10 Energy and Work A greyhound can rapidly go from a standstill to a very speedy run—meaning a very rapid increase in kinetic energy, the energy of motion. How does the greyhound’s ability to convert energy from one form to another compare to that of other animals? LOOKING AHEAD ▶▶ Forms of Energy Work and Energy Conservation of Energy This dolphin has lots of kinetic energy The woman does work on the jack, applying As they slide, their potential energy as it leaves the water. At its highest a force to the handle and pushing it down. This decreases and their kinetic energy increases, point its energy is mostly potential is a transfer of energy into the system, increas- but their total energy is unchanged: It is energy. ing the potential energy as the car is lifted. conserved. You’ll learn about several of the most You’ll learn how to calculate the work done How fast will they be moving when they important forms of energy—kinetic, potential, by a force, and how this work is related to the reach the bottom? You’ll use a new before- and thermal. change in a system’s energy. and-after analysis to find out. GOAL To introduce the concept of energy and to learn a new problem-solving strategy based on conservation of energy. LOOKING BACK ◀◀ Motion with Constant Acceleration In Chapter 2 you learned how to au STOP TO THINK describe the motion of a particle vu that has a constant acceleration. A car pulls away from a stop sign with a constant acceleration. After In this chapter, you’ll use the A particle’s final velocity is traveling 10 m, its speed is 5 m/s. What will its speed be after traveling constant-acceleration equations related to its initial velocity, 40 m? to connect work and energy. its acceleration, and its displacement by A. 10 m/s B. 20 m/s 2 2 C. 30 m/s D. 40 m/s v v 2a x x f = x i + x ∆ 1 2 1 2 318 CHAPTER 10 Energy and Work 10.1 The Basic Energy Model Energy. It’s a word you hear all the time. We use chemical energy to heat our homes and bodies, electric energy to run our lights and computers, and solar energy to grow our crops and forests. We’re told to use energy wisely and not to waste it. Athletes and weary students consume “energy bars” and “energy drinks.” But just what is energy? The concept of energy has grown and changed over time, and it is not easy to define in a general way just what energy is. Rather than starting with a formal definition, we’ll let the concept of energy expand slowly over the course of several chapters. In this chapter we introduce several fundamental forms of energy, including kinetic energy, potential energy, and thermal energy. Our goal is to under- stand the characteristics of energy, how energy is used, and, especially important, how energy is transformed from one form into another. Understanding these transforma- tions will allow us to understand and explore a wide variety of physical phenomena. Anything that happens involves a transformation of energy from one form to another, so the range of topics we’ll consider in this chapter is extensive. In solving problems, we’ll use a key fact about energy: Energy is neither created nor destroyed: If one form of energy in a system decreases, it must appear in an equal amount in another form. Many scientists consider this law of conservation of energy to be the most important of all the laws of nature. Systems and Forms of Energy FIGURE 10.1 A system and its energies. In Chapter 9 we introduced the idea of a system of interacting objects. A system can be as simple as a falling acorn or as complex as a city. But whether simple or com- A system can have many System boundary plex, every system in nature has associated with it a quantity we call its total energy E. dierent kinds of energy. The total energy is the sum of the different kinds of energies present in the system. System In the table below, we give a brief overview of some of the more important forms of K, Ug, Us, Eth, Echem, c energy; in the rest of the chapter, we’ll look at several of these forms of energy in greater detail. E K U U E E c = + g + s + th + chem + A system may have many of these kinds of energy at one time. For instance, a moving car has kinetic energy of motion, chemical energy stored in its gasoline, The total energy E is the sum of thermal energy in its hot engine, and many other forms of energy. FIGURE 10.1 illus- the energies present in the system. trates the idea that the total energy of the system, E, is the sum of all the different energies present in the system: E = K + Ug + Us + Eth + Echem + g (10.1) The energies shown in this sum are the forms of energy in which we’ll be most inter- ested in this and the next chapter. The ellipses ( g) stand for other forms of energy, such as nuclear or electric, that also might be present. We’ll treat these and others in later chapters. Some important forms of energy Kinetic energy K Gravitational potential energy Ug Elastic or spring potential energy Us Kinetic energy is the energy of motion. All Gravitational potential energy is stored Elastic potential energy is energy stored moving objects have kinetic energy. The energy associated with an object’s height when a spring or other elastic object, such as heavier an object and the faster it moves, above the ground. As this coaster ascends, this archer’s bow, is stretched. This energy the more kinetic energy it has. The wreck- energy is stored as gravitational potential can later be transformed into the kinetic ing ball in this picture is effective in part energy. As it descends, this stored energy energy of the arrow. because of its large kinetic energy. is converted into kinetic energy. Continued 10.1 The Basic Energy Model 319 Thermal energy Eth Chemical energy Echem Nuclear energy Enuclear Hot objects have more thermal energy Electric forces cause atoms to bind The forces that hold together the particles in than cold ones because the molecules in a together to make molecules. Energy can the nucleus of the atom are much stronger hot object jiggle around more than those in be stored in these bonds, energy that can than the electric forces that hold together a cold object. Thermal energy is the sum later be released as the bonds are rear- molecules, so they store a great deal more of the microscopic kinetic and potential ranged during chemical reactions. All energy. Certain nuclei break apart into energies of all the molecules in an object. animals eat, taking in chemical energy to smaller fragments, releasing some of this provide energy to move muscles and fuel nuclear energy. The energy is transformed processes of the body. into the kinetic energy of the fragments and then into thermal energy. Energy Transformations If the amounts of each form of energy never changed, the world would be a very dull place. What makes the world interesting is that energy of one kind can be trans- formed into energy of another kind. The following table illustrates a few common energy transformations. In this table, we use an arrow S as a shorthand way of representing an energy transformation. Some energy transformations A weightlifter lifts a barbell over her head The barbell has much more gravitational potential energy when high above her head than when on the floor. To lift the barbell, she transforms chemical energy in her body into gravitational potential energy of the barbell. Echem S Ug A base runner slides into the base When running, he has lots of kinetic energy. After sliding, he has none. His kinetic energy is transformed mainly into thermal energy: The ground and his legs are slightly warmer. K S Eth A burning campfire The wood contains considerable chemical energy. When the carbon in the wood combines chemically with oxygen in the air, this chemical energy is transformed largely into thermal energy of the hot gases and embers. Echem S Eth A springboard diver Here’s a two-step energy transformation. At the instant shown, the board is flexed to its maximum extent, so that elastic potential energy is stored in the board. Soon this energy will begin to be transformed into kinetic energy; then, as the diver rises into the air and slows, this kinetic energy will be transformed into gravitational potential energy. Us S K S Ug 320 CHAPTER 10 Energy and Work FIGURE 10.2 Energy transformations FIGURE 10.2 reinforces the idea that energy transformations are changes of within the system. energy within the system from one form to another. (The U in this figure is a generic potential energy; it could be gravitational potential energy Ug, spring poten- KU tial energy Us, or some other form of potential energy.) There are two types of arrows in the figure. The arrow between K and U is a two-way arrow; it’s easy to transform energy back and forth between these forms. When the springboard diver Echem goes up in the air, his kinetic energy is transformed into gravitational potential energy; when he comes back down, this process is reversed. But the arrow between Eth K and Eth is a one-way arrow pointing toward Eth.