CHAPTER12 CHAPTER Work and Energyparhamscience.pbworks.com/w/file/fetch/50020787/Holt_Physical...Work and Energy srthe s CHAPTER 12 1 Work, Power, and Machines What Is Work? Power

Work and Energy

Work and Energy

srthe s

C H A P T E R 12

1 Work, Power, and Machines

What Is Work?PowerMachines and Mechanical

Advantage

2 Simple MachinesThe Lever FamilyThe Inclined Plane FamilyCompound Machines

3 What Is Energy?Energy and WorkPotential EnergyKinetic EnergyOther Forms of Energy

4 Conservation of EnergyEnergy TransformationsThe Law of Conservation

of EnergyEfficiency of Machines

Chapter Preview

OverviewThis chapter covers work, power, and the mechanical advantage of machines. This chapter thenexplores the six simple machinesand relates work to energy, anddistinguishes between differentforms of energy. This chapterfinally covers energy transforma-tions, the conservation of energy,and the efficiency of machines.

Assessing PriorKnowledgeBe sure students understand thefollowing concepts:

• speed• velocity• forces• gravity• mass versus weight

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National Science Education Standards

The following descriptions summarize the National ScienceStandards that specifically relate to this chapter. For the fulltext of the standards, see the National Science EducationStandards at the front of the book.

Section 1 Work, Power, and MachinesPhysical Science PS 4aUnifying Concepts and Processes UCP 1–3, 5Science as Inquiry SAI 1

Section 2 Simple MachinesPhysical Science PS 4a

Unifying Concepts and Processes UCP 1–3, 5Science and Technology ST 2

Section 3 What Is Energy?Physical Science PS 1a, 1c, 2a–2e, 3b, 4b, 5a–5d, 6a, 6bLife Science LS 1b, 1f, 4a, 5a–5c, 5fEarth and Space Science ES 1aUnifying Concepts and Processes UCP 1–3Science in Personal and Social Perspectives SPSP 2

Section 4 Conservation of EnergyPhysical Science PS 5a, 5dLife Science LS 5fUnifying Concepts and Processes UCP 1–3

Standards Correlations

376 Chapter 12 • Work and Energy

C H A P T E R 12

Science education research hasidentified the following miscon-ceptions about work andenergy.

• Students often use energy,force, and work interchangeably.

• Some students think energy is only associated with inani-mate objects, or only withhumans, or that it is a fluid,ingredient, or fuel.

• Students believe that energytransformations involve onlyone form of energy at a time.

• The idea of energy conserva-tion is counter-intuitive tomany students.

Kinetic sculptures aresculptures that havemoving parts. Thechanges in the motionof different parts of akinetic sculpture canbe explained in termsof forces or in terms ofenergy transformations.

ACTIVITYACTIVITYFocusFocus

Background The collection of tubes, tracks, balls, and blocks ofwood shown at left is an audio-kinetic sculpture. A conveyor beltlifts the balls to a point high on the track, and the balls wind theirway down as they are pulled by the force of gravity and pushedby various other forces. They twist through spirals, drop straightdown tubes, and sometimes go up and around loops as if on aroller coaster. Along the way, the balls trip levers and bounce offelastic membranes. The sculpture uses the energy of the fallingballs to produce sounds in wood blocks and metal tubes.

This kinetic sculpture can be considered a machine or a col-lection of many small machines. Other kinetic sculptures mayincorporate simple machines such as levers, wheels, and screws.The American artist Alexander Calder, shown at left, is well knownfor his hanging mobiles that move in response to air currents.

This chapter introduces the basic principles of energy that explain the motions and interactions of machines.

Activity 1 Look around your kitchen or garage. What kinds of tools or utensils do you see? How do these tools help with different kinds of projects? For each tool, consider where force isapplied to the tool and how the tool may apply force to anotherobject. Is the force transferred to another part of the tool? Is theforce that the tool can exert on an object larger or smaller thanthe force exerted on the tool?

Activity 2 Any piece of artwork that moves is a kinetic sculpture.Design one of your own. Some ideas for materials include hang-ers, rubber bands, string, wood and metal scraps, and old toys.

Pre-Reading Questions1. How would you define work and energy?

Do these words have the same meaning in everyday speech and in science?

2. What different types of energy do youknow about?

www.scilinks.orgTopic: Machines SciLinks code: HK4081

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Chapter 12 • Work and Energy 377

Background The artistAlexander Calder was born in Philadelphia, Pennsylvania, in 1898. He is best known forinventing the mobile, a type of kinetic sculpture in whichbalanced weights could movein elaborate ways when onlylightly touched. Calder died at the age of 78, after creating16 000 works of art.Activity 1 Answers may vary.Student lists should includetools around the home andshould indicate some thoughtto the function of each tool,where forces act on the tools,and how the tools apply forcesto other objects. Kinesthetic

Activity 2 Encourage studentsto begin modeling their sculp-ture using the ideas of simplemachines from this chapter.Students may then construct akinetic sculpture by combiningsimple machines into a com-pound machine. Kinesthetic

Answers to Pre-ReadingQuestions1. Answers will vary. Discuss

student definitions of workand energy and emphasizethat in science work refersspecifically to the quantity of energy produced by a forcewhen it is applied to a bodyand causes that body to movein the direction of the force.

2. Answers will vary. Studentsmay say that they know about chemical, nuclear, elec-trical, sound, and solar energy.

LS

LS

ACTIVITYACTIVITYFocusFocus

• Pretest• Teaching Transparency Preview• Answer Keys

GENERAL

Chapter Resource File

Work, Power, and Machines> Define work and power.> Calculate the work done on an object

and the rate at which work is done.> Use the concept of mechanical advantage to explain

how machines make doing work easier.> Calculate the mechanical advantage of various machines.

I f you needed to change a flat tire, you would probably use a carjack to lift the car. Machines—from complex ones such as a car

to relatively simple ones such as a car jack, a hammer, or aramp—help people get things done every day.

What Is Work?Imagine trying to lift the front of a car without using a jack. Youcould exert a lot of force without moving the car at all. Exertingall that force might seem like hard work. In science, however, theword has a very specific meaning.

Work is done only when force causes a change in the positionor the motion of an object in the direction of the applied force.Work is calculated by multiplying the force by the distance overwhich the force is applied. We will always assume that the forceused to calculate work is acting along the line of motion of theobject.

In the case of trying to lift the car, you might apply a largeforce, but if the distance that the car moves is equal to zero, thework done on the car is also equal to zero.

However, once the car moves even a small amount, you havedone some work on it. You could calculate how much by multi-plying the force you have applied by the distance the car moves.

The weightlifter in Figure 1 is applying a force to the barbellas she holds it overhead, but the barbell is not moving. Is shedoing any work on the barbell?

work

O B J E C T I V E S

SECTION

1

378

K E Y T E R M

workpowermechanical advantage

▲work = force × distance

W = F × d

Work Equation

Figure 1As this weightlifter holds the barbell over her head, is shedoing any work on the barbell?

work the transfer of energyto a body by the application ofa force that causes the bodyto move in the direction of theforce

▲

OverviewBefore beginning this section,review with your students theobjectives listed in the StudentEdition. This section introduceswork and the specific conditions inwhich work is done. Power, therate at which work is done, is alsodiscussed. The section concludeswith a discussion of the mechanicaladvantage of various simplemachines.

Use the Bellringer transparency toprepare students for this section.

OpeningDiscussionHave students brainstorm all the words, phrases, and ideas thatthey associate with the term work.Write each term on the board, andlead students in a discussion aboutthe listed terms. Allow students to ask you and other students forclarification of the listed ideas. As part of the discussion, ask thefollowing: Which of the examplesinvolve work in the scientificsense? Which examples use adifferent definition of work?

VerbalLS

MotivateMotivate

Bellringer

FocusFocus

Alternative AssessmentWork Students may confuse the scientificmeaning of work with the common, everydaymeaning. In order to clarify the proper scien-tific meaning, point out that when used in the scientific sense, work is always done by aforce, on an object, changing the motion of theobject. Have students come up with sentencesusing work in both the common sense and thescientific sense. VerbalLS

Historical Perspective James Prescott Joule The unit of work and energy was named in honor of the Englishphysicist James Prescott Joule (1818–1889).Joule was one of the first scientists to recog-nize that mechanical work and non-mechanicalenergy could be interchangeable, which wasthe foundation of the law of conservation of energy.


378

SECTION

1

GENERAL


Work is measured in joulesBecause work is calculated as force times distance, it is measuredin units of newtons times meters, N•m. These units are alsocalled joules (J). In terms of SI base units, a joule is equivalent to1 kg•m2/s2.

1 N•m = 1 J = 1 kg•m2/s2

Because these units are all equal, you can choose whichever unitis easiest for solving a particular problem. Substituting equiva-lent units will often help you cancel out other units in a problem.

You do about 1 J of work when you slowly lift an apple, whichweighs about 1 N, from your arm’s length down at your side tothe top of your head, a distance of about 1 m.

379

Disc Two, Module 10: WorkUse the Interactive Tutor to learn moreabout this topic.

Math SkillsMath Skills

PracticePracticeWork1. A crane uses an average force of 5200 N to lift a girder 25 m.

How much work does the crane do on the girder?2. An apple weighing 1 N falls through a distance of 1 m.

How much work is done on the apple by the force of gravity? 3. The brakes on a bicycle apply 125 N of frictional force to the

wheels as the bicycle travels 14.0 m. How much work have thebrakes done on the bicycle?

4. While rowing in a race, John uses his arms to exert a force of165 N per stroke while pulling the oar 0.800 m. How muchwork does he do in 30 strokes?

5. A mechanic uses a hydraulic lift to raise a 1200 kg car 0.5 m off the ground. How much work does the lift do on the car?

PracticeHINT

> In order to use the workequation, you must use unitsof newtons for force and units of meters for distance.Practice Problem 5 gives amass in kilograms instead of a weight in newtons. Toconvert from mass to force(weight), use the definition of weight:

w = mgwhere m is the mass in kilograms and g = 9.8 m/s2.Then plug the value for weight into the work equation as the force.

Work Imagine a father playing with his daughter by lifting herrepeatedly in the air. How much work does he do with eachlift, assuming he lifts her 2.0 m and exerts an average force of190 N?

List the given and unknown values.Given: force, F = 190 N

distance, d = 2.0 mUnknown: work, W = ? J

Write the equation for work.work = force × distance W = F × d

Insert the known values into the equation, and solve.W = 190 N × 2.0 m = 380 N•m = 380 J

3

2

1

DemonstrationWork(Time: About 15 minutes)

Materials:• spring scale• string• textbookStep 1 Hang the book from thescale with string. Have studentsnote the scale reading. Is there aforce acting on the book? (Yes, grav-ity pulls down and the spring exertsan upward force.) Is work beingdone on the book? (No, because thebook’s displacement is zero.)Step 2 Now lift the book (usingthe scale) about 1 m at a constantvelocity. Does the scale readingchange? (Yes, at the beginning andthe end of the motion) Is work beingdone on the book? (Yes, becausea force moves the book through adistance.)Step 3 Now hold the scale atshoulder height and carry the book at a constant speed across theroom. Does the reading on thescale change? (No) Is work beingdone on the book? (No, because themotion is perpendicular to the force.)

Visual

1. W � (5200 N)(25 m) � 1.3 � 105 J2. W � (1 N)(1 m) � 1 J3. W � (125 N)(14.0 m) � 1750 J4. W � (30)(165 N)(0.800 m) �

3960 J5. W � (1200 kg)(9.8 m/s2)(0.5 m) �

6000 JLogicalLS

PracticePractice

LS

TeachTeach

379

• Lesson Plan• Cross-Disciplinary Worksheet

Integrating Biology—Muscles andWork

• Math Skills Work GENERAL


Transparencies

TT Bellringer

PowerRunning up a flight of stairs doesn’t require more work thanwalking up slowly does, but it is more exhausting. The amount oftime it takes to do work is an important factor when consideringwork and machines. The quantity that measures work in relationto time is Power is the rate at which work is done, thatis, how much work is done in a given amount of time.

Running takes less time than walking does. How does reduc-ing the time in this equation affect the power if the amount ofwork stays the same?

Power is measured in wattsPower is measured in SI units called watts (W). A watt is theamount of power required to do 1 J of work in 1 s, about as muchpower as you need to lift an apple over your head in 1 s. Do notconfuse the abbreviation for watts, W, with the symbol for work,W. You can tell which one is meant by the context in which itappears and by whether it is in italics.

power.

380

Materials

What is your power output when you climb the stairs?

✔ flight of stairs ✔ stopwatch ✔ meterstick

1. Determine your weight in newtons. If yourschool has a scale that reads in kilograms, multi-ply your mass in kilograms by 9.8 m/s2 to deter-mine your weight in newtons. If your school hasa scale that weighs in pounds, multiply yourweight by a factor of 4.45 N/lb.

2. Divide into pairs. Have your partner use the stopwatch to time how long it takes you to walkquickly up the stairs. Record the time. Thenswitch roles and repeat.

3. Measure the height of one step in meters. Multi-ply the number of steps by the height of onestep to get the total height of the stairway.

4. Multiply your weight in newtons by the height of the stairs in meters to get the work you did in

joules. Recall the work equation:work � force � distance, orW � F � d.

5. To get your power in watts, dividethe work done in joules by the time inseconds that it took you to climb the stairs.

Analysis1. How would your power output change if you

walked up the stairs faster?

2. What would your power output be if you climbedthe same stairs in the same amount of timewhile carrying a stack of books weighing 20 N?

3. Why did you use your weight as the force in thework equation?

power a quantity that measures the rate at whichwork is done or energy istransformed

▲

power = �wtim

orek

� P = �Wt�

Power Equation

Teaching TipWork versus Power Use thefollowing analogy to help studentsunderstand the difference betweenwork and power. Consider a sum-mer lawn-mowing job. If you haveto mow 30 lawns in one month,you could mow six lawns each day and finish in five days, or mowone lawn each day and take theentire month. The total number of mowed lawns (30) is the same,but the rate is different (either 6per day or 1 per day). Ask studentswhat is analogous to the totalnumber of lawns mowed (work)and to the rate of mowing (power).

VerbalLS

Teach, continuedTeach, continued

Scientists Around the World James Watt The unit of power was namedfor James Watt (1736–1819), a Scottish inven-tor who played an important role in the devel-opment of the steam engine. Watt was born inGreenock, Scotland in 1736. Although he didnot invent the steam engine, as is commonlystated, his contributions—which dramaticallyimproved its efficiency—were fundamental toits development. Inventions on his first patentof 1769 included a separate condensing cham-ber for the steam engine (which preventedhuge amounts of steam loss), oil lubrication,

and cylinder insulation. He later developed a steam indicator to measure the amount ofsteam pressure in an engine.

Watt also made contributions to otherfields throughout his lifetime. In addition tohis physical science work, he conducted sur-veys of canal routes as a civil engineer. Healso invented an adaptor for telescopes to aidin distance measuring. Watt died in England in 1819.


380

GENERAL

GENERAL

What is your power outputwhen you climb the stairs?Safety Caution: Instructstudents not to run on thestairs. Also caution studentsnot to overexert themselves.Emphasize to students that thisis not a contest.

Analysis1. Your power output would be

greater if you walked up the stairs faster.

2. Answers will vary dependingon data. Answer should beslightly larger than the poweroutput calculated in item 5 ofthe procedure.

3. Students are lifting themselves up the stairs against the forceof gravity. The gravitationalforce is equivalent to theirweight.KinestheticLS


381


PracticePracticePower1. While rowing across the lake during a race, John does 3960 J of

work on the oars in 60.0 s. What is his power output in watts?2. Every second, a certain coal-fired power plant produces enough

electricity to do 9 × 108 J (900 MJ) of work. What is the poweroutput of this power plant in units of watts (or in units ofmegawatts)?

3. Using a jack, a mechanic does 5350 J of work to lift a car0.500 m in 50.0 s. What is the mechanic’s power output?

4. Suppose you are moving a 300 N box of books. Calculate yourpower output in the following situations:a. You exert a force of 60.0 N to push the box across the floor

12.0 m in 20.0 s.b. You lift the box 1 m onto a truck in 3 s.

5. Anna walks up the stairs on her way to class. She weighs 565 Nand the stairs go up 3.25 m vertically.a. Calculate her power output if she climbs the stairs in 12.6 s.b. What is her power output if she climbs the stairs in 10.5 s?

PracticeHINT

> In order to calculate power inPractice Problems 4 and 5,you must first use the workequation to calculate thework done in each case.

Another common unit ofpower is horsepower (hp).This originally referred to theaverage power output of adraft horse. One horsepowerequals 746 W. With that muchpower, a horse could raise aload of 746 apples, weighing1 N each, by 1 m every second.

Power It takes 100 kJ of work to lift an elevator 18 m. If this isdone in 20 s, what is the average power of the elevator duringthe process?

List the given and unknown values.Given: work, W = 100 kJ = 1 × 105 J

time, t = 20 sThe distance of 18 m will not be needed to calculate power.

Unknown: power, P = ? W

Write the equation for power.

power = �wtim

orek

� P = �Wt�

Insert the known values into the equation, and solve.

P = �1 ×

2010

s

5 J� = 5 × 103 J/s

P = 5 × 103 WP = 5 kW

3

2

1

Additional ExamplesPower A student lifts a 12 N text-book 1.5 m in 1.5 s and carries thebook 5 m across the room in 7 s.

a. How much work does thestudent do on the textbook? (18 J)

b. What is the power output of the student? (12 W)

Compare the work and power usedin the following cases:

a. A 43 N force is exerted througha distance of 2.0 m over a timeof 3.0 s. (W � 86 J, P � 29 W)

b. A 43 N force is exerted througha distance of 3.0 m over a timeof 2.0 s. (W � 130 J, P � 65 W)Logical

1. P � �Wt� � �

36906.00

sJ

� � 66.0 W

2. P � �90

10

sMJ� � 900 MW

3. P � �55305.00

sJ

� � 107 W

4. a. W � (60.0 N)(12.0 m) � 720 J

P � �Wt� � �

2702.00

Js

� � 36 W

b. W � (300 N)(1 m) � 300 J

P � �Wt� � �

3030s

J� � 100 W

5. a. P � �Wt� ��

(5651N2).(63.

s25 m)

� �

146 W

b. P ��(565

1N0).(53.

s25 m)

�� 175 W

LogicalLS

PracticePractice

LS


381

• Math Skills Power• Quick Lab Datasheet What is your

power output when you climb thestairs? GENERAL

GENERAL


Electric Power Most utility companies billcustomers in units of kilowatt-hours, whichis actually a unit of energy, not power. Onekilowatt-hour, which equals 3 600 000 joules,is the amount of energy used at the rate ofone kilowatt (1000 watts, or 1000 joules/second) over a time period of one hour(1000 J/s � 3600 s/h � 1 h � 3 600 000 J).

Have students obtain a recent power bill anddetermine the average number of kilowatt-hours used each day. Also ask them to convertthis value to joules. IntrapersonalLS

REAL-LIFEREAL-LIFECONNECTIONCONNECTION

Machines and Mechanical AdvantageWhich is easier, lifting a car yourself or using a jack as shown in Figure 2? Which requires more work? Using a jack is obviouslyeasier. But you may be surprised to learn that using a jackrequires the same amount of work. The jack makes the work eas-ier by allowing you to apply less force at any given moment.

Machines multiply and redirect forcesMachines help us do work by redistributing the work that we putinto them. Machines can change the direction of an input force.Machines can also increase or decrease force by changing thedistance over which the force is applied. This process is oftencalled multiplying the force.

Different forces can do the same amount of workCompare the amount of work required to lift a box straight ontothe bed of a truck, as shown in Figure 3A, with the amount of work required to push the same box up a ramp, as shown inFigure 3B. When the mover lifts straight up, he must apply 225 Nof force for a short distance. Using the ramp, he can apply asmaller force over a longer distance. But the work done is aboutthe same in both cases.

Both a car jack and a loading ramp make doing work easierby increasing the distance over which force is applied. As aresult, the force required at any point is reduced. Therefore, amachine allows the same amount of work to be done by eitherdecreasing the distance while increasing the force or by decreas-ing the force while increasing the distance.

382

W = F � dW = 75.0 N � 3.00 mW = 225 N•m = 225 J

F = 75.0 N

d = 3.00 m

W = F � dW = 225 N � 1.00 mW = 225 N•m = 225 J

F = 225 N

d = 1.00 m

Figure 3When lifting a box straight up,

a mover applies a large force overa short distance.

Using a ramp to lift the box,the mover applies a smaller forceover a longer distance.

B

A

Figure 2A jack makes it easier to lift a carby multiplying the input force and spreading the work out over a large distance.

A B

Teaching TipMachines Be sure to emphasizethat machines do not increase the quantity of work that one cando. Given a specific amount ofwork to be done, a machine takesadvantage of the fact that forceand distance are inversely propor-tional. Either one can be increasedby decreasing the other.

As an example, you can use theequation W � F � d to show thata longer distance implies a smallerforce for the same amount of work.For instance, to lift a 225 N box in-to the back of a truck that is 1.00 moff the ground requires 225 J ofwork. If you lift the box straightup into the truck, the force neededis 225 N, but if you use a 3.00 mramp, the force needed is only 75 N(ignoring friction).

Interpreting Visuals Use Figure 3with the concrete example above tohelp students learn the concept ofmechanical advantage. Be sure topoint out that whether or not youuse the ramp, the box ends up inthe same place—a sure sign thatthe work done on the box is thesame in either case. LogicalLS



382

Alternative AssessmentConservation of Mechanical EnergyThe statement that different forces can

do the same amount of work is really anexpression of the law of conservation ofenergy. The law is implicit throughout thischapter, but it is not stated explicitly untilSection 4. Have students recall how theconservation of energy in Chapter 3 indicated

Writing that energy took different forms or was trans-ferred in different ways. Ask students to writea paragraph explaining how energy trans-ferred to objects by work is conserved inmachines. Be sure they give special attentionto how changes in force and displacement, thefactors affecting work, vary so that energy isconserved. VerbalLS

GENERAL


Mechanical advantage tells how much a machine multipliesforce or increases distanceA ramp makes doing work easier by increasing the distance overwhich force is applied. But how long should the ramp be? An extremely long ramp would allow the mover to use very littleforce, but he would have to push the box a long distance. A veryshort ramp, on the other hand, would be too steep and would nothelp him very much.

To solve problems like this, scientists and engineers use anumber that describes how much the force or distance is multi-plied by a machine. This number is called the

and it is defined as the ratio between the outputforce and the input force. It is also equal to the ratio between theinput distance and the output distance if friction is ignored.

A machine with a mechanical advantage greater than 1 mul-tiplies the input force. Such a machine can help you move or liftheavy objects, such as a car or a box of books. A machine with amechanical advantage of less than 1 does not multiply force, butincreases distance and speed. When you swing a baseball bat,your arms and the bat together form a machine that increasesspeed without multiplying force.

advantage,mechanical

383

mechanical advantage = �oiun

tppuuttffoorrccee

� =�oiuntppuuttddiissttaannccee

�

Mechanical Advantage Equation

mechanical advantagea quantity that measures howmuch a machine multipliesforce or distance

▲

www.scilinks.orgTopic: Mechanical

AdvantageSciLinks code: HK4085

BIOLOGYYou may not do anywork on a car if youtry to lift it without ajack, but your body

will still get tired from the effortbecause you are doing work onthe muscles inside your body.

When you try to lift some-thing, your muscles contractover and over in response to a series of electrical impulsesfrom your brain. With each con-traction, a tiny bit of work isdone on the muscles. In just afew seconds, this can add up tothousands of contractions and a significant amount of work.

Math SkillsMath SkillsMechanical Advantage Calculate the mechanical advantage ofa ramp that is 5.0 m long and 1.5 m high.

List the given and unknown values.Given: input distance = 5.0 m

output distance = 1.5 mUnknown: mechanical advantage = ?

Write the equation for mechanical advantage.Because the information we are given involves only distance, we only need part of the full equation:

mechanical advantage =�oiuntppuuttddiissttaannccee

�


mechanical advantage = �51..05

mm

� = 3.3

3

2

1

Teaching TipMechanical Advantage Pointout to students that the actualmechanical advantage must takeinto account all of the forcesinvolved, including any frictionalforces that must be overcome. Tell students that the mechanicaladvantage calculations they areperforming are ideal predictions,based on distances, and that fric-tion is not taken into account.

Because the force of frictionopposes the direction of motion,part of the input force is dissipatedin opposing friction. Thus, theresult of friction is the loss of someof the input energy. For example,due to friction, if a ramp has anideal mechanical advantage of 3 (it is three times longer than it is high), the true input force will be greater than one-third of theoutput force.

Additional ExamplesMechanical Advantage Askstudents: What are the units ofmechanical advantage? (Thereare none; all units cancel out in the equation.)

A mover uses a pulley systemwith a mechanical advantage of10.0 to lift a piano 3.5 m.Disregarding friction, how far mustthe mover pull the rope? (35 m)

A person pushes a 950 N boxup an incline. If the person exerts aforce of 350 N along the incline,what is the mechanical advantageof the incline? (2.7) LogicalLS


383

• Math Skills MechanicalAdvantage

• Science Skills Equations with ThreeParts

GENERAL


Conservation of Energy No machine canincrease both the force and the distance atthe same time. An increase in one alwayscorresponds to a decrease in the other. Thisis another way to express the idea that youcannot ever get more work out of a machinethan you put in. This is because energy isalways conserved; it cannot be created ordestroyed. Machines are not useful because

they increase the amount of work done, butbecause they make work easier.

If there were no friction, the work outputwould be exactly equal to the work input.However, because friction acts against workinput, the actual work output is always lessthan the work input.

384

S E C T I O N 1 R E V I E W

1. Define work and power. How are work and power related to each other?

2. Determine if work is being done in these situations:a. lifting a spoonful of soup to your mouthb. holding a stack of books motionless over your headc. letting a pencil fall to the ground

3. Describe how a ramp can make lifting a box easier withoutchanging the amount of work being done.

4. Critical Thinking A short ramp and a long ramp both reacha height of 1 m. Which has a greater mechanical advantage?

5. How much work in joules is done by a person who uses aforce of 25 N to move a desk 3.0 m?

6. A bus driver applies a force of 55.0 N to the steering wheel,which in turn applies 132 N of force on the steering column.What is the mechanical advantage of the steering wheel?

7. A student who weighs 400 N climbs a 3 m ladder in 4 s.a. How much work does the student do?b. What is the student’s power output?

8. An outboard engine on a boat can do 1.0 � 106 J of work in50.0 s. Calculate its power in watts. Convert your answer tohorsepower (1 hp � 746 W).


S U M M A R Y

> Work is done when a forcecauses an object to move.This meaning is differentfrom the everyday meaningof work.

> Work is equal to force timesdistance. The most com-monly used SI unit for workis joules.

> Power is the rate at whichwork is done. The SI unit forpower is watts.

> Machines help people byredistributing the work putinto them. They can changeeither the size or the direc-tion of the input force.

> The mechanical advantageof a machine describes howmuch the machine multi-plies force or increases distance.

PracticePracticeMechanical Advantage1. Calculate the mechanical advantage of a ramp that is 6.0 m

long and 1.5 m high.2. Determine the mechanical advantage of an automobile jack

that lifts a 9900 N car with an input force of 150 N.3. A sailor uses a rope and pulley to raise a sail weighing 140 N.

The sailor pulls down with a force of 140 N on the rope. Whatis the mechanical advantage of the pulley?

4. Alex pulls on the handle of a claw hammer with a force of 15 N.If the hammer has a mechanical advantage of 5.2, how muchforce is exerted on a nail in the claw?

5. While rowing in a race, John pulls the handle of an oar 0.80 mon each stroke. If the oar has a mechanical advantage of 1.5,how far does the blade of the oar move through the water oneach stroke?

PracticeHINT

> The mechanical advantageequation can be rearranged to isolate any of the variableson the left.

> For practice problem 4, youwill need to rearrange theequation to isolate outputforce on the left.

> For practice problem 5, youwill need to rearrange to isolate output distance. Whenrearranging, use only the part of the full equation that you need.

1. MA � input distance/outputdistance � 6.0 m/1.5 m � 4.0

2. MA � output force/inputforce � 9900 N/150 N � 66

3. MA � 140 N/140 N � 1.04. output force � (MA)(input force) �

(5.2)(15 N) � 78 N5. output distance � input distance/

MA � 0.80 m/1.5 � 0.53 m Logical

QuizMatch each term at the top withthe correct description below. Thenwrite the equation and the SI unitfor each term.left column:

1. work (c; force � distance; joules)

2. power (b; work/time; watts)

3. mechanical advantage (a; outputforce/input force; no units)

right column:

a. the amount that a machine mul-tiplies force or distance

b. the rate at which work is done

c. what is done when a forcemakes an object moveLogicalLS

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PracticePractice


Answers to Section 1 Review

1. Work is the quantity of energy transferred by a force applied to an object that moves in thedirection of the force. Power is a quantity thatmeasures the rate at which work is done. Powerequals work divided by time.

2. a. yesb. noc. yes (by gravity)

3. A ramp allows the use of a smaller input forceexerted over a longer distance, so that work isunchanged.

4. The long ramp has a greater mechanicaladvantage than the short ramp.

5. W � 75 J6. MA � 2.407. a. W � 1200 J

b. P � 300 W8. P � 2.0 � 104 W (27 hp)



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• Concept Review• Quiz

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> Name and describe the six types of simple machines.> Discuss the mechanical advantage of different types of

simple machines.> Recognize simple machines within compound machines.

Simple Machines

The most basic machines of all are called Other machines are either modifications of simple machines

or combinations of several simple machines. Figure 4 shows exam-ples of the six types of simple machines. Simple machines aredivided into two families, the lever family and the inclined planefamily.

The Lever FamilyTo understand how levers do work, imagine using a claw ham-mer to pull out a nail. As you pull on the handle of the hammer,the head turns around the point where it meets the wood. Theforce you apply to the handle is transferred to the claw on theother end of the hammer. The claw then does work on the nail.

simple machines.

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K E Y T E R M Ssimple machinescompound machines

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Simple inclined plane Wedge Screw

The inclinedplane family

The lever family

Simple lever Pulley Wheel and axle

Figure 4The Six SimpleMachines

simple machine oneof the six basic types of machines, which are the basis for all other forms ofmachines

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OverviewBefore beginning this section,review with your students theObjectives listed in the StudentEdition. This section discusses each of the six simple machines indetail, then explains what a com-pound machine is.


Opening ActivityHave students read this sectionbefore class. Write the followingstatement on the board: “Allmachines are simple machines.”Separate students into pairs orsmall groups and have the groupsdebate the statement. Each groupshould decide whether it agrees ordisagrees with the statement andshould provide some evidence tosupport its opinion. Have a classdiscussion to compare opinionsand rationales.

Students who disagree with thestatement will usually point outthat compound machines are morecomplicated because they are com-binations of simple machinesworking intricately together. Onthe other hand, students who agreewith the statement may point outthat a compound machine is reallynothing more than a collection ofsimple machines. InterpersonalLS

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• Lesson Plan


Transparencies

TT Bellringer

Have students examine the chapter openingphotographs and identify as many simplemachines in the kinetic sculptures as theycan. Students may refer to Figure 4 for exam-ples of the six simple machines. VisualLS

FINE ARTSFINE ARTSCONNECTIONCONNECTION

HISTORYHISTORYCONNECTIONCONNECTION

Have students research the history of one ofthe simple machines shown in Figure 4. Youmay wish to divide students into six groupsand assign one machine to each group.Research topics could include first knownuses of the machine and interesting inven-tions throughout history that have relied onthe machine. VerbalLS

Levers are divided into three classesAll levers have a rigid arm that turns around a point called thefulcrum. Force is transferred from one part of the arm to another.In that way, the original input force can be multiplied or redi-rected into an output force. Levers are divided into three classesdepending on the location of the fulcrum and of the input andoutput forces.

Figure 5A shows a claw hammer as an example of a first-classlever. First-class levers are the most common type. A pair of pliersis made of two first-class levers joined together.

Figure 5B shows a wheelbarrow as an example of a second-classlever. Other examples of second-class levers include nutcrackersand hinged doors.

Figure 5C shows the human forearm as an example of a third-class lever. The biceps muscle, which is attached to the bone nearthe elbow, contracts a short distance to move the hand a largedistance.

Outputforce

InputforceFulcrum

Outputforce

Inputforce

Fulcrum

Outputforce

Inputforce

Fulcrum

Figure 5The Three Classes of Levers

All first-class levershave a fulcrum locatedbetween the points of appli-cation of the input and out-put forces.

In a second-class lever,the fulcrum is at one end ofthe arm and the input forceis applied to the other end.The wheel of a wheelbarrowis a fulcrum.

Third-class levers multi-ply distance rather than force.As a result, they have amechanical advantage ofless than 1. The humanbody contains many third-class levers.

C

B

A

A

B

C

Forearm

Wheelbarrow

Hammer

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Interpreting Visuals Figure 5shows the three classes of levers.Ask students: For each of the threeexamples, where is force input and where is force output? Do thelevers multiply force or increasedistance on the output side?(Second-class levers always multiplyforce, third-class levers alwaysincrease distance, and first-classlevers may either multiply force or increase distance.) VisualLS

TeachTeach

single or double. Have other students checkthe classifications for accuracy. (Responsescould include the following: hammer claw, 1st class, single; see-saw, 1st class, single; scissors,1st class, double; pliers, 1st class, double; wheel-barrow, 2nd class, single; bottle opener, 2nd class,single; nutcracker, 2nd class, double; fishing rod,3rd class, single; tweezers, 3rd class, double;tongs, 3rd class, double.) IntrapersonalLS


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Double Levers Many common levers, suchas scissors (first-class), nutcrackers (second-class), and tweezers (third-class), are actuallycompound machines combining two leverstogether. Ask students to look for everydayexamples of both single and compound(double) levers. Have students add theirexamples to a list on the chalkboard, notingthe class of the lever and whether the lever is


Alternative AssessmentSimilar Features of Simple Machines Havestudents read the explanation of how Figure 6Ais like a first-class lever with the fulcrum in themiddle. Tell students that Figure 6B is like asecond class lever. Have students discuss this.

Next tell students that in pulley systems, themechanical advantage may be found by simplycounting the number of weight-supportingropes. Ask students to find the mechanical ad-vantage of the pulley systems in Figure 6A (1),6B (2), and 6C (3). VisualLS


Pulleys are modified leversYou may have used pulleys to lift things, as when raising a flag tothe top of a flagpole or hoisting a sail on a boat. A pulley isanother type of simple machine in the lever family.

Figure 6A shows how a pulley is like a lever. The point in themiddle of a pulley is like the fulcrum of a lever. The rest of thepulley behaves like the rigid arm of a first-class lever. Because thedistance from the fulcrum is the same on both sides of a pulley,a single, fixed pulley has a mechanical advantage of 1.

Using moving pulleys or more than one pulley at a time canincrease the mechanical advantage, as shown in Figure 6B andFigure 6C. Multiple pulleys are sometimes put together in a singleunit called a block and tackle.

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Outputforce =150 N

Inputforce =150 N

MA = 1

Outputforce =150 N

Inputforce =50 N

MA = 3

Outputforce =150 N

Inputforce =75 N

MA = 2

Figure 6The Mechanical Advantage of Pulleys

Lifting a 150 N weight with a single, fixed pulley,the weight must be fully supported by the rope oneach side of the pulley. This type of pulley has amechanical advantage of 1.

A Using a moving pulley, the 150 N force isshared by two sections of rope pulling upward.The input force on the right side of the pulley hasto support only half of the weight. This pulley sys-tem has a mechanical advantage of 2.

B

In this arrangement of multiple pulleys, all of the sections of rope pull up against the downwardforce of the weight. This gives aneven higher mechanical advantage.

C

DemonstrationPulley Power(Time: About 10 minutes)

Materials:• masses, 75 g and 100 g• pulleys, 2 fixed, 1 free• ring stand with horizontal clamp• stringStep 1 Arrange the free pulley and one fixed pulley as shown inFigure 6C. Attach the other fixedpulley to the clamp, and threadover it the string from beneath thefree pulley.Step 2 Attach the 100 g mass tothe bottom of the free pulley andthe 75 g mass to the string’s freeend. Hold the masses in place, andask students what they think willhappen when you let go.Step 3 Release the masses. The 75 gmass should fall and the 100 gmass should rise, showing that alighter mass can lift a heavier masswith the help of simple machines.

Visual

Teaching Tip“Massless” Pulleys Some stu-dents may ask about the weight ofthe pulleys and the rope in Figure 6.Point out that students are correctto consider this. Explain that inparts B and C of the figure, thepulley’s mass adds to the overallweight. In these cases, the inputforce would have to be greaterthan 75 N and 50 N by smallamounts. Much of the rope’sweight is evenly distributed oneither side of the stationary pulley.Explain that in most cases, theweight of the rope and pulleys ismuch smaller than the weight ofthe load, and can be ignored.

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Transparencies

TT LeversTT Pulleys

StrategiesStrategiesINCLUSIONINCLUSION

Using Figure 4, ask students to create aposter or bulletin board showing the six sim-ple machines in the lever and inclined planefamilies. Students can use cut out pictures ortheir own drawings to show their understand-ing of the different types of machines. If possi-ble, the students can tour the school buildingand take pictures or list machines in each cate-gory they find. Additionally, they can add thecategory of compound machines.

• Attention Deficit Disorders• Learning Disabled

• English LanguageLearners

A wheel and axle is a lever or pulley connected to a shaftThe steering wheel of a car is another kind of simple machine: awheel and axle. A wheel and axle is made of a lever or a pulley(the wheel) connected to a shaft (the axle), as shown in Figure 7.When the wheel is turned, the axle also turns. When a small inputforce is applied to the steering wheel, the force is multiplied tobecome a large output force applied to the steering column,which turns the front wheels of the car. Screwdrivers and cranksare other common wheel-and-axle machines.

The Inclined Plane FamilyEarlier we showed how pushing an object up a ramp requires lessforce than lifting the same object straight up. A loading ramp isanother type of simple machine, an inclined plane.

Inclined planes multiply and redirect forceWhen you push an object up a ramp, you apply a force to theobject in a direction parallel to the ramp. The ramp then redi-rects this force to lift the object upward. This is why the outputforce of the ramp is shown in Figure 8A as an arrow pointingstraight up. The output force is the force needed to lift the objectstraight up.

An inclined plane turns a small input force into a large outputforce by spreading the work out over a large distance. Pushingsomething up a long ramp that climbs gradually is easier thanpushing something up a short, steep ramp.

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Fulcrum

Outputforce

Inputforce

Figure 7How is a wheel and axle like a lever? How is it different from a pulley?

Figure 8 The Inclined Plane Family

Outputforce

Inputforce

An inclined planechanges both themagnitude and thedirection of force.

A

ACTIVITYACTIVITYQuickQuickQuick

A Simple Inclined Plane1. Make an inclined plane

out of a board and astack of books.

2. Tie a string to an objectthat is heavy but has lowfriction, such as a metaltoy car or a roll of wire.Use the string to pull theobject up the plane.

3. Still using the string, try to lift the object straightup through the same distance.

4. Which action requiredmore force? In which casedid you do more work?

Interpreting Visuals Havestudents examine Figure 7. Lead a discussion about the similaritiesbetween a wheel and axle and alever. Have students note that thesmall input force acts through alarge distance—the radius of thelarge wheel, while the large outputforce acts through a small distance—the radius of the axle. The wheel’s center is the fulcrumaround which the wheel and axlepivot. The mechanical advantageof a wheel and axle is equal to the ratio of the wheel radius to the axle radius. VisualLS


Historical Perspective Archimedes’ Machines Archimedes was aGreek mathematician (287 B.C.–212 B.C.) ofSyracuse, Sicily. Although his first love waspure mathematics, he also figured out how touse simple machines in a variety of practicalapplications. In response to a challenge by theKing, Archimedes developed a system of leversand pulleys to launch a heavy ship. The Kingwas astonished to see the fully-loaded ship glideinto the water with a simple pull of a rope.

Later, when the Romans were attackingSyracuse, Archimedes designed machines to

defend the city. He made cranes that wouldpick up Roman ships and smash them againstrocks. He also created catapults to hurl hugestones at ships and soldiers.

The Romans were forced to withdraw, butthey eventually gained control by starving thecitizens. The Roman leader Marcellus orderedhis men to “Spare that mathematician” but,tragically, Archimedes was killed. Encourageinterested students to find out more about thelife, death, and scientific contributions ofArchimedes.


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ACTIVITYACTIVITYQuickQuick

A Simple Inclined PlaneMaterials (per group): • board• stack of books• string• heavy object with low friction

Teacher’s Notes: The objectused in this activity can be anyheavy rolling object (such as awheeled dynamics cart) or sim-ply a heavy object with low fric-tion. A roll of wire with stringtied through the hollow shaft sothat the roll moves freely whendragged up the ramp will workwell.

Answer

4. Lifting the object straight uprequires more force than drag-ging it up the ramp. The workdone is the same in either case,if friction is ignored.KinestheticLS

GENERAL

Alternative AssessmentSimple Machine Acrostic Ask students tocreate an acrostic they can use as a memoryaid for the six simple machines. Use the fol-lowing example (or create one of your own) to give students the idea:Louis Plank Was an Interesting, Witty Scholar.(Lever, Pulley, Wheel and axle, Inclined plane,Wedge, Screw)Tell students to create their own examplebecause they will probably remember theirown words better than an acrostic written bysomeone else. Also remind them that they canlist the machines in any order. VerbalLS


A wedge is a modified inclined planeWhen an ax blade or a splitting wedge hits apiece of wood, it pushes through the wood andbreaks it apart, as shown in Figure 8B. An axblade is an example of a wedge, another kind ofsimple machine in the inclined plane family. Awedge functions like two inclined planes backto back. Using a wedge is like pushing a rampinstead of pushing an object up the ramp. Awedge turns a single downward force into twoforces directed out to the sides. Some types ofwedges, such as nails, are used as fasteners.

A screw is an inclined plane wrapped arounda cylinderA type of simple machine that you probably useoften is a screw. The threads on a screw looklike a spiral inclined plane. In fact, a screw is aninclined plane wrapped around a cylinder, asshown in Figure 8C. Like pushing an object up aramp, tightening a screw with gently slopingthreads requires a small force acting over alarge distance. Tightening a screw with steeperthreads requires more force. Jar lids are screwsthat people use every day. Spiral staircases arealso common screws.

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A wedge turns adownward force into twoforces directed out to thesides.

B A screw is aninclined planewrapped arounda cylinder.

C

Connection toSOCIAL STUDIESSOCIAL STUDIES

The ancient Egyptians builtdozens of large stone pyr-

amids as tombs for the bodiesof kings and queens. Thelargest of these is the pyramidof Khufu at Giza, also calledthe Great Pyramid. It is madeof more than 2 million blocksof stone. These blocks have anaverage weight of 2.5 tons, and the largest blocksweigh 15 tons. How did the Egyptians get thesehuge stones onto the pyramid?

Making the Connection1. The Great Pyramid is about 140 m tall. How

much work would be required to raise an average-sized pyramid block to this height? (2.5 tons � 2.2 � 104 N)

2. If the Egyptians used ramps with a mechani-cal advantage of 3, then an average blockcould be moved with a force of 7.3 � 103 N.If one person can pull with a force of 525 N,how many people would it take to pull anaverage block up such a ramp?

Wedge

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• Quick Activity Datasheet A SimpleInclined Plane

• Cross-Disciplinary Worksheet SocialStudies Connection—The Pyramids

GENERAL


There is some uncertainty abouthow the blocks were lifted,although simple machines musthave been involved. One hypoth-esis posits that the Egyptians pri-marily used ramps coated withmud to reduce friction. Theexercise here is based on thatmethod. Another hypothesisholds that the Egyptians usedlevers, mounted on either side ofeach block, to lift the blocks tosuccessively higher levels.

Answers1. W � Fd � (2.2 � 104 N)(140 m)

W � 3.1 � 106 J � 3.1 MJ2. 7.3 � 103 N/(525 N/person) �

14 people LogicalLS

Connection toSOCIAL STUDIESSOCIAL STUDIES

Compound MachinesMany devices that you use every day are made of more than onesimple machine. A machine that combines two or more simplemachines is called a A pair of scissors, forexample, uses two first class levers joined at a common fulcrum;each lever arm has a wedge that cuts into the paper. Most carjacks use a lever in combination with a large screw.

Of course, many machines are much more complex than these.How many simple machines can you identify in the bicycleshown in Figure 9? How many can you identify in a car?

compound machine.


1. List the six types of simple machines.

2. Identify the kind of simple machine represented by each of these examples:a. a drill bit b. a skateboard ramp c. a boat oar

3. Describe how a lever can increase the force without chang-ing the amount of work being done.

4. Explain why pulleys are in the lever family.

5. Compare the mechanical advantage of a long, thin wedge with that of a short, wide wedge. Which is greater?

6. Critical Thinking Can an inclined plane have a mechanicaladvantage of less than 1?

7. Critical Thinking Using the principle of a lever, explain why it is easier to open a door by pushing near the knob than bypushing near the hinges. What class of lever is a door?

8. Creative Thinking Choose a compound machine that you useevery day, and identify the simple machines that it contains.

S U M M A R Y

> The most basic machines are called simple machines.There are six types of simplemachines in two families.

> Levers have a rigid arm anda fulcrum. There are threeclasses of levers.

> Pulleys and wheel-and-axlemachines are also in thelever family.

> The inclined plane familyincludes inclined planes,wedges, and screws.

> Compound machines aremade of two or more sim-ple machines.

compound machinea machine made of more than one simple machine

▲

Figure 9A bicycle is made of many simplemachines.

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QuizList the two families of simplemachines and the type of simplemachines that belong to eachfamily. Then describe what acompound machine is.1. Lever family: levers, pulleys, and

wheel-and-axle machines2. Inclined plane family: inclined

planes, wedges, and screws3. A compound machine is any

machine made up of two or moresimple machines.

(Answers 1 and 2 could also be inthe reverse order.) LogicalLS

CloseClose


1. lever, pulley, wheel and axle, inclined plane,wedge, screw

2. a. screwb. inclined planec. lever

3. A lever can increase the force without increasingthe work done, because the output force willbe exerted through a smaller distance.

4. The middle of the pulley is the fulcrum; thewheel of the pulley is like a lever-arm extendedinto a circle. Pulleys are different from ordi-nary levers because you can change the loca-tion of the fulcrum of a lever.

5. A long, thin wedge has a greater mechanicaladvantage than a short, wide wedge becausethe ratio of its length to its height is greater.

6. If the MA were 1, the plane would be as longas it is tall. Because you cannot travel a dis-tance shorter than the actual height you needto lift an object, you cannot build an inclinedplane with a MA less than 1.


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• Concept Review • Quiz

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Presents Physical Science• Segment 3 Trebuchet Design• Critical Thinking Worksheet 3

See the Science in the News video guide for more details.

Videos

See “Continuation of Answers” at the end of the chapter.

Alternative AssessmentUnits of Energy Have groups of stu-dents research one of the different types

of units used to measure energy. These shouldinclude mechanical units (such as the erg andfoot-pound) and nonmechanical units (calorie,British thermal unit, kilowatt-hour, electronvolt, etc.). Each student should write a fewparagraphs describing some aspect of their

Writing assigned energy unit: the origins of the unit,the situations to which it is applied, why theunit is suitable to that situation (for instance,why kilowatt-hours are more convenientunits than joules for electric energy usage).The members of the group can then reporttheir findings in a group presentation to theclass. InterpersonalLS


> Explain the relationship between energy and work.> Define potential energy and kinetic energy.> Calculate kinetic energy and gravitational potential energy.> Distinguish between mechanical and nonmechanical

energy.

What Is Energy?

The world around you is full of energy. When you see a flashof lightning and hear a thunderclap, you are observing light

and sound energy. When you ride a bicycle, you have energy justbecause you are moving. Even things that are sitting still haveenergy waiting to be released. We use other forms of energy, likenuclear energy and electrical energy, to power things in ourworld, from submarines to flashlights. Without energy, livingorganisms could not survive. Our bodies use a great deal ofenergy every day just to stay alive.

Energy and WorkWhen you stretch a slingshot, as shown in Figure 10, you aredoing work, and you transfer energy to the elastic band. Whenthe elastic band snaps back, it may in turn transfer that energyagain by doing work on a stone in the slingshot. Whenever workis done, energy is transformed or transferred to another system.In fact, one way to define energy is as the ability to do work.

Energy is measured in joulesWhile work is done only when an object experiences a change inits position or motion, energy can be present in an object or asystem when nothing is happening at all. But energy can beobserved only when it is transferred from one object or system toanother, as when a slingshot transfers the energy from its elasticband to a stone in the sling.

The amount of energy transferred from the slingshot can bemeasured by how much work is done on the stone. Becauseenergy is a measure of the ability to do work, energy and workare expressed in the same units—joules.

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K E Y T E R M S

potential energy kinetic energymechanical energy

▲

Figure 10A stretched slingshot has the ability to do work.

OverviewBefore beginning this section,review with your students theObjectives listed in the StudentEdition. This section begins byrelating energy and work. Studentsthen will learn how to identify andcalculate potential and kineticenergy. The section concludes witha discussion of several examples ofnonmechanical energy.


Opening ActivityWrite the words work and energyon the chalkboard. Ask students to come up with words or phrasesthat relate to the concepts of workand energy. Have two studentvolunteers write down students’contributions in a list under eachword. Have students use the sec-tion headings and objectives in the chapter to devise a hypothesisabout how the terms are related.After they have read the section,have them develop a concept mapthat further explores the relationbetween the two terms. VerbalLS

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• Lesson Plan• Cross-Disciplinary Worksheet

Connection to Language Arts—The Concept of Energy


Transparencies

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GENERAL

www.scilinks.orgTopic: Potential EnergySciLinks code: HK4108

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potential energy theenergy that an object hasbecause of the position,shape, or condition of theobject

▲

Figure 11This apple has gravitational poten-tial energy. The energy resultsfrom the gravitational attractionbetween the apple and Earth.

Potential EnergyStretching a rubber band requires work. If you then release thestretched rubber band, it will fly away from your hand. Theenergy used to stretch the rubber band is stored as potentialenergy so that it can do work at a later time. But where is theenergy between the time you do work on the rubber band and thetime you release it?

Potential energy is stored energyA stretched rubber band stores energy in a form called

Potential energy is sometimes called energy ofposition because it results from the relative positions of objects ina system. The rubber band has potential energy because the twoends of the band are far away from each other. The energy storedin any type of stretched or compressed elastic material, such asa spring or a bungee cord, is called elastic potential energy.

The apple in Figure 11 will fall if the stem breaks off thebranch. The energy that could potentially do work on the appleresults from its position above the ground. This type of storedenergy is called gravitational potential energy. Any system of twoor more objects separated by a distance contains gravitationalpotential energy resulting from the gravitational attractionbetween the objects.

Gravitational potential energy depends on both mass and heightAn apple at the top of the tree has more gravitational potentialenergy with respect to the Earth than a similar apple on a lowerbranch. But if two apples of different masses are at the sameheight, the heavier apple has more gravitational potential energythan the lighter one.

Because it results from the force of gravity, gravitationalpotential energy depends both on the mass of the objects in a sys-tem and on the distance between them.

In this equation, notice that mg is the weight of the object innewtons, which is the same as the force on the object due to grav-ity. So this equation is really just a calculation of force times dis-tance, like the work equation.

potential energy.

grav. PE = mass × free-fall acceleration × heightPE = mgh

Gravitational Potential Energy Equation

Teaching TipWork and Energy When definingenergy as the ability to do work,point out that an acceptable defini-tion for work is the transfer ofmechanical energy from one object(or system) to another. When aforce is applied through a distance,work is done by one object onanother object. The energy to do the work comes from the firstobject, and is transferred to thesecond object. Energy transfer andconservation of energy will be dis-cussed in Section 4 in more detail,but the idea may be introducedhere.

Teaching TipGravitational Potential EnergyEquation Gravitational potentialenergy is different from weightbecause height is taken intoaccount. The equation for gravita-tional potential energy is reallyweight, mg, times height, h. This is also a measurement of the workthat the gravitational field woulddo on an object if it were to fallthrough a certain distance (theheight).

TeachTeach


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Potential Energy Potential energy is a termthat encompasses many types of energy.Other forms of potential energy include elas-tic, chemical, electrical, and magnetic. Thesemay seem like very different concepts to stu-dents, but all forms of potential energy dealwith position. Just as gravitational potentialenergy depends on distances between masses,

elastic potential energy depends on the elon-gation of elastic materials. Chemical poten-tial energy depends on bonds (position)between atoms within molecules. Electricalpotential energy depends on distancesbetween charged particles, and magneticpotential depends on the orientation of mag-netic particles in a magnetic field.


Height can be relativeThe height used in the equation for gravitational potential energyis usually measured from the ground. However, in some cases, arelative height might be more important. For example, if anapple were in a position to fall into a bird’s nest on a lowerbranch, the apple’s height above the nest could be used to calcu-late the apple’s potential energy relative to the nest.

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PracticePracticeGravitational Potential Energy1. Calculate the gravitational potential energy in the following

systems:a. a car with a mass of 1200 kg at the top of a 42 m high hillb. a 65 kg climber on top of Mount Everest (8800 m high)c. a 0.52 kg bird flying at an altitude of 550 m

2. Lake Mead, the reservoir above Hoover Dam, has a surface areaof approximately 640 km2. The top 1 m of water in the lakeweighs about 6.3 × 1012 N. The dam holds that top layer of water220 m above the river below. Calculate the gravitational potentialenergy of the top 1 m of water in Lake Mead.

3. A science student holds a 55 g egg out a window. Just before thestudent releases the egg, the egg has 8.0 J of gravitational poten-tial energy with respect to the ground. How far is the student’sarm from the ground in meters? (Hint: Convert the mass to kilograms before solving.)

4. A diver has 3400 J of gravitational potential energy after steppingup onto a diving platform that is 6.0 m above the water. What isthe diver’s mass in kilograms?

PracticeHINT

> The gravitational potentialenergy equation can be rearranged to isolate heighton the left.

mgh = PEDivide both sides by mg, and cancel.

�mm

ggh

� = �mPE

g�

h = �mPE

g�

> You will need this version of the equation for practice problem 3.

> For practice problem 4, youwill need to rearrange theequation to isolate mass onthe left. When solving theseproblems, use g = 9.8 m/s2.

Gravitational Potential Energy A 65 kg rock climber ascends acliff. What is the climber’s gravitational potential energy at apoint 35 m above the base of the cliff?

List the given and unknown values.Given: mass, m = 65 kg

height, h = 35 mfree-fall acceleration, g = 9.8 m/s2

Unknown: gravitational potential energy, PE = ? J

Write the equation for gravitational potential energy.

PE = mgh

Insert the known values into the equation, and solve.PE = (65 kg)(9.8 m/s2)(35 m)

PE = 2.2 × 104 kg•m2/s2 = 2.2 × 104 J

3

2

1

Additional ExamplesGravitational Potential EnergyA spider has 0.080 J of gravita-tional potential energy as it reachesthe halfway point climbing up a2.8 m wall. What is the potentialenergy of the spider at the top of thewall? (HINT: You do not need tofind the mass first.) (0.16 J)

A 0.50 g leaf falls from a branch4.0 m off the ground to a bird’snest 2.5 m off the ground. Howmuch gravitational potential energydid the leaf lose? ( 7.4 � 10�3 J)

Logical

1. a. PE � mgh � (1200 kg)(9.8 m/s2)(42 m) = 4.9 � 105 J

b. PE � (65 kg)(9.8 m/s2)(8800 m) � 5.6 � 106 J

c. PE � (0.52 kg)(9.8 m/s2)(550 m) � 2.8 � 103 J

2. PE � (6.3 � 1012 N)(220 m) �1.4 � 1015 J

3. h � �mPE

g� �

� 15 m

4. m � �PgEh� ��

(9.8 m34

/s020)(6

J.0 m)

� �

58 kg LogicalLS

8.0 J��

(0.055 kg)(9.8 m/s2)

PracticePractice

LS


393

• Math Skills Gravitational PotentialEnergy GENERAL


Potential Energy in Food Whenever weeat food, we are supplying our bodies withenergy. The body constantly uses that energyto perform actions and to stay alive, forexample to breathe and to pump blood. Aperson who exercises regularly needs morecalories of energy each day than someone whois inactive. In fact, each individual has a dailycaloric requirement based on their size andactivity level. The daily requirements listedin nutrition labels on food are for a personwho needs 2000 calories per day, but many

individuals actually need more or less thanthis average value.

If someone eats more calories than theirdaily requirement, the body stores the extraenergy in the form of fat. The energy—which is now in the form of potentialenergy—can be used at a later time when itis needed. Losing body fat requires using upthis potential energy by using more caloriesthan are taken in every day. This is bestaccomplished by a combination of caloriereduction and exercise.

Kinetic EnergyOnce an apple starts to fall from the branch of a tree, as in Figure 12A, it has the ability to do work. Because the apple ismoving, it can do work when it hits the ground or lands on thehead of someone under the tree. The energy that an object hasbecause it is in motion is called

Kinetic energy depends on mass and speedA falling apple can do more work than a cherry falling at thesame speed. That is because the kinetic energy of an objectdepends on the object’s mass.

An apple that is moving at 10 m/s can do more work than anapple moving at 1 m/s can. As an apple falls, it accelerates. Thekinetic energy of the apple increases as it speeds up. In fact, thekinetic energy of a moving object depends on the square of theobject’s speed.

Figure 12B shows a graph of kinetic energy versus speed for afalling apple that weighs 1.0 N. Notice that kinetic energy isexpressed in joules. Because kinetic energy is calculated usingboth mass and speed squared, the base units are kg•m2/s2, whichare equivalent to joules.

kinetic energy.

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kinetic energy the energyof a moving object due to theobject’s motion

▲

kinetic energy = ⎯12

⎯ × mass × speed squared

KE = ⎯12

⎯ mv2

Kinetic Energy Equation

Speed (m/s)

Kin

etic

ene

rgy

(J)

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

v = 8.0 m/sKE = 3.2 J

v = 2.0 m/sKE = 0.2 J

2.0 4.0 6.0 8.0 10.00

Kinetic comes from the Greekword kinetikos, which means“motion.”

V

Figure 12A falling apple can

do work on the groundunderneath—or onsomeone’s head.

A small increase inthe speed of an appleresults in a largeincrease in kineticenergy.

B

A

A B

Teaching TipKinetic Energy Kinetic energy,like all other kinds of energy, is anability to do work. Kinetic energyis probably the most obvious formof energy. If students have hadproblems grasping energy, now is agood time to drive it home. Whenyou think of an “energetic” person,you may think of someone whomoves around a lot. Somethingmoving has, by nature of itsmotion, an ability to do work.

Interpreting Graphs Havestudents examine the graph in Figure 12B. The graph showskinetic energy versus speed for afalling apple that weighs 1 N. Pointout that as the speed increases, thekinetic energy increases rapidly.That is because kinetic energydepends on the square of the speed.The curve on this graph is half of aparabola. Visual

Teaching Tip Kinetic Energy and MomentumSome students may be confusedabout the distinction betweenkinetic energy and momentum. Forthose students, write the equationsfor momentum and for kineticenergy side-by-side. Have studentsconsider how they are similar andhow they are different. (Both quan-tities depend on mass and velocity,but kinetic energy has a moresensitive dependence on velocitybecause of the squared quantity.)

LogicalLS

LS


Alternative AssessmentPotential and Kinetic Energy Have stu-dents write a brief paragraph describing thechanges in potential and kinetic energy in aroller coaster as it sits motionless at the top ofa rise, then begins rolling down the rise until it reaches the bottom. (At the top of the rise, the energy is all PE1 based on the coaster’sheight. Because the coaster is motionless, it hasno KE. As it starts rolling down the hill, itsheight decreases so it loses PE. At the same time,its speed increases, so it gains KE. At the bottomof the hill, the relative height is zero, so there is

no longer any PE. The speed has been graduallyincreasing, so KE is at a maximum at thispoint.)

After students have read Section 4, askthem to reread their paragraphs in light oftheir new understanding of energy conver-sions and conservation. (At that point theyshould recognize that, disregarding friction, thesum of PE and KE at any given time is a con-stant, so that the PE at the top equals the KE atthe bottom.) VerbalLS


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www.scilinks.orgTopic: Kinetic EnergySciLinks code: HK4075

Kinetic energy depends on speed more than massThe line on the graph of kinetic energy versus speed curvessharply upward as speed increases. At one point, the speed is 2.0 m/s and the kinetic energy is 0.20 J. At another point, thespeed has increased four times to 8.0 m/s. But the kinetic energyhas increased 16 times, to 3.2 J. In the kinetic energy equation,speed is squared, so a small increase in speed produces a largeincrease in kinetic energy.

You may have heard that car crashes are much more danger-ous at speeds above the speed limit. The kinetic energy equationprovides a scientific reason for that fact. Because a car has muchmore kinetic energy at higher speeds, it can do much morework—which means much more damage—in a collision.

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PracticePracticeKinetic Energy1. Calculate the kinetic energy in joules of a 1500 kg car moving

at the following speeds:a. 29 m/sb. 18 m/sc. 42 km/h (Hint: Convert the speed to meters per second

before substituting into the equation.)2. A 35 kg child has 190 J of kinetic energy after sledding down

a hill. What is the child’s speed in meters per second at the bottom of the hill?

3. A bowling ball traveling 2.0 m/s has 16 J of kinetic energy. Whatis the mass of the bowling ball in kilograms?

PracticeHINT

> The kinetic energy equationcan be rearranged to isolatespeed on the left.

⎯12

⎯ mv2 = KE

Multiply both sides by �m2

�.

��m2

�� × ⎯12

⎯ mv2 = ��m2

�� × KE

v2 = �2mKE�

Take the square root of each side.

�v�2� = ��2�mK�E��

v = ��2�mK�E��

You will need this version of the equation for Practice Problem 2.

> For Practice Problem 3, you will need to use the equationrearranged with mass iso-lated on the left:

m = �2vK2E

�

Math SkillsMath SkillsKinetic Energy What is the kinetic energy of a 44 kg cheetahrunning at 31 m/s?

List the given and unknown values.Given: mass, m = 44 kg

speed, v = 31 m/sUnknown: kinetic energy, KE = ? J

Write the equation for kinetic energy.

kinetic energy = ⎯12

⎯ × mass × speed squared

KE = ⎯12

⎯ mv2


KE = ⎯12

⎯(44 kg)(31 m/s)2

KE = 2.1 × 104 kg•m2/s2 = 2.1 × 104 J

3

2

1

Additional ExamplesKinetic Energy A 2 kg ball and a4 kg ball are traveling at the samespeed. If the kinetic energy of the 2 kg ball is 5 J, what is the kineticenergy of the 4 kg ball? (HINT:You do not have to solve for thespeed.) (10 J)

A 2.0 kg ball has 4.0 J of kineticenergy when traveling at a certainspeed. What is the kinetic energyof the ball when traveling at twicethe original speed? (HINT: You donot have to solve for the originalspeed.) (16 J) Logical

1. a. KE � 1/2 mv2 � (1/2)(1500 kg)(29 m/s)2 � 6.3 � 105 J

b. KE � (1/2)(1500 kg)(18 m/s)2 �2.4 � 105 J

c. v � (42 km/h)(1000 m/km)(1 h/3600 s) � 12 m/s KE � (1/2)(1500 kg)(12 m/s)2 �1.1 � 105 J

2. v � �2 KE/m� � ��(2

3)(519

k0�g

J)��

3.3 m/s

3. m � ��2vK2E

��

�(2(2.0)(1

m6

/Js))2

� � 8.0 kg

LogicalLS

PracticePractice

LS


395

• Math Skills Kinetic Energy• Science Skills Squares and Square

Roots

GENERAL


Transparencies

TT Kinetic Energy Graph

Rearranging the kinetic energy equationinvolves working with squares and squareroots. Ask an algebra teacher to visit yourclass to review these concepts with students.The Practice Hint shows students how tosolve the equation for velocity and also givesthem the equation rearranged to isolate mass.

MATHMATHCONNECTIONCONNECTIONStrategiesStrategies

INCLUSIONINCLUSION

Using note cards, ask students to label eachcard with a different form of energy. Includeat least five different forms of energy in theirnote cards. On the back of each card, askstudents to write a definition of each typeof energy and list examples of how the energyis used. Any additional information, such asequations, may be added to the note cards.These cards may be used as study tools andto show understanding of the section.

• Learning Disabled• English Language Learners

• Attention DeficitDisorder

Other Forms of EnergyApples have potential energy when they are hanging on a branchabove the ground, and they have kinetic and potential energywhen they are falling. The sum of the potential energy and the kinetic energy in a system is called Mechanical energy can also be thought of as the amount of workan object can do because of the object’s kinetic and potentialenergies.

Apples can also give you energy when you eat them. Whatkind of energy is that? In almost every system, there are hiddenforms of energy that are related to the motion and arrangementof atoms that make up the objects in the system.

Energy that lies at the level of atoms and that does not affectmotion on a large scale is sometimes called nonmechanicalenergy. However, a close look at the different forms of energy in asystem usually reveals that they are in most cases just specialforms of kinetic or potential energy.

Atoms and molecules have kinetic energyYou have learned that atoms and molecules are constantly inmotion. Therefore, these tiny particles have kinetic energy. Like abowling ball hitting pins, kinetic energy is transferred betweenparticles through collisions. The average kinetic energy of parti-cles in an object increases as the object gets hotter and decreasesas it cools down. In another chapter, you will learn more abouthow the kinetic energy of particles relates to heat and temperature.

Figure 13 shows the motion of atoms in two parts of an ironobject at different temperatures. In both parts, the iron atoms

inside the object are vibrating. The atoms in the hot-ter part of the object are vibrating more rapidly thanthe atoms in the cooler part, so they have greaterkinetic energy.

If a scientist wanted to analyze the motion of ahorseshoe in a game of “horseshoes,” the motion ofparticles inside the shoes would not be important.For the sake of that study, the energy due to themotion of the atoms would be considered nonme-chanical energy.

However, if the same scientist wanted to study thechange in the properties of iron when heated in ablacksmith’s shop, the motion of the atoms wouldbecome significant to the study, and the kineticenergy of the particles within the horseshoe wouldthen be viewed as mechanical energy.

mechanical energy.

396

mechanical energythe amount of work an objectcan do because of the object’skinetic and potential energies

▲

Figure 13The atoms in a hot object, such asa horseshoe, have kinetic energy.The kinetic energy is related to theobject’s temperature.

Teaching TipNonmechanical Energy Thedistinction between mechanicalenergy and nonmechanical energyis vague by nature. Nonmechanicalenergy is often called “internalenergy,” also a vague concept. Inmost cases, nonmechanical energycan be reduced to some kind ofmechanical energy (for instance, thekinetic energy of atoms in a gas asthe basis for thermal energy). Foreach type of energy introduced inthe next few pages, discuss how itcan also be considered as eitherkinetic or potential energy.

Teaching TipApproximations in ScienceExplain to students that the prac-tice of considering only majoreffects and ignoring small effects isa very common practice in science.As students read this page they mayask how scientists can considersome energy to be nonmechanicalat some times and not at others.Explain that scientists are quiteoften investigating one certainaspect of things.

For example, a physicist tryingto explain the flight of a horseshoecould include the motion of themolecules (with the help of a com-puter), but the physicist wouldprobably ignore the motion of themolecules because that motion isso small compared to the horse-shoe flying through the air.


Teacher ResourcesFor the New Teacher The fundamental con-cepts about energy that are explored in thissection will be used and built upon in the cov-erage of many other physics topics throughoutthe book. Topics that are especially relatedinclude the following: the kinetic theory ofmatter; heat and temperature; chemical reac-tions; energy derived from natural resources;nuclear energy; electricity; energy processes instars.

When working with those topics, be surestudents remember the information covered inthis section. For topics you have already stud-ied, you could have students review the topicsagain with their new understanding of energy.For upcoming topics, you may wish to brieflyreview this fundamental material before cov-ering the related topic.


396


Chemical reactions involve potential energyIn a chemical reaction, bonds between atoms break apart. Whenthe atoms bond together again in a new pattern, a different sub-stance is formed. Both the formation of bonds and the breakingof bonds involve changes in energy. The amount of chemicalenergy associated with a substance depends in part on the relativepositions of the atoms it contains.

Because chemical energy depends on position, it is a kind ofpotential energy. Reactions that release energy involve a decreasein the potential energy within substances. For example, when amatch burns, as shown in Figure 14, the release of stored energyfrom the match head produces light and a small explosion of hot gas.

Living things get energy from the sunWhere do you get the energy you need to live? It comes in theform of chemical energy stored in the food you eat. But wheredid that energy come from? When you eat a meal, you are eatingeither plants or animals, or both. Animals also eat plants or otheranimals, or both. At the bottom of the food chain are plants andalgae that derive their energy directly from sunlight.

Plants use photosynthesis to turn the energy in sunlight intochemical energy. This energy is stored in sugars and otherorganic molecules that make up cells in living tissue. When yourbody needs energy, some of these organic molecules are brokendown through respiration. Respiration releases the energy yourbody needs to live and do work.

397

Figure 14When a match burns, the chemi-cal energy stored inside the headof the match is released, produc-ing light and a small explosion ofhot gas.

REAL WORLDAPPLICATIONS

REAL WORLD

The Energy in FoodWe get energy from the food weeat. This energy is often measuredby another unit, the Calorie. OneCalorie is equivalent to 4186 J.

Applying Information1. Look at the nutrition label on

this “energy bar.” How manyCalories of energy does the bar contain?

2. Calculate how many joules of energy the bar contains bymultiplying the number of Calories by the conversion factor of 4186 J/Cal.

3. An average person needs totake in about 10 million joulesof energy every day. How manyenergy bars would you have toeat to get this much energy?

397

Effects of Energy It is notclear to many students thatforms of energy such as light,chemical, and sound energy can make things happen. Usethe examples on these pages to make the effects of energyclearer. For example, chemicalenergy makes a match burn.Return to this idea again inSection 4 when discussingenergy conversions.

The Energy in Food You canintroduce the idea that a foodCalorie is actually what scien-tists would call a kilocalorie, or1000 calories. So, to a scientist,one calorie (with a small “c”)equals 4.186 J. This is impor-tant if you are comparing thework you do exercising to theenergy in the food you eat.

Applying Information

1. 230 Cal2. 230 Cal � 4186 J/Cal �

9.6 � 105 J3. 1 � 107 J/9.6 � 105 J � 10

LogicalLS

A P P L I C A T I O N S

• Cross-Disciplinary Worksheet RealWorld Applications—Calories andNutrition

• Cross-Disciplinary WorksheetIntegrating Chemistry—ChemicalReactions


Energy Equivalence A piece of toast withbutter contains about 315 000 J of chemicalenergy. This is enough energy for the follow-ing tasks:

• running a car for 7 seconds (at 80 km/h)• jogging for 6 minutes• bicycling for 10 minutes• walking quickly for 15 minutes• sleeping for 1�

12

� hours• using a 60 W light bulb for 1�

12

� hours


Have students use the information in theReal-Life Connection to figure out how long each task could be performed with the energy from 230 Cal energy bar. (runninga car: 21 s; jogging: 18 min; bicycling: 30 min;walking quickly: 45 min; sleeping: 4�

12

� h; using a 60-watt light bulb: 4�

12

� h)As an extension, have students plot these

values on a bar graph to visually comparethe amount of time different tasks can beperformed with a given amount of energy.

LogicalLS

MATHMATHCONNECTIONCONNECTION

The sun gets energy from nuclear reactionsThe sun, shown in Figure 15, not only gives energy toliving things but also keeps our whole planet warmand bright. And the energy that reaches Earth fromthe sun is only a small portion of the sun’s totalenergy output. How does the sun produce so muchenergy?

The sun’s energy comes from nuclear fusion, atype of reaction in which light atomic nuclei com-bine to form a heavier nucleus. Nuclear powerplants use a different process, called nuclear fission,to release nuclear energy. In fission, a single heavynucleus is split into two or more lighter nuclei. Inboth fusion and fission, small quantities of mass areconverted into large quantities of energy.

You have learned that mass is converted to energyduring nuclear reactions. This nuclear energy is akind of potential energy stored by the forces holdingsubatomic particles together in the nuclei of atoms.

Electricity is a form of energyThe lights and appliances in your home are powered by anotherform of energy, electricity. Electricity results from the flow ofcharged particles through wires or other conducting materials.Moving electrons can increase the temperature of a wire andcause it to glow, as in a light bulb. Moving electrons also createmagnetic fields, which can do work to power a motor or otherdevices. The lightning shown in Figure 16 is caused by electronstraveling through the air between the ground and a thundercloud.

398

Figure 15The nuclei of atoms contain enor-mous amounts of energy. The sunis fueled by nuclear fusion reac-tions in its core.

Figure 16Electrical energy is derived fromthe flow of charged particles, as ina bolt of lightning or in a wire. Wecan harness electricity to powerappliances in our homes.

Teaching TipNuclear Fission Tell students toimagine a large water balloon filledalmost to the breaking point. Youhave to carry a balloon like thatvery carefully because the slightestbump will cause it to break. Nowhave students imagine two smallerwater balloons that are not as full.There is still a large amount offlexibility in the “wrapper” (orballoon). Large nuclei are like an overfilled water balloon. Thewrapper (strong nuclear forces that hold the nucleus together) is stretched to the breaking point.When a nucleus undergoes fission,it splits into smaller nuclei, where the nuclear forces are not“stretched” as much. The energythat is released is the difference in the energy required to hold thenuclei together. It takes less energyto contain two small nuclei than itdoes to contain one very large one.



398

What is Energy? Studentscommonly believe that energy isa fluid, an ingredient, or a fuel.Emphasize that energy is not amaterial substance. The defini-tion of energy as the ability todo work may seem vague tosome students; remind themthat the amount of energy asso-ciated with an object or systemcan be precisely quantified, asfor example with the KE andPE equations they have learnedin this section.

Tons of TNT Nuclear energy, especially as contained in nuclear weapons, is some-times expressed in units of tons of TNT.One ton of TNT is equal to the amount of energy released from the explosion of1 ton of TNT explosive. 1 ton of TNT �4.2 � 109 J.


1. Answers may include: kinetic energy, potentialenergy (gravitational or elastic), mechanicalenergy, nonmechanical energy, chemical energy,electrical energy, nuclear energy, light energy.

2. Energy is the ability to do work. Or whenwork is done, energy is transferred from oneobject to another.

3. Potential energy is energy due to position.Kinetic energy is the energy of motion.

4. a. gravitational PE and KE (both mechanical)b. kinetic energy of the molecules (nonme-

chanical), chemical energy of the molecules(nonmechanical)

c. elastic potential energy, kinetic energy asthe spring unwinds (both mechanical)

d. light energy (nonmechanical)e. gravitational PE (mechanical)

5. Storing the water up high gives the watergravitational potential energy, so the waterwill naturally flow out of the tank if needed.

6. The water tank in item 5 is a case wheregravitational PE is useful. Gravitational PEis dangerous to people hanging from the sideof a cliff or building.



Light can carry energy across empty spaceAn asphalt surface on a bright summer day is hotterwhere light is shining directly on it than it is in the shade.Light energy travels from the sun to Earth across emptyspace in the form of electromagnetic waves.

A beam of white light can be separated into a colorspectrum, as shown in Figure 17. Light toward the blueend of the spectrum carries more energy than light towardthe red end.

399


S U M M A R Y

> Energy is the ability to dowork.

> Like work, energy is meas-ured in joules.

> Potential energy is storedenergy.

> Elastic potential energy isstored in any stretched or compressed elasticmaterial.

> The gravitational potentialenergy of an object isdetermined by its mass, itsheight, and g, the free-fallacceleration due to gravity.PE � mgh.

> An object’s kinetic energy,or energy of motion, isdetermined by its mass andspeed. KE � �

12

�mv2.

> Potential energy and kineticenergy are forms ofmechanical energy.

> In addition to mechanicalenergy, most systems con-tain nonmechanical energy.

> Nonmechanical energydoes not usually affect sys-tems on a large scale.

Figure 17Light is made of electromagnetic wavesthat carry energy across empty space.

1. List three different forms of energy.

2. Explain how energy is different from work.

3. Explain the difference between potential energy and kineticenergy.

4. Determine what form or forms of energy apply to each ofthe following situations, and specify whether each form ismechanical or nonmechanical:a. a Frisbee flying though the airb. a hot cup of soupc. a wound clock springd. sunlighte. a boulder sitting at the top of a cliff

5. Critical Thinking Water storage tanks are usually built ontowers or placed on hilltops. Why?

6. Creative Thinking Name one situation in which gravitationalpotential energy might be useful, and name one situationwhere it might be dangerous.

7. Calculate the gravitational potential energy of a 93.0 kg skydiver who is 550 m above the ground.

8. What is the kinetic energy in joules of a 0.02 kg bullet traveling 300 m/s?

9. Calculate the kinetic or potential energy in joules for eachof the following situations:a. a 2.5 kg book held 2.0 m above the groundb. a 15 g snowball moving through the air at 3.5 m/sc. a 35 kg child sitting at the top of a slide that is 3.5 m

above the groundd. an 8500 kg airplane flying at 220 km/h


Quiz1. What is the SI unit of energy?

(a joule)

2. How is energy related to work?(Energy is the ability to do work.)

3. What are the two types ofmechanical energy, and what is the equation for each type?(potential energy: PE � mgh;kinetic energy: KE � �

12

� mv2)

4. List two examples of nonme-chanical energy. (Answers couldinclude any two of the following:energy of atoms and molecules;chemical energy; nuclear energy;electrical energy; energy of electro-magnetic waves)LogicalLS

CloseClose

399


GENERAL


Conservation of Energy

> Identify and describe transformations of energy.> Explain the law of conservation of energy.> Discuss where energy goes when it seems to disappear.> Analyze the efficiency of machines.

Imagine you are sitting in the front car of a roller coaster, suchas the one shown in Figure 18. The car is pulled slowly up the

first hill by a conveyor belt. When you reach the crest of the hill,you are barely moving. Then you go over the edge and start torace downward, speeding faster and faster until you reach thebottom of the hill. The wheels are roaring along the track. Youcontinue to travel up and down through a series of smallerhumps, twists, and turns. Finally, you climb another hill almostas big as the first, drop down again, and then coast to the end ofthe ride.

Energy TransformationsIn the course of a roller coaster ride, energychanges form many times. You may not havenoticed the conveyor belt at the beginning, butin terms of energy it is the most important partof the ride. All of the energy required for theentire ride comes from work done by the con-veyor belt as it lifts the cars and the passengersup the first hill.

The energy from that initial work is stored asgravitational potential energy at the top of thefirst hill. After that, the energy goes through aseries of transformations, or changes, turninginto kinetic energy and turning back into poten-tial energy. A small quantity of this energy istransferred as heat to the wheels and as vibra-tions that produce a roaring sound in the air.But whatever form the energy takes during theride, it is all there from the very beginning.

O B J E C T I V E S

SECTION

4

400

K E Y T E R M

efficiency

▲

Figure 18The tallest roller coaster in theworld is the Fujiyama, in FujikyuHighland Park, Japan. It spans 70 m from its highest to lowestpoints.

OverviewBefore beginning this section,review with your students theObjectives listed in the StudentEdition. In this section, studentslearn about energy transformationsand the law of energy conserva-tion. The section concludes with a discussion of the efficiency ofmachines.


Opening ActivityHave students devise a hypothesisabout the subject of the sectionbased on the objectives and head-ings. Have students create a con-cept map or graphic organizer toshow the structure of the section.Ask students to add details to theirconcept map or graphic organizeras they read the section. Verbal

Interpreting Visuals Have stu-dents discuss how the roller-coastercar in Figure 18 behaves going upand down the hills. Ask them todescribe the types and magnitudesof energy the car has at the highestand lowest points. VisualLS

TeachTeach

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MotivateMotivate

Bellringer

FocusFocus


400

SECTION

4

GENERAL

Plants use energy from the sun to carry outphotosynthesis. Invite a biology teacher to bea guest lecturer during your discussion ofenergy transformations. Have the biologyteacher explain the energy transformationsthat take place during the process ofphotosynthesis.

LIFE SCIENCELIFE SCIENCECONNECTIONCONNECTION

Invite a history teacher to be a guest lecturerduring your discussion of energy transforma-tion. Have the history teacher explain theimpact of new sources of power during theIndustrial Revolution.

SOCIAL STUDIESSOCIAL STUDIESCONNECTIONCONNECTION

Historical Perspective The First Roller Coasters The first rollercoasters were giant ice slides made in Russia.The first of these ice slides, which was in St.Petersburg, consisted of a 70-foot woodenframe packed with watered-down snow thatturned into ice. The sleds were made of two-foot ice blocks with seats carved into them.


Potential energy can become kinetic energyAlmost all of the energy of a car on a roller coaster is potentialenergy at the top of a tall hill. The potential energy graduallychanges to kinetic energy as the car accelerates downward. At thebottom of the lowest hill, the car has a maximum of kineticenergy and a minimum of potential energy.

Figure 19A shows the potential energy and kinetic energy of acar at the top and the bottom of the biggest hill on the Fujiyamaroller coaster. Notice that the system has the same amount ofenergy, 354 kJ, whether the car is at the top or the bottom of thehill. That is because all of the gravitational potential energy at thetop changes to kinetic energy as the car goes down the hill. Whenthe car reaches the lowest point, the system has no potentialenergy because the car cannot go any lower.

Kinetic energy can become potential energyWhen the car is at the lowest point on the roller coaster, it has nomore potential energy, but it has a lot of kinetic energy. Thiskinetic energy can do the work to carry the car up another hill.As the car climbs the hill, the car slows down, decreasing itskinetic energy. Where does that energy go? Most of it turns backinto potential energy as the height of the car increases.

At the top of a smaller hill, the car will still have some kinetic energy, along with some potential energy, as shown inFigure 19B. The kinetic energy will carry the car forward over thecrest of the hill. Of course, the car could not climb a hill tallerthan the first one without an extra boost. The car does not haveenough energy.

401

PE = 0 kJKE = 354 kJ v = 37.1 m/s

m = 515 kg

PE = 354 kJKE = 0 kJ v = 0 m/s

h = 70.0 mKE = 354 kJ PE = 0. kJv = 37.1 m/s

KE = 177 kJ PE = 177 kJv = 26.2 m/s

h = 35.0 m

m = 515 kg

Figure 19

As a car goes down a hill on a roller coaster,potential energy changes to kinetic energy.A At the top of this small hill, half the kinetic energy

has become potential energy. The rest of the kineticenergy carries the car over the crest of the hill at highspeed.

B

Teaching TipFriction Point out to students thatin a world with no friction, theexchange of energy—from poten-tial to kinetic and back again—could go on forever. In the realworld, some energy is lost to fric-tion as the car rolls along thetrack, so the roller coaster couldnot continue forever without someenergy input (such as that providedby the motor that pulls the cars upthe first hill).

Interpreting Diagrams Figure 19shows diagrams of two differenthills on a roller coaster. Walk stu-dents through the energy quanti-ties, which are generated by theequations learned in Section 3.What assumption is made in eachdiagram about the energy of theroller-coaster car? (The totalmechanical energy of the car at a later time is equal to the totalmechanical energy of the car at any earlier time. This is based on the law of conservation of energy.)

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• Lesson Plan


Transparencies

TT BellringerTM Energy Graphs

Because ice has a low coefficient of friction,the ice “cars” easily rolled down the ice slide.The seats were lined with straw or fur forinsulation. Sand was placed near the end ofthe slide. Friction between the sand and thesleds slowed them down near the bottom ofthe slide.

www.scilinks.orgTopic: Energy

TransformationsSciLinks code: HK4049

Energy transformations explain the flight of a ballThe relationship between potential energy and kinetic energy canexplain motion in many different situations. Let’s look at someother examples.

A tennis player tosses a 0.05 kg tennis ball into the air to setup for a serve, as shown in Figure 20. He gives the ball 0.5 J ofkinetic energy, and it travels straight up. As the ball rises higher,the kinetic energy is converted to potential energy. The ball willkeep rising until all the kinetic energy is gone. At its highestpoint, the ball has 0.5 J of potential energy. As the ball falls downagain, the potential energy changes back to kinetic energy.

Imagine that a tennis trainer wants to know how high the ballwill go when it is given 0.5 J of initial kinetic energy by a tennisplayer. The trainer could make a series of calculations using forceand acceleration, but in this case using the concept of energytransformations is easier. The trainer knows that the ball’s initialkinetic energy is 0.5 J and that its mass is 0.05 kg. To find out howhigh the ball will go, the trainer has to find the point where thepotential energy equals its initial kinetic energy, 0.5 J. Using theequation for gravitational potential energy, the height turns out tobe 1 m above the point that the tennis player releases the ball.

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Figure 20The kinetic energy of the ball atthe bottom of its path equals the potential energy at the top of the path.

KE = 0.5 J

h

PE � mgh

h �

h �

h � 1 m

0.5 J��(0.05 kg)(9.8 m/s2)

PE�mg

Teaching TipFlight of a Ball On the board,draw the flight of a ball thrownfrom one person to another. Thisshould be drawn as an invertedparabola. Ask students to identifywhere the ball has the maximumkinetic energy (at the bottom oneither side of the curve) and wherethe ball has the maximum potentialenergy (at the top). Point out tostudents that the ball you have justdrawn on the board does not have0 J KE at the top, because it istraveling sideways as well as upand down. Therefore, the ball stillhas some KE at the top. If it didnot, it would fall straight down,because there would be no energyat the top of the path to carry theball sideways. Visual

Interpreting Visuals Ask stu-dents if a greater initial kineticenergy from the tennis playerwould make the ball go higher or lower (higher). Then have themcalculate how high the tennis ballwould go if the tennis player givesit 0.8 J of initial kinetic energy(about 1.6 m). LogicalLS

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Tennis, anyone? When tossing a ball fora serve in tennis, the height of the ball tossis important. This is because the tennisplayer wants to hit the ball near the top ofthe arc, when it is not moving or is barelymoving. If the ball is thrown too high, itwill be harder to time the serve and hit theball at the right point. If the ball is toolow, the tennis player will not be able toextend his or her arm and therefore willnot hit the ball with as much force.

Alternative AssessmentAccounting for Energy Many exam-ples in the chapter so far have assumed

“ideal” circumstances, disregarding frictionand air resistance. However, once the ideathat mechanical energy can change to nonme-chanical energy is introduced, deviations fromthe ideal in “real world” situations can beexplained.

Writing Have students, after they have finishedreading this page, return to earlier examples in the chapter to consider if energy would betransferred from the system in realistic cir-cumstances (for instance, pushing a box up aramp, or a roller coaster). Have them write afew paragraphs about a given example, mak-ing sure that they account for as much of the“lost” energy as possible.


Energy transformations explain a bouncing ballBefore a serve, a tennis player usually bounces the ball a fewtimes while building concentration. The motion of a bouncingball can also be explained using energy principles. As the tennisplayer throws the ball down, he adds kinetic energy to the poten-tial energy the ball has at the height of her hand. The kineticenergy of the ball then increases steadily as the ball falls becausethe potential energy is changing to kinetic energy.

When the ball hits the ground, there is a sudden energy trans-formation as the kinetic energy of the ball changes to elastic potential energy stored in the compressed tennis ball. The elasticpotential energy then quickly changes back to kinetic energy asthe ball bounces upward.

If all of the kinetic energy in the ball changed to elastic poten-tial energy, and that elastic potential energy all changed back tokinetic energy during the bounce, the ball would bounce up tothe tennis player’s hand. Its speed on return would be exactly thesame as the speed at which it was thrown down. If the ball weredropped instead of thrown down, it would bounce up to the sameheight from which it was dropped.

Mechanical energy can change to other forms of energyIf changes from kinetic energy to potential energy and back againwere always complete, then balls would always bounce back tothe same height they were dropped from and cars on roller coast-ers would keep gliding forever. But that is not the way thingsreally happen.

When a ball bounces on the ground, not all of the kinetic energy changes to elastic potential energy. Some of the kinetic energy compresses the air around the ball, making a sound, andsome of the kinetic energy makes the ball, the air, and the groundslightly hotter. Because these other forms of energy are notdirectly due to the motion or position of the ball, they can beconsidered nonmechanical energy. With each bounce, the ballloses some mechanical energy, as shown in Figure 21.

Likewise, a car on a roller coaster cannot keepmoving up and down the track forever. The totalmechanical energy of a car on a roller coaster con-stantly decreases due to friction and air resistance.This energy does not just disappear though. Some ofit increases the temperature of the track, the car’swheels, and the air. Some of the energy compressesthe air, making a roaring sound. Often, when energyseems to disappear, it has really just changed to anonmechanical form.

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Figure 21With each bounce of a tennis ball,some of the mechanical energychanges to nonmechanical energy.

ACTIVITYACTIVITYQuickQuickQuick

Energy Transfer1. Flex a piece of thick wire

or part of a coat hangerback and forth about 10times with your hands. Are you doing work?

2. After flexing the wire, cautiously touch the partof the wire where youbent it. Does the wirefeel hot? What happenedto the energy you putinto it?

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ACTIVITYACTIVITYQuickQuick

Materials:• thick wire or coat hanger

Teacher’s Notes: Cautionstudents to avoid flexing the wire too many times, as itmay break or heat up enoughto cause burns. Performing this activity before theDemonstration on p. 404 willincrease students’ ability toidentify “missing” energy.

Answers1. The wire is displaced by a

force during the flexing, sowork is done on the wire.

2. The wire feels hot. This isbecause the mechanical energyinvolved in moving the wire istransformed into nonmechani-cal energy, namely, the kineticenergy of atoms in the wire.KinestheticLS

Energy TransformationsMany students believe thatenergy transformations involveonly one form of energy at atime. The transformation fromkinetic to thermal energy isespecially hard to visualize. Usethe Quick Activity to show howkinetic energy (the motion ofthe wire) can be converted intothermal energy (the increasedtemperature of the wire). Pointout that both types of energyinvolve motion; the first is on alarge scale (motion of a movingwire) and the second is on a molecular scale (motion ofatoms in the wire).

Transparencies

TT Kinetic and Potential Energy

• Quick Activity Datasheet EnergyTransfer GENERAL


The Law of Conservation of EnergyIn our study of machines, we saw that the work done on amachine is equal to the work that it can do. Similarly, in ourstudy of the roller coaster, we found that the energy present at thebeginning of the ride is present throughout the ride and at theend of the ride, although the energy continually changes form.The energy in each system does not appear out of nowhere andnever just disappears.

This simple observation is based on one of the most impor-tant principles in all of science—the law of conservation of energy. Here is the law in its simplest form.

Energy cannot be created or destroyed.

In a mechanical system such as a roller coaster or a swingingpendulum, the energy in the system at any time can be calculatedby adding the kinetic and potential energy to get the totalmechanical energy. The law of conservation of energy requiresthat at any given time, the total energy should be the same.

Energy doesn’t appear out of nowhereEnergy cannot be created from nothing. Imagine a girl jumpingon a trampoline. After the first bounce, she rises to a height of 0.5 m. After the second bounce, she rises to a height of 1 m. Because she has greater gravitational potential energy after thesecond bounce, we must conclude that she added energy to herbounce by pushing with her legs. Whenever the total energy in asystem increases, it must be due to energy that enters the systemfrom an external source.

Energy doesn’t disappearBecause mechanical energy can change to nonmechanical energy due to friction, air resistance, and other factors, tracingthe flow of energy in a system can be difficult. Some of the energy may leak out of the system into the surrounding environment, as when the roller coaster produces sound as itcompresses the air. But none of the energy disappears; it justchanges form.

Scientists study energy systemsEnergy has many different forms and can be found almost every-where. Accounting for all of the energy in a given situation canbe complicated. To make studying a situation easier, scientistsoften limit their view to a small area or a small number of objects. These boundaries define a system.

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COMPUTERS ANDTECHNOLOGYIn order for a flash-

light to work, there must be a supply of energy.

A flashlight battery con-tains different chemicals thatcan react with each other torelease energy. When theflashlight is turned on, chemi-cal potential energy changesto electrical energy, and elec-trons begin to flow through awire attached to the battery.Inside the bulb, the wire fila-ment begins to glow, and theenergy is transformed intolight energy.

After the flashlight hasbeen used for a certainamount of time, the batterywill run out of energy. It will have to be replaced orrecharged.

DemonstrationBouncing Balls (Time: About 10 minutes)

Materials• several different types of balls

(super ball, tennis ball, racquetball, squash ball, ball made of clay,steel ball bearing, etc.)

Rotating through all the types ofballs, hold two at a time approxi-mately 1 m above the floor or adesk. Drop the balls simultaneously.

Lead a discussion about whyeach ball bounces to a differentheight. Discuss the energy conver-sions mentioned in the text. Askstudents to hypothesize about the“disappearance” of the energy.Explain to students that each ballhas a different ability to store elas-tic potential energy—the super ballis very elastic, while the ball of clayis definitely not. Students should be able to conclude that someenergy is lost in the collision withthe floor or table. Lead students to the realization that some energyis released as sound, and some isstored internally as the temperatureof the ball rises. VisualLS



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GENERAL

Conservation of Energy The idea ofenergy conservation is counter-intuitive tomany students. Students do not understandthat this law can be used to explain phenom-ena. Also, students often interpret the phrase“energy is neither created or destroyed” tomean that energy is stored up in a systemand then released in its original form.

Apply the law to various examples toshow students how it can be used to

interpret observed phenomena and to makeaccurate predictions. Also explain that thelaw of energy conservation does not makeany stipulations about the forms of energyinvolved; the energy can change form multi-ple times, but the sum of all forms of energy(in a closed system) will not change.Introducing the concept of energy dissipa-tion while teaching the conservation lawmay also help alleviate confusion.

Alternative AssessmentOpen and Closed Systems Have studentsthink of different systems (just about anythingcan be considered a system). For each idea, askwhat boundaries define the system. Is the sys-tem open or closed? (Almost all systems areopen to some degree.) If open, where doesenergy come into and leak out of the system?Ask each student to choose an open system todiagram. Diagrams should illustrate the systemboundaries and should also show places where energy comes in and out of the system.

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Materials

Is energy conserved in a pendulum?

✔ 1–1.5 m length of string ✔ level ✔ nail or hook in the wall

✔ pencil with an eraser ✔ pendulum bob above a chalkboard

✔ meterstick

1. Hang the pendulum bob from the string in frontof a chalkboard. On the board, draw the diagramas shown in the photograph at right. Use themeterstick and the level to make sure the hori-zontal line is parallel to the ground.

2. Pull the pendulum ball back to the “X.” Make sure everyone is out of the way; then release thependulum and observe its motion. How highdoes the pendulum swing on the other side?

3. Let the pendulum swing back and forth severaltimes. How many swings does the pendulummake before the ball noticeably fails to reach itsoriginal height?

4. Stop the pendulum and hold it again at the “X”marked on the board. Have another studentplace the eraser end of a pencil on the intersec-tion of the horizontal and vertical lines. Makesure everyone is out of the way again, especiallythe student holding the pencil.

5. Release the pendulum again. This time itsmotion will be altered halfway through theswing as the string hits the pencil. How highdoes the pendulum swing now? Why?

6. Try placing the pencil at different heights alongthe vertical line. How does this affect the motionof the pendulum? If you put the pencil downclose enough to the arc of the pendulum, thependulum will do a loop around it. Why does that happen?

Analysis1. Use the law of conservation of energy to explain

your observations in steps 2–6.

2. If you let the pendulum swing long enough, it will start to slow down, and it won’t rise to theline any more. That suggests that the system haslost energy. Has it? Where did the energy go?

Systems may be open or closedA system might include a gas burner and a pot of water. A scien-tist could study the flow of energy from the burner into the potand ignore the small amount of energy going into the pot fromthe lights in the room, from a hand touching the pot, and so on.

When the flow of energy into and out of a system is smallenough that it can be ignored, the system is called a closed system.Most systems are open systems, which exchange energy with thespace that surrounds them. Earth is an open system, as shown inFigure 22. Is your body an open or closed system?

Figure 22Earth is an open system because itreceives energy from the sun andradiates some of its own energyout into space.

Energyfromthe sun

Teaching TipConservation of Energy Studentsmay confuse the conservation ofenergy law with the kind of energyconservation that is important toecologists and environmentalists.They are related but not the same.Conservationists want to preserveenergy in a useable form. Mostenergy technologies are inefficient,and after the energy has been used,it is no longer useful. (For example,once gasoline is burned, the energyhas been used to move the car, heatthe tires and road, and so on.)

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Teacher’s Notes: Attach thestring and hooks or nails beforestudents arrive. Try to makesure that the string is farenough from the wall that theplumb bob and string do notrub against anything as theyswing.

Analysis1. The bob’s PE at the beginning

is converted into KE at thebottom of the swing. The KEat the bottom is convertedback into PE as the bob rises.When the pencil is lowenough, the bob cannot riseenough to convert all KE intoPE, so the bob continues totravel, looping over the pencil.

2. The energy of the pendulum is lost to friction between thestring and hook, and veryslightly to air friction. Thiscauses the string and nail toheat up and the air to move,respectively.

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• Cross-Disciplinary WorksheetIntegrating Technology—Batteriesand Emerging Technology

• Cross-Disciplinary WorksheetIntegrating Environmental Science—The Conservation of Energy

• Quick Lab Datasheet Is energy con-served in a pendulum? GENERAL


Efficiency of MachinesIf you use a pulley to raise a sail on a sailboat like the one in Figure 23, you have to do work against the forces of friction in thepulley. You also have to lift the added weight of the rope and thehook attached to the sail. As a result, only some of the energy thatyou transfer to the pulley is available to raise the sail.

Not all of the work done by a machine is useful workBecause of friction and other factors, only some of the workdone by a machine is applied to the task at hand; the machinealso does some incidental work that does not serve any intendedpurpose. In other words, there is a difference between the totalwork done by a machine and the useful work done by themachine, that is, work that the machine is designed or intendedto do.

Although all of the work done on a machine has some effecton the output work that the machine does, the output workmight not be in the form that you expect. In lifting a sail, forexample, some of the work available to lift the sail, which wouldbe useful work, is transferred away as heat that warms the pulleybecause of friction. This warming is not a desired effect. Theamount of useful work might decrease slightly more if the pulleysqueaks, because some energy is “lost” as it dissipates into forcesthat vibrate the pulley and the air to produce the squeakingsound.

Efficiency is the ratio of useful work out to work inThe of a machine is a measure of how much usefulwork it can do. Efficiency is defined as the ratio of useful workoutput to total work input.

Efficiency is usually expressed as a percentage. To change an answer found using the efficiency equation into a percentage,just multiply the answer by 100 and add the percent sign, “%.”

A machine with 100 percent efficiency would produce exactlyas much useful work as the work done on the machine. Becauseevery machine has some friction, no machine has 100 percentefficiency. The useful work output of a machine never equals—and certainly cannot exceed—the work input.

efficiency

406

Figure 23Like all machines, the pulleys on a sailboat are less than 100 percent efficient.

Efficiency Equation

efficiency a quantity, usuallyexpressed as a percentage,that measures the ratio of useful work output to work input

▲efficiency �

useful work output��

work input

Teaching TipUseful Work Compare the lastsentence on this page, “The usefulwork output of a machine neverequals—and certainly cannotexceed—the work input,” with the following phrase from the sub-section in Section 1 titled Machinesand Mechanical Advantage:“Therefore, a machine allows the same amount of work to bedone . . .” How can these both betrue? (The law of conservation ofenergy requires that the energy thatgoes into the machine does not dis-appear, although it may change form.If the energy changes form, it may nolonger be able do the work that themachine is designed to do, so theuseful work output decreases.)

VerbalLS


this scale. This shows consumers the relativeefficiency of the appliance.

For example, a clothes washer label mightshow that washers of this type use from 312 kW•h/y to 1306 kW•h/y, with thewasher in question operating at 860 kW•h/y.Thus, this washing machine’s efficiency isabout average. The EnergyGuide labels alsoshow the approximate yearly operating costfor the appliance. (The labels became manda-tory in the 1970s; appliances made beforethen do not have the labels.)


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EnergyGuide Labels In the United States,consumers can easily determine the relativeefficiency of many common appliances,including refrigerators, freezers, clotheswashers, dishwashers, and room air condi-tioners. All they need to do is consult themandatory yellow EnergyGuide labelplaced on appliances by the manufacturers.These labels indicate the lowest and highestamounts of average yearly energy use forappliances of this type. The energy use forthe appliance in question is indicated on


Alternative AssessmentPerpetual Motion Machines Have studentsresearch some of the ideas people have hadthroughout history for perpetual motionmachines. Remind them that perpetual motionmachines are not possible, because someenergy always leaks out of a system. With this in mind, ask each student to choose aparticular example to illustrate on posterboard. Alternately, advanced students candesign and illustrate their own perpetualmotion machines. Display students’ postersaround the classroom. VerbalLS


Perpetual motion machines are impossibleFigure 24 shows a machine designed to keep on going foreverwithout any input of energy. These theoretical machines arecalled perpetual motion machines. Many clever inventors havedevoted a lot of time and effort to designing such machines. Ifsuch a perpetual motion machine could exist, it would require acomplete absence of friction and air resistance.

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PracticePracticeEfficiency1. Alice and Jim calculate that they must do 1800 J of work to

push a piano up a ramp. However, because they must also over-come friction, they actually must do 2400 J of work. What isthe efficiency of the ramp?

2. It takes 1200 J of work to lift the car high enough to change atire. How much work must be done by the person operating the jack if the jack is 25 percent efficient?

3. A windmill has an efficiency of 37.5 percent. If a gust of wind does 125 J of work on the blades of the windmill, howmuch output work can the windmill do as a result of the gust?

Efficiency A sailor uses a rope and an old, squeaky pulley toraise a sail that weighs 140 N. He finds that he must do 180 Jof work on the rope in order to raise the sail by 1 m (doing 140 J of work on the sail). What is the efficiency of the pulley? Express your answer as a percentage.

List the given and unknown values.Given: work input = 180 J

useful work output = 140 JUnknown: efficiency = ? %

Write the equation for efficiency.

efficiency �


To express this as a percentage, multiply by 100 and add the percent sign, “%.”efficiency = 0.78 × 100 = 78%

3

2

1

PracticeHINT

> The efficiency equation canbe rearranged to isolate anyof the variables on the left

> For practice problem 2, youwill need to rearrange theequation to isolate work input on the left side.

> For practice problem 3, youwill need to rearrange to isolate useful work output.

> When using these rearrangedforms to solve the problems,you will have to plug in val-ues for efficiency. Whendoing so, do not use a per-centage, but rather convertthe percentage to a decimalby dropping the percent signand dividing by 100.

Figure 24Theoretically, a perpetual motionmachine could keep going forever without any energy loss or energy input.

useful work output��

work input

efficiency = � 0.78140 J�180 J

Additional ExamplesEfficiency How much work mustyou do using a pulley that has anefficiency of 65 percent to raise a120 N box up to a 3.0 m shelf?(Hint: First solve for the workdone on the box.) (550 N)

If you improve the efficiency ofthe pulley to 85 percent by oiling it,how much work would you have todo? (420 N) Logical

1. efficiency � �((12840000

JJ))

� �

0.75 or 75%

2. work input ��usefu

elfwfic

oireknc

oyutput

��

�102.0205

J� � 4800 J

3. useful work output � (efficiency)(work input) � (0.375)(125 J) �46.9 JLogicalLS

PracticePractice

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• Science Skills Percentages• Math Skills Efficiency GENERAL


408


1. List three situations in which potential energy becomes kinetic energy and three situations in which kinetic energybecomes potential energy.

2. State the law of conservation of energy in your own words.Give an example of a situation in which the law of conser-vation of energy is demonstrated.

3. Describe the rise and fall of a basketball using the concepts of kinetic energy and potential energy.

4. Explain why machines are not 100 percent efficient.

5. Applying Knowledge Use the concepts of kinetic energy andpotential energy to describe the motion of a child on aswing. Why does the child need a push from time to time?

6. Creative Thinking Using what you have learned about energytransformations, explain why the driver of a car has to con-tinuously apply pressure to the gas pedal in order to keep thecar cruising at a steady speed, even on a flat road. Does thissituation violate the law of conservation of energy? Explain.

7. Efficiency When you do 100 J of work on the handle of a bicycle pump, it does 40 J of work pushing the air into thetire. What is the efficiency of the pump?

8. Efficiency and Power A river does 6500 J of work on a waterwheel every second. The wheel’s efficiency is 12 percent.a. How much work in joules can the axle of the wheel

do in a second?b. What is the power output of the wheel?

9. Efficiency and Work John is using a pulley to lift the sail onhis sailboat. The sail weighs 150 N and he must lift it 4.0 m.a. How much work must be done on the sail?b. If the pulley is 50 percent efficient, how much work must

John do on the rope in order to lift the sail?


S U M M A R Y

> Energy readily changesfrom one form to another.

> In a mechanical system,potential energy canbecome kinetic energy, andkinetic energy can becomepotential energy.

> Mechanical energy canchange to nonmechanicalenergy as a result of fric-tion, air resistance, or othermeans.

> Energy cannot be createdor destroyed, although itmay change form. This iscalled the law of conserva-tion of energy.

> A machine cannot do morework than the workrequired to operate themachine. Because of fric-tion, the work output of amachine is always some-what less than the workinput.

> The efficiency of a machineis the ratio of the usefulwork performed by themachine to the workrequired to operate themachine.

Machines need energy inputBecause energy always leaks out of a system, every machine needsat least a small amount of energy input to keep going. Unfor-tunately, that means that perpetual motion machines are impos-sible. But new technologies, from magnetic trains to high speedmicroprocessors, reduce the amount of energy leaking from sys-tems so that energy can be used as efficiently as possible.

Quiz1. What is one example of an

energy transformation? (Acceptall accurate responses. Exampleswould include gravitational poten-tial energy transferred to kineticenergy, or kinetic energy trans-formed to thermal energy.)

2. What is the law of the conserva-tion of energy? (Energy cannot becreated or destroyed.)

3. What is the efficiency of amachine, and how can it becalculated? (Efficiency is a meas-ure of how much useful work a machine can do for a givenamount of input work; efficiency �useful work output/work input.)LogicalLS

CloseClose


1. PE to KE: a falling ball, anything rollingdownhill, a pendulum on the downswing; KEto PE: a rising ball, anything rolling uphill, apendulum on the upswing

2. Energy can neither be created nor destroyed.In a swinging pendulum, energy is constantlytransformed from potential to kinetic energyand back again. In all of these transformations,the total mechanical energy remains the same.

3. The player throws the ball, giving it KE. Theball begins to rise and slow down as KE istransformed into PE. At its peak, the ball hasmaximum PE, then begins to fall, transform-ing PE into KE.

4. Friction prevents machines from being 100 percent efficient.

5. A child on a swing undergoes energy transfor-mations from maxium PE at the top (bothsides) to maximum KE at the bottom and backto maximum PE at the top of the oppositeside. The child needs a push every now andthen to make up for the energy lost to frictionbetween the rope and the support, as well assome energy lost to air resistance.


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GENERAL




409

Examine the graphs above and answer the following questions.

What type of graphs are these?

Identify the information provided by each graph.

Does the total mechanical energy change between 0.75 s and 1.5 s? What doeschange in this time interval?

Assume that the internal energy of the ball increases only when it bounces off thefloor. What can you tell about the number of times the ball has bounced between0.75 s and 1.5 s?

In which graph is the ball moving fastest? In which is the ball higher above theground? Explain your answers.

Suppose you are asked to design a ball that bounces to nearly the same height asthat from which it is dropped. In terms of energy, what property would this ballrequire?

Construct the type of graph best suited for the data given in the table below. Ismechanical energy conserved in this process? Explain your answer.

7

6

5

4

3

2

1

Graphing SkillsGraphing SkillsGraphing Skills

KineticEnergy55.8%

InternalEnergy15.0%

PotentialEnergy29.2%

t = 0.75 s

KineticEnergy18.4%

PotentialEnergy66.6%

InternalEnergy15.0%

t = 1.5 s

Time (s) Potential energy (J) Kinetic energy (J) Internal energy (J)

0 30.0 0 0

0.50 15.0 12.0 3.0

1.00 5.0 20.0 5.0

1.50 0 24.0 6.0

Total Mechanical Energy of a Bouncing Ball

Teaching TipInternal Energy Explain thatinternal energy is that portion ofenergy absorbed by the atoms ofan object, and accounts for the“lost” mechanical energy.

Answers1. pie charts2. the potential, kinetic, and internal

energy associated with the ballafter a particular time interval;The three types of energy arerelated by conservation of energy.

3. No. Total mechanical energy isconserved. KE decreases, PEincreases, internal energy remainsconstant

4. The ball has not bounced in thattime, as internal energy has notchanged.

5. The first graph has higher kineticenergy, so the ball is moving fasterat 0.75 s. Potential energy isgreater in the second graph, indi-cating that the ball is at a greaterheight with respect to the ground.

6. For the ball to bounce to nearlythe same height, it must notchange much mechanical energy to internal energy.

7. A bar graph would be best suitedfor the data. Mechanical energy isnot conserved, because the sum ofthe PE and KE values steadilydecreases. Total energy (PE, KE,and internal energy) is conservedin the process, because it equals30.0 J at all times.

Graphing SkillsGraphing Skills

409

7. _________ is determined by both mass and velocity.a. Work c. Potential energyb. Power d. Kinetic energy

8. Energy that does not involve the large-scalemotion or position of objects in a system is calleda. potential energy.b. mechanical energy.c. nonmechanical energy.d. conserved energy.

9. The law of conservation of energy states thata. the energy of a system is always

decreasing.b. no machine is 100 percent efficient.c. energy is neither created nor destroyed.d. Earth has limited energy resources.

10. Power is measured ina. watts.b. joules.c. newtons.d. kilograms.

11. Which of the following can a machine notdo?a. change the direction of a forceb. multiply or increase a forcec. redistribute workd. increase the total amount of work done

12. A machine with a mechanical advantage ofless than onea. increases speed and distance.b. multiplies force.c. increases output force.d. reduces distance and speed.

13. A perpetual motion machine is impossiblebecausea. machines require energy input.b. machines do not require energy input.c. machines have become too efficient.d. friction is negligible.

Chapter HighlightsBefore you begin, review the summaries of thekey ideas of each section, found at the end ofeach section. The key vocabulary terms arelisted on the first page of each section.

1. ________ is defined as force acting over adistance.a. Power c. Workb. Energy d. Potential energy

2. The quantity that measures how much amachine multiplies force is calleda. mechanical c. efficiency.

advantage. d. power.b. leverage.

3. Scissors are an example ofa. a lever. c. a wheel and axle.b. a wedge. d. a compound

machine.

4. The unit that represents 1 J of work doneeach second is thea. power. c. watt.b. newton. d. mechanical

advantage.

5. Units of joules could be used whenmeasuringa. the work done in lifting a bowling ball.b. the potential energy of a bowling ball

held in the air.c. the kinetic energy of a rolling

bowling ball.d. All of the above

6. Which of the following situations does notinvolve potential energy being changed into kinetic energy?a. an apple falling from a treeb. shooting a dart from a spring-loaded gunc. pulling back on the string of a bowd. a creek flowing downstream

UNDERSTANDING CONCEPTSUNDERSTANDING CONCEPTS

410

R E V I E WC H A P T E R 12

Understanding Concepts

1. c2. a3. d4. c5. d6. c7. d8. c9. c

10. a11. d12. a13. a

Using Vocabulary

14. Answers will vary. Work used inthe scientific sense should implya force acting on an object andchanging the object’s motion,while work in other contextsmay have other meanings.

15. Answers should contain somestatement that the word kineticrelates to motion.

16. wheel and axle, wedge, lever17. a. PE

b. KEc. PEd. KE


410

18. Because work is force times distance, the ele-phant does much more work than the mouse;the distance is the same, but the elephantweighs much more. Power is work divided bytime, and because the mouse beat the ele-phant by only a small amount of time, thefact that the elephant did much more workmeans that the power of the elephant is muchgreater than the power of the mouse.

19. Energy is the ability to do work. Doing workis transferring or transforming energy. Workis exerting a force through a distance tochange the motion, and thus the energy, of an

object. An object that has energy has the abil-ity to exert a force through a distance. Therate of changing energy, or work, per unittime is power.

20. Answers will vary. Students may say thatelectrical energy supplies the power forcomputers, light bulbs, air conditioners,refrigerators, and many other appliances andmachines, and that light energy providesplants with the energy that is converted byphotosynthesis into the chemical energy thatsustains living things.

C H A P T E R 12

R E V I EW

• Chapter Tests • Test Item Listing for ExamView®

Test Generator

GENERAL


14. Write one sentence using work in thescientific sense, and write anothersentence using it in a different,nonscientific sense. Explain thedifference in the meaning of work inthe two sentences.

15. The first page of this chapter shows an example of kinetic sculpture. You have nowalso learned the definition of kinetic energy.Given your knowledge of these two terms,what do you think the word kinetic means?

16. A can openeris a compoundmachine.Namethreesimplemachinesthat itcontains.

17. For each of the following, state whether thesystem contains primarily kinetic energy orpotential energy:a. a stone in a stretched slingshotb. a speeding race carc. water above a hydroelectric damd. the water molecules in a pot of boiling

water

18. An elephant and a mouse race up the stairs.The mouse beats the elephant by a full second, but the elephant claims, “I am morepowerful than you are, and this race hasproved it.” Use the definitions of work andpower to support the elephant’s claim.

19. How is energy related to work, force,and power?

20. List several examples of how electrical energyand light energy are useful to you.

21. You and two friends apply a force of 425 Nto push a piano up a 2.0 m long ramp.

a. Work How much work in joules hasbeen done when you reach the top of theramp?

b. Power If you make it to the top in 5.0 s,what is your power output in watts?

c. Mechanical Advantage If lifting thepiano straight up would require 1700 Nof force, what is the mechanical advan-tage of the ramp?

22. A crane uses a block and tackle to lift a2200 N flagstone to a height of 25 m.

a. Work How much work is done on theflagstone?

b. Efficiency In the process, the crane’s hydraulic motor does 110 kJ of work onthe cable in the block and tackle. What is the efficiency of the block and tackle?

c. Potential Energy What is the potentialenergy of the flagstone when it is 25 mabove the ground?

23. A 2.0 kg rock sits on the edge of a cliff 12 m above the beach.

a. Potential Energy Calculate the poten-tial energy in the system.

b. Energy Transformations The rock fallsoff the cliff. How much kinetic energywill it have just before it hits the beach?(Ignore air resistance.)

c. Kinetic Energy Calculate the speed ofthe rock just before it hits the beach.(For help, see Practice Hint on page395.)

d. Conservation of Energy What happensto the energy after the rock hits thebeach?

411

WRITINGS K I L L

USING VOC ABULARYUSING VOC ABULARY BUILDING MATH SKILLSBUILDING MATH SKILLS

Building Math Skills

21. a. 850 Jb. 170 Wc. 4.0

22. a. 55 000 J (or 55 kJ)b. 0.50 (or 50%)c. 55 kJ

23. a. 240 Jb. 240 Jc. 15 m/sd. It is transferred into the kinetic

energy of the sand, soundenergy (KE of molecules inair), and increased tempera-ture (KE of the molecules inthe rock and sand).

Thinking Critically

24. a. A, E, B, D, Cb. C, D, B, E, Ac. The lists are identical, except

in reverse order.25. Because energy cannot be cre-

ated, the machine can only putout an amount of work equal toor less than the energy within themachine, which is equal to orless than the work input.

26. nine times27. The work done by the hammer is

converted into kinetic energy ofthe nail and then into usefulwork on the wood, splitting itopen so the nail can enter. Muchof the energy goes into heatingthe hammer, nail, and wood.Some of the energy goes into theair as sound. This does not vio-late the law of conservation ofenergy.

28. The work done on the lever willbe greater than the work done onthe rock by the lever, becausesome energy is dissipated or“lost” as nonmechanical energyevery time energy is transferredfrom one object to another.

29. The advantage of using amachine lies in its ability toredistribute work by changingthe direction of an input force orchanging the distance over whichthe force is applied.

30. No, the design will not be suc-cessful, because the car will nothave enough kinetic energy toclimb a hill that is taller than thefirst one, without receiving anadditional input of energy.


411

Section Questions

Assignment GuideSection Questions

1 1, 2, 4, 10–12, 14, 18, 21, 29, 33, 372 3, 16, 28, 31, 34–36, 413 5–8, 15, 17, 19, 20, 26, 38–404 9, 13, 22–25, 27, 30, 32

29. Applying Knowledge If a machine cannotmultiply the amount of work, then what isthe advantage of using a machine?

30. Applying Knowledge You are designing aroller coaster in which a car will be pulledto the top of a hill and then will be releasedto roll freely down the hill toward the top ofthe next hill. The next hill is twice as high.Will your design be successful?

31. Applying Knowledge In two or three sen-tences, explain the force-distance trade-offthat occurs when a machine is used to makework easier. Use the lever as an example ofone type of trade-off.

32. Applying Knowledge Why do you think thatlevers have a greater mechanical efficiencythan other simple machines do?

33. Applying Knowledge You are trying to prythe lid off a paint can with a screwdriver,but the lid will not budge. Should you tryusing a shorter screwdriver or a longerscrewdriver? Explain.

34. Designing Systems Imagine you are tryingto move a piano into a second-floor apart-ment. It will not fit through the stairwell,but it will fit through a large window 3.0 moff the ground. The piano weighs 1740 Nand you can exert only 290 N of force.Design a system of machines you coulduse to lift the piano to the window.

35. Teaching Others Prepare a poster or aseries of models of common machines thatexplains their uses and how they work.Include a diagram next to each sample label-ing parts of each machine. Add your ownexamples of machines to the following list:nail clipper, wheelbarrow, can opener, nut-cracker, electric drill, screwdriver, tweezers,and a key in a lock.

24. Interpreting Graphics The diagram belowshows five different points on a roller coaster.

a. List the points in order from the pointwhere the car would have the greatestpotential energy to the point where itwould have the least potential energy.

b. Now list the points in order from thepoint where the car would have thegreatest kinetic energy to the point whereit would have the least kinetic energy.

c. How are your two lists related to each other?

25. Critical Thinking Use the law of conserva-tion of energy to explain why the workoutput of a machine can never exceed the work input.

26. Applying Knowledge If a bumper cartriples its speed, how much more work canit do on a bumper car at rest? (Hint: Use theequation for kinetic energy.)

27. Understanding Systems When a hammerhits a nail, there is a transfer of energy as the hammer does work on the nail.However, the kinetic energy and potentialenergy of the nail do not change very much.What happens to the work done by thehammer? Does this violate the law ofconservation of energy?

28. Critical Thinking You are attempting tomove a large rock using a long lever. Will thework you do on the lever be greater than,the same as, or less than the work done bythe lever on the rock? Explain your answer.

412

R E V I E WC H A P T E R 12

THINKING CR ITIC ALLYTHINKING CR ITIC ALLY

A

B

C

D

E

DEVELOPING LI FE/WORK SKILLSDEVELOPING LI FE/WORK SKILLS

31. Because work equals force multi-plied by distance, machines canbe used to decrease or increaseforce by changing the distanceover which the force is applied.A second-class lever, for example,multiplies input force by decreas-ing the distance over which thework occurs, whereas a third-class lever, decreases input forceby increasing distance.

32. Levers have a greater mechanicalefficiency than other simplemachines do, because there is less opportunity for energy to betransformed into unuseful non-mechanical energy in levers than in the other types of simplemachines. In most cases, usingpulleys, wheel and axles, inclinedplanes, wedges, and screwsinvolves more friction than usinglevers.

Developing Life/Work Skills

33. You should use a longer screw-driver. The output length remainsthe same (the distance from thefulcrum to the output force), butthe input length increases with a longer screwdriver, creating alarger mechanical advantage andtherefore a larger output force.


412

34. Answers may vary. One option is to use aramp that is 18 m long, but that is not practi-cal. Another option is a block and tacklewith a mechanical advantage of 6 (threemoving and three fixed pulleys).

35. Answers will vary. Student posters shouldreflect information from Section 2 of thischapter.

36. Mechanical energy is not conserved becauseof the longer distance travelled. However, thezigzag design acts as a series of inclinedplanes, so it provides the advantage ofspreading the work over a larger distance,

and thus decreasing the input force requiredat any given moment. The amount of powerprovided is lower because energy is spreadout over more time.

37. Work is done when the bag is lifted, becauseforce applied to the bag has moved the bag avertical distance in the direction of the force.Work, in the scientific sense, is not donewhen the bag is carried, because the motionof the bag is perpendicular to the direction ofthe force.

C H A P T E R 12

R E V I EW

36. Designing Systems Many mountain roadsare built so that they zigzag up a mountainrather than go straight up toward the peak.Discuss the advantage of such a design fromthe viewpoint of energy conservation andpower. Think of a winding road as a seriesof inclined planes.

37. Applying Knowledge Explain why you dowork on a bag of groceries when you pick itup, but not when you are carrying it.

38. Connection to Sports A baseball pitcher applies a force to the ball as his arm movesa distance of 1.0 m. Using a radar gun, thecoach finds that the ball has a speed of 18 m/s after it is released. A baseball has amass of 0.15 kg. Calculate the average forcethat the pitcher applied to the ball. (Hint:You will need to use both the kinetic energyequation and the work equation.)

39. Concept Mapping Copy the unfinished concept map below onto a sheet of paper.Complete the map by writing the correctword or phrase in the lettered boxes.

40. Connection to Earth Science Many fuelscome from fossilized plant and animal mat-ter. How is the energy stored in these fuels?How do you think that energy got into thefuels in the first place?

41. Connection to Biology When lifting anobject using the biceps muscle, the forearmacts as a lever with the fulcrum at the elbow.The input work is provided by the bicepsmuscle pulling up on the bone. Assumethat the muscle is attached 1.0 cm from theelbow and that the total length of the fore-arm from elbow to palm is 32 cm. Howmuch force must the biceps exert to lift anobject weighing 12 N? What class of leveris the forearm in this example?

Art Credits: Figs. 6,7, 8A, 8B, 13, Stephen Durke/Washington Artists; Fig. 22, Uhl Studios, Inc.

Photo Credits: Chapter Opener photo of George Rhodes’ auto-kinetic sculpture by Wayne Source;portrait of Alexander Calder by Tony Vaccaro/AKG Photo, London; Fig. 1, Amwell/GettyImages/Stone; Inquiry Lab, Sam Dudgeon/HRW; Figs. 2-3, Peter Van Steen/HRW; Fig. 4 (hammer),Michelle Bridwell/HRW; (pulley), Visuals Unlimited/A. J. Copley; (wheel), Peter Van Steen/HRW;(ramp), Sam Dudgeon/HRW; (wedge), Superstock; (drill bit), Dr. E. R. Degginger/Color-Pic, Inc.;Fig. 5 (hammer) Michelle Bridwell/HRW; (wheelbarrow), John P. Kelly/Getty Images/The ImageBank; (arm), Sam Dudgeon/HRW; Fig. 7, Peter Van Steen/HRW, Fig. 8 (ramp), Sam Dudgeon/HRW;(wedge), Superstock; (drill bit), Dr. E. R. Degginger/Color-Pic, Inc.; “Connection to Social Studies,”M. O’Neill/Getty Images/The Image Bank; Figs. 9-10, Peter Van Steen/HRW; Fig. 11, Picture Perfect;Fig. 12, Kindra Clineff/The Picture Cube/Index Stock; Fig. 13, Randy Ury/Corbis Stock Market; Fig. 14,Al Francekevich/Corbis Stock Market; “Real World Applications,” Peter Van Steen/HRW; Fig. 15,NASA/Phototake; Fig. 16, Steve Bloom/Picture Perfect; Fig. 17, E. R. Degginger/Color-Pic, Inc.; Fig. 18,AFP/CORBIS; Fig. 20, Getty Images/FPG International; Fig. 21, Henry Groskinsky/Peter Arnold, Inc.;“Inquiry Lab,” Sam Dudgeon/HRW; Fig. 23, Visuals Unlimited/Albert J. Copley; Fig. 37, HankMorgan/Rainbow Inc.; “Chapter Review,” (can opener), Peter Van Steen/HRW; “Skill Builder Lab,”Peter Van Steen/HRW, “Career Link,” Ken Kinzie/Latent Image Photography/HRW.

413

INTEGR ATING CONCEPTSINTEGR ATING CONCEPTS

b.

c. d.position

or

which measures

Energy a.

includes

kinetic energy

distance

destroyed

transformed e.

includes can be

is the abilityto do

but neverwhich is energyassociated with

which isenergy of

actingover a

www.scilinks.orgTopic: Energy and Sports SciLinks code: HK4047

Integrating Concepts

38. 24 N;

W � KE, F � d � �12�mv2

F � �m2vd

2� ��

(0.152k(1g.)0(1

m8

)m/s)2

�

� 24 N39. a. work

b. potential energy c. motiond. createde. force

40. chemical energy; Light (solar)energy was converted into chemi-cal energy through photosynthesis.

41. 380 N; The forearm is acting as athird-class lever. work input � work output;Fi � di � Fo � do

Fi � Fo �ddo

i� � 12 N ��13.

20

ccmm��

� 380 N


413

Transparencies

TT Concept Mapping

Raised objects have gravitational potential energy. Moving objects havekinetic energy. How are these two quantities related in a system that involves a ball rolling down a ramp?

> Measure the height, distance traveled, and time interval for aball rolling down a ramp.

> Calculate the ball’s potential energyat the top of the ramp and its kineticenergy at the bottom of the ramp.

> Analyzethe results to find the relationshipbetween potential energy and kineticenergy.

balanceboard, at least 90 cm (3 ft) longboxgolf ball, racquet ball, or handballmasking tapemeterstickstack of books, at least 60 cm (2 ft) highstopwatch

USING SCIENTIFIC METHODS

Introduction

Objectives

Materials

414

Determining Energy for a Rolling Ball

� Procedure

Preparing for Your Experiment1. On a blank sheet of paper, prepare a table

like the one shown below.

Table I Potential Energy and Kinetic Energy

2. Measure the mass of the ball, and record it in your table.

3. Place a strip of masking tape across the board closeto one end, and measure the distance from the tapeto the opposite end of the board. Record this dis-tance in the row labeled “Length of ramp.”

4. Make a catch box by cutting out one side of a box.

5. Make a stack of books approximately 30 cm high.Build a ramp by setting the taped end of the board ontop of the books, as shown in the photograph on thenext page. Place the other end in the catch box.Measure the vertical height of the ramp at the tape,and record this value in your table as “Height of ramp.”

Height 1 Height 2 Height 3

Mass of ball (kg)

Length of ramp (m)

Height of ramp (m)

Time ball traveled, first trial (s)

Time ball traveled, second trial (s)

Time ball traveled, third trial (s)

Average time ball traveled (s)

Final speed of ball (m/s)

Final kinetic energy of ball (J)

Initial potential energy of ball (J)

DETERMINING ENERGYFOR A ROLLING BALL

Teacher’s Notes

Time Required 1 lab period

RatingsTEACHER PREPARATION 1

STUDENT SETUP 2

CONCEPT LEVEL 2

CLEANUP 1

Skills Acquired• Collecting data• Communicating• Identifying/Recognizing patterns• Interpreting• Measuring• Organizing and analyzing data

The Scientific MethodIn this lab, students will:• Make Observations • Analyze the Results • Draw Conclusions• Communicate Results

MaterialsMaterials are listed for each group.

Safety CautionsThe balls used for the experimentcould cause trip and fall hazards.Be sure that students use a catchbox at the end of the ramp.

E A S Y H A R D

1 32 4E A S Y

414



Making Time Measurements6. Place the ball on the ramp at the tape. Release the ball, and measure how long it

takes the ball to travel to the bottom of the ramp. Record the time in your table.

7. Repeat step 6 two more times and record the results in your table. After three trials, calculate the average travel time and record it in your table.

8. Repeat steps 5–7 with a stack of books approximately 45 cm high, and repeat thesteps again with a stack approximately 60 cm high.

� Analysis1. Calculate the average speed of the ball using the following equation:

2. Multiply average speed by 2 to obtain the final speed of the ball, and record thefinal speed.

3. Calculate and record the final kinetic energy of the ball by using the following equation:

4. Calculate and record the initial potential energy of the ball by using the followingequation:

grav. PE � mass of ball � (9.8 m/s2) � height of ramp

PE � mgh

� Conclusions5. For each of the three heights, com-

pare the ball’s potential energy atthe top of the ramp with its kineticenergy at the bottom of the ramp.

6. How did the ball’s potential andkinetic energy change as theheight of the ramp was increased?

7. Suppose you perform this experi-ment and find that your kineticenergy values are always just a lit-tle less than your potential energyvalues. Does that mean you didthe experiment wrong? Why orwhy not?

average speed �length of ramp

��average time ball traveled

KE � � mass of ball � (final speed)2

KE � mv21�2

1�2

415

Tips and TricksBefore the lab, review the law ofconservation of energy with stu-dents and discuss the concepts ofkinetic and potential energy. Givestudents examples such as a speed-ing car or a skydiver for kineticenergy and a coconut in a tree or a book on the edge of a desk forpotential energy.

ProcedureExplain to students that they mayhave some difficulty obtaining pre-cise measurements of the time ittakes the ball to roll down theramp. Have the students try theexperiment a few times to decideon their best method for timing.

Answers to Analysis1. Answers will vary. All answers

should be between 0.25 s and0.35 s for the ramp heights usedin the experiment.

2. Answers will vary.3. Answers will vary. Answers should

all be less than 1.0 J.4. Answers will vary. Answers should

all be less than 1.0 J.

Answers to Conclusions5. The gravitational potential energy

at the top and the kinetic energyat the bottom should be nearly thesame.

6. The higher the ramp, the greaterthe potential and kinetic energies.

7. No. Not all of the gravitationalpotential energy is converted tokinetic energy because someenergy is given up to the sur-roundings by friction.

415

Sample Data TablePotential Energy and Kinetic Energy

Height 1 Height 2 Height 3

Mass of ball (kg) 0.045 0.045 0.045

Length of ramp (m) 1.513 1.513 1.513

Height of ramp (m) 0.28 0.445 0.583

Time ball traveled, first trial (s) 1.59 1.31 1.09

Time ball traveled, 1.62 1.28 1.06second trial (s)

Time ball traveled, third trial (s) 1.56 1.25 1.04

Average time ball traveled (s) 1.59 1.28 1.06

Final speed of ball (m/s) 1.90 2.36 2.86

Final kinetic energy of ball (J) 0.081 0.125 0.184

Initial potential energy of ball (J) 0.123 0.196 0.257

• Datasheet Determining Energy for aRolling Ball

• Observation Lab Exploring Work andEnergy

• CBL™ Probeware Lab DeterminingWhich Ramp Is More Efficient

GENERAL


415A Chapter 12 • Work and Energy

Continuation of Answers

Continuation of Answers from p. 390

Section 2 Review

7. A door is normally a second-class lever. Pushing near the knob iseasier because the input distance is longer. If you push near thehinges, the input arm is shorter than the output arm, and the doorbecomes a third-class lever, with an MA of less than 1.

8. Answers will vary. A pencil sharpener, for example, is a compoundmachine that consists of a couple of screws (the blades to sharpenthe pencil), wedges (the edges of those blades), and a wheel andaxle (the crank).


Section 3 Review

7. PE � mgh � (93.0 kg)(9.8 m/s2)(550 m) � 5.0 � 105 J8. KE � �

12

� mv2 � (�12

�)(0.02 kg)(300 m/s)2 � 900 J9. a. PE � mgh � (2.5 kg)(9.8 m/s2)(2.0 m) � 49 J

b. KE � �12

� mv2 � (�12

�)(0.015 kg)(3.5 m/s)2 � 0.092 Jc. PE � mgh � (35 kg)(9.8 m/s2)(3.5 m) � 1200 Jd. KE � �

12

� mv2 � (�12

�)(8500 kg)[(220 km/h)(1000 m/km)(1 h/3600 s)]2 � 1.6 � 107 J


Section 4 Review

6. The driver must keep transferring potential energy from the gas tothe kinetic energy of the car to make up for the losses due to fric-tion within the car’s mechanism and between the tires and the road.This does not violate the law of conservation of energy becausemechanical energy is transformed into nonmechanical forms.

7. efficiency � useful work output/work input � (40 J)/(100 J) � 0.4or 40%

8. a. useful work output � (efficiency)(work input) �(0.12)(6500 J) � 780 J

b. P � W/t � 780 J/1 s � 780 W 9. a. W � Fd � (150 N)(4.0 m) � 6.0 � 102 J

b. work input � useful work output/efficiency �6.0 � 102 J/0.50 � 1200 J



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CareerLinkCareerLinkCareerLink

In a sense, civil engineering has beenaround since people started to buildstructures. Civil engineers plan and design public projects, such as roads,bridges, and dams, and private proj-ects, such as office buildings. To learnmore about civil engineering as a ca-reer, read the profile of civil engineer Grace Pierce, who works at Traffic Systems, Inc., in Orlando, Florida.

Civil Engineer

What do you do as a civil engineer?

I’m a transportation engineer with a bache-lor’s degree in civil engineering. I do a lot of transportation studies, transportationplanning, and engineering—anything to dowith moving cars. Right now, my clients areabout a 50-50 mix of private and public.

What part of your job doyou like best?

Transportation planning. On the planningside, you get to be involved in developmentsthat are going to impact the community . . .being able to tap into my creative sense tohelp my clients get what they want.

What do you find most rewarding about your job?

Civil engineering in civil projects. They arevery rewarding because I get to see myinput on a very fast time scale.

??

??

??

What kinds of skills do youthink a good civil engineerneeds?

You need a good solid academic back-ground. You need communication skills and writing ability. Communication is key.You should get involved in activities orclubs like Toastmasters, which can help youwith your presentation skills. You should getinvolved with your community.

What part of your educa-tion do you think was most important?

Two years before graduation, I was giventhe opportunity to meet with the owner ofa company who gave me a good preview ofwhat he did. It’s really important to get outthere and get the professional experienceas well as the academic experience beforeyou graduate.

??

??

“I get to help inprojects that pro-vide a betterquality of life forpeople. It’s agood feeling.”

As a civil engineer,Grace Pierce designsroads and intersections.

416

CIVIL ENGINEER

Teaching TipCivil engineers rely on many of theprinciples of physics to plan theirprojects and be certain they areappropriate. In Grace Pierce’s workwith Traffic Systems, Inc., she usesthe concepts of speed, acceleration,and force that were all discussed inthis textbook

Career LinkCareer Link

According to the Southern CaliforniaAssociation of Governments, by the year2020, traffic in Los Angeles will movetwice as slow as it does now.


You didn’t enter collegeimmediately after highschool. Did you have to doanything differently from ayounger student?

I went to school as an older student. Ididn’t go back to college until age 27. Iknew that because I was competing withyounger folks, I really had to hustle.

“ I think my industry is going toward the ‘smart’ movement of vehicles and people. The future is intelligent transportation systems using automated systems.”

—Grace Pierce

??

??

www.scilinks.orgTopic: EngineerSciLinks code: HK4156

What advice do you havefor anyone interested incivil engineering?

Have a vision. Have a goal, whatever thatmight be, and envision yourself in thatarena. Work as hard as you can to realizethat vision. Find out what you want to do,and find someone who can mentor you.Use every resource available to you in highschool and college, including professors andpeople in the community. And in the pro-cess, have fun. It doesn’t have to be dreary.

417

COMPUTERS AND TECHNOLOGY One fast-growing area of traffic researchis building new models that canpredict traffic flow patterns.Many of these models are com-puter simulations of traffic situ-ations, either generated with afew key equations or with sim-ulations of independent vehicleswhose movement is governedby a few basic rules. Anotherpromising field of inquiry com-pares the creation and dilutionof traffic jams by individualdrivers’ behaviors to the behav-ior of the particles in a liquidas the liquid undergoes a phasechange to become a solid.

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CHAPTER12 CHAPTER Work and Energyparhamscience.pbworks.com/w/file/fetch/50020787/Holt_Physical...Work and Energy srthe s CHAPTER 12 1 Work, Power, and Machines What Is Work? Power