section 12.1 12.1 forces -...

12.1 Forces

Reading StrategyRelating Text and Visuals Copy the tablebelow. As you read, look carefully at Figures 2,3, and 5. Complete the table by describing theforces and motion shown in each figure.

Key ConceptsHow do forces affect themotion of an object?

What are the four maintypes of friction?

How do gravity andair resistance affect afalling object?

In what direction doesEarth’s gravity act?

Why does a projectilefollow a curved path?

Vocabulary◆ force◆ newton◆ net force◆ friction◆ static friction◆ sliding friction◆ rolling friction◆ fluid friction◆ air resistance◆ gravity◆ terminal velocity◆ projectile motion

A powerful storm is approaching. The weather forecast calls forgale-force winds. Many people in the city decide to leave work earlyin order to get home before things get worse. As shown in Figure 1, a

man pushes ahead into a strong wind and shields himself from thedriving rain with an umbrella. The strong wind makes it very

difficult for him to hold onto his umbrella. To keep theumbrella from being pulled from his hands, he tightlysqueezes the umbrella handle. Elsewhere, a store ownerattempts to bring in a folding sign that hasn’t blown awaybecause it is chained to a pole.

Wind is but one example of the many forces you expe-rience every day. The study of forces is a very important part ofphysics. As you read this section you’ll learn what forces are andhow they make things move.

What Is a Force?The man out in the storm is battling the forces of wind. A forceis a push or a pull that acts on an object. A force can causea resting object to move, or it can accelerate a moving object bychanging the object’s speed or direction. The force of the windpushing against the man slows his speed. A strong gust couldeven change the direction in which he was moving.

2B

3

a. ?

c. ?

e. ?

g. ?

i. ?

b. ?

d. ?

f. ?

h. ?

j. ?

2A

5A

5B

Figure Is Net Force 0? Effect on Motion

Figure 1 The wind pushesagainst the man and hisumbrella. The push from thewind is a force.

356 Chapter 12

FOCUS

Objectives12.1.1 Describe examples of force

and identify appropriate SIunits used to measure force.

12.1.2 Explain how the motion of an object is affected whenbalanced and unbalancedforces act on it.

12.1.3 Compare and contrastthe four kinds of friction.

12.1.4 Describe how Earth’s gravity and air resistance affect falling objects.

12.1.5 Describe the path of a projectileand identify the forces thatproduce projectile motion.

Build VocabularyLINCS Have students use the LINCSstrategy to learn and review the termsforce, friction, air resistance, and gravity.In LINCS exercises, students List theparts that they know (list the word andits definition on an index card). Imaginea picture (create a mental image of theterm’s meaning and describe the imageusing real words). Note a sound-alikeword (think of a familiar word thatsounds like the term or part of it).Connect the terms (make up a shortstory about each term’s meaning thatuses the sound-alike word). Self-test(quiz themselves).

Reading Strategya. Yes b. No motion c. Yesd. No motion e. Yes f. No motiong. Yes h. No motion i. No j. Pottedtree accelerates

INSTRUCT

What Is a Force?Use VisualsFigure 1 Emphasize that the wind actsas a force because it pushes against theman. Ask, In what ways can the forceof the wind alter the man’s motion?(It can change the speed or direction ofmotion.) Will these changes cause theman to accelerate? (Yes)Visual

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Reading Focus

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Section 12.1

Print• Reading and Study Workbook With

Math Support, Section 12.1• Transparencies, Chapter Pretest and

Section 12.1

Technology• Interactive Textbook, Section 12.1• Presentation Pro CD-ROM, Chapter Pretest

and Section 12.1• Go Online, NSTA SciLinks, Forces

Section Resources

356 Chapter 12

Forces and Motion 357

Measuring Force Forces are often easy to measure. In fact, ifyou’ve ever shopped at a grocery store, you may have measured forcesusing a spring scale like the one shown in Figure 2. The stretch of thespring in the scale depends on the amount of weight (a type of force)acting on it. As more fruit is placed on the scale, the spring is stretchedfarther and the scale reading increases.

Units of Force Force is measured in newtons, abbreviated as N.One newton is the force that causes a 1-kilogram mass to accelerate ata rate of 1 meter per second each second (1 m/s2). In fact, 1 newton isequal to 1 kilogram-meter per second squared (1 N � 1 kg•m/s2). Thenewton is named after Sir Isaac Newton (1642–1727), the English sci-entist who explained how force, mass, and acceleration are related.You’ll learn more about forces and mass in the next section.

Representing Force You can use anarrow to represent the direction and strength ofa force. The direction of the arrow representsthe direction of the force. The length of thearrow represents the strength, or magnitude, ofthe force.

In Figure 2, the force arrows represent theweight of the items on the scale. Both arrowspoint down because weight always acts down-ward. The lengths of the arrows show you thatmore weight acts on the scale in Figure 2B thanthe one in Figure 2A.

Combining ForcesHave you ever helped to push a car that has runout of gas? If you have, you were taking advan-tage of the fact that forces can be combined. Theindividual force of each person’s push adds withthe others into a larger force that allows you tomove the car.

You can combine force arrows to show theresult of how forces combine. That is, forces inthe same direction add together and forces inopposite directions subtract from one another.The net force is the overall force acting on anobject after all the forces are combined.

What amount of force accelerates a 1-kilogrammass at 1 m/s2?

A B

Figure 2 The downward force arrows representthe weight (a type of force) on the scales. The dialindicator gives a visual measure of the weight.Calculating What is the approximate weightdifference between the two scale readings?

Build Science Skills

Measuring

Purpose Students learn to measure force and sketch force arrows.

Materials 5-N spring scale, centimeterruler, book, string, 5 objects (such asbooks) weighing from 1 to 5 newtons

Class Time 30 minutes

Procedure Have students pull eachobject at a slow, constant speed across aflat surface using the spring scale. Theymay need to attach the scale to the objectusing string. Students should record theforce required to pull each object. Next,have them draw force arrows for eachobject. The arrows should be drawn toscale using a scale factor of 1 centimeterper newton of force.

Expected Outcome Students willdraw scaled force arrows for eachobject. Logical

Combining ForcesBuild Reading LiteracyIdentify Main Ideas/Details Refer topage 98D in Chapter 4, which providesthe guidelines for identifying main ideasand details.

Ask students to explain the main conceptin the first two short paragraphs underthe head Combining Forces on p. 357.(Forces can be combined.) Encouragestudents to illustrate the main idea witha diagram. Ask, What would be theeffect on the direction of the net forceif some of the people push the carforward while others push it back-wards? (The net force would be in thedirection of the people who were pushingwith a greater force.)Logical, Portfolio

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Customize for English Language Learners

Illustrate Content You may assist English language learners byusing diagrams, illustrations, or other visuals toexplain the content of the lesson. Studentsmay also benefit from keeping a “picturedictionary” with their own visuals to illustrateimportant concepts. For example, studentsmay include diagrams to illustrate how forces

combine and to show the meaning of balancedforce and unbalanced force. This strategy can beespecially helpful for students who are in thebeginning stages of learning English. Studentswho have a greater mastery of English mayalso benefit from sharing their picture diction-aries with each other and explaining theconcepts for which they have included visuals.

Answer to . . .

Figure 2 The difference in weightbetween the two scale readings isabout 3 pounds.

The amount of forcethat accelerates 1 kg

at 1 m/s2 is one newton.

0354_hsps09te_Ch12.qxp 4/18/07 3:47 PM Page 357

Balanced Forces Sometimes, the net force acting on an object iszero. Look at the tug of war in Figure 3. Each group pulls on the ropewith the same amount of force, but they pull in opposite directions.Neither group wins the tug of war because the forces on the rope arebalanced. Balanced forces are forces that combine to produce a netforce of zero. When the forces on an object are balanced, the netforce is zero and there is no change in the object’s motion.

Examples of balanced forces are common. For example, imagine twopeople locked in an arm wrestling match. Although neither person’s armmay be moving, a pair of equal and opposite balanced forces are acting.An unlimited number of individual forces can act on an object and stillproduce a net force of zero. As shown in Figure 3, the individual forceexerted by each person still results in a zero net force on the rope.

Unbalanced Forces Often, the forces on an object are unbal-anced. If you push hard against the side of a book that is resting on atable, the book will begin to move. This is an example of an unbalancedforce. An unbalanced force is a force that results when the net forceacting on an object is not equal to zero. When an unbalanced forceacts on an object, the object accelerates.

Forces acting in opposite directions can also combine to producean unbalanced force. When a team of people win a tug of war, theywin by pulling with a greater force than the losing team. The twounequal forces act in opposite directions but combine to produce anunbalanced net force. The net force equals the size of the larger forceminus the size of the smaller force. This unbalanced force causes therope, the winning team, and the losing team to accelerate in the direc-tion of the unbalanced force. Figure 4 shows several examples of howforces combine.

What is the net force of a pair of balanced forces?

Figure 3 In this tug of war, thetwo groups pull with equal forcesin opposite directions. The forcescombine by subtracting from each other. Interpreting Photos What isthe net force acting on the rope?

Figure 4 Forces can add togetheror subtract from one another. A Two forces acting in the samedirection add together. B Forcesin opposite directions subtractfrom each other. C Forces thatare equal in size and opposite indirection result in no net force.

358 Chapter 12

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B

C

Adding forces

=

Subtracting forces

=

Equal and opposite forces

= 0

358 Chapter 12

Integrate HealthFigure 3 illustrates a group exercise (tugof war). Emphasize to students the valueof regular exercise. According to theAmerican Academy of Family Physicians,regular exercise reduces risk of someserious diseases including heart disease,diabetes, and obesity. Exercise alsoenhances flexibility so that bodymovement is easier. Regular exercisehelps to relieve stress, increase energyand endurance, and—because it raisesthe rate at which the body burnscalories—maintain a healthy weight.

Ask students to hypothesize why aperson with normal (not high) bloodpressure and a normal body weight is at lower risk for heart disease. (Thatperson’s heart does not have to do extra work.) Verbal, Logical

Some students may think that onlypeople and animals can exert a force. You may dispel this fallacy by pointingout that moving automobiles or othermoving vehicles are not living organisms.In addition, explain that the force ofgravity is also inanimate. You could alsouse figures in the text to show that thereare many examples all around students offorces that are not animate.Visual, Logical

Use Visuals

Figure 4 Emphasize that the arrows in Figure 4 help students understand howforces combine. Tell students that thelength of the arrows represents magni-tude (size) of force. Ask, When twoarrows directly oppose one anotherand are different in size, what will bethe direction of the net force? (Thedirection of the net force will be the same as the direction of the longer arrow.) Howis the net force determined when twoforces act in the same direction on anobject? (The forces are added. The direc-tion is the same as the forces.) Which ofthe combinations of forces shown inthe figure would cause an object tomove? (Only the unbalanced forces shownin A and B would cause the object to move.)Visual

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Section 12.1 (continued)

Virtual Reality Forces A knowledge ofbalanced and unbalanced forces is importantfor virtual reality applications. Sensors detectthe direction and magnitude of force exertedon an object by a user. The system thenprovides resistive force feedback to the user

that corresponds to the desired virtualmaterial. For example, the resistive force canbe increased to simulate a stiff material such as hard rubber. The resistive force can bedecreased to simulate a soft material such as a cloth.

Facts and Figures


FrictionAll moving objects are subject to friction, a force that opposes themotion of objects that touch as they move past each other. Withoutfriction, the world would be a very different place. In a frictionlessworld, every surface would be more slippery than a sheet of ice. Yourfood would slide off your fork. Walking would be impossible. Carswould slide around helplessly with their wheels spinning.

Friction acts at the surface where objects are in contact. Note that“in contact” includes solid objects that are directly touching oneanother as well as objects moving through a liquid or a gas. Thereare four main types of friction: static friction, sliding friction, rollingfriction, and fluid friction.

Static Friction Imagine trying to push a large potted tree acrossa patio. Although you apply force to the pot by pushing on it, you can’tget the pot to move. As shown in Figure 5A, the force of static frictionopposes your push. Static friction is the friction force that acts onobjects that are not moving. Static friction always acts in the directionopposite to that of the applied force.

You experience static friction every time you take a step. As youpush off with each step, static friction between the ground and yourshoe keeps your shoe from sliding.

Sliding Friction With the help of a friend, you push on the potwith enough force to overcome the static friction. The pot slides acrossthe patio as shown in Figure 5B. Once the pot is moving, static frictionno longer acts on it. Instead, a smaller friction force called sliding fric-tion acts on the sliding pot. Sliding friction is a force that opposes thedirection of motion of an object as it slides over a surface. Because slid-ing friction is less than static friction, less force is needed to keep anobject moving than to start it moving.

For: Links on forces

Visit: www.SciLinks.org

Web Code: ccn-2121

A B

Push

Staticfriction

Push

Slidingfriction

Pottedtreeaccelerates.

Figure 5 Different types of friction act on moving and nonmoving objects. A Static friction acts opposite the direction of the force you apply to move theplant. The potted tree does not move. B When you push with more force, thepotted tree begins to slide. Sliding friction acts to oppose the direction of motion.

A B

FrictionUse Community ResourcesAsk a civil engineer to visit your class andtalk about the effects of friction betweenroad surfaces and the tires of a movingcar. Have the engineer emphasize thenecessity of friction in controlling a car.Suggest that the engineer explain to the students what happens when a carhydroplanes because of lack of frictionbetween the tires and the surface of the road. Encourage students to askquestions about how engineers takefriction into account when designingroads and bridges.Interpersonal

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Answer to . . .

Figure 3 The net force on the rope is zero.

The net force is zero.

Download a worksheet on forcesfor students to complete, and findadditional teacher support fromNSTA SciLinks.


360 Chapter 12

Rolling Friction When a round object rolls across a flat floor,both the object and the floor are bent slightly out of shape. This changein shape at the point of rolling contact is the cause of rolling friction,the friction force that acts on rolling objects. For a given set of materi-als, the force of rolling friction is about 100 to 1000 times less than theforce of static or sliding friction. Because of this, professional moversoften use wheeled dollies to move heavy objects.

Ball bearings like those shown in Figure 6 are often used to reducefriction in machines. A ball bearing is made up of a set of round ballslocated between two smooth surfaces. The balls roll as the surfacesmove past each other. Friction is greatly reduced between the surfacesbecause rolling friction replaces sliding friction. Inline skates, skate-boards, bicycles, and automobiles are just a few of the many machinesthat use ball bearings.

Fluid Friction Friction also acts on a submarine moving throughwater and on an airplane flying through air. Water and a mixture ofgases such as air are known as fluids. The force of fluid frictionopposes the motion of an object through a fluid. You feel fluid frictionwhen stirring thick cake batter. The motion of the spoon through thebatter is slowed by fluid friction. Fluid friction increases as the speedof the object moving through the fluid increases. Thus the faster youstir, the greater the friction is.

Fluid friction acting on an object moving through the air is knownas air resistance. At higher speeds, air resistance can become a signifi-cant force. For this reason, bicyclists and speed skaters often wear slickracing suits to reduce air resistance.

What are two common examples of fluid friction?

Observing theEffects of FrictionProcedure1. Attach a sticky note to the

widest side of a rectangulareraser. The note must coverthe entire side of the eraser.Trim off excess paper with scissors.

2. Place the eraser from Step 1note-side down, next to asecond eraser so that oneend of each eraser extends2 cm over the edge of a table.

3. Use a ruler to strike botherasers firmly and evenly atthe same time. Record thedistance each eraser slides.

4. Repeat Steps 2 and 3 twomore times. Calculate andrecord the average distanceeach eraser slides.

Analyze and Conclude 1. Observing Which eraser

slid farther?

2. Formulating HypothesesWhy did the erasers slidedifferent distances?

3. Drawing ConclusionsHow does friction affect themotion of a sliding object?

4. Revising What could youdo to make the erasers slideeven farther?

Figure 6 Ball bearingsin these wheels greatlyreduce friction by replacing sliding frictionwith rolling friction.

360 Chapter 12

Observing the Effects Of Friction

Objective After completing this activity, studentswill be able to • describe the effect of friction on

motion.

Skills Focus Observing, DrawingConclusions

Prep Time 5 minutes

Materials 2 rubber erasers, stickynotes, scissors, metric ruler


Teaching Tips• Have students construct data tables in

which to record their observations.• You may need to show students how to

arrange the erasers so that the ruler willstrike both of them at the same time.

• Tell students to repeat the experiment ifan eraser flips over or falls off the table.

Expected Outcome Students willobserve that the sticky note increasesthe distance that the eraser slides.

Analyze and Conclude1. The eraser with the sticky noteattached slid farther.2. The sticky note enabled one eraser toslide farther by reducing friction.3. Friction produces a force that opposesmotion. The greater the frictionbetween two surfaces, the stronger thatforce is.4. The erasers would slide farther if theforce of friction were reduced by coatingthe erasers or the tabletop with asmoother material, or if the erasers werestruck more firmly, providing a greaterforce in the direction of motion.Logical

For EnrichmentStudents can use a spring scale to pull amass across surfaces that provide moreor less friction, to observe the differencebetween the forces required toovercome static and sliding friction. Ingeneral, more force is required toovercome static friction and beginsliding than to continue sliding atconstant velocity.Kinesthetic

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Friction and Tennis You may mention to thestudents that, if they have ever played tennison a clay court, they may have discovered thatclay courts are covered with a layer of finesand. The sand granules act as ball bearings for a short distance and then cause the playerto slide. Ask, With clay courts, what types of friction is the player experiencing?

(The player first experiences rolling friction whenthe sand granules are still rolling. The player thenexperiences sliding friction when the granules stoprolling and start sliding. The sliding friction isactually occurring between the grains of sand andthe surface below the sand, as the sand sticks tothe shoes of the player.)

Facts and Figures

GravityWhy do leaves fall to the ground? The answer is gravity. Gravity is aforce that acts between any two masses. Gravity is an attractive force,that is, it pulls objects together. Earth’s gravitational force exerts a forceof attraction on every other object that is near Earth. That includesyou—the force of Earth’s gravity holds you on the ground. Note thatthe force of gravity does not require objects to be in contact for it to acton them. Unlike friction, gravity can act over large distances.

Earth’s gravity acts downward toward the center of Earth.Fortunately, an upward force usually balances the downward force ofgravity. What forces act on the boulder in Figure 7? Gravity pulls downon the boulder. An upward force supplied by the supporting rock actsupward and balances the downward gravitational force. Because theforces on the boulder are balanced, it remains at rest as it has for thou-sands of years.

Falling Objects What forces affect the motion of a dollar billdropped from the top of a tall building? Both gravity and air resist-ance affect the motion of a falling object. Gravity causes objectsto accelerate downward, whereas air resistance acts in the directionopposite to the motion and reduces acceleration.

In Figure 8, a flying squirrel has jumped from atree and is falling toward the ground. As you can see,the squirrel has positioned its body parallel to Earth’ssurface and spread its arms and legs. By doing this,the squirrel creates a very large surface area. Thelarge area maximizes the force of air resistance actingto slow the squirrel’s downward acceleration.Because of the squirrel’s slower downward accelera-tion, it is able to travel farther through the air thanwould otherwise be possible.

As objects fall to the ground, they accelerate andgain speed. With increasing speed comes increasingair resistance. If an object falls for a long time, theupward force of air resistance becomes equal to thedownward force of gravity. At this point, the forcesacting on the object are balanced. Acceleration iszero and the object continues falling at a constantvelocity. Terminal velocity is the constant velocityof a falling object when the force of air resistanceequals the force of gravity. Read the Concepts inAction pages later in this chapter to learn how skydivers reach terminal velocity.

Gravity

Supportingforce

Air resistance

Gravity

Figure 7 Earth exerts anattractive, downward force onthis boulder. Inferring Because the boulder isat rest, what do you know aboutthe net force acting on it?

Figure 8 This flyingsquirrel takesadvantage of airresistance to slow itsfall and increase thedistance covered inthe jump.


Gravity

Students may think that no forces areacting on an object at rest. Help stu-dents see that this is false. Reinforce that resting objects have no net forceacting on them. Show students thatanything that has weight has at leasttwo forces on it (if it is not in free fall).Forces of gravity pull the object down-ward toward Earth, and a reaction forcepushes against that object, in accordancewith Newton’s third law of motion. Askstudents to explain why a book whichhas weight (a type of force) rests on adesk without moving.Visual, Logical

Use VisualsFigure 8 The spread-out wings of theflying squirrel increase the air resistancethat opposes the force of gravity, slowingthe squirrel’s fall. Have students examinethe two force arrows in the figure. Ask,What is the direction of the net forceacting on the squirrel? (Downward)Why is the squirrel able to increase thedistance covered when it jumps if theair resistance increases? (Because thesquirrel’s downward acceleration is slowedby the increased air resistance, the squirrelhas more time to travel through the air. Thesquirrel’s forward speed is not noticeablychanged by the increased air resistance,and thus it travels a greater horizontaldistance because it falls through the air agreater period of time.)Visual

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Answer to . . .

Figure 7 The net force on the boulderis zero.

Answers may includestirring cake batter and

air resistance.

Flying Squirrels Southern flying squirrels arefound mostly from southern Ontario to theGulf Coast. The length of an adult squirrel,including the tail, is about 23 to 25 cm, and itsweight is usually between 55 and 110 g. Its furis long, soft, and silky. On each side of thesquirrel’s body is a gliding membrane between

the wrist of the front leg and the ankle of thehind leg. When the front and hind legs areextended, the membranes help the squirrel toglide in a motion that appears to be flying,giving the animal the name “flying squirrel.”The tail acts as a rudder and helps to stabilizethe squirrel as it glides.

Facts and Figures


362 Chapter 12

Section 12.1 Assessment

Reviewing Concepts1. How is the motion of an object affected

when a force acts on it?

2. List the four types of friction.

3. How does air resistance affect theacceleration of a falling object?

4. Earth’s gravitational force acts inwhat direction?

5. Describe why a projectile follows acurved path.

Critical Thinking6. Comparing and Contrasting Compare the

strengths of static, sliding, and rolling friction.

Projectile MotionWhen you throw a ball forward, you’ll notice that it actually followsa curved path. This curved path is an example of projectile motion,the motion of a falling object (projectile) after it is given an initialforward velocity. Air resistance and gravity are the only forces actingon a projectile.

Figure 9 shows the motion of two balls released at the same time.Figure 9A shows that balls of different mass fall at the same rate. InFigure 9B the curved path of the yellow ball is the result of the forceof gravity and the initial horizontal velocity. The combination ofan initial forward velocity and the downward vertical force of grav-ity causes the ball to follow a curved path. The two balls fall with thesame acceleration and strike the ground at the same time.

Figure 9 Gravity acts on fallingobjects. A Although their massesare different, the blue and greenballs fall at the same rate. B The yellow ball is a projectile,following a curved path.Applying Concepts What forcesact on each of the falling balls?

Velocity and Acceleration Makesketches of Figures 9A and 9B. Use themto relate the concepts of velocity andacceleration from Section 11.3 to fallingobjects. Add velocity and accelerationarrows at three locations on each sketch.

7. Applying Concepts Explain why fallingleaves often do not fall in a straight-line pathto the ground.

8. Predicting Two coins are knocked off a tableat the same time by different forces. Which coinwill hit the floor first?

A B

362 Chapter 12

Projectile MotionUse VisualsFigure 9 Have students read the textunder Projectile Motion. Then, askquestions to reinforce the idea thatprojectile motion is the result of theinitial horizontal velocity and the vert-ical force of gravity. Ask, Why does the yellow ball in Figure 9B continuedownward at the same rate as theblue and green balls in Figure 9A?(They all accelerate downward by theforce of gravity, approximately 9.8 m/s2.)Why does the yellow ball (in 9B) con-tinue horizontally? (The ball’s initialhorizontal velocity is not affected by thedownward force of gravity.)Visual, Logical

ASSESSEvaluate UnderstandingHave students write a review questionand its answer for each objective at thebeginning of this section. Studentsshould also be able to discuss thesection objectives.

ReteachHave students use Figure 4 tosummarize the concepts of balancedand unbalanced forces. Use Figures 5and 8 to review friction, gravity, and air resistance.

Students’ sketches should showconstant horizontal velocity, steadilyincreasing downward velocity, and constant downward acceleration.

If your class subscribesto the Interactive Textbook, use it toreview key concepts in Section 12.1.

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5. The combination of initial horizontalvelocity and downward vertical force causes aprojectile to follow a curved path.6. The force of static friction is greater than thatof sliding friction. The force of sliding friction isgenerally greater than that of rolling friction.7. Varying air resistance acting on the leafresults in a fluttering motion.8. Both coins hit the ground at the same time.


1. A force can set an object at rest intomotion, or it can accelerate a moving objectby changing its speed or direction. 2. Static friction, sliding friction, rollingfriction, and fluid friction3. It acts opposite the direction of motion andslows the acceleration of a falling object.4. Downward toward the center of Earth

Answer to . . .

Figure 9 Forces acting on both of the falling balls are air resistance and gravity. In addition, the projectilein Figure 9B was briefly acted on by the force that gave it its initialhorizontal velocity.


12.2 Newton’s First and Second Laws of Motion

Reading StrategyBuilding Vocabulary Copy the tablebelow. Then as you read the section, write adefinition for each vocabulary term in yourown words.

Key ConceptsHow does Newton’s firstlaw relate change inmotion to a zero net force?

How does Newton’ssecond law relate force,mass, and acceleration?

How are weight andmass related?

Vocabulary◆ inertia◆ mass◆ weight

Why do some cars accelerate faster than others? How does an iceskater glide far across the ice after pushing off only once? The answersto these questions involve the concepts of mass and inertia.

Aristotle, Galileo, and NewtonModern scientists understand the relationships between force andmotion. However, it took about 2000 years to develop this understanding.

Aristotle The ancient Greek scientist and philosopher Aristotle(384 B.C.–322 B.C.) made many scientific discoveries through carefulobservation and logical reasoning. He was not always correct. Aristotleincorrectly proposed that force is required to keep an object moving atconstant speed. This error held back progess in the study of motionfor almost two thousand years.

Galileo Italian scientist Galileo Galilei (1564–1642) experi-mented to find out about the world. By rolling balls downwooden ramps, he studied how gravity produces constant accel-eration. Galileo concluded that moving objects not subjected tofriction or any other force would continue to move indefinitely.Galileo’s portrait and the title page from the book that presentedhis work are shown in Figure 10.

b. ?

a. ?

c. ?

d. ? e. ?

Inertia

Vocabulary Definition

Figure 10Galileo’s workhelped correctmisconceptionsabout force andmotion that hadbeen widely heldsince Aristotle’stime.



FOCUS

Objectives12.2.1 Describe Newton’s first law

of motion and its relation to inertia.

12.2.2 Describe Newton’s second lawof motion and use it tocalculate acceleration, force,and mass values.

12.2.3 Relate the mass of an object to its weight.

Build VocabularyVocabulary Rating Chart Havestudents make a four-column chart withthe headings Term, Can Define or Use It,Heard or Seen It, and Don’t Know. Havethem put inertia, mass, and weight inthe first column, rating their knowledgeof each term by putting a checkmark inone of the other columns. Give studentsa purpose for reading by asking them tocheck their expectations as they read.Ask them to make another chart afterthey have read the section.

Reading Strategya. The tendency of an object to resist achange in its motion b. Mass c. Theamount of matter an object contains asmeasured by its inertia d. Weight e. Theforce of gravity acting on an object

INSTRUCT

Aristotle, Galileo, and NewtonIntegrate Social StudiesAristotle did not correctly explain why anobject falls toward Earth. Later, Galileo’sobservations led him to confirm thatEarth is one of many planets, all gov-erned by the same laws of gravity.Galileo prepared the way for IsaacNewton, whose laws are presented inthis chapter. To demonstrate these ideas,have students further research the ideasAristotle and Newton had on gravity.Then, drop an object to the floor, andhave student volunteers play the roles of “Aristotle” and “Newton” and debatewhat caused the object to fall.Verbal, Interpersonal

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Reading Focus

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Print• Lab Manual, Investigations 12A and 12B• Reading and Study Workbook With

Math Support, Section 12.2 and Math Skill: Calculating Acceleration

• Math Skills and Problem SolvingWorkbook, Section 12.2

• Transparencies, Section 12.2

Technology• Interactive Textbook, Section 12.2• Presentation Pro CD-ROM, Section 12.2• Go Online, NSTA SciLinks, Mass

Section 12.2

Section Resources

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Newton In 1665, the plague broke out in London, forcing IsaacNewton to leave Trinity College in Cambridge, England, where he wasa student. Over the next two years, Newton built on the work of sci-entists such as Galileo. He published his results many years later in abook entitled Principia. In this important work, Newton first had todefine mass and force. He then introduced his laws of motion. Newton’sportrait and the title page of Principia are shown in Figure 11.

Newton’s First Law of MotionNewton summarized his study of force and motion in several laws ofmotion. According to Newton’s first law of motion, the state ofmotion of an object does not change as long as the net force actingon the object is zero. Thus, unless an unbalanced force acts, an objectat rest remains at rest, and an object in motion remains in motion withthe same speed and direction. For example, a soccer ball resting on thegrass remains motionless until a force is applied to it in the form of akick. The kicked ball begins rolling. Because friction between the grassand the ball acts on the ball as it rolls, the ball slows. The force of fric-tion slows the ball and brings it to a stop.

Newton’s first law of motion is sometimes called the law of inertia(in UR shuh). Inertia is the tendency of an object to resist a change inits motion. In other words, an object at rest tends to remain at rest, andan object in motion tends to remain in motion with the same directionand speed. Note that as the soccer ball sat motionless in the grass, theforces acting on it were balanced. The ball remained at rest until anunbalanced force acted on it. The ball has inertia.

How does a zero net force affect an object’s motion?

Figure 11 Isaac Newtonpublished his work on forceand motion in the bookentitled Principia.

This crash sequence illustrates inertia—the tendencyof an object in motion to remain in motion.

At impact, the air bag deploys. Note that thetest dummy continues its forward motion asthe collision begins to slow the car.

Figure 12

A B

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Build Science SkillsInferring Before studying Newton’sfirst law of motion, have students look atFigures 12A and 12B. Ask, What wouldhave happened to the test dummy ifthe air bag had not deployed and the dummy had not been wearing aseatbelt? (Students should infer from thephotos that the dummy’s forward motioncontinues after the crash, and that thedummy might have gone through thewindshield.) Visual, Logical

Newton’s First Law of MotionUse VisualsFigures 12A and 12B Have studentsexamine Figures 12A and 12B. Ask, What is the effect of inertia on the car? (Inertia causes the mass of the car to continue forward, crushing the front ofthe car.) What effect does inertia haveon the dummy? (After the car stops, thedummy continues to move forward until it isstopped by the air bag and seatbelt.) Howis the mass of a passenger related tothe passenger’s inertia? (Passengers withgreater mass have more inertia. It is harderto stop the forward motion of passengerswith greater mass.) Visual, Logical

Investigating Inertia

Objective After completing this activity, studentswill be able to • use the concept of inertia to explain

the movement of objects.

This lab can help to correct the miscon-ception that inertia refers to the tendencyof objects to resist motion, rather than the tendency to resist a change in motion.Use student answers to Question 1 as thebasis of a discussion about the nature ofinertia.

Skills Focus Observing,Formulating Hypotheses

Prep Time 5 minutes

Materials index card, coin

Advance Prep Checkers may besubstituted for coins.


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Expected Outcome Fast changes in themovement of the card can occur with little effecton the movement of the coin. When the cardmoves slowly, it carries the coin along.

Analyze and Conclude1. In Step 1, the inertia of the coin resistedacceleration by the card. The force of friction wasnot strong enough to hold the coin in place onthe accelerating card. In Step 2, the accelerationof the card was not as great. Therefore, the forceof friction was strong enough to hold the coin inplace on the card. In Step 3, the situation was

identical to that in Step 2 at first. However, whenthe card suddenly stopped moving, the inertia ofthe coin was great enough to keep it moving inthe same direction, in spite of the force of friction.

2. If the mass of the coin were greater, its inertiaalso would be greater. Therefore, the coin wouldagain have resisted acceleration in Step 1 andmoved with the card in Step 2 if the card wasnot moving too quickly. In Step 3, the coinwould have continued moving longer after thecard stopped moving. Logical


Think about what happens if you are in a moving car that isinvolved in a front-end collision. The collision makes the car stop sud-denly. What happens to you? Because you have inertia, you continuemoving forward. The series of photos in Figure 12 shows you howdangerous a front-end collision can be. If a seat belt and airbag hadnot restrained the test dummy, it would have crashed into the steeringwheel and windshield with great force. The seat belt and airbag workby exerting force against the body of the dummy, opposing its for-ward motion.

Newton’s Second Law of MotionHow do unbalanced forces affect the motion of an object? An unbal-anced force causes an object’s velocity to change. In other words, theobject accelerates. For example, you apply a net force to a ball when youthrow it. The harder you throw, the more the ball accelerates. In fact, theacceleration of the ball is directly proportional to the net force acting onit. If you double the force, the acceleration of the ball doubles as well.Newton also learned that the acceleration of an object depends upon itsmass. Mass is a measure of the inertia of an object and depends on theamount of matter the object contains.

According to Newton’s second law of motion, the accelerationof an object is equal to the net force acting on it divided by theobject’s mass. Thus, doubling the mass of an object cuts its accelera-tion in half. Newton was able to put these ideas into a single formula.

Newton’s Second Law

Acceleration � , or a �Fm

Net forceMass

Investigating InertiaProcedure1. Place an index card on a

flat table. Place a coin inthe middle of the card. Asquickly as you can, try topull the card out fromunder the coin. Observewhat happens to the coin.

2. Repeat Step 1 whilemoving the card slowly.

3. Repeat Step 1 again. Thistime, slowly accelerate thecard, and then suddenlybring it to a stop.

Analyze and Conclude1. Applying Concepts Use

the concepts of inertia andfriction to explain thebehavior of the coin eachtime you moved the card.

2. Predicting How wouldyour observations bedifferent with a coinof greater mass? Testyour predictions.

As the car comes to a stop, the air bag prevents thetest dummy from striking the steering wheel.

Interpreting Photographs What objects anddevices absorb the energy of the crash?

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Newton’s Second Law of Motion

Force and AccelerationPurpose Students observe thatacceleration is directly proportional toforce applied

Materials 2 identical toy cars (ordynamics carts), 2 student volunteers,identical floor surface for each car

Procedure Tell students that the cars’masses are identical. Ask a student topush one car along the floor with littleforce. Have a second student push theother car with greater force.

Expected Outcome The car pushedwith little force will accelerate very little.The car pushed with greater force willaccelerate much more. Visual, Group

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Customize for Inclusion Students

Learning Disabled Experiential and visual learning are goodstrategies for many learning-disabled students.Encourage students to do the followingexperiments to gain hands-on knowledge andto see the results themselves.

Use a wheeled toy to teach Newton’s firstand second laws of motion. Have studentsplace a small object on the toy, push the toyforward, and suddenly stop the forward

movement. Students will observe that thesmall object’s inertia causes it to continuemoving. Then allow students to push thewheeled toy with varying degrees of force.They will observe that when the mass does notchange, acceleration varies in direct proportionto the force applied. In Section 12.3, studentswill learn Newton’s third law by observingthat, while they are standing on the floor, thefloor exerts force in opposition to their weight.

Answer to . . .

Figure 12 The crushing of the car’sbody absorbs much of the energy. The air bag and seatbelt also absorbcrash energy.

The object’s motion doesnot change.


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Corner collisionOne standard test involvescrashing a car into a solidconcrete wall at nearly 60kilometers an hour. Other testsinvolve crashing a sled into theside or corner of the car.

Crash-Test DummiesDummies are used in simulated car crashes to study whatmight happen to passengers in a real crash. They are fittedwith a range of measuring devices that track the motionof the dummies throughout the crash. By analyzing thedata, scientists learn how injuries occur and how they canbe prevented. Interpreting Diagrams What forces acton the crash-test dummy to slow its forward movement?

Impact Upon initialimpact, the frontof the car stopsabruptly, butinertia keeps thedummy movingforward.

Seatbelt The seatbeltimmediately tightens toslow down the dummy andto absorb energy.

Inflating air bag The air bag exerts aforce that slows down the dummy’sforward motion, absorbs its energy, andprevents it from hitting the steering wheel.

Markers Camerasfocus on the markersto record how thebody moves duringthe collision.

Car’s initialvelocity

SensorsComputersconnected tosensors on thelegs, chest,abdomen, and head measure andrecord movementand acceleration.

Paint Layers ofdifferent coloredpaints on thedummy recordthe directionand effects ofimpact forces.

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Crash-Test DummiesDefining the way a body will respond to acrash is difficult because different parts ofthe human body behave in different waysin a crash. For that reason, developing acrash-test dummy that behaves like ahuman body in a crash has been difficult.

Early automotive crash test dummieswere based on dummies used in aero-space. Because head, spine, and neckinjuries can be life-threatening, dummies’heads, necks, and spines were a majorfocus of research. In 1973, dummies wereimproved. Injuries to lower extremitiesare rarely fatal, but they can reduce aperson’s quality of life. Further researchand development of crash-test dummieswill focus on lower extremities.

Interpreting Diagrams Forces fromboth the seatbelt and the air bag slowthe dummy’s movement.Visual

For EnrichmentHave students research the methods usedby the National Highway Traffic SafetyAdministration (NHTSA) to test a vehicle’scrash worthiness and its likelihood ofrolling over. Also have students createtables explaining the meaning of the starrating system used by the NHTSA. Selecta method for students to use to presenttheir findings to the class.Logical

Use Community ResourcesArrange for a police officer to speak toyour class about seatbelt safety laws. Havethe officer reinforce the importance ofseatbelts in preventing injury. The policedepartment may have a video that couldvisually reinforce the concept of seatbeltsafety and its relationship to Newton’s firstlaw of motion in sudden stops.Logical, Visual

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Bike Helmets You may help your studentsunderstand that Newton’s first law of motionis a reason for wearing helmets when cycling.During an accident, the foam padding in ahelmet is deformed, absorbing the energy ofthe impact. Explain that each year, almost400,000 children ages 14 and under aretreated in emergency rooms for bicycle-related

injuries. Head injuries account for more than two thirds of bicycle-related hospitaladmissions and more than half of bicycle-related deaths. If each child wore a bicyclehelmet, between 39,000 and 45,000 headinjuries, and between 18,000 and 55,000scalp and face injuries could be preventedannually.

Facts and Figures


The acceleration of an object is always in the same direction as thenet force. In using the formula for Newton’s second law, it is helpful torealize that the units N/kg and m/s2 are equivalent. The Math Skillsbox reinforces this relationship.

Note that Newton’s second law also applies when a net force acts inthe direction opposite to the object’s motion. In this case, the force pro-duces a deceleration that reduces the speed. This is the principle usedby automobile seat belts. In a collision, the seat belt applies a force thatopposes a passenger’s forward motion. This force decelerates the pas-senger in order to prevent serious injury.

Newton’s Second LawAn automobile with a mass of 1000 kilograms accelerates whenthe traffic light turns green. If the net force on the car is 4000 newtons, what is the car’s acceleration?

Read and UnderstandWhat information are you given?

Mass, m = 1000 kg

Force, F = 4000 N (in the forward direction)

Plan and SolveWhat unknown are you trying to calculate?

Acceleration, a = ?

What formula contains the given quantitiesand the unknown?

Acceleration � , a �

Replace each variable with its known value and solve.

a � � � � 4 m/s2

a � 4 m/s2 in theforward direction

Look Back and CheckIs your answer reasonable?

Powerful sports cars can accelerate at 6 m/s2 or more.Thus, a smaller acceleration of 4 m/s2 seems reasonable.

4kg•m

kg4 N kg

4000 N1000 kg

Fm

Net forceMass

1. A boy pushes forward a cart ofgroceries with a total mass of40.0 kg. What is the accelerationof the cart if the net force on thecart is 60.0 N?

2. What is the upward accelerationof a helicopter with a mass of5000 kg if a force of 10,000 Nacts on it in an upwarddirection?

3. An automobile with a mass of1200 kg accelerates at a rate of3.0 m/s2 in the forward direction.What is the net force acting onthe automobile? (Hint: Solvethe acceleration formulafor force.)

4. A 25-N force accelerates a boy ina wheelchair at 0.5 m/s2 What isthe mass of the boy and thewheelchair? (Hint: SolveNewton’s second law for mass.)

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a � 4 m/s2 in the forward direction

Newton’s Second Law of Motion Purpose Students observe thatacceleration is inversely proportional tomass. (a � F/m)

Materials wind-up toy car, 3 metalwashers, tape

Procedure Have students wind the toycar completely and observe its motionalong a flat surface. Next, have themtape metal washers to the car, wind it,and watch its motion along the flatsurface again.

Expected Outcome Students willnotice that the car’s accelerationdecreases because of the increased mass.Visual

Solutions1. a � F/m � 60.0 N/40.0 kg �1.50 m/s2

2. a � F/m � 10,000 N/5000 kg �2 m/s2

3. a � F/m; F � ma � 1200 kg �3.0 m/s2 � 3600 N4. a � F/m; m � F/a � 25 N/0.50 m/s2 �50 kgLogical

For Extra HelpRemind students that they first need to solve the equation a � F/m for theunknown. Also ask students to identifyall the known and unknown variablesbefore using the equation. Logical

Direct students to the Math Skills in the Skills and Reference Handbookat the end of the student text foradditional help.

Additional Problems1. A 20-N net force acts on an objectwith a mass of 2.0 kg. What is theobject’s acceleration? (10 m/s2)2. A box has a mass of 150 kg. If a netforce of 3000 N acts on the box, what is the box’s acceleration? (20 m/s2)3. What is the acceleration of a 1000 kgcar subject to a 500 N net force? (0.5 m/s2) Logical, Portfolio

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The shopping carts in Figure 13 further illustrate Newton’s secondlaw. What happens if you push on a single shopping cart? The unbal-anced force causes the cart to accelerate. What happens when you pushwith the same force on a chain of eight shopping carts? The accelera-tion of the chain of carts is much less than that of the single cart. Thechain of carts accelerates less because it has more mass.

Weight and Mass Do you sometimes talk about weight and mass as if they were the samething? Although related to each other, mass and weight are not the same.Weight is the force of gravity acting on an object.An object’s weight is theproduct of the object’s mass and acceleration due to gravity acting on it.

Weight Formula

Weight � Mass � Acceleration due to gravity

W � mg

The weight formula is basically Newton’s second law. However,weight (W) is substituted for force (F) and acceleration due to gravity(g) is substitutued for acceleration (a). In other words, W � mg is a dif-ferent form of a � , that is when the equation is solved for force,

F � ma. The value of g in the formula is 9.8 m/s2.

In using the weight formula or Newton’s second-law formula, makesure you use the correct units. The force (F or W) should be in new-tons, the acceleration (a or g) in meters per second squared, and themass (m) in kilograms. The following example shows how to use theweight formula.

If an astronaut has a mass of 112 kilograms, what is his weight onEarth where the acceleration due to gravity is 9.8 m/s2?

Weight � Mass � Acceleration due to gravity

� 112 kg � 9.8 m/s2

� 1100 kg•m/s2 � 1100 N

FM

Figure 13 Acceleration dependsdirectly on force and inversely onmass. Neglecting friction, whenthe same force acts, the singlecart accelerates eight times fasterthan the chain of eight carts.Predicting How would theacceleration of a chain of twocarts compare with theacceleration of a single cart ifthe same force acted on both?

Force Force

Acceleration Acceleration

For: Links on mass


Web Code: ccn-2122

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Use VisualsFigure 13 Use this figure to be surethat students understand the equation F � ma before asking the followingquestion about the mass-accelerationratio. Ask, Why would one cart accel-erate eight times as fast as the chainof eight carts with the same forceapplied in each case? Explain usingthe second-law equation. (If the forceremains the same in the equationF � ma, then as mass increases, theacceleration has to decrease in proportionto the increase in mass.) How would theforce have to change in order to havethe same acceleration for eight cartsas for one cart? (The force would have tobe eight times greater.) How wouldanother force directed to the left onthe cart affect the cart’s acceleration?(The acceleration would depend on the netforce acting on the cart. The net forcewould be the force acting to the rightminus the force acting to the left.)Visual

Build Reading LiteracyVisualize Refer to page 354D inChapter 12, which provides theguidelines for visualizing.

Tell students that forming a mentalimage of concepts they are learninghelps them remember new concepts. For example, this section discussesweight in newtons, but students maythink of weight in terms of pounds. Helpstudents to visualize that the poundequals 4.448 newtons. Tell them, that inapproximate weights, pound is slightlymore than one newton. Encouragestudents to think of something the sizeof a pound, such as a pound of butter. If the butter is divided into four sticks,each stick is slightly more than theweight of one newton. Likewise, aquarter-pound hamburger could becalled a “newton” burger. Visual

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Download a worksheet on mass forstudents to complete, and findadditional teacher support fromNSTA SciLinks.


Reviewing Concepts1. State Newton’s first law of motion in your

own words.

2. What equation states Newton’s second lawof motion?

3. How is mass different from weight?

Critical Thinking4. Applying Concepts Describe several

examples of Newton’s first and second lawsthat you observe during a normal day.

5. Making Judgments A steel ball is the samesize as a wooden ball, but weighs twice asmuch. If both balls are dropped from anairplane, which of them will reach terminalvelocity more quickly? Explain.

6. During a test crash, an air bag inflatesto stop a dummy’s forward motion.The dummy’s mass is 75 kg. If the netforce on the dummy is 825 N towardthe rear of the car, what is thedummy’s deceleration?

7. A bicycle takes 8.0 seconds to accelerateat a constant rate from rest to a speed of4.0 m/s. If the mass of the bicycle andrider together is 85 kg, what is the netforce acting on the bicycle? (Hint: Firstcalculate the acceleration.)

If you study the weight formula, you’ll see that mass and weight areproportional. Doubling the mass of an object also doubles the object’sweight. Mass is a measure of the inertia of an object; weight is ameasure of the force of gravity acting on an object. Consider the sameastronaut shown on Earth and on the moon in Figure 14. On the moon,the acceleration due to gravity is only about one sixth that on Earth.Thus, the astronaut weighs only about one sixth as much on the moonas on Earth. In both locations, the mass of the astronaut is the same.


Figure 14 Weight is a measure ofthe force of gravity acting on anobject. A An astronaut with amass of 88 kg weighs 863 N onEarth. B An astronaut with a massof 88 kg weighs 141 N on themoon. Calculating If the sameastronaut stood on Mars wherethe acceleration due to gravity isabout 3.7 m/s2, how much wouldthe astronaut weigh?

Astronaut on EarthMass = 88.0 kg; Weight = 863 N

Astronaut on MoonMass = 88.0 kg; Weight = 141 N

BA

ASSESSEvaluate UnderstandingHave students work in pairs to writethree math problems (with solutions)based on Newton’s second law, a � F/m.Then have them do the same for theweight equation, W � mg. Ask studentsto present their problems and solutionsin class.

ReteachUse Figure 12 to review inertia and itsrelationship to Newton’s first law ofmotion. Use Figure 13 to review Newton’ssecond law of motion. Use Figure 14 toreview how Newton’s second law isrelated to the weight formula.

Solutions6. a � F/m � 825 N/75 kg � 11 m/s2,toward the rear of the car7. a � d v/t � (4.0 m/s)/(8.0 s) �0.50 m/s2; F � ma � 85 kg x 0.50 m/s2

� 43 N

If your class subscribesto the Interactive Textbook, use it toreview key concepts in Section 12.2.

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4. Students should cite examples in whichobjects at rest remain at rest or tend tocontinue moving (first law) and in which a net force acting on an object causes a changein the object’s state of motion (second law).5. The heavier steel ball will take longer toreach terminal velocity. A greater speed isneeded to produce the air resistance requiredto balance the steel ball’s greater weight. Thesteel ball must fall for a longer period of timein order to reach this greater speed.


1. Students should paraphrase the following:According to Newton’s first law of motion, thestate of motion of an object does not changeas long as the net force acting on the object is zero.2. a � F/m3. Mass is a measure of the inertia of anobject; weight is a measure of the force ofgravity acting on an object.

Answer to . . .

Figure 13 The two-cart chain would accelerate at half the rate of the single cart.

Figure 14 330 N

Terminal Speed

Sky diving relieson two principles ofphysics. First, if there is nothing tosupport you, the force of gravity will cause youto accelerate downward. Second, all fluids—includingair—produce a drag force that opposes the motion ofan object moving through the fluid. The speed of afalling object increases until the drag force equals theforce of gravity. At this point, the net force is zero andthe sky diver falls at a constant, terminal speed.

The actual terminal speed depends on severalfactors. For example, an object with greater mass hasa greater gravitational force on it, increasing itsterminal speed. Thinner air, such as air at very highaltitudes, increases velocity by decreasing the dragforce. A sky diver can also partially control the dragforce, and terminal speed, by changing shape.Opening the parachute dramatically increases thedrag force and lowers the terminal speed to about 4.5meters per second—a speed suitable for landing.

Downwardforce of gravity

Upward drag force

Harness

Imagine you are a sky diver about to step out ofa plane and fall through the air. What forceswill you experience during your fall? How canyou use these forces to combine anexhilarating experience with a safe landing?

Helmet forprotection

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Terminal Speed BackgroundThe skydiver’s weight, the gravitationalforce downward, is constant and iscalculated with the formula W � mg.The variable g is 9.8 m/s/s, usuallywritten 9.8 m/s2. The opposing dragforce, D, from the air, continues toincrease until terminal velocity isreached. The drag force depends on theshape and position of the skydiver. Dragis calculated from a complex formula.

The skydiver’s net force is weightminus drag, W � D. Using net force W � D for F, acceleration is found asfollows: a � F/m � (W � D)/m.

When weight equals drag, W � Dbecomes zero; therefore, accelerationbecomes zero. The skydiver stopsaccelerating and reaches maximumvelocity, which is called terminal velocity.

Build Science Skills

Observing

Purpose Students investigate air resistance and its effect on the rate of acceleration.

Materials sheet of paper, stopwatch,auditorium stage


Procedure Have one student drop theflat sheet of paper from the auditoriumstage while another times the paper’sdescent with the stopwatch. A thirdstudent can record the time.

Repeat the experiment, but this timehave the student crumple the sheet ofpaper. Compare the descent times. Ask,What variables remained constantand what variables changed? (Airresistance changed. Weight (mass) andacceleration due to gravity, g, remainedthe same.) Why are the times differ-ent? (A greater air resistance force acts on the flat sheet, causing it to fall moreslowly.) If both the flat and crumpledsheets were dropped in a vacuumwhere there is no air resistance, whatwould happen? (The time it takes thesheet to fall would be the same.)

Expected Outcome The increasedforce of air resistance acting on the flatsheet causes it to fall more slowly thanthe crumpled sheet. Visual, Logical

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■ Research the development and use of theparachute and prepare a poster presentationof your findings. Be sure toinclude a development timeline listing names and dates ofsignificant contributions andadvances.

■ Take a Discovery Channel VideoField Trip by watching “AirForces.”

Going Further

■2 Falling freelySky divers usually

jump from a height of about 3000 meters and

fall freely for about 45 secondsbefore opening the parachute.The top speed reached, known asterminal speed, is about 52 metersper second. Falling from very highaltitudes, where the air is thinnerand the drag force is less, canproduce higher terminal speeds.

■3 Slowing the fallUsually the parachute isfully open by the time thesky diver is 300 meters abovethe ground. The parachute causesrapid deceleration and allows thesky diver to make a steady descent,using the control lines to steer.

■4 Landing The skydiver pulls down onthe control lines toachieve a safe andsteady low-speedlanding.

Altimetershowingaltitude

The Sky Diving SequenceNo matter what the starting altitude,any sky dive consists of the samebasic stages, starting with thejump from the plane.

■1 Jumping out Uponjumping, the sky diverbegins accelerating at a rate of 9.8 meters persecond per second in free fall. Within a fewseconds she will reachmaximum speed.

Parachute

Sky diver landsstanding up


Video Field Trip

Students may think that objects in avacuum fall at a constant speed. Helpthem to realize that objects accelerate asthey fall. Earth’s gravitational accelerationin a vacuum is approximately 9.8 m/s/s,meaning that the velocity increases 9.8 m/s every second, or 9.8 m/s2, as the object falls.

Without a vacuum, however, airresistance increases as the object fallsuntil the object reaches terminalvelocity. Reinforce that all objects in avacuum accelerate at the same rate, butthat they do not fall at a constant speeduntil they reach terminal velocity.Logical

Going FurtherStudent poster presentations mayinclude references to Leonardo da Vinci,Fauste Veranzio, and Joseph and JacquesMontgolfier. Visual, Verbal

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After students have viewed the Video Field Trip, askthem the following questions: What is the net forceon the skydiver just before stepping out of theplane? Explain your answer. (Zero. The force ofgravity is balanced by the force the aircraft exerts sothat the skydiver is not yet accelerating.) How do theforce of gravity and air resistance compare as theskydiver is falling and gaining speed? Explainyour answer. (The force of gravity is greater than the

air resistance because the gravitational force isdownward and the air resistance is upward, resulting ina net force downward.) How does the force of airresistance change as the skydiver gains speedwhile falling? (The air resistance increases.) Whathappens to the skydiver’s speed when the forceof air resistance becomes equal to the force ofgravity? Explain your answer. (The skydiver’s speedstays the same. Gravity and air resistance balance eachother. Because the net force is zero, there is noacceleration.) How does the force of air resistancechange when the skydiver’s parachute opens? (Itsuddenly increases.)

Video Field Trip

Air Forces


12.3 Newton’s Third Law of Motion and Momentum

Reading StrategySummarizing Read the section onmomentum. Then copy and complete theconcept map below to organize what youknow about momentum.

Key ConceptsWhat is Newton’s third lawof motion?

What is needed for anobject to have a largemomentum?

How is momentumconserved?

Vocabulary◆ momentum◆ law of conservation

of momentum

is calculatedby multiplying

is measuredin

b. ? c. ?a. ?

Momentum

and

Think physics the next time you go to an amusementpark. There is no better place than an amusement parkto see Newton’s laws in action. As you experience suddenstarts, stops, changes in direction, and possibly even freefall, you can be sure that the laws of physics control yourmotion. The bumper cars in Figure 15 illustrate momen-tum and Newton’s third law of motion, the subjects ofthis section.

If you have ever driven a bumper car, you know yourgoal is to slam into another car head on. When you col-lide with the other car, you do so with enough force tojolt the other driver almost out of the seat. There are twoparts to this collision, however—the collision also causesyour own car to rebound sharply. Newton’s third law ofmotion explains the behavior of the bumper cars duringa collision.

Figure 15 When this bumper carcollides with another car, two forcesare exerted. Each car in the collisionexerts a force on the other.

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FOCUS

Objectives12.3.1 Explain how action and

reaction forces are relatedaccording to Newton’s thirdlaw of motion.

12.3.2 Calculate the momentum ofan object and describe whathappens when momentum isconserved during a collision.

Build VocabularyParaphrase Have students work with apartner to write an explanation in theirown words for the law of conservationof momentum. They may do so byreading this section and by using whatthey have already learned about mass,inertia, and velocity. Have studentgroups read their explanation aloud.Encourage other students to react to the explanation they hear.

Reading Strategya. kg•m/s b. Mass (or velocity) c. Velocity (or mass)

Build Reading LiteracyRelate Text and Visuals Refer topage 190D in Chapter 7, whichprovides the guidelines for relating text and visuals.

Ask questions that will help studentsunderstand how the visuals help clarifyand extend concepts presented in thetext. Point out Figure 15. Ask, Describethe forces created when the bumpercar strikes another car. (There is a forcefrom each car toward the other car.) If amoving car hits a car at rest, will thecar at rest exert a force on the movingcar? Explain your answer. (Yes, accor-ding to Newton’s third law, the car at restexerts an equal and opposite force on themoving car.)Visual, Verbal

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Reading Focus

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Section 12.3


Math Support, Section 12.3 • Math Skills and Problem Solving

Workbook, Section 12.3• Transparencies, Section 12.3

Technology• Probeware Lab Manual, Lab 4• Interactive Textbook, Section 12.3• Presentation Pro CD-ROM, Section 12.3• Go Online, NSTA SciLinks, Newton’s laws

Section Resources

Newton’s Third LawA force cannot exist alone. Forces always exist in pairs. Accordingto Newton’s third law of motion, whenever one object exerts a forceon a second object, the second object exerts an equal and oppositeforce on the first object. These two forces are called action and reaction forces.

Action and Reaction Forces The force your bumper car exertson the other car is the action force. The force the other car exerts on yourcar is the reaction force. These two forces are equal in size and oppositein direction.

Pressing your hand against a wall also produces a pair of forces. Asyou press against the wall, your hand exerts a force on the wall. This isthe action force. The wall exerts an equal and opposite force againstyour hand. This is the reaction force.

A similar situation occurs when you use a hammer to drive a nailinto a piece of wood. When the hammer strikes the nail, it applies aforce to the nail. This action force drives the nail into the piece ofwood. Is there a reaction force? According to Newton’s third law theremust be an equal and opposite reaction force. The nail supplies thereaction force by exerting an equal and opposite force on the hammer.It is this reaction force that brings the motion of the hammer to a stop.

Action-Reaction Forces and MotionCan you determine the action and reaction forcesoccurring in Figure 16? The swimmer uses her armsto push against the water and create an action force.The action force causes the water to move in thedirection of the action force. However, the wateralso exerts its equal and opposite reaction force onthe swimmer. The reaction force acts on the swim-mer and pushes her forward through the water.

Unlike the swimmer in Figure 16, not all action and reaction forcesproduce motion. Pushing against the wall with your hand is an exam-ple of an action-reaction force pair that does not result in motion.

Action-Reaction Forces Do Not Cancel You may be won-dering why the action and reaction forces acting on the swimmer inFigure 16 do not cancel each other and produce a net force of zero.The reason is that the action and reaction forces do not act on the sameobject. The action force acts on the water, and the reaction force actson the swimmer. Only when equal and opposite forces act on the sameobject do they result in a net force of zero.

Why don’t action and reaction forces cancel eachother out?


Figure 16 Action-reaction forcespropel the swimmer through thewater. The swimmer pushes againstthe water, and the water pushesthe swimmer ahead. Comparing and ContrastingDescribe the magnitude anddirection of the action andreaction forces acting on the swimmer.

For: Links on Newton’s laws


Web Code: ccn-2123

INSTRUCT

Newton’s Third LawBuild Science SkillsPredicting

Purpose Students use Newton’s third law of motion to predict the effect of objects that hit against one another.

Materials soccer ball, several heavy books


Procedure Ask students to useNewton’s third law to predict the out-come of each activity before performingit. First, have students lift several heavybooks above their heads and notice thedownward force they feel against theirhands. Next, place a soccer ball against a wall. Have a student kick the ball gently.The student should notice the opposingforce he or she feels against his or herfoot. Afterwards, have students discussthe origin of the forces they felt in each activity.

Expected Outcome Students willrealize that the force they exerted on the books and ball caused an equal andopposite force against them.Visual, Logical

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Customize for English Language Learners

Use InteractionOne of the best ways to teach science contentand language to all students, including Englishlanguage learners, is to encourage verbalinteraction, such as that which occurs in agroup. You may help English language learnersby using group activities in this section, as thesection lends itself well to activities involving

action-reaction forces. Since all force involvesaction-reaction, you may start with activitiesthat make the concept easy to learn. Forexample, demonstrate that standing on thefloor results in a reaction force of the floor,which is actually pushing back. Encouragestudents to work in groups to list other action-reaction forces.

Answer to . . .

Figure 16 The action force is theforce the swimmer exerts on the water.The equal and opposite reaction forceis the force the water exerts on theswimmer.

They do not cancel eachother out because they

act on different objects.

Download a worksheet on Newton’slaws for students to complete, andfind additional teacher support fromNSTA SciLinks.


374 Chapter 12

1846 The firstrailway to turn itspassengers upsidedown opens at apark in Paris, France.

1884 The first trueroller coaster in Americaappears at Coney Island,New York.

Amusement Park Rides

Acceleration Ridersexperience an acceleration

toward the loop’s centeras they move around it.

Start turret,13 metersabove the

ground

LOOPING GRAVITY RAILWAY

1845 1875 1905

For more than one hundred years, engineershave been designing rides that subject ridersto jarring motions, large accelerations,terrifying heights, soakings, or free falls.

The ridePassengersmove at aspeed ofabout 0.5 m/s.

Wood-paneledcar Each carhas a mass of13 tons andholds as manyas 60 people.

FERRIS WHEEL

1900 Trolleycompanies buildamusement parksto encourageweekend travel.

Maximum heightThe first Ferriswheel is 80.5 mtall.

1893 The George Ferris GiantWheel, named after the inventor,debuts at the ColumbianExposition in Chicago. A ridecosts 50 cents.

MomentumImagine a loaded shopping cart and a small glass marble are both slowlyrolling toward you at the same speed. The marble is easier to stop.Intuitively, you know that a loaded shopping cart is harder to stop becauseit has a greater mass. If the marble were moving 100 times faster than theshopping cart, which would be easier to stop? Momentum is the prod-uct of an object’s mass and its velocity. An object with large momentumis hard to stop. An object has a large momentum if the product ofits mass and velocity is large. The momentum for any object at rest iszero. A huge rocket such as the space shuttle has zero momentum as itsits on the launch pad. A small 1-kilogram meteor traveling at the veryhigh speed of 20 kilometers per second has a very large momentum.

374 Chapter 12

Momentum

MomentumPurpose Students observe that force is related to the time during which anobject’s momentum changes.

Materials water-filled balloons, pillow

Procedure Before beginning thedemonstration, explain to students thatforce can be written as a function ofmomentum and time: F � m � a �m � (v/t) � (m � v)/t. Therefore, F � t � m � v, where momentum is m � v, and F � t is the quantity knownas impulse. Point out that force has aninverse relationship to time in theequation. Therefore, the longer the timeperiod over which momentum changeoccurs, the smaller the force will be.

Take students outdoors to a paved area.Drop a water-filled balloon to the groundand let it burst on the pavement. Next,drop a water-filled balloon so that it landson the pillow without bursting.

Safety Caution students to stand a safedistance away from you when you dropthe balloons.

Expected Outcome Students shouldrealize that when the balloon stopsquickly, the momentum change occursover a short time. This results in a largeforce acting on the balloon—the largeforce breaks the balloon. When theballoon lands on the pillow, itsmomentum change occurs over a muchlonger period of time. The balloondoesn’t burst because the force actingon it is much less.Visual, Logical

FYIThe coverage of momentum in this text is limited to linear momentum—angular momentum and conservationare not covered.Momentum is a vectorquantity, having both magnitude anddirection.

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1996 A free-fall ride with adrop of 46meters opens inMaryland.

1934 The firstwild mouse coaster,with sharp turnsand abrupt drops,is built in Germany.

1963 Theworld’s first log-in-water ride is aninstant success ata park in Texas.Similar rides aresoon being builtaround the world.

FREE FALLRIDE

Sharp dropRiders reach a

maximum speedof about 25 m/s

during the drop.

THEME PARKSun wheel, amodern twiston the Ferriswheel.Rubber bumper

This prolongs thetime of impactand decreases the force of thecollisions.

1955 The firstcartoon-themedamusement parkopens in Anaheim,California.

1935 1965 1995

Roller coasterThis version,about three

kilometerslong,

catapults riders to

about25 m/s in the

first 4 seconds.

Explain a Sequence Write aparagraph about one of theamusement park rides shownon the time line. Describe themotion of the ride usingNewton’s laws of motion.(Hint: Before you write, use adiagram to analyze the forcesacting on the ride at aparticular moment.)

You can calculate momentum by multiplying an object’s mass(in kilograms) and its velocity (in meters per second).

Momentum FormulaMomentum � Mass � Velocity

Momentum is measured in units of kilogram-meters per second.Which has more momentum, a 0.046-kilogram golf ball with a

speed of 60.0 meters per second, or a 7.0-kilogram bowling ball witha speed of 6.0 meters per second?

Momentumgolf ball � 0.046 kg � 60.0 m/s � 2.8 kg•m/s

Momentumbowling ball � 7.0 kg � 6.0 m/s � 42 kg•m/s

The bowling ball has considerably more momentum than the golf ball.

1928 The firstfully steerablebumper car isinvented.

BUMPER CAR

Amusement Park RidesHave students read about the amuse-ment park inventions shown in thetimeline. Then, ask them what otherscience-related events they would addto the timeline. Suggestions may includethese events: Orville and Wilbur Wright’sfirst flight at Kitty Hawk, North Carolina,in 1903; Henry Ford’s initial Model-Tproduction in 1908; the opening of the 50-mile Panama Canal in 1914; orCharles Lindbergh’s 33 -hour, non-stopflight in a monoplane from New York to Paris in 1927. Then, ask students howall of the events in the timeline affectedboth science and society, includingthose events that students have added.Verbal

Build Math SkillsEquations and Formulas Many studentshave difficulty relating the description ofa relationship given in the text with theequation used to solve problems. Havestudents read Momentum. Ask them touse the description from the text towrite the momentum equation(Momentum � Mass � Velocity). Oncethey have written the equation, havethem practice solving the equation foreach of the three possible unknowns:momentum, mass, and velocity. Tellthem that it is important to practiceworking with the units (kg•m/s). Refer students to the text samples on this page. Logical, Portfolio

Direct students to the Math Skills in the Skills and Reference Handbookat the end of the student text foradditional help.

Explanations describing the forces and resulting motion that occur as asequence of events will vary dependingon which amusement park ride ischosen. Paragraphs should discussforces, acceleration, and momentum.Verbal, Portfolio

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376 Chapter 12

Conservation of MomentumWhat happens to momentum when objects collide? Look at the colli-sions in Figure 17. Under certain conditions, collisions obey the law ofconservation of momentum. In physics, the word conservation meansthat something has a constant value. That is, conservation of momen-tum means that momentum does not increase or decrease.

Imagine two trains colliding as shown in Figure 17A. If the two carsare part of a closed system, then momentum is conserved. A closedsystem means other objects and forces cannot enter or leave a system.Objects within the system, however, can exert forces on one another.According to the law of conservation of momentum, if no net force actson a system, then the total momentum of the system does not change.

Thus, if we consider the two train cars as a closed system, the carscan exert forces on each other. But overall, the total momentum of thesystem is conserved. In a closed system, the loss of momentum ofone object equals the gain in momentum of another object—momentum is conserved.

Figure 17 Three differentcollisions between equal-masstrain cars are shown above. Thedifferent collisions betweenequal-mass train cars are shownabove. In each collision, the totalmomentum of the train cars doesnot change—momentum isconserved. Calculating What isthe mass of each train car?

One car moving.

Before collision10 m/s

Momentum =300,000 kg·m/s


0 m/s 5 m/s

Momentum before collision = 300,000 kg·m/s

After collision

Momentum after collision = 300,000 kg·m/s

Momentum = 0

One car moving.



Momentum = 0Momentum = 0Momentum =300,000 kg·m/s

0 m/s 0 m/s 10 m/s


After collision


Both cars moving.






5 m/s 5 m/s 10 m/s


After collision


A Cars bounce off each other.

B Cars bounce off each other.

C Cars couple.

For: Activity on momentum

Visit: PHSchool.com

Web Code: ccp-2123

376 Chapter 12

Conservation ofMomentumUse VisualsFigure 17 To help teach conservation ofmomentum, point out to students thateach car’s momentum is written on thecar, and its velocity is written above thecar. Ask students to describe the motionin 17A before and after the collision. (Theblue car, going in the same direction as thegreen car, but faster, catches the green carand collides with it. After the collision, partof the momentum from the blue car istransferred to the green car, but the totalmomentum is still the same.) Ask, What isthe momentum of the blue car and thegreen car before and after the collisionin 17A? (Before the collision, the blue car’smomentum is 300,000 kg•m/s and thegreen car’s momentum is 150,000 kg•m/s.After the collision, the blue car’s momentumis 150,000 kg•m/s and the green car’smomentum is 300,000 kg•m/s.) What is the sum of the momentum beforeand after the collision? (The totalmomentum is 450,000 kg•m/s before and after the collision.) How does thisshow conservation of momentum?(The total momentum doesn’t change.)Repeat the above questions for Figures17B and 17C.Visual, Logical

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For: Activity on momentumVisit: PHSchool.comWeb Code: ccp-2123

Students can interact with simulationsof momentum and conservation ofmomentum online.


Reviewing Concepts1. Using Newton’s third law, explain what is

meant by action and reaction pairs of forces.

2. State in your own words the formula formomentum.

3. What is a necessary condition for theconservation of momentum?

4. If an eagle and a bumblebee are traveling at8 km/hr, which has more momentum? Explain.

Critical Thinking5. Applying Concepts A friend tells you that a

rowboat is propelled forward by the force ofits oars against the water. First, explainwhether the statement is correct, and thenidentify the action and reaction forces.

6. Inferring Explain how Newton’s third law ofmotion is at work when you walk.

7. Applying Concepts Explain in terms ofNewton’s third law why someone who tries tojump from a canoe to a riverbank may fall intothe water.


Explanatory Paragraph Write a paragraphexplaining why it is impossible to identifya single isolated force. State in your firstsentence the main idea of Newton’s thirdlaw of motion.

Momentum

A class studied the speed and momentum of a0.25-kilogram ball dropped from a bridge. Thegraph shows the momentum of the ball from thetime it was dropped until the time it hit the riverflowing below the bridge.

1. Applying Concepts At what time did theball have zero momentum? Describe this pointin the ball’s motion.

2. Using Graphs At what time did the ball havethe greatest momentum? What was the peakmomentum value?

3. Calculating What is the ball’s speed after1.25 seconds? (Hint: Use the graph and themomentum formula.)

Time (s)

Mo

men

tum

(kg

m/s

)

7

6

5

4

3

2

1

00 0.5 1.0 1.5

Momentum of a 0.25-kg Ball

2.0 2.5

Three different closed systems are shown in Figure 17. Each systemconsists of two train cars with the same mass that collide. In Figures17A and 17B, the train cars collide and then bounce apart. In Figure17C, the cars collide and then join together. Examine the momentumof each train car before and after the collision. Note that the totalmomentum before and after each collision does not change. Themomentum is conserved.

ASSESSEvaluate UnderstandingAsk students to write their own examplesillustrating the key concepts of Newton’sthird law of motion, momentum, andconservation of momentum.

ReteachDemonstrate a force acting on an objectand ask the students to identify the actionand reaction forces. Have them identifythe direction of each force on the objecton which it acts. Use Figure 17 to reviewmomentum. Emphasize that momentumis mass times velocity.

MomentumAnswers1. At t � 0 s; the ball has zeromomentum before it is released. 2. At t � 2.5 s; about 6.5 kg•m/s3. (m)(v) � 3.25 kg•m/sv � (3.25 kg•m/s)/(0.25 kg)v � 13 m/s, upwardThe speed is 13 m/s.

For Extra HelpShow students how they can locate thedesired momentum value by moving their finger up the vertical axis until theyreach the value. Then, they can movehorizontally to the right until they hit theplotted line. Finally, they can move downto the horizontal axis and determine thetime. For question 3, have students findthe momentum for a time of 1.25 s.Then, demonstrate how students can find the ball’s velocity by rewriting themomentum equation as velocity equalsmomentum divided by mass. Logical

Student paragraphs will vary but mustmention that forces always exist in pairs,and that according to Newton’s thirdlaw, every action force has an equal andopposite reaction force.

If your class subscribes tothe Interactive Textbook, use it toreview key concepts in Section 12.3.

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the action force, and the water pushing backagainst the oars is the reaction force.6. As you walk, you bend your foot and pushoff against the ground. This action forceproduces the reaction force of the groundpushing against your shoe. The reaction forcepushes you forward.7. When you jump, you push against the canoe.However, the canoe also moves in the oppositedirection of your jump. Because the canoemoves away, it produces a smaller reaction forceon you. This small reaction force is not strongenough to propel you to the riverbank.


1. Whenever one object exerts a force on asecond object, the second object exerts anequal and opposite force on the first object.2. Momentum � Mass � Velocity3. The objects involved must be part of aclosed system.4. Because the speeds are equal, the eagle’sgreater mass gives it more momentum.5. It is incorrect because it is the force of thewater against the oars that propels the boatforward. The oars pushing against the water is

Answer to . . .

Figure 17 30,000 kg


12.4 Universal Forces

Key ConceptsWhat force can attractand repel?

What force holds thenucleus together?

What is Newton’s law ofuniversal gravitation?

Vocabulary◆ electromagnetic force◆ strong nuclear force ◆ weaknuclear force ◆ gravitationalforce ◆ centripetal force

Reading StrategyComparing and Contrasting Copy the table below. After readingthe section, compare the two universal nuclear forces by completingthe table.

If you could travel to a distant planet in another galaxy, what wouldyou expect to find? The scene shown in Figure 18 is one possibility.Although this world looks so different from the one you know, somethings on this distant planet would be familiar—the forces.

Observations of planets, stars, and galaxies strongly suggest fourdifferent forces exist throughout the universe. These forces are knownas universal forces. The four universal forces are the electromagnetic,strong nuclear, weak nuclear, and gravitational. All the universal forcesact over a distance between particles of matter, which means that theparticles need not be in contact in order to affect one another. In addi-tion, each of these forces is affected by the distance between theparticles of matter.

Electromagnetic ForcesElectric and magnetic force are two differ-ent aspects of the electromagnetic force.Electromagnetic force is associated withcharged particles. Electric force andmagnetic force are the only forces thatcan both attract and repel. To understandelectric and magnetic forces, recall whatyou learned about charged particles inChapter 4.

Figure 18 An artist’s depiction ofa planet’s surface shows a worldvery different from Earth. Regard-less of location, however, certainuniversal forces are present.

378 Chapter 12

c. ? a. ?

d. ?

b. ?

e. ? f. ?

Strong nuclear

Weak nuclear

Force Acts on Which Particles?

Acts Over What Distance?

RelativeStrength

FOCUS

Objectives12.4.1 Identify the forms of electro-

magnetic force that can bothattract and repel.

12.4.2 Identify and describe theuniversal forces acting withinthe nucleus.

12.4.3 Define Newton’s law ofuniversal gravitation anddescribe the factors affectinggravitational force.

12.4.4 Describe centripetal force andthe type of motion it produces.

Build VocabularyCompare-Contrast Table Havestudents each make a table similar tothe table on p. 378. Have students useelectromagnetic force, nuclear forces, andgravitational force as the entries underthe heading Force. For Relative Strength,have students use words such as weak,weaker, weakest, strong, stronger, andstrongest. Suggest that students makethis table as they read in order to helpthem learn the section’s content.

Reading Strategya. Neutrons and protons b. Very short(decreases rapidly beyond the diameterof a few protons) c. Very strong (100times stronger than electrical repulsionforce at that distance) d. All particlese. Short f. Weaker than the strongnuclear force.

INSTRUCT

Electromagnetic ForcesBuild Reading LiteracyRelate Cause and Effect Refer to page260D in Chapter 9, which provides theguidelines on relating cause and effect.

Encourage students to make a list ofcause-and-effect relationships as they readabout electromagnetic forces. Then, havestudents compare their lists. Students maylist the behavior of charged objects whenthey approach one another, the clingingof clothes that have become charged, andthe repulsion or attraction of magneticpoles. Verbal, Logical

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Reading Focus

1

Section 12.4


Math Support, Section 12.4 • Transparencies, Section 12.4

Technology• Interactive Textbook, Section 12.4• Presentation Pro CD-ROM, Section 12.4• Go Online, NSTA SciLinks, Gravity

Section Resources

378 Chapter 12


Electric Forces Electric forces act between charged objects orparticles such as electrons and protons. Objects with oppositecharges—positive and negative—attract one another. Objects withlike charges repel one another. Figure 19 shows that clothes often clingtogether when they are removed from a dryer. Some clothes, such ascotton socks, lose electrons easily and become positively charged.Other clothes, such as polyester shirts, gain electrons easily andbecome negatively charged. Because the oppositely charged particlesattract one another, the clothes cling together.

Magnetic Forces Magnetic forces act on certain metals, on thepoles of magnets, and on moving charges. Magnets have two poles,north and south, that attract each other. Two poles that are alike repeleach other. If you have handled magnets, you know that when oppo-site magnetic poles are brought close, they almost seem to jumptogether. On the other hand, when two similar poles approach eachother, you can feel them pushing apart.

Figure 20 shows a child’s wooden train set whose cars are linkedwith magnets. Each car has a north pole on one end and a south poleon the other. Children quickly learn that if a train car won’t stick tothe one in front of it, the car must be turned around.

Nuclear ForcesThink about the nucleus of an atom, with its protons crammed into anincredibly small space. Because protons are positively charged, you wouldexpect that an electric force of repulsion would break the nucleus apart.Scientists believe the nucleus would fly apart if there were not another,much stronger, attractive force holding the protons within the nucleus.

Two forces, the strong nuclear force and theweak nuclear force, act within the nucleus to hold ittogether. The strong nuclear force overcomes the elec-tric force of repulsion that acts among the protons in thenucleus. The weak nuclear force is involved in certaintypes of radioactive processes.

Strong Nuclear Force The strong nuclear forceis a powerful force of attraction that acts only on theneutrons and protons in the nucleus, holding themtogether. The range over which the strong nuclear forcesacts is approximately equal to the diameter of a proton(10-15 m). Although this force acts over only extremelyshort distances, it is 100 times stronger than the elec-tric force of repulsion at these distances.

What type of force acts between particles withthe same electrical charge?

Figure 20 A magnetic force ofattraction holds the two traincars together. Applying Concepts How arethe two magnetic poles of themagnets related?

Figure 19 Clothes often acquireelectric charges in the dryer.Clothes with opposite chargestend to cling together.

Some students may think that for anobject to become positively charged, itmust gain one or more protons.Reinforce the concept that electrontransfer leads to charged particles.Electrons have a negative charge.Therefore, gaining electrons makes anobject more negative, and losingelectrons makes an object more positive.Logical

Nuclear Forces

Nuclear ForcesPurpose Students observe forcesrepresenting the strong force in anatom’s nucleus and the electric forcebetween protons.

Materials 2 magnetic toy train cars orany 2 magnets, wide adhesive tape on aroll (or rubber band)

Procedure Use the toy train cars ormagnets to show students that like poles repel. With the cars touching eachother, bind them together with adhesivetape. Be sure to tape the cars in such away that the tape can be easily cut to freethe cars. Tell students that the toy traincars are like protons, whose electriccharges repel each other, and that thetape is like the strong nuclear force,overcoming the electric charge of theprotons. Cut the tape and have studentsobserve the energy released as the carspush away from each other. Relate this tothe force released in a nuclear explosionwhen the nucleus of an atom is split.

Expected Outcome The studentsrealize that the strong nuclear force inan atom’s nucleus is stronger than theelectric force between protons.Visual, Logical

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Customize for Inclusion Students

Physically ChallengedTo accommodate students who have physicalchallenges, look for opportunities to includethem in tasks that are suited to their motorskills. For example, have students with limitedbody movements explain the similarities in the

way electrically charged particles attract andrepel each other and the behavior of oppositemagnetic poles. Then, provide them with barmagnets and ask them to demonstrateattractive and repulsive magnetic forces. Answer to . . .

Figure 20 The opposite poles, northand south, are touching one another.

Electric force


380 Chapter 12

Weak Nuclear Force The other powerful force in the nucleus isthe weak nuclear force. As the name implies, the weak force is weakerin strength than the strong nuclear force. The weak nuclear force isan attractive force that acts only over a short range. The short rangeover which the weak nuclear force acts, about 10-18 meters, is less thanthe range of the strong nuclear force.

Gravitational ForceGravity, the weakest universal force, is so much a part of your life thatyou probably take it for granted. You know from experience thatobjects fall toward Earth. It was Newton who discovered that gravityaffects all objects in the universe. The same force acting on a fallingapple is also acting on the moon to keep it in its orbit.

Gravitational force involves much more than just Earth’s gravita-tional field. Gravitational force is an attractive force that acts betweenany two masses. Newton’s law of universal gravitation states thatevery object in the universe attracts every other object.

Thus, Earth exerts a force on an apple, and the apple exerts an equalforce on Earth. You exert a gravitational force on your textbook, andyour textbook exerts an equal gravitational force on you. The reasonyou don’t notice gravity pulling your textbook toward you is that yourmass and the mass of the textbook are so small. It takes a huge masssuch as Earth’s to exert a large gravitational force. The attractive forceof gravity acting between two objects is shown in Figure 21.

Investigating Forceand Distance

Materials balloon, bubble solution,bubble wand

Procedure1. Inflate a balloon and then

make a knot in its neck toclose it. Rub the balloonback and forth against yourhair to charge it.

2. Blow several bubbles intothe air and hold the chargedballoon above them.Observe how the distancebetween the balloon andthe bubbles affects thespeed at which the bubblesfall. CAUTION Quickly wipeup any spilled bubble solu-tion to avoid slips and falls.

3. Try to temporarily suspend abubble in the air withouttouching it with the balloon.

Analyze and Conclude1. Drawing Conclusions

How does the distancebetween two objects affectthe force of attractionbetween them?

2. Predicting If a bubblewere suspended below theballoon, what do you thinkwould happen when youmoved the balloon closerto the bubble?

Gravitational force of attraction of mass Y by mass X

Gravitational force of attraction of mass X by mass Y

X Y

X Y

X Y

A

B

C

Figure 21 Gravitational force depends upon mass and distance. A Two masses,X and Y, attract each other. B The larger mass of X results in a largergravitational force. C Increasing the distance between the masses significantlyreduces the gravitational force.

380 Chapter 12

Gravitational Force

Investigating Force and Distance

ObjectiveAfter completing this activity, studentswill be able to• describe how the force of electrostatic

attraction is affected by distance.


Prep Time 5 minutes

Advance Prep Select a day when therelative humidity is moderate or low toperform this lab.


Teaching Tips• Demonstrate how to charge the

balloon and hold it above the bubble.• Some hair products will interfere with

the balloon. In this case, have studentsrub the balloon against their clothes.

Expected Outcome The bubbles willbe attracted to the charged balloon. The force of this attraction will increaseas students bring the balloon closer tothe bubbles.

Analyze and Conclude1. There is very little electricalinteraction between objects that are farapart. As the distance is decreased, theattraction between the two objectsbecomes stronger.2. If the balloon were brought closer tothe bubble, the force of attractionwould increase and the bubble wouldmove upwards toward the balloon.Visual, Logical

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Law of Universal Gravitation Newtoncame to the conclusion that any two objects in the universe exert a gravitational force ofattraction on each other. The force is directedalong a line joining the objects’ centers.Newton concluded that the gravitationalattraction (G) is proportional to the productof the objects’ masses (m1 and m2) andinversely proportional to the square of thedistance (d) between them. That equation is

F � G(m1m2/d2). Because the value of G isvery small, the gravitational force is onlysignificant if one or both objects has a largemass and the distance between the objects is not very large. Earth’s gravitationalacceleration g is related to the equation ofuniversal gravitation by the expression g �g(me/d2), where me is Earth’s mass. In thiscase, the equation for universal gravitationreduces to the familiar equation F � mg.

Facts and Figures


Gravity Acts Over Large Distances The gravitational forcebetween two objects is proportional to their masses and decreases rap-idly as the distance between the masses increases. The greater the massof the objects, the greater is the gravitational force. Gravitational forcedecreases with the square of the distance between the objects. As shownin Figures 21A and 21C, if the distance between masses doubles, theforce of gravity is only one fourth as strong.

Gravity is the weakest universal force, but it is the most effectiveforce over long distances. Gravity holds you on Earth. It keeps the moonin orbit around Earth, the planets in orbit around the sun, and the starsin orbit in their galaxies. The sun’s mass is about 300,000 times the massof Earth, so the sun’s gravitational force is much stronger than that ofEarth. The influence of the sun’s gravitational force extends well beyondEarth. Pluto, which is almost 40 times farther from the sun than Earthis, has its orbit determined by the gravitational pull of the sun.

The Earth, Moon, and Tides How is themoon kept in orbit around Earth? Recall that the moonhas inertia, so according to Newton’s first law, it shouldcontinue to move along a straight path until actedupon by a force. That force is Earth’s gravitational force,which acts continuously to pull the moon toward it, asshown in Figure 22.

Earth’s gravitational attraction keeps the moon in anearly circular orbit around Earth. It works in much thesame way that a string tied to an eraser allows you to twirlthe eraser in a circle over your head. As you twirl theeraser, the string exerts a centripetal force on the eraser.Acentripetal force is a center-directed force that continu-ously changes the direction of an object to make it movein a circle. This center-directed force causes a continuouschange in the direction of the eraser. The result is a cir-cular path. The center-directed force of Earth’s gravitypulls the moon into a nearly circular orbit around Earth.

If you have spent time at the seashore, you have probably noticedthat the level of the tide changes throughout the day. The gravitationalpull from the moon produces two bulges in Earth’s oceans. One bulgeis on the side of Earth closest to the moon. The other bulge is on theside of Earth farthest from the moon. Earth rotates once per daybeneath theses two bulges. This rotation results in two high and twolow tides per day on Earth.

What factors affect gravitational force?

Figure 22 The moon’s inertiaand the gravitational pull ofEarth result in a nearly circularorbit. The gravitational pull ofthe moon is the primary cause of Earth’s ocean tides.

Earth

Moon

Gravity

Motion of Moon

For: Links on gravity


Web Code: ccn-2124

Build Science SkillsObserving Take students outside. Tie a string around an eraser, as describedin the second paragraph of The Earth,Moon, and Tides. Ask a volunteer totwirl the eraser over his or her head.CAUTION Make sure the studentsobserving this demo stand far away fromthe student twirling the eraser. Havestudents observe that the eraser followsa circular orbit. Remind students thatinertia causes an object to resist changein motion. Explain that this means thatthe eraser would travel in a straight pathif a force did not pull it into an orbit. Askthe volunteer to slowly twirl the eraserand then let go of the string. Havestudents observe what happens. Ask,What force kept the eraser moving ina circular orbit? (The centripetal forcefrom the string kept the eraser moving in acircular orbit.) What proof do you havethat a centripetal force was acting onthe twirling eraser to change itsmotion? (As soon as the string wasreleased, the eraser moved in a straightline path.) As the eraser is twirled at a constant speed, is it accelerating?Explain your answer. (Yes, accelerationoccurs because the eraser is constantlychanging direction.) Visual, Logical

Use VisualsFigure 22 Use Figure 22 to reinforcethe concept of centripetal force andinertia, as discussed in Build ScienceSkills. Help students to see thatgravitational pull is the centripetal(center-directed) force in planetaryorbits. Ask, What is the direction of the moon’s velocity in Figure 22? (The moon’s velocity is tangent to itscircular path. At the instant shown, thedirection of the moon’s velocity is straightdown toward the bottom of the page.)Visual, Logical

L1

L2


Answer to . . .

Mass and distance

Download a worksheet on gravityfor students to complete, and findadditional teacher support fromNSTA SciLinks.


382 Chapter 12


Reviewing Concepts1. Which universal force can repel as well

as attract?

2. Which universal force acts to hold thenucleus together?

3. State in your own words what is meant byNewton’s law of universal gravitation.

4. How does friction with the atmosphere affectthe speed of an artificial satellite?

Critical Thinking5. Using Models The moon in its orbit around

Earth behaves like a ball at the end of a stringbeing swung above your head. Explain theforces involved.

6. Predicting If the speed of an orbitingsatellite decreases, how might you expectits orbit to change?

7. Inferring Explain how Newton’s third lawand his law of universal gravitation areconnected.

Satellites in Orbit Artificial satellites are launched into orbit bya rocket or space shuttle. Why doesn’t a satellite in a high orbit need tofire rocket engines continuously to remain in orbit? Much like themoon, the satellite needs only the centripetal force provided by grav-ity and its inertia to maintain its orbit. Satellites in a low orbit, however,are slowed by friction with Earth’s atmosphere. As a satellite losesspeed, it loses altitude. Eventually the satellite reenters Earth’s atmos-phere and burns up.

Uses of Satellites Currently, there are hun-dreds of artificial satellites orbiting Earth. Thesesatellites perform many functions. They monitorEarth’s weather, create detailed radar maps ofEarth’s surface, use telescopes to gaze deep intospace, and study Earth’s climate. Some satellites,like the one shown in Figure 23, receive and trans-mit radio and microwave signals. Numerouscommunication satellites are used to receive andtransmit cell phone and satellite television signals.

The next time you watch an event on televi-sion transmitted by satellite from another part ofthe world, you should thank Isaac Newton. Hiswork to discover the laws of motion and universalgravitation have led to the development of count-less modern technologies.

Compare-Contrast Paragraph Write a shortparagraph comparing the similarities and differ-ences of the universal forces. Discuss the dis-tances over which the forces act and whethereach force attracts, repels, or can do either.

Satellite

Dishreceiver

Transmitter

Figure 23 Satellites are used to receive and transmitelectromagnetic waves over great distances.

382 Chapter 12

ASSESSEvaluate UnderstandingHave students make a poster with information about electromagneticforces, nuclear forces, and gravitationalforce. Students should include examplesof each type of force along with sketchesor diagrams that illustrate the mainconcepts.

ReteachAsk students to list all examples ofelectromagnetic, nuclear, andgravitational forces they can think of,both from the text and from everydayexamples. Have them explain the actionof each of the forces they list.

The electromagnetic force is bothrepulsive and attractive. The other threeforces are only attractive. The electro-magnetic force and the gravitationalforce act at all distances. The strongforce and the weak force act only at veryshort distances.

If your class subscribes tothe Interactive Textbook, use it toreview key concepts in Section 12.4.

L1

L2

3


5. Earth’s gravitational attraction acts as acentripetal force on the moon.6. It would gradually be pulled closer to Earthand eventually fall out of orbit.7. According to Newton’s third law, wheneverone object exerts a force on a second object,the second object exerts an equal andopposite force on the first object. Newton’slaw of gravitation is a special case of this inwhich the force is gravity.


1. Electromagnetic force is the only force thatcan both attract and repel.2. The strong nuclear force acts within thenucleus to hold it together.3. According to Newton’s law of universalgravitation, every object in the universe attractsevery other object.4. Friction with the atmosphere slows artificialsatellites in low orbit.

354 Chapter 12

Forces and MotionC H A P T E R

A kayaker maneuvers his way downstream �using a paddle.

How do science concepts apply to yourworld? Here are some questions you’ll beable to answer after you read this chapter.

■ Why doesn’t the pulling by each team in a tug of war always result in motion? (Section 12.1)

■ Why do flying squirrels spread their arms and legs when they jump through the air? (Section 12.1)

■ What happens to the forward motion of a passenger in a head-on auto accident? (Section 12.2)

■ What factors affect the fall of a sky diver? (page 370)

■ What brings the head of a hammer to a stop when you drive a nail into a board?(Section 12.3)

■ What causes tides? (Section 12.4)

354 Chapter 12

ASSESS PRIORKNOWLEDGEUse the Chapter Pretest below to assessstudents’ prior knowledge. As needed,review these Science Concepts andMath Skills with students.

Review Science ConceptsSection 12.1 Review with studentswhat motion is and how it is measured.Encourage students to describe what aforce is and what it can do.

Section 12.2 Ask students to reviewalgebraic equations and exponents.Suggest that they observe physicalforces in their everyday lives and beprepared to discuss how they thinkthese forces affect motion.

Section 12.3 Encourage students to review the concepts of mass andvelocity, making sure they do notconfuse mass with weight or velocitywith speed. Reinforce that mass andweight are not the same and that speedwith direction is velocity.

Section 12.4 Review models of theatom if this concept has been covered.Remind students of their prior knowledgeof gravitational force and forces that actbetween magnets and charged particles.

Review Math SkillsFormulas and Equations,Exponents, and Line Graphs Students will need to work with equationsand exponents to solve problems usingNewton’s second law of motion.

Direct students to the Math Skills in theSkills and Reference Handbook at theend of the student text.

PHYSICS

Chapter 12

Chapter Pretest

1. What is relative motion? (Relative motion is movement in relation to a frame of reference.) 2. What is the difference between distanceand displacement? (Distance is the length ofa path between two points. Displacement isthe direction from the starting point and thelength of a straight line from the starting pointto the ending point.)

3. How is average speed calculated? (Totaldistance is divided by total time.)4. On a distance-time graph, what does theslope represent? (The slope represents the speed.)5. What is velocity? (Velocity is speed with direction.)6. How is acceleration related to velocity?(Acceleration is change in velocity, that is, anychange in speed, direction, or both.)

7. A backpack falls out of an open window.The backpack starts from rest and hits theground 1.0 second later with a velocity of9.8 m/s. What is the average acceleration of the backpack? (c)

a. 9.8 m/s b. 9.8 mc. 9.8 m/s2 d. All of the above

8. How are mass and weight different? (Massis a measure of inertia. Weight is the measureof the force of gravity acting on an object.)

PHYSICS

12.1 Forces

12.2 Newton’s First andSecond Laws of Motion

12.3 Newton’s Third Law ofMotion and Momentum


Chapter Preview

What Starts an Object Moving?Procedure1. On a flat surface, arrange four pennies in a

row so that they are touching one another.

2. Using your index finger, slide a fifth pennyacross the surface in line with the row ofpennies so that it strikes a penny at one endof the row.

Think About It1. Observing Describe how the row of pennies

moves in response to the collision.

2. Formulating Hypotheses What doyou think caused the pennies to moveafter the collision? Why didn’t the penniesmove before the collision?

Video Field Trip

Air Forces



Encourage students to view the Video Field Trip“Air Forces.”

ENGAGE/EXPLORE

Video Field Trip

What Starts an Object Moving?PurposeIn this activity, students begin to use theconcept of force to explain movement.

Students may hold the misconceptionthat only a moving object can exertforce. To help dispel this misconception,after completing this activity askstudents what caused the penny on theend of the row to move. Each pennyexerts a force on the next, although onlythe last penny in the row moves.


Prep Time 5 minutes

Materials 5 pennies

Advance Prep Checkers or gamechips can be substituted for pennies.


Safety Students should wear safetygoggles. Caution students not toobserve from a position in which the pennies move toward them.

Teaching Tips • If students are having difficulty striking

the row of coins head-on, they cantape a pair of rulers to the table oneither side of the row of coins tocreate a linear track for the coins totravel along.

Expected Outcome As the row ofcoins is struck, the moving coin will stopat the head of the row while the coin atthe far end of the row will move away.

Think About It1. Only the coin at the far end of therow moved away.2. During the collision, a force wastransferred from one coin to the next inthe row. Because no horizontal force wasacting on the coins before the collision,they did not move at that time. Studentsmay not articulate the abstract conceptof a force well at this stage. Althoughstudents can reasonably be expected tostart developing this concept, they maynot express it in formally correctscientific language at this stage.Visual

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ENGAGE/EXPLORE

Video Field Trip

Air Forces



In this lab, you will examine the relationships amongforce, mass, and motion.

Problem How does a jet-powereddevice move?

Materials

For the probeware version of this lab, seethe Probeware Lab Manual, Lab 4.

Skills Applying Concepts

Procedure1. On a separate sheet of paper, make a copy of

the data table shown.

2. Insert the string through the straw and tieeach end of the string to the back of aseparate chair. Pull the chairs apart until thestring is tight and horizontal.

3. Blow up the balloon and then hold theballoon’s opening closed. Record the length ofthe balloon. Have a classmate attach theballoon lengthwise to the straw using tape.

4. While continuing to hold the balloon’sopening closed, slide the balloon jet to theend of the string as shown.

5. Release the balloon. Measure the time duringwhich the balloon jet moves. Measure thedistance that the balloon jet travels along the

• string, 3 m in length• drinking straw• 4 long balloons• masking tape

• stopwatch• meter stick• 2 threaded nuts• 2 chairs

string. Record the distance and time valuesin the data table for 0 Nuts Used, Trial 1.

6. Repeat Steps 3 through 5 with a new balloon.Make sure to inflate the balloon to the samesize as in Step 3. Record your results in thedata table for 0 Nuts Used, Trial 2.

7. Repeat Steps 3 through 6 twice more with anew balloon. This time, tape two nuts to theballoon before releasing it. Record your resultsin the data table for 2 Nuts Used, Trials 1 and 2.

8. Calculate and record the average speed foreach trial. The average speed is equal to thedistance divided by the time.

Analyze and Conclude1. Applying Concepts Use Newton’s second

and third laws to explain the motion of theballoon jet.

2. Analyzing Data How did adding mass(nuts) to the balloon jet affect its motion?

Investigating a Balloon Jet

Data Table

0022

Length of Inflated Balloon (centimeters)

Number of Nuts Used

1212

TrialNumber

Time(seconds)

Distance(centimeters)

Average Velocity(cm/s)

Investigating a Balloon Jet Objective After completing this activity, studentswill be able to • use Newton’s second and third laws of

motion to explain the movement of ajet-powered device.

• use Newton’s second and third laws ofmotion to describe how the mass ofan object affects its acceleration inresponse to a force.

Many students hold the misconceptionthat a jet functions by pushing againstthe surrounding air. Point out thatrockets work in the vacuum of outerspace. Then, ask students to explain how they think the balloon jet moves.As the air in the balloon jet is pushedout the end, it produces an equal andopposite reaction in the balloon, whichaccelerates the balloon forward.

Skills Focus Measuring,Calculating, Applying Concepts

Prep Time 5 minutes


Expected Outcome As the balloon isreleased it will accelerate along the lengthof the string. Adding the nuts to the massof the balloon will reduce the time anddistance that the balloon travels.

Analyze and Conclude1. The jet’s movement depends onNewton’s third law of motion. Thepressurized air inside the sealed balloonpushes outward in all directions, but aslong as the air can’t go anywhere,neither can the balloon. As soon as theair inside the balloon is allowed toescape, the force of the air on theopened end of the balloon no longerbalances the force of air on the oppositeend. The reaction to this action is themovement of the balloon in theopposite direction. Newton’s second lawof motion predicts that the balloon willaccelerate at a rate that is directlyproportional to the force of thecompressed air, and inverselyproportional to the balloon’s mass.2. Adding nuts increased the mass of the balloon jet, which reduced its acceleration.Logical

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Probeware Lab Manual Versions of this labfor use with probeware available from Pasco,Texas Instruments, and Vernier are in theProbeware Lab Manual.


354A Chapter 12

Planning Guide

SECTION OBJECTIVES STANDARDS ACTIVITIES and LABSNATIONAL STATE

A-1, A-2, B-4,F-1, G-1, G-2,G-3

B-4, G-1, G-2,G-3

A-1, A-2, B-4,G-1

12.2 Newton’s First and Second Laws of Motion, pp. 363–369

1 block or 2 periods

12.2.1 Describe Newton’s first law of motion andits relation to inertia.

12.2.2 Describe Newton’s second law of motionand use it to calculate acceleration,force, and mass values.

12.2.3 Relate the mass of an object to its weight.

12.3 Newton’s Third Law of Motion and Momentum, pp. 372–377


12.3.1 Explain how action and reaction forcesare related according to Newton’s thirdlaw of motion.

12.3.2 Calculate the momentum of an object anddescribe what happens when momentumis conserved during a collision.

12.1 Forces, pp. 356–362


12.1.1 Describe examples of force and identifyappropriate SI units used to measureforce.

12.1.2 Explain how the motion of an object isaffected when balanced and unbalancedforces act on it.

12.1.3 Compare and contrast the four kinds of friction.

12.1.4 Describe how Earth’s gravity and airresistance affect falling objects.

12.1.5 Describe the path of a projectile and identify the forces that produceprojectile motion.

SE Quick Lab: Investigating Inertia,p. 365

TE Teacher Demo: Force and Acceleration, p. 365

TE Teacher Demo: Newton’s Second Law of Motion, p. 367

LM Investigation 12A: InvestigatingGravitational Acceleration and Fluid Resistance

LM Investigation 12B: Testing Galileo’sHypothesis L1

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SE Exploration Lab: Investigating a Balloon Jet, p. 383

TE Build Science Skills: Predicting,p. 373

TE Teacher Demo: Momentum,p. 374 L2

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SE Inquiry Activity: What Starts an Object Moving? p. 355

SE Quick Lab: Observing the Effects of Friction, p. 360

TE Build Science Skills: Measuring,p. 357 L2

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Easy Planner Teacher Express

A-1, A-2, B-1,B-4, E-2, G-1,G-2, G-3

12.4 Universal Forces, pp. 378–382


12.4.1 Identify the forms of electromagneticforce that can both attract and repel.

12.4.2 Identify and describe the universalforces acting within the nucleus.

12.4.3 Define Newton’s law of universalgravitation and describe the factorsaffecting gravitational force.

12.4.4 Describe centripetal force and the type of motion it produces.

SE Quick Lab: Investigating Force and Distance, p. 380

TE Teacher Demo: Nuclear Forces,p. 379 L2

L2

Forces and Motion 354B

Quantities for each group

STUDENT EDITION

Inquiry Activity, p. 355 5 pennies

Quick Lab, p. 360 2 rubber erasers, sticky notes,scissors, metric ruler

Quick Lab, p. 364 index card, coin

Quick Lab, p. 380balloon, bubble solution,bubble wand

Exploration Lab, p. 383 string (3 m in length), drinkingstraw, 4 long balloons, maskingtape, stopwatch, meter stick, 2 threaded nuts, 2 chairs

TEACHER’S EDITION

Build Science Skills, p. 357 5-N spring scale, centimeterruler, book, string, 5 objects(such as books) weighing from1 to 5 newtons

Teacher Demo, p. 365 2 identical toy cars (ordynamics carts), 2 studentvolunteers, identical floorsurface for each car

Teacher Demo, p. 367 wind-up toy car, 3 metalwashers, tape

Build Science Skills, p. 370 sheet of paper, stopwatch,auditorium stage

Build Science Skills, p. 373 soccer ball, several heavy books

Teacher Demo, p. 374 water-filled balloons, pillow

Teacher Demo, p. 379 2 magnetic toy train cars or any2 magnets, wide adhesive tapeon a roll (or rubber band)

Materials for Activities and Labs

Chapter Assessment

CHAPTER ASSESSMENT

SE Chapter Assessment, pp. 385–386

CUT Chapter 12 Test A, BCTB Chapter 12iT Chapter 12PHSchool.com GOWeb Code: cca-2120

STANDARDIZED TEST PREP

SE Chapter 12, p. 387TP Diagnose and Prescribe

Go online for these Internet resources.

Web Code: cca-2120Web Code: ccn-2121Web Code: ccn-2122Web Code: ccn-2123Web Code: ccn-2124

Interactive Textbook withassessment at PHSchool.com

Ability Levels Components

For students who need additional help

For all students

For students who need to be challengedL3

L2

L1 SE Student EditionTE Teacher’s EditionLM Laboratory ManualPLM Probeware Lab

Manual

RSW Reading & StudyWorkbook

MSPS Math Skills &Problem SolvingWorkbook

CUT Chapter & Unit TestsCTB Computer Test BankTP Test Prep ResourcesDC Discovery Channel

Videotapes & DVDs

T TransparenciesiT Interactive TextbookP Presentation Pro

CD-ROMGO Internet Resources

RESOURCES SECTION

PRINT and TECHNOLOGY ASSESSMENT

RSW Section 12.1

T Chapter 12 Pretest

Section 12.1

P Chapter 12 Pretest

Section 12.1

GO Forces L2

L2

L2

L2

L2

L1 SE Section 12.1Assessment, p. 362

iT Section 12.1

RSW Section 12.2

RSW Math Skill

MSPS Section 12.2

DC Air Forces

T Section 12.2

P Section 12.2

GO Mass L2

L2

L2

L2

L2

L2

L1 SE Section 12.2 Assessment, p. 369

iT Section 12.2

PLM Lab 4: Investigating a Balloon Jet

RSW Section 12.3

MSPS Section 12.3

T Section 12.3

P Section 12.3

GO Newton’s laws L2

L2

L2

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L2SE Section 12.3

Assessment, p. 377

iT Section 12.3

RSW Section 12.4

T Section 12.4

P Section 12.4

GO Gravity L2

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L1 SE Section 12.4 Assessment, p. 382

iT Section 12.4

354C Chapter 12

Physics Refresher

Forces 12.1

A force, which can be simplydefined as any push or pull, isthe cause of acceleration(change in velocity). Force is avector, that is, it has magnitudeand direction. The SI unit offorce is the newton (N), theamount of force that producesan acceleration of 1 m/s2 on a1 kg mass.

If all forces on an object arecombined and the net force iszero, the object does not accel-erate. If the net force is notzero, velocity remains constant.

Friction 12.1

Friction is the opposing force that touching objects experienceas they move past one another. Static friction is the force ofresistance to motion when two contacting surfaces are station-ary. Kinetic friction (which includes sliding, rolling, and fluidfriction) is the force of resistance that opposes the relativemotion of two contacting surfaces moving past one another.

Laws of Motion 12.2 and 12.3

Newton’s first law of motion says that an object at rest willremain at rest, and an object in motion will continue in motionwith constant velocity unless it experiences a net force.

Newton’s second law of motion says that an object’s accelera-tion is directly proportional to the net force acting on it and

Before you teach

Big IdeasThere are four distinct forces in our universe: gravita-tional, electromagnetic, and strong and weak nuclearforces. At the time of the big bang, these four forces werelikely unified as a single force, but they fragmented asthe universe expanded and cooled.

Space and Time Gravity is the most important forceover large distances, and is responsible for large-scalemotions in space. Gravity is the weakest of all the forces,but because it acts between all matter and because itdecays at a moderate rate with distance, it is the mostdominant force over large distances.

The strong and weak nuclear forces act between atomicparticles. The strong force holds the nuclei of atomstogether. The weak force is responsible for radioactivedecay. These forces are immense at subatomic distances,but decay rapidly with distance.

The electromagnetic force is best known for effectssuch as electricity and magnetism. However, it alsoprovides most of the everyday “forces” in our lives. Holdsomething up, and the electrons around the atoms ofyour hand are repelling the electrons around the atomsof the object you are holding. Pushing, pulling, hitting,and holding all result from the repelling electromagneticforces supplied by the electrons on the outsides of theatoms of objects.

Forces and Motion The most important equation inall of science is likely F � ma, which says that when youpush on an object, it accelerates. Push on a massive object,and it accelerates slowly. Push harder, and it acceleratesfaster. The most prevalent force on our planet’s surface isthe gravitational pull of Earth’s mass. As a result, the mostprevalent kind of motion is downward acceleration (i.e.,things fall downhill).

Matter and Energy As Einstein showed, gravity isbetter viewed as a distortion of the fabric of space bymatter. Very massive objects, like black holes and galaxies,create very large “warping” of the spatial dimensions ofspace. This explains why light from distant galaxies isbent around intervening galaxies.

From the AuthorMichael WysessionWashington University

Force Force

Acceleration Acceleration

Mass = 1 shopping cartA Mass = 8 shopping cartsB

Some students mayincorrectly think that onlyanimate objects can exerta force. However, gravityis inanimate, as are many other forces. For astrategy to overcome this misconception, seeAddress Misconceptionson page 358.

Acceleration depends on force and mass.

inversely proportional to its mass (a � F/m, F � ma). One appli-cation is the measurement of weight. Weight, W, is a force, whilethe gravity, g, is the acceleration (W � mg). On Earth’s surface,g is approximately 9.8 m/s2.

In the 1680s, Newton related the laws in his book PhilosophiaeNaturalis Principia Mathematica. He stated that force is propor-tional to change in momentum. Mathematically, this law is F � m � v. A change in velocity is the same as acceleration, so thisequation became F � ma.

Newton’s third law of motion says that, when object A exerts aforce on object B, object B exerts a force on object A that is equalin magnitude and opposite in direction.

Universal Forces 12.4

Three of the four universal forces are electromagnetic, strongnuclear, and weak nuclear. The range and relative strengths of theuniversal forces are summarized in the table below.

The electromagnetic force consists of both the electric force andthe magnetic force. These forces are found in regions in whichthere are electric and magnetic fields. Michael Faraday discoveredthat a changing magnetic field produces an electric field, andJames Clerk Maxwell illustrated that a changing electric field pro-duces a magnetic field.

The nucleus of an atomis held together by attractionsamong protons and neutronscalled the strong nuclear force and the weak nuclear force.The strong nuclear force isgreater than the electric repul-sion of the protons’ positiveforces and therefore overcomesthat repulsion, holding themtogether. The attraction due tothe strong force, however,occurs over a very short dis-tance, less than 3 � 10�15 m, orabout three protons’ width. Theweak nuclear force is stronger

than gravitational force.

Build Reading Literacy

Visualize

Forming Mental PicturesStrategy Help students understand and recall complex textby forming mental pictures as they read. In some cases, visualelements of the text can aid students in visualizing; in othercases students must rely solely on text descriptions. Chooseseveral paragraphs from Chapter 12, such as the four on p. 358. If possible, include at least one paragraph that has anaccompanying figure and at least one other paragraph thatrefers to concepts or events that are not illustrated in visualelements, such as diagrams, charts, graphs, or photographs.

Example1. Have students keep their books closed. Tell them to listenwhile you read and to visualize, or form mental pictures of,each object or action you read about.2. Then, read a paragraph or so aloud, pausing frequently todemonstrate, by thinking aloud, how to visualize each thingdescribed. When reading complex or technical text, pausingafter each phrase will often be appropriate.3. Tell students to continue visualizing. Slowly and clearly,read on. Then, select a logical stopping point and discuss withstudents the images they visualized.4. If there is an accompanying figure, have students open to itand see how it compares with their visualizing. Point out thatvisuals in the text help readers picture what they are reading.5. Have students work with partners to practice by taking turnsreading and visualizing aloud. Tell them to expand on visualsthat appear in the text and to describe their own mental imagesof ideas or events that are not shown in visuals.

See p. 368 for a script on how to use the visualize strategywith students. For additional Build Reading Literacystrategies, see pp. 357, 372, and 378.

Some students may thinkthat objects become posi-tively charged because theyhave gained protons. Whattakes place is electron (notproton) transfer. Electronshave a negative charge.For a strategy to overcomethis misconception, seeAddress Misconceptionson page 379.

Forces and Motion 354D

For: Teaching methods for forces and motionVisit: www.SciLinks.org/PDLinksWeb Code: ccn-1299

Universal Force CharacteristicsForce Relative Strength Range

Strong nuclear 1 ~10�15 m

Electromagnetic 10�2 �

Weak nuclear 10�13 < 10�18 m

Gravitational 10�38 � 1r2

1r2

384 Chapter 12

12.1 Forces

Key Concepts

• A force can cause a resting object to move, or itcan accelerate a moving object by changing theobject’s speed or direction.

• When the forces on an object are balanced, thereis no change in the object’s motion. When anunbalanced force acts on an object, the object accelerates.

• There are four main types of friction: static friction,sliding friction, rolling friction, and fluid friction.

• Earth’s gravity acts downward toward the centerof Earth. Gravity causes objects to acceleratedownward, whereas air resistance acts in thedirection opposite to the motion and reducesacceleration.

• The combination of initial forward velocity anddownward vertical force of gravity cause aprojectile to follow a curved path.

Vocabulary

force, p. 356; newton, p. 357; net force, p. 357;friction, p. 359; static friction, p. 359; sliding friction,p. 359; rolling friction, p. 360; fluid friction, p. 360;air resistance, p. 360; gravity, p. 361; terminal velocity,p. 361; projectile motion, p. 362

12.2 Newton’s First and SecondLaws of Motion

Key Concepts

• According to Newton’s first law of motion, thestate of motion of an object does not change aslong as the net force acting on the object is zero.

• According to Newton’s second law of motion, theacceleration of an object is equal to the net forceacting on it divided by the object’s mass.

• Acceleration �

• Weight � Mass � Acceleration due to gravity

• Mass is a measure of the inertia of an object;weight is a measure of the force of gravity actingon an object.

Vocabulary

inertia, p. 364; mass, p. 365; weight, p. 368

Net forceMass

12.3 Newton’s Third Law of Motionand Momentum

Key Concepts

• According to Newton’s third law of motion, forcesexist as equal and opposite force pairs.

• Momentum � Mass � Velocity An object has a large momentum if the product of its mass and velocity is large.

• Momentum is conserved in a closed system.

Vocabulary

momentum, p. 374; law of conservation ofmomentum, p. 376


Key Concepts

• Electric and magnetic forces are the only forcesthat can both attract and repel.

• The strong and weak nuclear forces hold thenucleus together.

• Newton’s law of universal gravitation statesthat every object in the universe attracts everyother object.

Vocabulary

electromagnetic force, p. 378; strong nuclear force,p. 379; weak nuclear force, p. 380; gravitationalforce, p. 380; centripetal force, p. 381

Concept Map Use the information on forces fromthe chapter to complete the concept map below.

Thinking Visually

CHAPTER

12 Study Guide

is measuredin units of

can becan be represented

by

b. ? c. ? a. ?

Force

unbalanced

d. ? e. ?

which causesno changein objects’

which causesobject to

384 Chapter 12

Study Guide

Study TipChoose a Quiet Place Tell students that being able toconcentrate while studying will increasetheir comprehension. Therefore, a quietplace where they will not be distractedcan help them to achieve a better graspof the subject material and will maketheir study time more efficient.

Thinking Visuallya. Arrowsb. Newtonsc. Balancedd. State of motione. Accelerate

Assessment

If your class subscribes to the Interactive Textbook, your students can go online to access aninteractive version of the StudentEdition and a self-test.

Reviewing Content1. c 2. a 3. a4. d 5. a 6. c7. b 8. a 9. d

10. b

Chapter 12

Print• Chapter and Unit Tests, Chapter 12

Test A and Test B• Test Prep Resources, Chapter 12

Technology• Computer Test Bank, Chapter Test 12• Interactive Textbook, Chapter 12• Go Online, PHSchool.com, Chapter 12

Chapter Resources


Choose the letter that best answers the question orcompletes the statement.

1. Which is not a force?a. friction b. gravityc. momentum d. weight

2. You push on a box and are unable to move it.What force opposes your push?

a. static friction b. rolling frictionc. sliding friction d. air resistance

3. Air resistance depends ona. the velocity of a moving object.b. the weight of a moving object. c. the mass of a moving object.d. the inertia of a moving object.

4. What force besides gravity acts on a projectile?a. weak nuclear b. electrical c. magnetic d. air resistance

5. Newton’s first law of motion is sometimes calledthe law of

a. inertia. b. conservation. c. momentum. d. resistance.

6. A change in which of the following affects theweight of an object?

a. momentumb. velocityc. acceleration due to gravityd. friction

7. Which represents Newton’s second law?a. v � b. a �

c. F � mv d. F � 0

8. For every action force there is aa. reaction force. b. net force.c. friction force. d. unbalanced force.

9. Momentum depends upona. force only. b. velocity and friction.c. weight and mass. d. mass and velocity.

10. What force holds the nucleus together?a. magneticb. strong nuclear c. gravitational d. centripetal

Fm

dt

Reviewing Content

11. Three forces act on a wooden crate that isinitially at rest as shown below. Determine thenet force acting on the crate and describe theresulting motion of the crate.

12. Suppose two 4-newton forces act on an objectin the same direction. What is the net force onthe object?

13. Five different forces act on an object. Is it possiblefor the net force on the object to be zero? Explain.

14. What happens to an object when an unbalancedforce acts on it?

15. You push harder and harder on a box until itbegins sliding across the floor. Which was thestronger of the forces acting on the box, staticfriction or sliding friction?

16. How do ball bearings reduce friction in machinery?

17. Explain why a falling object subjected to Earth’sgravity does not continue to accelerate forever.

18. What is the difference between mass and weight?

19. What is an action-reaction pair?

20. What must you know to determine which of twovehicles traveling at the same velocity, has thegreater momentum?

21. What force is responsible for your socks stickingtogether after they have been in a clothes dryer?

22. What particles do the strong and weak nuclearforces act on?

23. What force is responsible for the orbits of theplanets in the solar system?

Understanding Concepts

CHAPTER

12 Assessment

8 N5 N

3 N

Interactive Textbook withassessment at PHSchool.com

Assessment (continued)

Understanding Concepts11. The net force is zero and the cratedoes not move.12. 8 N13. Yes, all of the forces can cancel oneanother. 14. It accelerates. 15. Static friction16. A machine part rubs against a rollingsurface rather than a flat surface, thusreducing the size of the surfaces incontact and the amount of friction.17. As the velocity of the falling objectincreases, the air resistance acting on italso increases. Eventually the opposingforce of air resistance equals the object’sweight, and the object reaches itsterminal velocity.18. Weight is a measure of the force ofgravity acting on an object. Mass is theamount of matter an object contains asmeasured by its inertia. 19. When a force is exerted on anobject, the object responds with anequal and opposite force. The forcesgenerated in this way are called action-reaction pairs.20. The mass of each vehicle21. Electric force22. Strong: protons and neutrons; weak:all particles23. Gravitational force


Homework GuideSection

12.112.212.312.4

Questions1–4, 11–17, 24, 28–29, 34–365–7, 18, 26–27, 30–31, 338–9, 19–20, 25, 32, 3710, 21–23

386 Chapter 12

24. Applying Concepts When shooting an arrowat a target, why is it advisable to aim above thebull’s-eye rather than directly at it?

25. Inferring When a tennis player practices byhitting a ball against a wall, which of Newton’slaws of motion is the player making use of?

26. Comparing and Contrasting The moon’sgravity is only one sixth that of Earth’s. Explainhow the weight and mass of an object differbetween the two locations.

27. Interpreting Graphs The graph below showsthe relationship between the force acting on anobject and the acceleration of the object. What isthe acceleration of the object when a 3-newtonforce acts on it? What is the object’s mass?

28. Comparing and Contrasting Consider tworocks with masses of 1 and 10 kilograms. What isthe relation between their inertias? Between theirmasses? Between their weights on Earth?

29. Relating Cause and Effect During a fuel-economy test of a sports car, the car achievedmore miles per gallon of gasoline when itsconvertible top was up. Explain how theconvertible top being up or down is related tothe car’s fuel economy.

30. Applying Concepts What are the two ways in which the acceleration of an object can be increased?

Critical Thinking

CHAPTER

12 Assessment (continued)

Acceleration (m/s2)

Forc

e (N

)

6

5

4

3

2

1

00 0.2 0.4 0.6

Force vs. Acceleration

0.8 1.0

For: Self-grading assessment

Visit: PHSchool.com

Web Code: cca-2120

31. Using Formulas A 100-kg crate, sliding on afloor, is brought to a stop by 25-N force. What isthe deceleration of the crate?

32. Calculating What is the momentum of an 80-kg runner moving at the speed of 2.5 m/s?

33. Using Formulas What is the weight on Earth ofa girl with a mass of 30 kg? The acceleration dueto gravity on Earth is 9.8 m/s2.

34. Inferring Hovercraft, which move over wateron a cushion of air, can achieve greater speedsthan ordinary boats. Explain why this is possible.

35. Making Judgments Imagine that you havedesigned clothing for professional bicycle racers.How could you judge the effectiveness of theclothing at improving a racer’s speed?

36. Designing an Experiment Explain how youcould determine the force of static friction actingon a box that is resting on a rough floor.

37. Writing in Science Consider an automobilecruising at a constant speed on the highway.Write a paragraph summarizing the forces actingon the car. Be sure to include the force suppliedby the engine and at least two types of frictionacting on the car.

Communicating Results Draw a cartoon thatillustrates one of Newton’s laws in an amusing way.You and your classmates might display your cartoonsfor the whole school to enjoy.

Performance-Based Assessment

Concepts in Action

Math Skills

386 Chapter 12

Critical Thinking24. The arrow follows a projectile path.It begins to fall as soon as it leaves thebow. Thus, if the arrow is aimed directlyat the target, it will hit the target belowthe bull’s-eye.25. Newton’s third law of motiondescribes the action and reaction forcesthat occur when the ball is struck by theracquet and when the ball strikes the wall.Newton’s second law of motion describesthe acceleration of the tennis ball when aforce from the racquet or the wall isapplied to it.26. An object’s weight is six timesgreater on Earth; however, its mass isthe same in both locations.27. 0.6 m/s2; 5 kg28. The inertia, mass, and weight of the10-kg rock are 10 times greater thanthat of the 1-kg rock.29. The air resistance is greatly increasedwhen the top is down resulting in fewermiles per gallon.30. Increasing the force applied to theobject or decreasing the mass of theobject will increase the acceleration ofthe object.

Math Skills31. 0.25 m/s2

32. 200 kg•m/s33. 290 N

Concepts in Action34. The fluid friction from the hover-craft’s contact with the air is less than an ordinary boat’s fluid friction fromcontact with the water.35. The racer could be tested in a wind tunnel or out on a road. If theclothing is effective, the force on theracer in the wind tunnel will decrease.The racer’s maximum speed on the road will increase. 36. Attach a spring scale to the box.Gradually increase the force applied by pulling on the spring scale. Thesmallest measured force on the springscale that moves the box equals theforce of static friction.37. Student paragraphs will vary butshould include the force applied at thedrive wheels (supplied by the engine),the action-reaction force pair where thetires are in contact with the road, the air resistance (fluid friction), the rollingfriction of the tires on the road, and therolling friction of the ball bearings in theengine and wheels.

Chapter 12

Performance-Based AssessmentDrawings will vary but must properly illustrateone of Newton’s laws.

Your students can independentlytest their knowledge of the chapterand print out their test results foryour files.


Standardized Test Prep

Choose the letter that best answers the question orcompletes the statement.

1. Which of the following correctly lists frictiontypes (excluding fluid friction) from weakest to strongest? (A) sliding, static, magnetic(B) static, rolling, sliding(C) weak, strong, nuclear(D) rolling, sliding, static(E) static, sliding, rolling

2. Which statement about an object falling atterminal velocity is TRUE?(A) Unbalanced forces act on the object.(B) The net force acting on the object is zero.(C) The object is accelerating.(D) The object is traveling in a circular path.(E) No fluid friction acts on the object.

3. An object changes direction as it moves. Whichof the following is FALSE?(A) The acting net force is not zero.(B) An unbalanced force acts on the object.(C) The object is accelerating. (D) A centripetal force must act on the object.(E) The object’s inertia remains unchanged.

4. Which has the greatest momentum?(A) a huge boulder at rest(B) a small pebble that is tossed into the air (C) a baseball after it is hit with a bat(D) a small pebble at rest(E) a car traveling on a highway

Use the diagram below to answer Questions 5 and 6.The diagram shows how five forces act on a woodencrate as it slides across the floor.

5. If A � 60 N, B � 20 N, C � 30 N, D � 30 N,and E � 30 N, which of the following statementsis FALSE?(A) A net force of 50 N acts on the crate and

the crate moves to the right.(B) The crate accelerates to the right. (C) The net force in the vertical direction is zero.(D) Force C represents the weight of the crate.(E) Forces C and E represent balanced forces

acting in the vertical direction.

6. Which force represents the sliding friction force?(A) A(B) B(C) C(D) D(E) E

Test-Taking Tip

Using a CalculatorKeep the following tips in mind when solvingproblems that require a calculator. Write downthe equation that you will be solving beforeusing the calculator. Next, substitute the knownvalues for each term in the equation. Then,enter the numbers into your calculator andcalculate the answer. It is also important tobecome familiar with the order in which yourcalculator performs operations. Most calculatorsoperate using an algebra-based operatingsystem. If time permits, double-check youranswer by performing the calculations a second time.

What is the acceleration of a 1200-kg car actedon by a net force of 250 N?

(A) 0.21 m/s2 (B) 2.4 m/s2

(C) 4.8 m/s2 (D) 950 m/s2

(E) 300,000 m/s2

(Answer: A) DB

A

E

C

Standardized Test Prep1. D 2. B 3. D4. E 5. D 6. D


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