4 Conservation of Energy

Transcription

1 CHAPTER 13 4 Conservation of Energy SECTION Work and Energy KEY IDEAS As you read this section, keep these questions in mind: How can energy change from one form to another? What is the law of conservation of energy? How much of the work done by a machine is useful work? What is efficiency? How Can Energy Change from One Form to Another? Imagine you are sitting in a roller coaster car. A conveyer belt pulls the car slowly up the first hill. When you reach the top of the hill, you are barely moving. Then the car goes over the top, and you race down the hill. You speed faster and faster down the hill to the bottom. You continue moving up and down through smaller hills, twists, and turns until you coast to the end. READING TOOLBOX List As you read this section, make a list of real-life examples that demonstrate the law of conservation of energy. This roller coaster, like many others, relies on the fact that energy is conserved to move riders up and down hills. 1. Identify Where does the roller coaster car have the most gravitational potential energy? During your roller coaster ride, energy changes from one form to another many times. All of the energy required for the whole ride comes from the conveyer belt on the first hill. It does work as it lifts the car and passengers up the hill. The energy from that work is stored as gravitational potential energy at the top of the hill. Before the ride is over, the energy changes from potential energy into kinetic energy and back again several times. In addition, a small amount of the stored energy is transferred to the wheels as heat. Some energy also makes the air vibrate and creates the roaring sound. The energy changes easily from one form to another, but the total amount of energy always remains the same. Interactive Reader 289 Work and Energy

2 2. Identify On the figure, circle the location at which the roller coaster car has the least gravitational potential energy. The energy of a roller coaster car changes from potential energy to kinetic energy and back again many times during a ride. Discuss In a small group, identify several situations in everyday life in which an object s energy changes from one form to another. For each situation, identify the different types of energy the object has at different times. 3. Explain Why can t a roller coaster ride continue forever? POTENTIAL ENERGY TO KINETIC ENERGY AND BACK At the top of a hill, all the energy of a roller coaster car is potential energy. The potential energy slowly changes to kinetic energy as the car accelerates down the hill. At the bottom of the hill, almost all of the potential energy has changed to kinetic energy. However, the system has the same total energy whether the car is at the top or bottom. This kinetic energy of the car at the bottom of the hill can carry the car up another smaller hill. As the car climbs the hill, the car slows down and its kinetic energy decreases. Where does that energy go? Most of it turns back into potential energy. At the top of the smaller hill, the car still has some kinetic energy, along with some potential energy. The kinetic energy carries the car forward over the top of the hill. This process continues to the end of the ride potential energy to kinetic energy and back again. Remember that the initial energy for the ride came from the work the conveyer belt did to lift the car. The roller coaster cannot climb a hill as tall or taller than the first hill without more work being done. The car does not have enough energy. The car also cannot glide on forever. If the changes from potential energy to kinetic energy were complete, the roller coaster ride would never have to end. Where does the energy go? It is transformed into other forms of energy. Interactive Reader 290 Work and Energy

3 MECHANICAL ENERGY TO OTHER FORMS OF ENERGY Imagine dropping a tennis ball on the ground. With each bounce, the ball loses height. Eventually, it stops bouncing. If no energy were lost, the ball would bounce to its starting height forever. The ball stops bouncing because not all of its kinetic energy changes to elastic potential energy when it bounces. With each bounce, the ball loses some of its mechanical energy. 4. Apply Concepts Identify two forms of potential energy that the tennis ball has. At the top of a bounce, the ball s kinetic energy is zero. All of its kinetic energy has been converted to potential energy. When the ball hits the ground, some of its kinetic energy is changed into sound and heat. 5. Identify On the figure, circle a place where the ball has both kinetic and gravitational potential energy. Is the energy really lost? When the ball bounces, some of its kinetic energy compresses the air around the ball, which makes a sound. Some of the kinetic energy also heats the ball, air, and ground. Sound and heat are forms of nonmechanical energy. In most cases, when it seems that an object has lost mechanical energy, the energy has just changed form. Similarly, a moving roller coaster car loses mechanical energy as it rolls, because of friction and air resistance. This energy is not lost. Some of it increases the temperature of the track, the car s wheels, and the air. Some of the energy compresses the air around the wheels and causes a roaring sound. The car s mechanical energy has not disappeared. Some mechanical energy has just changed to nonmechanical forms. Interactive Reader 291 Work and Energy

4 GRAPHING MECHANICAL ENERGY Graphs are a useful way to show relationships between variables. The bar graph below presents data about the mechanical energy of a roller coaster car. Graphing Skills 6. Read a Graph At which location does the roller coaster car have the most kinetic energy? 7. Identify Name two things about the roller coaster car that you cannot learn by examining the graph. Mechanical Energy of a Roller Coaster Car Total mechanical energy (kj) If the roller coaster car did not lose energy to friction, its total energy would stay the same throughout the ride. It would change from kinetic to potential energy and back again. A B C D Location Kinetic energy Potential energy Use the steps below to learn about the relationship between potential and kinetic energy that is illustrated in the graph: Step 1: Study the axes to determine the variables being plotted. x-axis variable: location y-axis variable: mechanical energy Step 2: Identify the dependent and independent variables. Location is the independent variable, because location does not depend on the energy of the car. Kinetic and potential energy are the dependent variables, because the car s energy depends on its location. Step 3: Examine the legend and decide what it tells you about how it relates to the graph. The legend indicates that mechanical energy consists of both kinetic and potential energy. Step 4: Examine the graph to decide what the data tell you about the relationship between kinetic and potential energy. The graph shows that total mechanical energy stays the same. An increase in kinetic energy produces an equal decrease in potential energy. A decrease in kinetic energy produces an equal increase in potential energy. Interactive Reader 292 Work and Energy

5 What Is the Law of Conservation of Energy? The energy present in a roller coaster car at the beginning of the ride is present throughout the ride. The same amount of energy is present at the end of the ride, even though the energy has changed form. The energy of a bouncing ball changes form, but none is lost. The work done on a machine is equal to the work it can do. These simple observations are based on one of the most important principles in science the law of conservation of energy. Simply put, the law of conservation of energy states that energy cannot be created or destroyed. In other words, the total amount of energy in the universe never changes. Energy may change from one form to another, but energy never disappears. Mechanical energy can change to nonmechanical forms of energy, such as heat, light, and sound. Energy in a system may move into the surrounding environment, but the total amount of energy does not change. Energy does not disappear. 8. Describe What does the law of conservation of energy state? When fireworks explode, chemical potential energy is converted into other kinds of energy. However, the total energy of the system remains the same. 9. Identify What are two kinds of energy that the chemical energy in fireworks changes into? Energy also cannot be created from nothing. The total energy in a system can increase only if energy enters the system. Energy can enter a system by doing work on a system. Imagine a boy bouncing on a trampoline. His second bounce is higher than his first bounce. How could his second bounce be bigger? Because energy cannot just appear from nowhere, he must have added energy by doing work with his legs. Interactive Reader 293 Work and Energy

6 10. Explain Why is it impossible to consider all the energy in the universe when doing energy calculations? OPEN AND CLOSED SYSTEMS If we had to include all the energy in the universe during energy calculations, the calculations would be impossible. Therefore, to make studying a process easier, scientists often limit their view of the world. They may decide to study only a small area or small number of objects. Scientists call such small parts of the universe systems. System Boundary Surroundings Brainstorm In a small group, think of different processes or events that scientists may study. For each case, identify an appropriate system for a scientist to use. What objects or processes should be within the system? What objects or processes do not have to be included? 11. Compare How is a closed system different from an isolated system? A system is the object or group of objects that are being studied. A system is separated from its surroundings by a boundary. A system might include a gas burner and a beaker of water. A scientist could study the flow of energy from the burner to the beaker of water. There is also energy in the room from the lights and heat. However, the scientist can ignore this energy because she has defined her system as the burner and the beaker. Scientists describe systems based on whether matter and energy can flow across their boundaries. An open system is a system that can exchange both matter and energy with its surroundings. A closed system is a system that can exchange energy, but not matter, with its surroundings. An isolated system is a system that cannot exchange matter or energy with its surroundings. Interactive Reader 294 Work and Energy

7 THERMODYNAMICS AND ENERGY CONSERVATION Thermodynamics is the study of how energy moves during different processes. The process may be bouncing a ball, sanding wood, riding a roller coaster, or a plant converting sunlight into food. Thermodynamics can describe the movements of energy in each of these situations. Remember that work can transfer energy from one object to another. When you lift a ball, you do work on it. The ball gains potential energy. Energy can also be transferred as heat. For example, when you place a piece of bread in a toaster, energy moves from the toaster to the bread. The energy causes the bread to heat up. In any closed system, a change in energy must be caused by work or heat being gained or lost. When no energy is transferred as work or heat, energy is conserved. This form of the law of energy conservation is called the first law of thermodynamics. What Is Useful Work? We use machines to make work easier, but only part of the work done by any machine is useful work. Useful work is work that a machine is designed to do. For example, suppose you want to raise the sail on a sailboat. You can raise the sail with a pulley, but you must do work against the force of friction in the pulley. You also must lift the added weight of the rope and hook connected to the sail. As a result, only some of the energy that you transfer to the pulley is available to raise the sail. Therefore, only some of the work the pulley does to lift the sail is useful work. 12. Define What is thermodynamics? 13. Define What is useful work? 14. Identify What happens to the energy you put into the pulley that is not used to raise the sail? The pulleys on a sailboat can do work. However, like all machines, not all the work they do is useful work. Interactive Reader 295 Work and Energy

8 15. Explain Why is the work done by a machine always less than the work put into it? What Is Incidental Work? Work that a machine does that does not serve its intended purpose is incidental work. Think again of the pulley on the sailboat. There is friction between the rope and the pulley. This friction causes some of the work you put into the rope to change into heat. The heat does not help to raise the sail, so it is incidental work. In addition, some of the energy in the pulley causes air to vibrate, producing sound. This is another form of incidental work. Because of friction and other factors, only some of the work of any machine is applied to its intended purpose. The useful work done by a machine is always less than the total work put into it. EFFICIENCY The efficiency of a machine is a measure of how much useful work the machine can do. Efficiency is the ratio of useful work output to total work input. The mathematical equation for efficiency is: useful work output efficiency work input Efficiency is usually expressed as a percentage. You can use the equation below to calculate percent efficiency: useful work output % efficiency 100 work input 16. Describe If a machine were 100% efficient, how much work could you get out of it? A machine that is 100% efficient would produce exactly as much useful work as the work done on the machine. However, every machine has some friction, so no machine is 100% efficient. Because no machine is 100% efficient, all machines need at least a small amount of energy input to keep going. People use machines to make work easier. Because of this, we must always put more energy into a machine than the machine can produce. The more efficient a machine is, the less extra energy we have to put into it. Therefore, scientists and engineers are always trying to design more efficient machines. Interactive Reader 296 Work and Energy

9 CALCULATING EFFICIENCY A student uses a ramp to lift a 150 N box to a height of 2 m. The student uses 400 J of energy to push the box up the ramp. What is the percent efficiency of the ramp? The useful work output of the ramp is the work done on the box. You can calculate the work done on the box using the work equation. Step 1: List the given and unknown values. Step 2: Write the equations. Step 3: Insert the known values and solve for the unknown values. Given: weight, w = 150 N height, h = 2 m work input, = 400 J W = Fd efficiency = Unknown: efficiency useful work output work input W = (150 N) (2 m) W = 300 J = useful work output efficiency = 300 J 400 J efficiency = 0.75 To convert the decimal efficiency to a percent, multiply by 100. This gives the percent efficiency of the ramp: 75%. Math Skills 17. Calculate A sailor uses a rope and an old, squeaky pulley to raise a sail. It takes 140 J of work to lift the sail 1 m. Using the pulley, he must do 180 J of work to raise the sail. What is the percent efficiency of the pulley? Show your work. PERPETUAL MOTION MACHINES Many clever inventors have tried to design machines that will keep going forever without any input of energy. Such a machine is called a perpetual motion machine. However, even with a lot of time and effort, no inventor will ever create a perpetual motion machine. This is because a perpetual motion machine can only work in the absence of friction and air resistance. These conditions are not found in our universe. In theory, a perpetual motion machine is 100% efficient. However, in our universe, perpetual motion machines cannot exist. 18. Explain Why are perpetual motion machines impossible? Interactive Reader 297 Work and Energy

10 Section 4 Review SECTION VOCABULARY efficiency a quantity, usually expressed as a percentage, that measures the ratio of work output to work input 1. Describe State the law of conservation of energy in your own words. 2. Calculate John uses a pulley to lift the sail on his sailboat. The sail weighs 150 N, and he must lift it 4.0 m. The pulley is 50% efficient. How much work must be done to lift the sail? How much work must John do on the rope to lift the sail? Show your work. 3. Calculate A student does 100 J of work on the handle of a bicycle pump. The pump does 40 J of work pushing the air into the tire. What is the efficiency of the pump? Show your work. 4. Apply Concepts Imagine a bouncing ball that does not lose any energy as it bounces. Could it ever bounce to a greater height than it was dropped from? Explain your answer. 5. Explain Why are machines never 100% efficient? 6. Apply Concepts Are living things open or closed systems? Explain your answer. Interactive Reader 298 Work and Energy