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CHAPTERCHAPTER 44
Make a three-tab book. Label it as shown. Use it to organize your notes on energy.
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Concepts in Motion
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Work and EnergyWork and Energy
Launch Lab
Doing Work with a Simple Machine
Did you know that you can lift several times your weight with the help of a pulley? Before the hydraulic lift was invented, a car mechanic used pulleys to raise a car off the ground. In this lab, you will see how a pulley can increase a force.
For a lab worksheet, use your StudentWorks™ Plus Online.
??^ Inquiry Launch Lab
Chapter 4 • Work and Energy 105
THEME FOCUS Energy Energy can be transformed among its many forms, but energy cannot be created or destroyed.
BIG Idea Energy has many forms and can be transferred through work.
Section 1 • Work and Machines
Section 2 • Describing Energy
Section 3 • Conservation of Energy
Force parallel to motion Imagine that you push on the lawn mower in Figure 1 with a force of 25 N and through a distance of 4 m. In what direction would you push to do the maximum amount of work on the mower? You do the maximum amount of work when you push the lawn mower in the same direction as it is moving. When force and motion are parallel, which means they are in the same direction, work is equal to force multiplied by distance.
Work Equation
work (in joules) = applied force (in newtons) × distance (in meters)
W = Fd
If force is measured in newtons (N) and distance is measured in meters (m), then work is measured in joules (J). You do about 1 J of work on a cell phone when you pick it up off the floor.
Section 1 • Work and Machines 107
EXAMPLE Problem 1
Solve for Work You push a refrigerator with a horizontal force of 100 N. If you move the refrigerator a distance of 5 m while you are pushing, how much work do you do?
Identify the Unknown:
List the Knowns:
Set Up the Problem:
Solve the Problem:
Check the Answer:
PRACTICE Problems Find Additional Practice Problems in the back of your book.
1. A couch is pushed with a horizontal force of 80 N and moves a distance of 5 m across the floor. How much work is done in moving the couch? 2. How much work do you do when you lift a 100-N child 0.5 m? 3. The brakes on a car do 240,000 J of work in stopping the car. If the car travels a distance of 40 m while the brakes are being applied, how large is the average force that the brakes exert on the car? 4. Challenge The force needed to lift an object is equal in size to the gravitational force on the object. How much work is done in lifting an object that has a mass of 5 kg a vertical distance of 2 m?
Review Additional Practice Problems
work: W
applied force: F = 100 N distance: d = 5 m
Check to see whether the units match on both sides of the equation. units of W = (units of F) × (units of d) = N × m = J
W = ( 100 N )( 5 m ) = 500 J
W = Fd
SC.912.P.10.3: Compare and contrast work and power qualitatively and quantitatively. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment.
Force perpendicular to motion When you carry books while walking at a constant velocity, you might think that your arms are doing work on those books. After all, you are exerting a force on the books to hold them, and the books are moving with you. Your arms might even feel tired. However, in this case, the force exerted by your arms does zero work on the books. This is because there is a 90° angle between this force on the books and the motion of the books. When a force is perpendicular to motion, the work from that force is zero.
Reading Check Describe the work done on an object when the force on that object and the motion of that object are perpendicular.
Other directions If a force on an object and that object’s motion are parallel, then the work from that force equals that force’s magnitude multiplied by distance. If the force on an object and that object’s motion are perpendicular, then the work from that force equals zero. How much work is done when the angle between force and motion is not parallel or per- pendicular? For these other directions, the work done is less than the force multiplied by the distance but more than zero. Figure 2 shows a graph of how direction affects work. When is work done? Suppose you give a book a push; it leaves your hand and slides along a table for a distance of 1 m before it comes to a stop. The distance that you used to calcu- late the work you did on the book is how far the object moves while you apply a force. Even though the book moved a total of 1 m, you do work on the book only while you touch it. You can only do work on an object while you are applying a force to that object. In Figure 3, the girl only did work on the softball while her hand was in contact with the softball.
Work vs. Angle
0.0 10 20 30 40 50 60 70 80 90
0 Angle between force and motion (°)
Work (J)
108 Chapter 4 • Work and Energy
VOCABULARY
ACADEMIC VOCABULARY Contact union or junction of surfaces Your hand must be in contact with the book to push on it.
■ (^) Figure 2 This graph shows the work done on an object for different angles between force and motion when 1 N is applied to the object and the object moves 1 m. Interpret Graphs At what angle between force and motion is work one-half as much as when force and motion are in the same direction?
■ (^) Figure 3 This pitcher does work on a ball only while that ball is in her hand. After the ball leaves her hand, she is no longer exerting any force on the ball. Identify a force that is doing work on a ball when that ball is falling through the air.
Efficiency Machines can increase force or increase speed. You might think this means that you get more work out of a machine than you put into a machine because work is related to force and motion. However, no machine can increase both force and speed at the same time. In fact, you always put more work into a machine than you get out of that machine. This is a fundamental scientific law that cannot be broken by building better machines. Efficiency is the ratio of output work to input work. Efficiency is often measured in percent.
Efficiency Equation
efficiency (%) = ___ output work^ (in joules) input work (in joules)
× 100
e = _ Wout Win^ ×^100
Machines can be made more efficient by reducing friction. This is usually done by adding a lubricant, such as oil or grease, to surfaces that rub together. However, all machines are less than one hundred percent efficient.
110 Chapter 4 • Work and Energy
EXAMPLE Problem 2
Solve for Efficiency You do 20 J of work in pushing a crate up a ramp. If the output work from the inclined plane is 11 J, then what is the efficiency of the inclined plane?
Identify the Unknown:
List the Knowns:
Set Up the Problem:
Solve the Problem:
Check the Answer
PRACTICE Problems Find Additional Practice Problems in the back of your book.
5. Find the efficiency of a machine that does 800 J of work if the input work is 2,000 J. 6. The input work on a pulley system is 75 J. If the pulley system is 84 percent efficient, then what is the output work from the pulley system? 7. Challenge Workers do 8,000 J of work on a 2,000-N crate to push it up a ramp. If the ramp is 2 m high, then what is the efficiency of the ramp?
Review Additional Practice Problems
efficiency: e
work in: Win = 20 J work out: Wout = 11 J
The work out is about half of the work in. Therefore, an answer close to 50 percent is reasonable.
e = _ 11 J 20 J × 100 e = 55 percent
e = W _ Wout in
× 100
SC.912.P.10.3: Compare and contrast work and power qualitatively and quantitatively. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment.
How are machines useful? How are machines useful if a machine’s output work is always less than its input work? Machines change the way work is done. They can increase speed, change the direction of a force, or increase force.
Increase speed Bicycles are machines that increase speed. A person can travel more quickly on a bicycle than on foot. However, to increase speed, a bicycle decreases force. Look at the cyclist pedaling up the hill in the top panel of Figure 5. He might get to the top more quickly than if he walked, but his legs must apply a larger force to the pedals to get up that hill.
Change direction of force Some machines change the direction of an applied force. The wedge-shaped blade of the ax in Figure 5 is one example. You exert a downward force on an ax to split wood. The blade changes this downward force into outward forces that split the wood.
Increase force A car jack, such as the one in the bottom panel of Figure 5, increases force but decreases speed. The upward force exerted on the car is greater than the downward force that you exert on the handle. However, you move the car jack handle faster than you lift the car. We can describe the effectiveness of a machine at increasing force by its mechanical advantage. Mechanical advantage is the ratio of the output force to input force.
Mechanical Advantage Equation
mechanical advantage = ___ output force^ (in newtons) input force (in newtons) MA = _ Fout Fin
The input force is the force that a person or device such as a motor applies to the machine. The output force is the force that the machine applies to another object. In the car jack example in Figure 5, the man applies an input force to the car jack, and the car jack applies an output force to the car. The mechanical advantage of the car jack is greater than one because the output force is greater than the input force.
Increase Speed
C04 04A 894583
Applied force
Resulting force
Change Direction of Force
Your force Distance you push
Distance car is raised
Force exerted by jack
Increase Force
Section 1 • Work and Machines 111
Concepts in Motion Animation ■ (^) Figure 5 A machine can change work to increase speed, change the direction of a force, or increase force.
LAB Mechanical Advantage and Efficiency
??^ Inquiry Lab^ Chapter 4 •^ Lab^113
YOUR DATA
Compare your results with others in the class. Discuss whether you agree about how you might improve the efficiency of the inclined plane.
Objectives
n Model lifting devices based on an inclined plane. n Calculate the work needed to lift a weight straight up. n Calculate the work needed to pull a weight up an inclined plane. n Calculate mechanical advantage and efficiency for an inclined plane.
Background: Have you ever tried to lift a heavy box onto a truck? If you pushed the box up a ramp, then your job was probably easier. A ramp is an inclined plane. In this lab, you will find the efficiency and mechanical advantage of an inclined plane. Question: How can an inclined plane be used to make doing work easier?
Materials
wooden board, 40 cm long support for board, 10 cm high 1-kg mass spring scale, 0–10 N range
Safety Precautions
1. Read the procedure and safety information, and complete the lab form. 2. Set up your inclined plane. It should be 40 cm long and 10 cm high. 3. Using the spring scale, find how much force is needed to lift the 1-kg mass straight up. This is the output force.
Preparation
Procedure
4. Calculate the work needed to lift the 1-kg mass 10 cm. This is the inclined plane’s output work. 5. Using the spring scale, find how much force is needed to pull the 1-kg mass up the inclined plane. This is the input force. 6. Calculate the work done on the mass as it is pulled up the inclined plane. This is the input work. 7. Using the output force and input force, calculate the mechanical advantage of the inclined plane. 8. Using the output work and input work, calculate the efficiency of the inclined plane. 1. Explain how you might improve the efficiency of your inclined plane. 2. Predict how you might increase the mechanical advantage of your inclined plane. Try it. 3. Identify situations in which an inclined plane would be useful.
Conclude and Apply
SC.912.P.10.3: Compare and contrast work and power qualitatively and quantitatively. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment.
114 Chapter 4 • Work and Energy
Describing Energy
MAIN Idea Energy is the ability to cause change. Real-World Reading Link Think about what is written on the side of a cereal box. The side of the box tells you how many Calories are in each serving. A Calorie is a unit of energy. It takes energy to run, jump, grow, and even think.
Change Requires Energy When something is able to change its surroundings or itself, it has energy. Energy is the ability to cause change. Without energy, nothing would ever change. The moving tennis racket in Figure 6 has energy. That racket causes change when it deforms the tennis ball and changes the tennis ball’s motion. Work transfers energy The tennis racket in Figure 6 also does work on the tennis ball, applying a force to that ball through a distance. When this happens, the racket transfers energy to the ball. Therefore, energy can also be described as the ability to do work. Because energy can be described as the ability to do work, energy can be measured with the same units as work. Energy, like work, can be measured in joules. Imagine that the tennis racket in Figure 6 does 250 J of work on the tennis ball. Then, 250 J of energy are transferred from the racket to the ball. Systems The tennis racket and the tennis ball in Figure 6 are systems. A system is anything around which you can imagine a boundary. A system can be a single object, such as a tennis ball, or a group of objects, such as the solar system. When one system does work on a second system, energy is transferred from the first system to the second system.
Reading Preview
Essential Questions
◗ What is the difference between kinetic energy and potential energy? ◗ How can you calculate kinetic energy? ◗ What are some different forms of potential energy? ◗ How can you calculate gravitational potential energy?
Review Vocabulary work: a force applied through a distance
New Vocabulary energy system kinetic energy potential energy elastic potential energy chemical potential energy gravitational potential energy
gg Multilingual eGlossary
Section 22
■ (^) Figure 6 The tennis racket causes changes to occur when it hits the tennis ball. Describe the changes that are occurring.
SC.912.P.10.1: Differentiate among the various forms of energy and recognize that they can be transformed from one form to others. ALSO COVERS: MA.912.S.1.
Kinetic energy When you think of energy, you might think of objects in motion. Objects in motion can collide with other objects and cause change. Therefore, objects in motion have energy. Kinetic energy is energy due to motion. A car moving along a highway and a ballet dancer leaping through the air have kinetic energy. The kinetic energy from an object’s motion depends on that object’s mass and speed.
Kinetic Energy Equation
kinetic energy (in joules) = _^1 2 mass^ (in kg)^ ×^ [ speed^ (in m/s)]
2
KE = _^12 mv^2
If mass is measured in kg and speed is measured in m/s, then kinetic energy is measured in joules. If you drop a softball from just above your knee, the kinetic energy from that ball’s falling motion is about 1 J, just before the ball reaches the floor.
116 Chapter 4 • Work and Energy
EXAMPLE Problem 4
Solve for Kinetic Energy A jogger with a mass of 60.0 kg is moving forward at a speed of 3.0 m/s. What is the jogger’s kinetic energy from this forward motion?
Identify the Unknown:
List the Knowns:
Set Up the Problem:
Solve the Problem:
Check the Answer:
PRACTICE Problems Find Additional Practice Problems in the back of your book.
16. A baseball with a mass of 0.15 kg is moving at a speed of 40.0 m/s. What is the baseball’s kinetic energy from this motion? 17. Challenge A 1,500-kg car doubles its speed from 50 km/h to 100 km/h. By how many times does the kinetic energy from the car’s forward motion increase?
Review Additional Practice Problems
kinetic energy: KE
mass: m = 60.0 kg speed: v = 3.0 m/s
Check the last step by estimating. Round 9.0 m^2 /s^2 upward to 10 m^2 /s^2. Then, _^12 (60.0 kg)(10 m^2 /s^2 ) = 300 J. This is close to 270 J, so the final calculation was reasonable.
KE = _^12 ( 60.0 kg )( 3.0 m/s )^2
KE = _^12 ( 60.0 kg )(9.0 m^2 /s^2 ) KE = 270 J
KE = _^12 mv^2
MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment.
Potential energy Energy does not always involve motion. Even motionless objects can have energy. Potential energy is energy that is stored due to the interactions between objects. One example is the energy stored between an apple hanging on a tree and Earth. Energy is stored between the apple and Earth because of the grav- itational force between the apple and Earth. Another example is the energy stored between objects that are connected by a compressed spring or a stretched rubber band.
Elastic potential energy If you stretch a rubber band and let it go, it sails across the room. As it flies through the air, it has kinetic energy due to its motion. Where did this kinetic energy come from? Just as there is potential energy due to gravita- tional forces, there is also potential energy due to the elastic forces between the particles that make up a stretched rubber band. The energy of a stretched rubber band or a compressed spring is called elastic potential energy. Elastic potential energy is energy that is stored by compressing or stretching an object.
Chemical potential energy The food that you eat and the gasoline in cars also have stored energy. This stored energy is due to the chemical bonds between atoms. Chemical potential energy is energy that is due to chemical bonds. You might notice chemical potential energy when you burn a substance. When an object is burned, chemical potential energy becomes thermal energy and radiant energy. Figure 8 shows the process for burning methane.
Section 2 • Describing Energy 117
■ (^) Figure 8 When methane burns, it combines with oxygen to form carbon dioxide and water. In this chemical reaction, chemical potential energy is converted to other forms of energy.
Interpret Data from a Slingshot
Procedure
- Read the procedure and safety information, and complete the lab form.
- Using two fingers, carefully stretch a rubber band on a table until it has no slack.
- Place a nickel on the table, slightly touching the midpoint of the rubber band.
- Push the nickel back 0.5 cm into the rubber band and release. Measure the distance that the nickel travels with a metric ruler.
- Repeat steps 3 and 4, each time pushing the nickel back an additional 0.5 cm. Analysis
- Describe how the distance that the nickel travels depends on the distance that you stretch the rubber band.
- Infer how the takeoff speed of the nickel depends on the distance that you stretch the rubber band.
- Infer how the kinetic energy from the nick- el’s motion depends on the distance that you stretch the rubber band.
Methane + Oxygen Carbon dioxide + Water
??^ Inquiry MiniLab
SC.912.P.10.1: Differentiate among the various forms of energy and recognize that they can be transformed from one form to others.
Assessment Online Quiz Section 2 •^ Describing Energy^119
EXAMPLE Problem 5
FL Solve for Gravitational Potential Energy A 4.0-k g ceiling fan is placed 2.5 m above the floor. What is the gravitational potential energy of the Earth-ceiling fan system relative to the floor? Identify the Unknown: List the Knowns
Set Up the Problem: Solve the Problem:
Check the Answer:
PRACTICE Problems Find Additional Practice Problems in the back of your book.
18. An 8.0-kg history textbook is placed on a 1.25-m high desk. How large is the gravitational potential energy of the textbook-Earth system relative to the floor? 19. Challenge How large is the GPE of the textbook-Earth system in problem 18, relative to the desktop?
Review Additional Practice Problems
gravitational potential energy: GPE mass: m = 4.0 kg gravity: g = 9.8 N/kg height: h = 2.5 m
Round 9.8 N/kg to 10 N/kg. Then, GPE = (4.0 kg)(10 N/kg)(2.5 m) = 100 J. This is very close to the answer above. Therefore, that answer is reasonable.
GPE = ( 4.0 kg )( 9.8 N/kg )( 2.5 m ) = 98 N • m = 98 J
GPE = mgh
Section 22 Review
A^ pply Math
- MAIN^ Idea^ Describe a change caused by kinetic energy as well as a change that involves potential energy.
- Infer whether a system can have kinetic energy and potential energy at the same time.
- Contrast elastic potential energy and chemical potential energy.
- Think Critically The different molecules that make up the air in a room have, on average, the same kinetic energy. How does the speed of the different molecules that make up the air depend on their masses?
Section Summary ◗◗ Forms of energy include mechanical, elec- trical, chemical, thermal, and radiant energy. ◗◗ Kinetic energy is the energy that a moving object has because of its motion. ◗◗ Potential energy is stored energy due to the interactions between objects. ◗◗ Different forms of potential energy include elastic potential energy, chemical potential energy, and gravitational potential energy.
- Calculate Kinetic Energy A 0.06-kg ball is moving at 5.0 m/s. How large is the kinetic energy from this motion?
- Calculate GPE A 0.50-kg apple is 2.0 m above the reference level. What is the GPE of the apple-Earth system?
SC.912.P.10.1, SC.912.P.10.2, MA.912.S.1.
MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment.
120 Chapter 4 • Work and Energy
Conservation of Energy
MAIN Idea Energy cannot be created or destroyed. Real-World Reading Link When you toss a ball into the air, you give it kinetic energy. This kinetic energy transforms into potential energy as the ball rises and then back into kinetic energy as the ball falls. What happens to the energy when you catch the ball?
The Law of Conservation of Energy Suppose you are riding on a roller coaster like the one in Figure 10. As your height above the ground changes, gravitational potential energy changes. As your speed changes, kinetic energy changes. Think about the motion of the roller-coaster cars. When the cars are high above the ground, GPE is large and kinetic energy is small. When the cars are low, GPE is small and kinetic energy is large. Energy is changing back and forth between GPE and kinetic energy. In addition, some kinetic energy is slowly con- verted into other forms of energy during a roller-coaster ride. However, the total energy remains constant. The law of conservation of energy states that energy cannot be created or destroyed. Energy can only be converted from one form to another or transferred from one place to another.
Reading Check State the law of conservation of energy.
Conserving resources You might have heard about energy conservation or have been asked to conserve energy. These ideas are related to using energy resources, such as coal and oil, wisely. The law of conservation of energy, on the other hand, is a universal principle that states that total energy remains constant.
Reading Preview
Essential Questions
◗ What is the law of conservation of energy? ◗ What is mechanical energy? ◗ Why is mechanical energy not always conserved? ◗ How are power and energy related?
Review Vocabulary friction: a force that opposes the sliding motion of two surfaces that are touching each other
New Vocabulary law of conservation of energy mechanical energy power
gg Multilingual eGlossary
Section 33
■ (^) Figure 10 Energy can be trans- ferred or transformed, but it cannot be created or destroyed. For the roller- coaster cars, energy is converted back and forth between kinetic energy and gravitational potential energy. In addition, some kinetic energy is converted to other forms of energy. However, the total amount of energy is constant.
SC.912.P.10.1: Differentiate among the various forms of energy and recognize that they can be transformed from one form to others. SC.912.P.10.2: Explore the Law of Conservation of Energy by differentiating among open, closed, and isolated systems and explain that the total energy in an isolated system is a conserved quantity. SC.912.P.10.3: Compare and contrast work and power qualitatively and quantitatively.
Projectile motion Energy transformations also occur during projectile motion when an object moves in a curved path. Look at Figure 12 and consider the ball-Earth system. When the ball leaves the bat, the ball is moving fast, so the system’s kinetic energy is relatively large. The ball’s speed decreases as it rises, so the system’s kinetic energy decreases. However, the system’s gravitational potential energy increases as the ball goes higher. At the top of the ball’s path, the system’s GPE is larger and kinetic energy is smaller. Then, as the baseball falls, the system’s GPE decreases as its kinetic energy increases. However, the mechanical energy of the ball-Earth system remains constant as the ball rises and falls. Swings The mechanical energy transformations for a swing, like the one shown in Figure 13, are similar to the mechanical energy transformations for a roller coaster. The ride starts with a push, which transfers kinetic energy to the rider. As the swing rises, the rider loses speed but gains height. In energy terms, kinetic energy changes to GPE. At the top of the rider’s path, GPE is at its greatest. Then, as the swing moves back downward, gravitational potential energy changes back to kinetic energy. At the bottom of each swing, the kinetic energy is at its maximum and the GPE is at its minimum. As the rider swings back and forth, energy is continually transformed between kinetic energy and GPE. However, the rider swings less and less on each cycle unless he or she pumps the swing or gets someone to provide a push. What is happening to the rider’s mechanical energy?
High KE Low GPE
Low KE High GPE
High KE Low GPE
122 Chapter 4 • Work and Energy
VOCABULARY
WORD ORIGIN Kinetic comes from the Greek word kinetikos, which means putting in motion A truck traveling on an interstate high- way has a lot of kinetic energy.
■ (^) Figure 12 Kinetic energy is trans- formed into gravitational potential energy as the ball rises. As the ball falls, gravitational potential energy is transformed back into kinetic energy. Predict How large will the mechanical energy of the ball-Earth system be after the ball has reached the ground and rolled to a stop? Use the ground as the reference level.
Concepts in Motion Animation
Section 3 • Conservation of Energy 123
A ride on a swing illustrates how kinetic energy changes to potential energy and back to kinetic energy.
FIGURE 13
Visualizing Energy Transformations
GPE
Energy
KE GPE
Energy
KE
GPE
Energy
KE GPE
Energy
KE GPE
Energy
KE
