
How do we characterize a piece of matter? First and most obviously we can measure its mass, a measure of the amount of matter present. Second, there is its size­length, for instance, or volume. These are not useful for making generalizations, though, since they are measures of a particular chunk of matter. From them we can find an object's density, which measures how much matter is in a given volume, or equivalently how much space a given mass of matter occupies:

where the Greek letter rho is used to denote density, m is mass and v is volume.

Right now, we are interested in the thermal properties of matter. We have noticed that the temperature of matter changes as we heat it. The temperature change for a given amount of heating seems to be different for different types of matter. We can characterize this differencein temperature change for a given amount of heating with a single parameter. We call this parameter the heat capacity. It is useful to define a specific heat. or specific heat capacity, usually denoted by the letter c. The relation between heat added or removed (Q), the mass of an object (m), its specific heat (c) and the change in temperature of the object (T) is:

Notice that this is a linear relation. That is, it has the form y = m x , where the dependent variable (y or T) depends on the first power (hence linear, not quadratic, cubic etc.) of the independent variable (x or Q). We can also define a molar specific heat. The usefulness of molar specific heat is that we easily compare specific heats of different substances to models of specific heat that depend on the number of particles explicitly, but not on mass. We will return to this in several weeks.

Another thermal property is latent heat. Latent heat is the amount of energy that must be added (or removed) as a substance changes phase while remaining at a constant temperature. For example, to melt ice, the ice must first be warmed to 0 C. Then, additional heat must be added to break bonds between the water molecules. The ice/water remains at 0 C during this process. The latent heat of a substance is given as the amount of energy per mass or as energy per mole of substance. The symbol L is usually used to designate latent heat.

Suppose we made an energy-interaction diagram for the example of melting ice. What energy systems are involved? As the ice is warmed to 0 ūC, the energy of the thermal system of the ice increases. But what happens when the ice reaches 0 C and begins to melt. The temperature doesn't change, so energy can't be increasing in the thermal system. Where is the energy going? There must be another system. The energy has to go somewhere. There must be a new energy system. We can define a bond energy system that increases in energy as bonds between water molecules are broken. To freeze water, we would have to remove energy from the bond system as bonds were formed.

Heating ice at 0 C. Heat from an external source is supplied goes into the thermal system of the ice, but does not raise its temperature, because it is all passed on through to the bond system.

Units for Energy We have not yet talked about units for anything. We can't put it off any longer. Since all energy is the same, all the ways of measuring energy must be related. The SI unit for energy is the joule (J) (rhymes with cool). The SI unit for mass is kilogram (kg). The SI unit for temperature is the kelvin (K). Note that the kelvin is the same size as the Celsius degree, so when talking about temperature differences, it is convenient to use Celsius degrees for T. Thus the SI unit for specific heat is J/kg K, which will often be written J/kgC.

Some common energy units and their conversions are listed here.

1 J = 107 erg = 0.7373 ft*lb = 9.869 L*atm

1 kW*h = 3.6 MJ

1 cal = 4.184 J

1 Cal (food Calorie) = 103 cal

1 eV = 1.602 x 10-19 J

1 BTU = 778 ft*lb = 252 cal = 1054 J

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page created: 30-Sep-96
Lawrence B. Coleman, Department of Physics, University of California, Davis
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