CHAPTER11 CHAPTER Forces -...

ForcesForcesC H A P T E R 11

Chapter Preview

1 Laws of MotionNewton’s First LawNewton’s Second Law

2 GravityLaw of Universal GravitationFree Fall and WeightFree Fall and MotionProjectile Motion and Gravity

3 Newton’s Third LawAction and Reaction ForcesMomentum

OverviewThis chapter covers Newton’s firstand second laws of motion, includ-ing problem-solving with the sec-ond law. It also discusses the lawof universal gravitation, free fall,and projectile motion. Finally, thechapter explores Newton’s thirdlaw of motion and also coversmomentum.

Assessing PriorKnowledgeBe sure students understand thefollowing concepts:

• mass• acceleration• balanced and unbalanced forces

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National Science Education Standards

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

Section 1 Laws of MotionPhysical Science PS4a

Section 2 GravityPhysical Science PS4b

Section 3 Newton’s Third LawPhysical Science PS4a

Standards Correlations

344 Chapter 11 • Forces

C H A P T E R 11

Science education research hasidentified the following miscon-ceptions about forces and freefall.

• Students believe that whenthere is no motion, there is no force.

• Students characterize equilib-rium as the result of thestrongest forces winning andbelieve that all forces ceaseto act at equilibrium.

• Students believe that heavierobjects fall faster, and theyare unable to separate theeffects of air resistance.

ACTIVITYACTIVITYFocusFocus

Pre-Reading Questions1. How is force used in other sports, such

as basketball, baseball, and hockey? Giveexamples.

2. Give as many examples as you can thinkof about how force is involved in drivinga car.

Background When you kick a soccer ball, you are applying forceto the ball. At the same time, the ball is also applying force toyour foot. Force is involved in soccer in many ways. Soccer players have to know what force to apply to the ball. They mustbe able to anticipate the effects of force so that they will knowwhere the ball is going and how to react. They sometimes experi-ence force in the form of collisions with other players.

Another illustration of force in soccer is a change in the ball’sdirection. Soccer players need to know how to use force to kickthe ball in a new direction or to continue to kick it in the samedirection it had been going.

Activity 1 Hold this textbook at arm’s length in front of yourshoulders. Move the book from left to right and back again.Repeat these actions with a piece of paper. What differences doyou notice between the effort needed to change the direction ofthe paper and the effort needed to change the direction of thetextbook? Why would there be a difference?

Activity 2 You can investigate Earth’s pull on objects by using astopwatch, a board, and two balls of different masses. Set one endof the board on a chair and the other end on the floor. Time eachball as it rolls down the board. Then, several more times, roll bothballs down the board at different angles by using books under oneend of the board and changing the number of books to change theangle. Does the heavier ball move faster, move more slowly, ortake the same amount of time as the lighter one? What factors doyou think may have affected the motion of the two balls?

www.scilinks.orgTopic: Forces SciLinks code: HK4055

Soccer gives usmany examples ofthe use of force.

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Chapter 11 • Forces 345

Background Soccer is themost popular sport in theworld, and the World Cup—a national soccer competitionthat occurs every four years—may be the world’s most popu-lar athletic event. A regulationsoccer ball has a mass of397g – 454g when inflatedproperly. When students studyNewton’s second law, givethem this range of values,and have them calculate whatforces are required for variousaccelerations of balls withmasses in this range. Logical

Activity 1 This activity allowsstudents to feel the effects ofinertia. Students should notethat the paper requires muchless effort to move than thetextbook. They should realizethat this is because the text-book has a greater mass.Activity 2 Do not allow stu-dents to use hollow balls forthis activity. (This is becausesolid balls act more nearly likeideal point masses. Hollowthin-walled balls roll differently,and do not behave ideally.) Theweight of the balls is not impor-tant. The closer the board isto vertical, the faster the ballaccelerates.

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ACTIVITYACTIVITYFocusFocus

• Pretest• Teaching Transparency Preview• Answer Keys

GENERAL

Chapter Resource File

Answers to Pre-ReadingQuestions1. Accept all answers in which stu-

dents describe examples of forcesin various sports.

2. Accept any examples of forcesinvolved in driving a car.

Laws of Motion> Identify the law that says that objects change their motion

only when a net force is applied.> Relate the first law of motion to important applications,

such as seat belt safety issues. > Calculate force, mass, and acceleration by using Newton’s

second law.

Every motion you observe or experience is related to a force.Sir Isaac Newton described the relationship between motion

and force in three laws that we now call Newton’s laws of motion.Newton’s laws apply to a wide range of motion—a caterpillarcrawling on a leaf, a person riding a bicycle, or a rocket blastingoff into space.

Newton’s First LawIf you slide your book across a rough surface, such as carpet, thebook will soon come to rest. On a smooth surface, such as ice, thebook will slide much farther before stopping. Because there isless frictional force between the ice and the book, the force mustact over a longer time before the book comes to a stop. Withoutfriction, the book would keep sliding forever. This is an exampleof Newton’s first law, which is stated as follows.

An object at rest remains at rest and an object in motion maintains its velocity unless it experiences an unbalanced force.

In a moving car, you experience the effect described byNewton’s first law. As the car stops, your body continues forward,as the crash-test dummies in Figure 1 do. Seat belts and othersafety features are designed to counteract this effect.

Objects tend to maintain their state of motionis the tendency of an object at rest to remain at rest or,

if moving, to continue moving at a constant velocity. All objectsresist changes in motion, so all objects have inertia. An objectwith a small mass, such as a baseball, can be accelerated with asmall force. But a much larger force is required to accelerate acar, which has a relatively large mass.

Inertia

O B J E C T I V E S

SECTION

1

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K E Y T E R M S

inertia

▲

Figure 1Crash-test dummies, used by carmanufacturers to test cars in crashsituations, continue to travel for-ward when the car comes to asudden stop, in accordance withNewton’s first law.

inertia the tendency of anobject to resist being movedor, if the object is moving, toresist a change in speed ordirection until an outside forceacts on the object

▲

OverviewBefore beginning this section,review with your students theObjectives listed in the StudentEdition. In this section, studentslearn Newton’s first law of motion,the law of inertia, and they learnthat mass is a measure of inertia.Next, students study and applyNewton’s second law of motion(F � ma).

Use the Bellringer transparency toprepare students for this section.

OpeningDemonstrationYou will need a toy dump truck, asmall doll, and a textbook. Set thedoll in the back of the truck. Placethe truck and the book on a flat sur-face, with the truck facing the book.Give the truck a push toward thebook. When the truck hits the bookand stops, the doll will fly out. Askstudents to explain this in terms ofinertia. (Since the doll and truck arein motion, they both have a tendencyto stay in motion until experiencing anunbalanced force. The book exerts anunbalanced force on the truck; thetruck stops. This force does not affectthe doll, so the doll continues movingand flies out of the truck.) VisualLS

MotivateMotivate

Bellringer

FocusFocus


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SECTION

1

Transparencies

TT Bellringer

GENERAL

Crash-Test Dummies Crash-test dummiescome in various sizes and shapes. Eachdummy is outfitted with sensors that recordhow the dummy moves and how hard itpresses against different parts of the car dur-ing a crash when the dummy is strapped inby a seatbelt. Automobile manufacturers usethis information to develop and improve seatbelts and other safety devices, such as airbags and padded dashboards.

REAL-LIFEREAL-LIFECONNECTIONCONNECTION


Inertia is related to an object’s massNewton’s first law of motion is often summed up in one sentence:Matter resists any change in motion. An object at rest will remainat rest until something makes it move. Likewise, a moving objectstays in motion at the same velocity unless a force acts on it tochange its speed or direction. Since this property of matter iscalled inertia, Newton’s first law is sometimes called the law ofinertia.

Mass is a measure of inertia. An object with a small mass hasless inertia than an object with a large mass. Therefore, it is eas-ier to change the motion of an object with a small mass. Forexample, a softball has less mass and less inertia than a bowlingball does. Because the softball has a small amount of inertia, it iseasy to pitch, and the softball’s direction will change easily whenit is hit with a bat. Imagine how difficult playing softball with abowling ball would be! The bowling ball would be hard to pitch,and changing its direction with a bat would be very difficult.

Seat belts and car seats provide protectionBecause of inertia, you slide toward the side of a car when thedriver makes a sharp turn. Inertia is also why it is impossible fora plane, car, or bicycle to stop instantaneously. There is always atime lag between the moment the brakes are applied and themoment the vehicle comes to rest.

When the car you are riding in comes to a stop, your seat beltand the friction between you and the seat stop your forwardmotion. They provide the unbalanced rearward force needed tobring you to a stop as the car stops.

Babies are placed in special backward-facing car seats, asshown in Figure 2. With this type of car seat, the force that isneeded to bring the baby to a stop is safely spread out over thebaby’s entire body.

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QuickQuickQuick ACTIVITYACTIVITY

1. Set an index card over a glass.Put a coin on top of the card.

2. With your thumb and forefinger,quickly flick the card sideways offthe glass. Observe what happensto the coin. Does the coin movewith the index card?

Newton’s First Law

Figure 2During an abrupt stop, this babywould continue to move forward.The backward-facing car seat dis-tributes the force that holds thebaby in the car.

3. Try again, but this time slowly pullthe card sideways and observewhat happens to the coin.

4. Use Newton’s first law of motionto explain your results.

Interpreting Visuals Have stu-dents examine Figure 2. Explain tostudents that very young babieshave little muscle control and areunable to even hold their head up.Have students discuss why infantcar seats for small babies facebackward while car seats for olderchildren face forward.

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TeachTeach

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GENERAL

ACTIVITYACTIVITYQuickQuick

Newton’s First LawMaterials:• index card• glass• coin

Teacher’s Notes: In step 2,students should observe thecoin fall into the glass. Thecoin may move slightly side-ways with the card. If studentsare having difficulty, emphasizethat they must flick the cardvery quickly.

Make sure that studentsunderstand that in step 3, thecoin should not fall into theglass; it should remain restingon the card. The force of fric-tion caused the coin to movesideways with the card.

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Presents Physical Science• Segment 4 Crash-Test Dummies• Critical Thinking Worksheet 4

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

Videos

Magic Trick A magician who pulls atablecloth out from under a table set withdishes—without moving or breaking thedishes—is taking advantage of the dishes’inertia.

Alternative AssessmentPerforming Magic Ask students to performthe dishes-under-the-tablecloth magic trick athome. Instruct them to start with a single, non-breakable dish and to use caution. If a studentis able to master the trick, have him or her per-form it for the class with non-breakable dishes.Be sure students are seated at a safe distance.Ask a volunteer to explain how inertia isinvolved in the demonstration. KinestheticLS

GENERAL

• Lesson Plan• Quick Activity Datasheet Newton’s

First Law GENERAL


and the Consumerand the ConsumerScienceScience

Should a Car’s Air Bags Be Disconnected?

Air bags are standard equipment in everynew automobile sold in the United States.These safety devices are credited with saving

almost 1700 lives between 1986 and 1996. However,air bags have also been blamed for the deaths of36 children and 20 adults during the same period.In response to public concern about the safety of airbags, the National Highway Traffic Safety Administrationhas proposed that drivers be allowed to disconnectthe air bags on their vehicles.

How Do Air Bags Work?When a car equipped with air bags comes to anabrupt stop, sensors in the car detect the suddenchange in speed (negative acceleration) and triggera chemical reaction inside the air bags. This reactionvery quickly produces nitrogen gas, which causes thebags to inflate and explode out of their storage com-partments in a fraction of a second. The inflated airbags cushion the head and upper body of the driverand the passenger in the front seat, who keep movingforward at the time of impact because of their inertia.Also, the inflated air bags increase the amount of timeover which the stopping forces act. So, as the ridersmove forward, the air bags absorb the impact.

What Are the Risks?Because an air bag inflates suddenly and with greatforce, it can cause serious head and neck injuries insome circumstances. Seat belts reduce this risk byholding passengers against the seat backs. Thisallows the air bag to inflate before the passenger’shead comes into contact with it. In fact, most of thepeople killed by air bags either were not using seatbelts or had not adjusted the seat belts properly.

Two groups of people are at risk for injury by airbags even with seat belts on: drivers shorter thanabout 157 cm (5 ft 2 in) and infants riding next tothe driver in a rear-facing safety seat.

Alternatives to Disconnecting Air BagsAlways wearing a seat belt and placing child safetyseats in the back seat of the car are two easy waysto reduce the risk of injury from air bags. Shorterdrivers can buy pedal extenders that allow them tosit farther back and still safely reach the pedals.Some vehicles without a back seat have a switch that can deactivate the passenger-side air bag.Automobile manufacturers are also working on air bags that inflate less forcefully.

1. Critical Thinking Are air bags useful if your caris struck from behind by another vehicle?

2. Locating Information Research “smart” air-bag systems, and prepare a report.

348

Your Choice

In a collision, air bags explode from a compartment tocushion the passenger’s upper body and head.

www.scilinks.orgTopic: Inertia SciLinks code: HK4072

Science and the ConsumerShould a Car’s Air Bags BeDisconnected? The key to an airbag’s success during a crash is thespeed at which it inflates. Insidethe bag is a gas generator that con-tains the compounds sodium azide,potassium nitrate, and silicon diox-ide. At the moment of a crash, anelectronic sensor in the vehicledetects the sudden decrease inspeed. The sensor sends a smallelectric current to the gas genera-tor, providing the energy needed tostart the chemical reaction.

The force that triggers the infla-tion of an air bag is approximatelythe same as that of hitting a solidbarrier head-on at 20 km/h. Thechemicals sodium azide and potas-sium nitrate react to form non-toxic, nonflammable nitrogen gas,which is what actually inflates thebag. (Several toxic chemicals arealso formed, but they quickly reactwith other substances to makethem less hazardous.)

The rate at which the reactionoccurs is very fast. In 0.04 s—lessthan the blink of an eye—the gasformed in the reaction inflates thebag. By filling the space betweenthe person and the car’s dashboard,the air bag protects the personfrom injury.

Answers to Your Choice1. No, because your body moves

toward the seat back and nottoward the dashboard, where theair bag deploys.

2. Students’ reports may vary.VerbalLS

Teach, continuedTeach, continued


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GENERAL

Reduced Risk In purely frontal crashes,drivers protected by front air bags have a31% reduction in fatality risk. The reduc-tion in fatality risk for all types of crashes(purely frontal, partially frontal, andother) is 11%.


Newton’s Second LawNewton’s first law describes what happens when the net forceacting on an object is zero: the object either remains at rest orcontinues moving at a constant velocity. What happens when thenet force is not zero? Newton’s second law describes the effect ofan unbalanced force on the motion of an object.

Force equals mass times accelerationNewton’s second law, which describes the relationship betweenmass, force, and acceleration, can be stated as follows.

The unbalanced force acting on an object equalsthe object’s mass times its acceleration.

Mathematically, Newton’s second law can be written as follows.

Consider the difference between pushing an empty shoppingcart and pushing the same cart filled with groceries, as shown inFigure 3. If you push with the same amount of force in each situation, the empty cart will have a greater acceleration becauseit has a smaller mass than the full cart does. The same amount offorce produces different accelerations because the masses aredifferent. If the masses are the same, a greater force produces agreater acceleration, as shown in Figure 4 on the next page.

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force = mass × accelerationF = ma

Newton’s Second Law

Figure 3Because the full cart has alarger mass than the emptycart does, the same forcegives the empty cart agreater acceleration.

www.scilinks.orgTopic: Newton’s Laws

of MotionSciLinks code: HK4094

Reading Skills Have studentsread silently the section entitledNewton’s Second Law, includingthe Math Skills example. Instructthem to mark on self-adhesivenotes those portions of the textthat they do not understand. Besure that students study all illustra-tions and legends that accompanythe passage. Group studentstogether in pairs, and have eachstudent in each pair discuss withthe other student the parts of thepassage that he or she found diffi-cult. The listener should either clar-ify the difficult passages or shouldhelp frame a common question for later explanation. Verbal

Teaching TipInterpreting Equations Use sim-ple examples to explore Newton’sSecond Law conceptually. Forexample, ask: What happens toacceleration when the force dou-bles and the mass remains con-stant? (acceleration doubles) Whathappens when the force is halved?(acceleration is halved) These ques-tions illustrate that force is propor-tional to acceleration. Use similarquestions to show that force isinversely proportional to mass.

LogicalLS

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• Cross-Disciplinary Worksheet RealWorld Applications—Car Seat Safety

• Cross-Disciplinary WorksheetIntegrating Mathematics—UsingForce Diagrams GENERAL

GENERAL

Chapter Resource FileForces and Motions Many students havethe misconception that when there is nounbalanced force, there is no motion. Inother words, forces cause motions, and con-stant motion requires a constant force. Youmay have addressed this misconceptionwhen studying balanced and unbalancedforces. When studying Newton’s laws, youcan address this misconception again.

As seen with Newton’s first law, an objectexperiencing no unbalanced force maintainsits state of rest or motion. An unbalancedforce is not needed to keep an object inmotion, but to change its state of motion orrest. Newton’s second law emphasizes thisfurther. Unbalanced forces cause changes ofmotion; they cause accelerations.

Transparencies

TT Newton’s Second Law

Force is measured in newtonsNewton’s second law can be used to derive the SI unit of force,the newton (N). One newton is the force that can give a mass of1 kg an acceleration of 1 m/s2, expressed as follows.

1 N � 1 kg � 1 m/s2

The pound (lb) is sometimes used as a unit of force. One new-ton is equivalent to 0.225 lb. Conversely, 1 lb is equal to 4.448 N.

350

Figure 4A small force on an object causes a small

acceleration.A A larger force on the object causes a larger

acceleration.B

Sir Isaac Newton (1642–1727)was a central figure in theScientific Revolution duringthe seventeenth century. Hewas born in 1642, the sameyear that Galileo died.

Math SkillsMath Skills

Newton’s Second Law Zookeepers lift a stretcher that holds asedated lion. The total mass of the lion and stretcher is 175 kg,and the upward acceleration of the lion and stretcher is 0.657m/s2. What is the unbalanced force necessary to produce thisacceleration of the lion and the stretcher?

List the given and unknown values.Given: mass, m � 175 kg

acceleration, a � 0.657 m/s2

Unknown: force, F � ? N

Write the equation for Newton’s second law.force � mass � accelerationF � ma

Insert the known values into the equation, and solve.F � 175 kg � 0.657 m/s2

F � 115 kg � m/s2 � 115 N

3

2

1

AdditionalExamplesNewton’s Second Law A 1200kg car has a force of 1500 N fromthe engine pushing it forward. Thecar also has a combined frictionalforce of 1100 N pushing it back-ward. What is the acceleration ofthe car? (Hint: You will need tocalculate the net force first.)Answer: 0.33 m/s2 forward

If the driver eases up on the gaspedal, the frictional force remainsthe same, and the engine is exert-ing a force of only 950 N, what isthe new acceleration?Answer: –0.13 m/s2 forward �0.13 m/s2 backward (The car is slowing down.) Logical

Teaching TipMass versus Weight The intro-duction of the pound as a unit offorce may bring up the issue ofweight. Remind students that massand weight are not the same. In theSI system, mass is measured inkilograms, and weight—a force—ismeasured in newtons. The weightof an apple is about 1 newton.Tell students they will learn moreabout weight in this section, whenthey study gravity.

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GENERAL

Alternative AssessmentIsaac NewtonIt is generally accepted that Isaac Newton was one of the greatest scientists in history. In addition to his work with forces, he madesignificant advancements in mathematics,astronomy, and other branches of physics.Have students research some aspect of his lifeor work. Possible topics include: his studies oflight and color, his invention of Calculus, hispersonal history, or his personality and char-acter. Ask each student to prepare a briefpresentation for the class. VerbalLS

Concept MapHave students create a concept map forNewton’s first and second laws. Instruct themto include all of the following terms in theirmaps: Newton’s first law, inertia, mass, unbal-anced force, balanced force, Newton’s secondlaw, acceleration, newtons. VerbalLS

Answers to Section 1 Review

1. Answers may vary. Students should say in theirown words that an object at rest remains atrest and an object in motion maintains itsvelocity unless it experiences an unbalancedforce. They should each give an example ofthis law.

2. Answers may vary. Students should say some-thing like this: When you have on a seat beltand the vehicle stops suddenly, the seat beltapplies a force that stops you and keeps youfrom flying forward, as the force of inertiakeeps you in motion after the car has stopped.

3. a. The car may be unable to turn. Newton’sfirst law states that the object (car) will

continue to travel in a straight line unlessan unbalanced force acts on the object.Since the road is icy, the friction betweenthe tires and the ice may not be largeenough to turn the car.

b. The car will slide for the same reasons in(a). Also, Newton’s second law states thatacceleration is proportional to force. Sincethe friction force is much smaller on an icyroad, the negative acceleration (decelera-tion) is much smaller.


PracticePractice

Newton’s second law can also be stated as follows:

The acceleration of an object is proportional to the net force on the object and inversely proportional to the object’s mass.

Therefore, the second law can be written as follows.

acceleration � �mfo

arcses

�

a � �mF

�

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

1. State Newton’s first law of motion in your own words, andgive an example that demonstrates that law.

2. Explain how the law of inertia relates to seat belt safety.

3. Critical Thinking Using Newton’s laws, predict what willhappen in the following situations:a. A car traveling on an icy road comes to a sharp bend.b. A car traveling on an icy road has to stop quickly.

4. What is the acceleration of a boy on a skateboard if theunbalanced forward force on the boy is 15 N? The totalmass of the boy and the skateboard is 58 kg.

5. What force is necessary to accelerate a 1250 kg car at a rateof 40 m/s2?

6. What is the mass of an object if a force of 34 N produces anacceleration of 4 m/s2?

S U M M A R Y

> An object at rest remains at rest and an object inmotion maintains a con-stant velocity unless itexperiences an unbalancedforce (Newton’s first law).

> Inertia is the property ofmatter that resists changein motion.

> Properly used seat beltsprotect passengers.

> The unbalanced force act-ing on an object equalsthe object’s mass times itsacceleration, or F � ma(Newton’s second law).

PracticeHINT

> When a problem requires youto calculate the unbalancedforce on an object, you canuse Newton’s second law (F � ma).

> The equation for Newton’ssecond law can be rearrangedto isolate mass on the leftside as follows.

F � maDivide both sides by a.

�Fa

� � �maa�

m � �Fa

�

You will need this form inPractice Problem 2.

> In Practice Problem 3, youwill need to rearrange theequation to isolate accelera-tion on the left.

Newton’s Second Law1. What is the net force necessary for a 1.6 x 103 kg automobile to

accelerate forward at 2.0 m/s2?

2. A baseball accelerates downward at 9.8 m/s2. If the gravitational force is the only force acting on the baseball and is 1.4 N, what is the baseball’s mass?

3. A sailboat and its crew have a combined mass of 655 kg. Ignoring frictional forces, if the sailboat experiences a net force of 895 N pushing it forward, what is the sailboat’s acceleration?


1. F � ma � (1.6 � 103 kg)(2.0 m/s2) � 3.2 � 103 N

2. m � �Fa� � �9

1.8.4

mN/s2� �

0.14 kg

3. a � �mF

� � �685955

kNg� � 1.37 m/s2

in the direction of the forceLogical

Quiz1. What is Newton’s first law of

motion? (When there is no unbal-anced force, an object at restremains at rest, and an object inmotion maintains its velocity.)

2. How is inertia related to mass?(Mass is a measure of inertia. Asmaller mass has less inertia thana larger mass does.)

3. Express Newton’s second lawmathematically. (F � ma, or a �F/m)

4. What acceleration would be pro-duced if a 25 N force acts on a5.0 kg mass? (a � F/m �25 N/5.0 kg � 5.0 m/s2)

CloseClose

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PracticePractice

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• Math Skills Newton’s Second Law

• Concept Review• Quiz

GENERAL

GENERAL


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

Answers from page 330

5. A cup of boiling water has a higher temperature thanLake Michigan, but Lake Michigan has more total kineticenergy since it has more particles.

6. �95�(20.0) + 32.0 = 68.0°F

20 + 273 = 293 K

7. �59�(−128.6 − 32.0) = −89.2°C

−89.2 + 273 = 184 K


4. The temperature differences on the moon’s surface aredue to two things. One is the composition of the moon’ssurface, which varies from place to place. The other fac-tor is whether or not the spot in question is on the sunnyside of the moon (hot) or the shadow side (cold).

5. The cookies near the turned-up edge receive conductionenergy from the cookie sheet, just like the cookies in themiddle. However, those near the edge also receive moreenergy from air convection currents and radiation fromthe turned up edge.

6. c � = 130 J/kg•K; lead

7. 228 J/kg•K

3250 J(1.32 kg)(292 K − 273 K)


S E C T I O N 10 . 2 R E V I E WS E C T I O N 10 . 2 R E V I E W


S E C T I O N 10 .1 R E V I E WS E C T I O N 10 .1 R E V I E W

CONTINUATION OF ANSWERS

351A

Design Your Own Lab from page 351

Investigating Conduction of Heat

�Analyzing Your Results

1. Answers will vary. See sample data.2. Answers will vary. See sample data.3. See sample graph. Results will vary, but times should be

greater for smaller-diameter wires. The line that best fits thedata points should decrease as diameter increases.

4. Students should find that thicker wires conduct energy asheat more quickly than thin wires.

5. A thicker skewer will conduct energy as heat more quicklythan a thin skewer.

�Defending Your Conclusions

6. Students could test wires made from different kinds of metals.

Sample Data Table Heat Conductivity for Copper Wire

Wire Time to melt wax (s)

diameter (mm) Trial 1 Trial 2 Trial 3 Average time

Wire 1 1.0 39.1 37.8 38.4 38.4

Wire 2 1.5 35.0 36.1 34.8 35.3

Wire 3 2.0 34.0 33.3 30.9 32.7

Wire Diameter (mm)

Tim

e to

mel

t bal

l of w

ax (s

)

1 1.5

39

38

37

36

35

34

33

32

31

30

29

2

S

S

DEVELOPING LIFE/ WORK SKILLS

DEVELOPING LIFE/ WORK SKILLS

INTEGRATING CONCEPTS

INTEGRATING CONCEPTS

33. Answers will vary.34. Statement (b) is correct. Energy can never be lost; it is al-

ways conserved.

35. a. kinetic energy b. Celsiusc. Kelvind. Fahrenheite. conductionf. convectiong. radiation

36. http://www.treasure-troves.com/bios/Rumford.html


351B


4. Answers will depend on your area, but some possibilities are:advantages—free energy from sun, less pollution;disadvantages—not much sun available, expensive to set up, difficult to install

5. Accept all reasonable responses.6. Students’ spreadsheets should calculate the following

values for rate of energy transfer:

drywall: �1.0 m

0

2

.4×520°C

� = 44

wood shingles: �1.0 m2

0.×87

20.0°C� = 23

flat glass: �1.0 m2

0.×89

20.0°C� = 22

hardwood siding: �1.0 m2

0.×91

20.0°C� = 22

vertical air space: �1.0 m2

1.×01

20.0°C� = 20.

insulating glass: �1.0 m2

1.×54

20.0°C� = 13

cellulose fiber: �1.0 m2

3.×70

20.0°C� = 5.4

brick:�1.0 m2

4.×00

20.0°C� = 5.0

fiberglass batting: �1.0 m

1

2

0×.9

200.0°C

� = 1.8

S E C T I O N 10 . 3 R E V I E WS E C T I O N 10 . 3 R E V I E W

W

S

S

S

S

Gravity> Explain that gravitational force becomes stronger as the

masses increase and rapidly becomes weaker as the dis-tance between the masses increases, F � G�

md1m

22�

> Evaluate the concept that free-fall acceleration nearEarth’s surface is independent of the mass of the falling object.

> Demonstrate mathematically how free-fall accelerationrelates to weight.

> Describe orbital motion as a combination of two motions.

Have you ever seen a videotape of the first astronauts on themoon? When they tried to walk on the lunar surface, they

bounced all over the place! Why did the astronauts—who werewearing heavy spacesuits—bounce so easily on the moon, asshown in Figure 5?

Law of Universal GravitationFor thousands of years, two of the most puzzling scientific ques-tions were “Why do objects fall toward Earth?” and “What keepsthe planets in motion in the sky?” A British scientist, Sir IsaacNewton (1642–1727), realized that they were two parts of thesame question. Newton generalized his observations on gravityin a law now known as the law of universal gravitation. The lawstates that all objects in the universe attract each other throughgravitational force.

This equation says that the gravitational force increases as one orboth masses increase. It also says that the gravitational forcedecreases as the distance between the masses increases. In fact,because distance is squared in the equation, even a smallincrease in distance can cause a large decrease in force. The sym-bol G in the equation represents a constant.

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free fallterminal velocityprojectile motion

▲

Figure 5Because gravity is less on themoon than on Earth, the Apolloastronauts bounced as theywalked on the moon’s surface.

F � G�m

d1m

22�

Universal Gravitation Equation

OverviewBefore beginning this section,review with your students theObjectives listed in the StudentEdition. In this section, studentsstudy gravitational force and thelaw of universal gravitation, free-fall acceleration, mass versusweight, terminal velocity, and projectile motion.


OpeningDiscussionAsk students if they would weighthe same at sea level, on MountEverest, and on the moon. Somestudents may already know thattheir weight would be less on themoon. Write the universal gravita-tion equation on the chalkboardand challenge students to use theequation to explain why weightwould vary. (Be sure to explainwhat each symbol in the equationrepresents.) Students should also beable to deduce from the equationthat they would weigh slightly lesson Mount Everest than at sea level.

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TT Bellringer

GENERAL

Universal Gravitation Equation Thesymbol G in the universal gravitationequation is a constant, sometimes calledthe constant of universal gravitation.Scientists have used experiments to deter-mine the value of G: 6.674 �10–11 N•m2/kg2.

For your discussion of gravity, rent and playthe video of Neil Armstrong’s first step on themoon during the Apollo 11 mission.

SOCIAL STUDIESSOCIAL STUDIESCONNECTIONCONNECTION


All matter is affected by gravityWhether two objects are very large or very small, there is a gravitational force between them. When something is very large,such as Earth, the force is easy to detect. However, we do notnotice that something as small as a toothpick exerts gravitationalforce. Yet no matter how small or how large the objects are, everyobject exerts a gravitational force, as illustrated by both parts ofFigure 6. The force of gravity between two masses is easier tounderstand if you consider it in two parts: (1) the size of themasses and (2) the distance between them. So, these two ideaswill be considered separately.

Gravitational force increases as mass increasesGravity is given as the reason why an apple falls down from atree. When an apple breaks its stem, it falls down because thegravitational force between Earth and the apple is much greaterthan the gravitational force between the apple and the tree.

Imagine an elephant and a cat. Because an elephant has alarger mass than a cat does, the gravitational force between anelephant and Earth is greater than the gravitational forcebetween a cat and Earth. That is why a cat is much easier to pickup than an elephant! There is also gravitational force between thecat and the elephant, but it is very small because the cat’s massand the elephant’s mass are so much smaller than Earth’s mass.The gravitational force between most objects around you is rela-tively very small.

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Figure 6The arrows indicate the gravitational force betweenobjects. The length of the arrows indicates thestrength of the force.

Gravitational forceis larger when one orboth objects havelarger masses.

B

Gravitational forceis small betweenobjects that have small masses.

A

BIOLOGYGravity plays a role in your body. Bloodpressure, for exam-ple, is affected by

gravity. Therefore, your bloodpressure will be greater in thelower part of your body than inthe upper part. Doctors andnurses take your blood pres-sure on your arm at the levelof your heart to see what theblood pressure is likely to be at your heart.

Teaching TipWeight Influences Shape Thedramatic necessity of having ashape correct for your size can beshown by comparing an ant’s legsto the legs of an elephant. An anthas very thin legs relative to the sizeof its body, while an elephant hasthick legs. Students may have seenscience fiction movies with giantants, but in reality these giant antscould never exist. If an ant weresomehow enlarged to the size of anelephant, it wouldn’t even be ableto walk. This is because strength isproportional to the cross-sectionalarea—how big the muscle is. Inorder to support its new, largerbody, the ant would have to growthick, strong legs like an elephant!

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• Science Skills Worksheet EquationsInvolving a Constant

• Cross-Disciplinary WorksheetIntegrating Biology—Blood Pressurein Space

• Cross-Disciplinary WorksheetConnection to Social Studies—The Great Plague and Isaac Newton

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Transparencies

TM Law of Universal Gravitation

Presents Physical Science• Segment 6 Egg Drop Contest• Critical Thinking Worksheet 6


Videos

Gravity Some students think of gravity as“holding,” or as “that which keeps thingsfrom floating away.” Students also believethat gravity requires air; these studentsthink that gravity is not present in space.Another common misconception is thatgravity stops acting on an object when ithas finished falling. Ask specific questionsto target these misconceptions, such as“Can gravity occur in space?” and “Doesgravity continue acting on a fallen objectafter it hits Earth’s surface?”

In the reduced gravity of space, astronautslose bone and muscle mass, even after a veryshort time. Sleep patterns may be affected,and so may cardiovascular strength and theimmune response. These same effects happenmore gradually as people age on Earth.Scientists are interested in studying the effectsof microgravity so they can find ways tocounteract them in space and here on Earth.

LIFE SCIENCELIFE SCIENCECONNECTIONCONNECTION

BIOLOGY The human bodymakes use of gravity. Oneexample is blood pressure.Gravity pulls blood to thelower part of the body; withoutgravity, blood would remaincloser to the heart. Musclesthen work as pumps to returnblood back to the heart.

Gravitational force decreases as distance increasesGravitational force also depends on the distance between twoobjects, as shown in Figure 7. The force of gravity changes as thedistance between the balls changes. If the distance between thetwo balls is doubled, the gravitational force between themdecreases to one-fourth its original value. If the original distanceis tripled, the gravitational force decreases to one-ninth its origi-nal value. Gravitational force is weaker than other types offorces, even though it holds the planets, stars, and galaxiestogether.

Free Fall and WeightWhen gravity is the only force acting on an object, the object issaid to be in The free-fall acceleration of an object isdirected toward the center of Earth. Because free-fall accelera-tion results from gravity, it is often abbreviated as the letter g.Near Earth’s surface, g is approximately 9.8 m/s2.

Free-fall acceleration near Earth’s surface is constantIn the absence of air resistance, all objects near Earth’s surfaceaccelerate at the same rate, regardless of their mass. As shown inFigure 8, the feather and the apple, dropped from the sameheight, would hit the ground at the same moment. In this book,we disregard air resistance for all calculations. We assume thatall objects on Earth accelerate at exactly 9.8 m/s2.

Why do all objects have the same free-fall acceleration?Newton’s second law shows that acceleration depends on bothforce and mass. A heavier object experiences a greater gravita-tional force than a lighter object does. But a heavier object is alsoharder to accelerate because it has more mass. The extra mass ofthe heavy object exactly compensates for the additional gravita-tional force.

free fall.

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1.0m

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Figure 7Gravitational force rapidly

becomes stronger as the distancebetween two objects decreases.

Gravitational force rapidlybecomes weaker as the distancebetween two objects increases.

B

A

free fall the motion of abody when only the force ofgravity is acting on the body

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Figure 8In a vacuum, a feather and anapple fall with the same accelera-tion because both are in free fall.

A

BTeaching TipFree-Fall Acceleration On theApollo 15 mission, astronautDavid Scott released a hammer anda feather on the moon at preciselyat the same moment. Ask studentsto hypothesize about what hap-pened in the experiment based ontheir knowledge of free-fall acceler-ation. (Since there is no air resistanceon the moon, the hammer andfeather fell with the same accelera-tion, and both hit the moon at thesame instant.) Explain that since themoon’s mass and radius are smallerthan Earth’s, free-fall accelerationon the moon is about 1/6 what it ison Earth. As a result, the accelera-tion of the hammer and featherwas less than it would be in a vac-uum on Earth, making the motionseasier to observe.

If you have Internet access, youcan show students a video of thisexperiment at the following NASAWeb site: http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo.html

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Interpreting Visuals Have stu-dents look at Figure 8. Ask: Whatwould happen if this experimentwere performed outside, on Earth’ssurface? (The feather would fallslower than the apple because of airresistance.) Assuming that the vac-uum is on Earth and that the appleand feather are dropped from ahigh enough distance that they donot hit the ground for 5 seconds,what would their speed be after 1 s, 2 s, and 3 s? (9.8 m/s, 19.6 m/s,29.4 m/s) LogicalLS

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MATHEMATICSMATHEMATICSCONNECTIONCONNECTION

Students can also substitute the values forG, mEarth, and radiusEarth to see that aobj �9.8 m/s2. (G � 6.674 � 10–11 N•m2/kg2;mEarth � 5.97 � 1024 kg; rEarth �6.38 � 106 m)aobj � GmEarth/(radiusEarth)2

aobj � (6.674 � 10–11 N•m2/kg2)(5.97 �1024 kg)/(6.38 � 106 m)2

aobj � 9.8 m/s2

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Challenge students to use the universal gravi-tation equation and Newton’s second law todemonstrate mathematically that free-fallacceleration is independent of the mass of theobject, disregarding air resistance.F � Gm1m2/d2 � GmobjmEarth/(radiusEarth)2

F � ma, so a � F/maobj � F/mobj � GmobjmEarth/(radiusEarth)2/mobj

aobj � GmobjmEarth/(radiusEarth)2/mobj

aobj � GmEarth/(radiusEarth)2


Weight is equal to mass times free-fall accelerationThe force on an object due to gravity is called its weight. OnEarth, your weight is simply the amount of gravitational forceexerted on you by Earth. If you know the free-fall acceleration, g,acting on a body, you can use F � ma (Newton’s second law) tocalculate the body’s weight. Weight equals mass times free-fallacceleration. Mathematically, this is expressed as follows.

weight � mass � free-fall accelerationw � mg

Note that because weight is a force, the SI unit of weight isthe newton. For example, a small apple weighs about 1 N. A 1.0 kg book has a weight of 1.0 kg � 9.8 m/s2 � 9.8 N.

You may have seen pictures of astronauts floating in the air,as shown in Figure 9. Does this mean that they don’t experiencegravity? In orbit, astronauts, the space shuttle, and all objects onboard experience free fall because of Earth’s gravity. In fact, theastronauts and their surroundings all accelerate at the same rate.Therefore, the floor of the shuttle does not push up against theastronauts and the astronauts appear to be floating. This situa-tion is referred to as apparent weightlessness.

Weight is different from massMass and weight are easy to confuse. Although mass and weightare directly proportional to one another, they are not the same.Mass is a measure of the amount of matter in an object. Weight isthe gravitational force an object experiences because of its mass.

The weight of an object depends on gravity, so a change in anobject’s location will change the object’s weight. For example, onEarth, a 66 kg astronaut weighs 66 kg � 9.8 m/s2 � 650 N (about150 lb), but on the moon’s surface, where g is only 1.6 m/s2, theastronaut would weigh 66 kg � 1.6 m/s2, which equals 110 N(about 24 lb). The astronaut’s mass remains the same every-where, but the weight changes as the gravitational force actingon the astronaut changes in each place.

Weight influences shapeGravitational force influences the shapes of living things. Onland, large animals must have strong skeletons to support theirmass against the force of gravity. The trunks of trees serve thesame function. For organisms that live in water, however, thedownward force of gravity is balanced by the upward force of thewater. For many of these creatures, strong skeletons are unnec-essary. Because a jellyfish has no skeleton, it can drift gracefullythrough the water but collapses if it washes up on the beach.

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Figure 9In the low-gravity environment of the orbiting space shuttle,astronauts experience apparentweightlessness.

SPACE SCIENCEPlanets in our solarsystem have differentmasses and differentdiameters. Therefore,

each has its own unique valuefor g. Find the weight of a 58 kg person on the followingplanets:

Earth, where g � 9.8 m/s2

Venus, where g � 8.9 m/s2

Mars, where g � 3.7 m/s2

Neptune, where g �

11.0 m/s2

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Mass and Weight Some stu-dents believe that the “feltweight” of an object is a prop-erty of the object, while mass issomething that “presses down.”Review the definition of masswith students, then discuss theconcept of weight. Emphasizethat weight is proportional tomass but the two are not thesame. When free-fall accelera-tion changes, mass (the measureof matter in an object) does notchange, but weight does changebecause weight � mass � free-fall acceleration.

SPACE SCIENCEEarth: 570 NVenus: 520 NMars: 210 NNeptune: 640 N

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• Cross-Disciplinary WorksheetIntegrating Space Science—Gravityand the Planets

• Cross-Disciplinary WorksheetIntegrating Biology—How FishMaintain Neutral Buoyancy


Apparent Weightlessness Many studentswill have experienced a temporary sensationof weightlessness in an elevator, on a rollercoaster, or on a free-fall type of ride as itbegins to descend. This is similar to whatastronauts experience. Because the seat andthe car around you begin descending at theacceleration of gravity, there is no gravita-tional force holding you into your seat. Thiscauses the sensation of weightlessness. Inreality, you do have weight, as evidenced byyour rapid fall toward the Earth!


Ask a biology teacher to visit your classroomand explain the effects of space flight on thehuman body.

LIFE SCIENCELIFE SCIENCECONNECTIONCONNECTION

Velocity is constant when air resistance balances weightBoth air resistance and gravity act on objectsmoving through Earth’s atmosphere. A fallingobject stops accelerating when the force of airresistance becomes equal to the gravitationalforce on the object (the weight of the object),as shown in Figure 10. This happens becausethe air resistance acts in the opposite directionto the weight. When these two forces areequal, the object stops accelerating andreaches its maximum velocity, which is calledthe

When skydivers start a jump, their para-chutes are closed, and they are acceleratedtoward Earth by the force of gravity. As theirvelocity increases, the force they experiencebecause of air resistance increases. When airresistance and the force of gravity are equal,skydivers reach a terminal velocity of about320 km/h (200 mi/h). But when they open theparachute, air resistance increases greatly. Fora while, this increased air resistance slowsthem down. Eventually, they reach a new ter-minal velocity of several kilometers per hour,which allows them to land safely.

Free Fall and MotionSkydivers are often described as being in free fall before theyopen their parachutes. However, that is an incorrect description,because air resistance is always acting on the skydiver. An objectis in free fall only if gravity is pulling it down and no other forcesare acting on it. Because air resistance is a force, free fall canoccur only where there is no air—in a vacuum (a place in whichthere is no matter) or in space. Thus, a skydiver falling to Earthis not in free fall.

Because there is no air resistance in space, objects in spaceare in free fall. Consider a group of astronauts riding in a space-craft. When they are in space, gravity is the only force acting onthe spacecraft and the astronauts. As a result, the spacecraft andthe astronauts are in free fall. They all fall at the same rate ofacceleration, no matter how great or small their individualmasses are.

terminal velocity.

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Figure 10When a skydiver reaches terminalvelocity, the force of gravity is bal-anced by air resistance.

Forces balanced:no acceleration

Force ofair resistance

Force ofgravity

terminal velocity the con-stant velocity of a falling objectwhen the force of air resist-ance is equal in magnitudeand opposite in direction tothe force of gravity

▲

Interpreting Visuals Have stu-dents examine Figure 10. Ask:Since the two forces are balanced,is the sky diver at rest? UseNewton’s laws to explain youranswer. (No. According to Newton’sfirst law, the sky diver will maintainhis state of rest or motion if there areno unbalanced forces acting on him.Since he was in motion before theforces became balanced, he remainsin motion at the same velocity thatwas reached at the moment theforces became balanced.) Logical

Teaching TipTerminal Velocity Students havelearned that, in the absence of airresistance, all objects accelerate atthe same rate. You can use the con-cept of terminal velocity to explainwhy, in the presence of air resist-ance, heavy objects fall faster.

A sky diver continues to acceler-ate until the force of gravity (thesky diver’s weight) is balanced bythe force of air resistance, whichincreases as speed increases. Themoment the two forces are equalwill occur later for a diver with agreater weight. For example, a 100 kg diver will accelerate untilthe force of air resistance is equalto the diver’s weight of 980 N (w � mg � 100 kg � 9.8 m/s2 �980 N), while a 50 kg diver would accelerate only until air resistanceequals 490 N (50 kg � 9.8 m/s2 �490 N). Since the heavier diveraccelerates longer and then fallswith a greater terminal velocity,that diver will reach Earth first.

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Falling Objects Many students believethat heavier objects fall faster, and theyhave trouble separating the effects of airresistance. Use discussion questions andthe examples discussed throughout thissection to address this misconception.

Spacediving In the 1950s, the Air Forcebegan conducting experiments to learnabout the hazards faced by flight crewsbailing from high-altitude aircraft. Theirexperiments included three high-altitude“spacedives” by Captain Joseph Kittinger.His final jump, in August of 1960, wasfrom the incredible height of 31,334meters (102,800 feet, or almost 20 miles)!Even today Kittinger holds the record for the highest jump and the fastest speed attained by a human being in theatmosphere.


Orbiting objects are in free fallWhy do astronauts appear to float inside a space shuttle? Is itbecause they are “weightless” in space? You may have heard thatobjects are weightless in space, but this is not true. It is impos-sible to be weightless anywhere in the universe.

As you learned earlier in this section, weight—a measure ofgravitational force—depends on the masses of objects and thedistances between them. If you traveled in space far away fromall the stars and planets, the gravitational force acting on youwould be almost undetectable because the distance between youand other objects would be great. But you would still have mass,and so would all the other objects in the universe. Therefore,gravity would still attract you to other objects—even if justslightly—so you would still have weight.

Astronauts “float” in orbiting spaceships, not because theyare weightless but because they are in free fall. The moon staysin orbit around Earth, as in Figure 11, and the planets stay inorbit around the sun, all because of free fall. To better under-stand why these objects continue to orbit and do not fall to Earth,you need to learn more about what orbiting means.

Two motions combine to cause orbiting An object is said to be orbiting when it is traveling in a circularor nearly circular path around another object. When a spaceshiporbits Earth, it is moving forward but it is also in free fall towardEarth. Figure 12 shows how these two motions combine to causeorbiting.

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Force of Earth‘s gravity on the moon

Path of the moon

Figure 11The moon stays in orbit aroundEarth because Earth’s gravitationalforce provides a pull on the moon.

Figure 12How an Orbit Is Formed

The shuttle is in free fallbecause gravity pulls it towardEarth. This would be its path if itwere not traveling forward.

B When the forward motioncombines with free fall, the shuttlefollows the curve of Earth’s sur-face. This is known as orbiting.

CThe shuttle moves forward at aconstant speed. This would be itspath if there were no gravitationalpull from Earth.

A

A

B

C

Vocabulary Tell students that inastronomy, the word orbit can beused as both a noun and a verb,and it also has several other relatedmeanings. Have students give anexample of each use in astronomy,then have them use a dictionary tofind out as many other meaningsas possible. As an extension, havestudents speculate about the rela-tionships between the variousmeanings they find. Students maywish to consult an etymologicaldictionary to check their specula-tions. Verbal

Group ActivityArtificial Satellites Tell studentsthat in addition to our moon, anatural satellite, thousands of man-made satellites are also in orbitaround Earth. Like the moon, theseartificial satellites have both a for-ward motion and a free fall accel-eration, and their orbits combinethese two motions. Likewise, theInternational Space Station (ISS)also orbits Earth.

Divide students into groups, andask each group to prepare a pres-entation about artificial satellites.Instruct each group to include avisual aid with their presentation,such as a poster or a transparencypage. Presentation topics couldinclude the following: types ofsatellites, uses of satellites, earlysatellite experiments, details abouta particular satellite, and theInternational Space Station.

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Transparencies

TT Terminal VelocityTT Two Motions Cause Orbiting

Historical Perspective Newton’s Idea of Gravity One of IsaacNewton’s amazing scientific achievements washis recognition that the force that pulls anapple toward Earth is the same force thatholds the moon in its orbit around Earth. The legend about Newton first realizing thiswhile watching an apple fall to the groundstems from an account written down by JohnConduitt, Newton’s assistant at the royalmint. (John Conduitt was also Newton’sniece’s husband.) Conduitt wrote:

In the year 1666 . . . while he was musing in a garden it came into his thought that thepower of gravity (which brought an applefrom a tree to the ground) was not limitedto a certain distance from earth, but that thispower must extend much further than wasusually thought. Why not as high as the Moonthought he to himself & that if so, that mustinfluence her motion & perhaps retain her inher orbit, whereupon he fell a-calculating whatwould be the effect of that superposition . . .

Projectile Motion and GravityThe orbit of the space shuttle around Earth is an example of

Projectile motion is the curved path anobject follows when thrown, launched, or otherwise projectednear the surface of Earth. The motions of leaping frogs, thrownballs, and arrows shot from a bow are all examples of projectilemotion. Projectile motion has two components—horizontal andvertical. The two components are independent; that is, they haveno effect on each other. In other words, the downward accelera-tion due to gravity does not change a projectile’s horizontalmotion, and the horizontal motion does not affect the downwardmotion. When the two motions are combined, they form a curvedpath, as shown in Figure 13.

Projectile motion has some horizontal motionWhen you throw a ball, your hand and arm exert a force on theball that makes the ball move forward. This force gives the ballits horizontal motion. Horizontal motion is motion that is per-pendicular (90°) to Earth’s gravitational field.

After you have thrown the ball, there are no horizontal forcesacting against the ball (if you ignore air resistance). Therefore,there are no forces to change the ball’s horizontal motion. So, thehorizontal velocity of the ball is constant after the ball leavesyour hand, as shown in Figure 13.

Ignoring air resistance allows you to simplify projectilemotion so that you can understand the horizontal and then thevertical components of projectile motion. Then, you can putthem together to understand projectile motion as a whole.

projectile motion.

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The twomotions combineto form a curvedpath.

C

Figure 13Two motions combine to formprojectile motion.

projectile motion thecurved path that an object follows when thrown,launched, or otherwise projected near the surface of Earth; the motion of objectsthat are moving in two dimen-sions under the influence ofgravity

▲

After the ball leaves thepitcher’s hand, its horizontalvelocity is constant.

A

The ball’s verticalvelocity increasesbecause gravitycauses it to acceler-ate downward.

B

Teaching TipNewton’s Thought ExperimentTo help students understand howan orbiting space station is anexample of projectile motion, youcan use Newton’s thought experi-ment. Newton imagined putting acannon on top of a tall mountain.When the cannon is fired, the can-nonball has projectile motion, andit eventually falls to Earth. Thegreater the ball’s speed, the moredistance it covers before hitting theground.

Draw a few examples of thisscenario on a chalkboard or over-head projector, with differentspeeds. Ask students what wouldeventually happen when the speedreached a high enough value.(Remind them that this is athought experiment, and the setupis purely hypothetical.) By extrapo-lating from the previous examples,students should realize that, if thecannonball’s speed were greatenough, it would continually “fall”around Earth, never touching theground; in other words, it wouldbe in orbit around Earth. This is todemonstrate that an object orbitingEarth is simply an example of pro-jectile motion. LogicalLS



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Black holes are objects so massive that the speed required to escape their gravita-tional pull is greater than the speed of light.Einstein found that no mass can travel at orgreater than the speed of light. As a result,no mass can escape the gravitational pull of ablack hole. Even light—which always travelsat the same speed, the fastest speed in theuniverse—cannot travel fast enough to escapea black hole!

When a rocket is sent into space, its velocitymust be great enough that it can escapeEarth’s gravitational field. With a lowervelocity, the rocket would either fall backtoward Earth in projectile motion or fall into orbit around Earth. The velocityrequired to escape Earth’s gravity—calledescape velocity—depends on Earth’s mass.Since the force of gravity is proportional tomass, a greater mass corresponds to a greaterescape velocity. For example, the sun has agreater escape velocity than Earth.

SPACE SCIENCESPACE SCIENCECONNECTIONCONNECTION


1. Sample answer: The law of universal gravita-tion says that the force of gravitational accel-eration is proportional to the attracting massesand inversely proportional to the square of thedistance between the masses. If you make themass of one or both of the attracting masseslarger, then the force will be larger. (Weight onJupiter is larger than weight on Earth becausethe mass of Jupiter is so much larger than themass of the earth.) The attraction of Earth fora satellite gets smaller as the satellite gets far-ther away from Earth.

2. The moon’s mass is much smaller than Earth’smass. Since the force of attraction depends on

the mass of both attracting objects, the forceof attraction between you and the moonwould therefore be smaller than the forcebetween you and Earth.

3. Mass is the resistance to change in motion ofone object, whereas weight is a pull betweentwo objects. Weight is proportional to themass of those two objects and inversely pro-portional to the square of the distance betweenthem. Mass is the amount of stuff, and doesn’tchange; weight is gravitational pull, anddepends on location.


Projectile motion also has some vertical motionIn addition to horizontal motion, vertical motion isinvolved in the movement of a ball that has beenthrown. If it were not, the ball would continue mov-ing in a straight line, never falling. Again imaginethat you are throwing the ball as in Figure 13. Whenyou let go of the ball, gravity pulls it downward,which gives the ball vertical motion. Verticalmotion is motion in the direction in which the forceof Earth’s gravity acts.

In the absence of air resistance, gravity on Earthpulls downward with an acceleration of 9.8 m/s2 onobjects that are in projectile motion, just as it doeson all falling objects. Figure 14 shows that the down-ward accelerations of a thrown object and of afalling object are identical.

Because objects in projectile motion acceleratedownward, you should always aim above a target ifyou want to hit it with a thrown or propelled object.This is why archers point their arrows above thebull’s eye on a target. If they aimed an arrowdirectly at a bull’s eye, the arrow would strike belowthe center of the target rather than the middle.

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1. State the law of universal gravitation, and use examples toexplain the effect of changing mass and changing distanceon gravitational force.

2. Explain why your weight would be less on the moon thanon Earth even though your mass would not change. Use thelaw of universal gravitation in your explanation.

3. Describe the difference between mass and weight.

4. Name the two components that make up orbital motion,and explain how they do so.

5. Critical Thinking Using Newton’s second law, explain whythe gravitational acceleration of any object near Earth is thesame no matter what the mass of the object is.

6. The force between a planet and a spacecraft is 1 millionnewtons. What will the force be if the spacecraft moves tohalf its original distance from the planet?

S U M M A R Y

> Gravitational force betweentwo masses strengthens asthe masses become moremassive and rapidly weak-ens as the distancebetween them increases.

> Gravitational accelerationresults from gravitationalforce, is constant, and doesnot depend on mass.

> Mathematically, weight �

mass � free-fall accelera-tion, or w � mg.

> Projectile motion is a com-bination of a downwardfree-fall motion and a for-ward horizontal motion.

Figure 14The red ball was dropped without a hori-

zontal push.

The yellow ball was given a horizontal pushoff the ledge at the same time it was dropped.It follows a projectile-motion path.

The two balls have the same accelerationdownward because of gravity. The horizontalmotion of the yellow ball does not affect itsvertical motion.

C

B

A


A

B

C

Teaching TipMicrogravity When an objectsuch as a satellite or a space stationis in free fall around Earth, a con-dition of microgravity is said toexist. Although astronauts inmicrogravity are not weightless,they appear to be so because theyare falling around Earth at thesame rate as their surroundings.

QuizChoose the word that completeseach sentence correctly.

1. The force of gravity is inverselyproportional to mass/distancesquared. (distance squared)

2. Disregarding air resistance, free-fall acceleration near Earth’s sur-face does/does not depend onmass. (does not)

3. The mass/weight of an astronauton the moon is the same as it ison Earth. (mass)

4. Terminal velocity is reachedwhen the forces on a skydiverbecome balanced/unbalanced.(balanced)

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• Concept Review • Quiz

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Transparencies

TM Projectile Motion

Presents Physical Science• Segment 7 Zero-Gravity Plane• Critical Thinking Worksheet 7


Videos


Newton’s Third Law> Explain that when one object exerts a force on a second

object, the second object exerts a force equal in size andopposite in direction on the first object.

> Show that all forces come in pairs commonly called actionand reaction pairs.

> Recognize that all moving objects have momentum.

When you kick a soccer ball, as shown in Figure 15, younotice the effect of the force exerted by your foot on the

ball. The ball experiences a change in motion. Is this the onlyforce present? Do you feel a force on your foot? In fact, the soc-cer ball exerts an equal and opposite force on your foot. The forceexerted on the ball by your foot is called the action force, and theforce exerted on your foot by the ball is called the reaction force.

Action and Reaction ForcesNotice that the action and reaction forces are applied to differentobjects. These forces are equal and opposite. The action forceacts on the ball, and the reaction force acts on the foot. This is anexample of Newton’s third law of motion, also called the law ofaction and reaction.

For every action force, there is an equal and opposite reaction force.

Forces always occur in pairsNewton’s third law can be stated as fol-lows: All forces act in pairs. Whenever aforce is exerted, another force occursthat is equal in size and opposite indirection. Action and reaction forcepairs occur even when there is nomotion. For example, when you sit on achair, your weight pushes down on thechair. This is the action force. The chairpushing back up with a force equal toyour weight is the reaction force.

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momentum

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Figure 15According to Newton’s third law,the soccer ball and the foot exertequal and opposite forces on oneanother.

OverviewBefore beginning this section,review with your students theobjectives listed in the StudentEdition. In the first part of this section, students learn aboutNewton’s third law, also called thelaw of action and reaction. Next,they study momentum, includingproblem solving with momentumand the conservation of momen-tum. The section concludes with adiscussion of rocket propulsionand additional examples of action-reaction pairs.


OpeningDemonstrationUse two identical horseshoe mag-nets and an overhead projector todemostrate Newton’s third law.Place the two magnets closetogether on the overhead projector,with the poles facing one another.Release the magnets at the samemoment, and have studentsobserve their motion and finalpositions. The magnets shouldmove away from one another andcome to rest in a symmetrical pat-tern. VisualLS

MotivateMotivate

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plants. Since the box-like structures remindedhim of the cells of a monastery, he coined theterm “cells” to describe them.

Soon afterward, Antony van Leeuwenhoek—inspired by Hooke’s work—learned how tomake simple microscopes which producedgreater clarity and brightness than other cur-rent microscopes. He observed a vast arrayof items over the next 50 years, and made anumber of significant discoveries, includinglittle “animalcules” (now known as bacteriaand protozoa), red blood cells, and sperm cells.

Newton’s three laws of motions were pub-lished in the Principia in 1686. There weremany significant developments in biologyaround the same time.

In 1665, Robert Hooke publishedMicrographia, which described his detailedobservations of insects, sponges, and similarobjects with one of the best compoundmicroscopes of the day. Observing the cellwalls in cork tissue, Hooke marveled at theregular pattern of repeating structures, whichhe also observed in other woods and in

BIOLOGYBIOLOGYCONNECTIONCONNECTION

Historical PerspectiveNewton’s Principia Students may be inter-ested in reading Newton’s formulation of thethree laws of motion. Obtain a copy of thePrincipia, and make copies of the appropriatepassage for students. Have students discusstheir interpretations. Ask them to compareNewton’s words with our modern formulationof the three laws. (Discuss Newton’s formula-tion of the second law again after studentsstudy momentum.) Encourage students to con-sult Newton’s definitions (which precede thelaws) as needed. Discuss why Newton calls thethree principles “axioms, or laws.” VerbalLS


Force pairs do not act on the same objectNewton’s third law indicates that forces always occur in pairs. Inother words, every force is part of an action and reaction forcepair. Although the forces are equal and opposite, they do not can-cel one another because they are acting on different objects. Inthe example shown in Figure 16, the swimmer’s hands and feetexert the action force on the water. The water exerts the reactionforce on the swimmer’s hands and feet. In this and all otherexamples, the action and reaction forces do not act on the sameobject. Also note that action and reaction forces always occur atthe same time.

Equal forces don’t always have equal effectsAnother example of an action-reaction force pair is shown inFigure 17. If you drop a ball, the force of gravity pulls the balltoward Earth. This force is the action force exerted by Earth onthe ball. But the force of gravity also pulls Earth toward the ball.That force is the reaction force exerted by the ball on Earth.

It’s easy to see the effect of the action force—the ball falls toEarth. Why don’t you notice the effect of the reaction force—Earth being pulled upward? Remember Newton’s second law: anobject’s acceleration is found by dividing the force applied to theobject by the object’s mass. The force applied to Earth is equal tothe force applied to the ball. However, Earth’s mass is muchlarger than the ball’s mass, so Earth’s acceleration is muchsmaller than the ball’s acceleration.

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Figure 16The action force is the swimmer

pushing the water backward.A The reaction force is the water pushing

the swimmer forward.B

Figure 17The two forces of gravity betweenEarth and a falling object are anexample of a force pair.

Action force

Reaction force

A

B

Teaching TipNewton’s Third Law Emphasizethat the equal but opposite forcesin Newton’s third law act on dif-ferent objects. As A acts on B, Bacts on A. Action/reaction forcesnever cancel out—they cannotbecause they act on differentobjects. The only time forces couldcancel out (add up to zero) wouldbe if they acted on the same object.

You can use the classic horse-cart problem as an example. If ahorse pulls a cart with a certainhorizontal force, the cart exerts an equal and opposite force on the horse. Challenge students toexplain how the cart accelerates.(Students should realize that theaction and reaction forces are actingon different objects. So, although theforces are equal and opposite, theydo not cancel.) Ask a volunteer todraw separate force diagrams forboth the horse and cart to empha-size this point. (In addition to thehorizontal action force exerted bythe horse on the cart and its equaland opposite reaction force, the dia-grams may include the force of fric-tion between the horse’s feet and theground, and between the cart wheelsand the ground. The net force onboth the horse and the cart should be shown to be in the forward direction.) LogicalLS

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• Lesson Plan• Cross-Disciplinary Worksheet

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momentum a quantitydefined as the product of themass and velocity of an object

▲

Figure 18Because of the large mass andhigh speed of this bowling ball, it has a lot of momentum and isable to knock over the pins easily.

www.scilinks.orgTopic: MomentumSciLinks code: HK4088

MomentumIf a compact car and a large truck are traveling with the samevelocity and the same braking force is applied to each, the trucktakes more time to stop than the car does. Likewise, a fast-movingcar takes more time to stop than a slow-moving car with thesame mass does. The truck and the fast-moving car have more

than the compact car and the slow-moving car do.Momentum is a property of all moving objects, which is equal tothe product of the mass and the velocity of the object.

Moving objects have momentumFor movement along a straight line, momentum is calculated bymultiplying an object’s mass by its velocity. The SI unit formomentum is kilograms times meters per second (kg•m/s).

The momentum equation shows that for a given velocity, themore mass an object has, the greater its momentum is. A massivesemi truck on the highway, for example, has much more momen-tum than a sports car traveling at the same velocity has. Themomentum equation also shows that the faster an object is mov-ing, the greater its momentum is. For instance, a fast-movingtrain has much more momentum than a slow-moving train withthe same mass has. If an object is not moving, its momentum iszero.

Like velocity, momentum has direction. An object’s momen-tum is in the same direction as its velocity. The momentum of thebowling ball shown in Figure 18 is directed toward the pins.

momentum

momentum = mass � velocityp = mv

Momentum Equation

Teaching TipMomentum Introduce the subjectof momentum by asking studentsfor examples of non-scientific usesof the term, such as, “The baseballteam started gaining momentumnear the end of the season.” Afterstudents read this page, discusshow the scientific use of the termmomentum relates to its use incommon speech. Also discuss howthe two are different. Verbal

Interpreting Visuals Have stu-dents examine Figure 18. Ask stu-dents: How could you increase themomentum of the bowling ball?(increase its velocity) Would a lessmassive ball at the same velocityhave more or less momentum? (less)Do the pins have any momentumbefore the ball hits them? How doyou know? (No, the pins do not haveany momentum because they do nothave any velocity.) LogicalLS

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Alternative AssessmentMomentum and Newton’s Second LawIf students have read Newton’s laws in thePrincipia, they have probably noticed thatNewton actually uses momentum ratherthan acceleration in his second law. If stu-dents did not read this, explain that in hissecond law of motion, Newton states thatforce is proportional to the “change ofmotion.” Also explain that he defines motionas velocity multiplied by the “quantity ofmatter,” or velocity times mass (momentum).Thus, Newton’s own version of the secondlaw states that force is proportional to

change in momentum. Have students provethat this is equivalent to our modern formu-lation of F � ma.force � change in momentum/time (F � �p/t)momentum � mass � velocity (p � mv)force � mass � change in velocity/time(F � m�v/t)change in velocity/time � acceleration (�v/t � a)force � mass � acceleration (F � ma)Symbolically:F � �p/t � �mv/t � m�v/t � ma

LogicalLS



Force is related to change in momentumTo catch a baseball, you must apply a force on the ball to make itstop moving. When you force an object to change its motion, youforce it to change its momentum. In fact, you are actually chang-ing the momentum of the ball over a period of time.

As the time period of the momentum’s change becomeslonger, the force needed to cause this change in momentumbecomes smaller. So, if you pull your glove back while you arecatching the ball, as in Figure 19, you are extending the time forchanging the ball’s momentum. Extending the time causes theball to put less force on your hand. As a result, the sting to yourhand is reduced.

As another example, when pole-vaulters, high jumpers, andgymnasts land after jumping, they move in the direction of themotion. This motion extends the time of the momentum change.As a result, the impact force decreases.

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PracticeHINT

> When a problem requires thatyou calculate velocity whenyou know momentum andmass, you can use themomentum equation.

> You may rearrange the equa-tion to isolate velocity on theleft side, as follows: v � �

mp�.

You will need this form ofthe momentum equation forPractice Problem 2.

Momentum Calculate the momentum of a 6.00 kg bowling ballmoving at 10.0 m/s down the alley toward the pins.

List the given and unknown values.Given: mass, m � 6.00 kg

velocity, v � 10.0 m/s down the alley Unknown: momentum, p � ? kg • m/s (and direction)

Write the equation for momentum.momentum � mass � velocity, p � mv

Insert the known values into the equation, and solve. p � mv � 6.00 kg � 10.0 m/s p � 60.0 kg • m/s down the alley

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Momentum1. Calculate the momentum of the following objects.

a. a 75 kg speed skater moving forward at 16 m/s

b. a 135 kg ostrich running north at 16.2 m/s

c. a 5.0 kg baby on a train moving eastward at 72 m/s

d. a seated 48.5 kg passenger on a train that is stopped

2. Calculate the velocity of a 0.8 kg kitten with a momentum of 5 kg • m/sforward.

Figure 19Moving the glove back duringthe catch increases the time ofthe momentum’s change anddecreases the impact force.

Additional ExamplesMomentum An athlete with amass of 73.0 kg runs with a con-stant forward velocity of 1.50 m/s.What is the athlete’s momentum? Answer: 110 kg • m/s forward(rounded to correct significant figures)

If a car with a mass of 925 kg hasthe same momentum as the athlete,what is the car’s speed? Answer: 0.119 m/s

Logical

1. p � mva. (75 kg)(16 m/s) �

1200 kg•m/s forwardb. (135 kg)(16.2 m/s) �

2187 kg•m/s north (using sig-nificant figures: 2190 kg•m/snorth)

c. (5.0 kg)(72 m/s) �360 kg•m/s eastward

d. (48.5 kg)(0 m/s) �0 kg • m/s

2. v � �mp

� � �5

0k.g8•mkg

/s��

6.3 m/s forward (using significantfigures: 6 m/s forward)LogicalLS

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• Math Skills Momentum• Cross-Disciplinary Worksheet

Connection to Fine Arts—Momentumof Line in Art

• Cross-Disciplinary WorksheetApplications—Driving Safety

GENERAL


Air Bags Air bags in automobiles takeadvantage of the fact that force decreaseswhen the time period of a change in momen-tum increases. If a driver is in a collision, thedriver keeps moving forward (in accordancewith Newton’s first law of motion), evenafter the vehicle stops. If the driver hits awindow or dashboard, his change in momen-tum occurs very quickly, so the force on thedriver is great. Air bags increase the timeinterval over which momentum changes and,as a result, the force on the driver is greatlyreduced.


Momentum is conserved in collisionsImagine that two cars of different massestraveling with different velocities collidehead on. Can you predict what will happenafter the collision? The momentum of thecars after the collision can be predicted.This prediction can be made because, in theabsence of outside influences, momentumis conserved. Some momentum may betransferred from one vehicle to the other,but the total momentum remains the same.This principle is known as the law of con-servation of momentum.

The total amount of momentum in an isolated system is conserved.

The total momentum of the two carsbefore a collision is the same as the total

momentum after the collision. This law applies whether the carsbounce off each other or stick together. In some cases, carsbounce off each other to move in opposite directions. If the carsstick together after a collision, the cars will continue in the direc-tion of the car that originally had the greater momentum.

Momentum is transferredWhen a moving object hits a second object, some or all of themomentum of the first object is transferred to the second object.If only some of the momentum is transferred, the rest of themomentum stays with the first object.

Imagine you hit a billiard ball with a cue ball so that the bil-liard ball starts moving and the cue ball stops, as shown in Figure 20.The cue ball had a certain amount of momentum before the col-lision. During the collision, all of the cue ball’s momentum wastransferred to the billiard ball. After the collision, the billiard ballmoved away with the same amount of momentum the cue ballhad originally. This example illustrates the law of conservation ofmomentum. Any time two or more objects interact, they mayexchange momentum, but the total momentum stays the same.

Newton’s third law can explain conservation of momentum.In the example of the billiard ball, the cue ball hit the billiard ballwith a certain force. This force was the action force. The reactionforce was the equal but opposite force exerted by the billiard ballon the cue ball. The action force made the billiard ball start mov-ing, and the reaction force made the cue ball stop moving.

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Figure 20The cue ball is moving forward

with momentum. The billiardball’s momentum is zero.

When the cue ball hits the bil-liard ball, the action force makesthe billiard ball move forward. Thereaction force stops the cue ball.

Because the cue ball’s momen-tum was transferred to the billiardball, the cue ball’s momentumafter the collision is zero.

C

B

A

B

C

ATeaching TipNewton’s Cradle You can use atoy called “Newton’s cradle” todemonstrate the conservation ofmomentum. Newton’s cradle—acommon office toy—consists offive or seven steel balls suspendedfrom a horizontal bar, hangingclose enough together that the ballsare all touching when they are atrest. If a ball from one side ispicked up and then released, a ballfrom the other side flies out, andthe motion continues back andforth. If two balls are used, twoballs move on the other side, andso on. Show students what hap-pens when you pick up one, two,and three balls, and discuss howthe toy demonstrates the conserva-tion of momentum. You can alsodiscuss the demonstration in termsof action/reaction forces.

Interpreting Visuals Ask stu-dents how they could calculate thevelocity of the billiard ball inFigure 20C, given the mass of eachball and the initial velocity of thecue ball. (Since momentum is con-served, the total momentum beforethe collision (mass of the cue ball �initial velocity of the cue ball) equalsthe total momentum after the colli-sion (mass of the billiard ball � finalvelocity of the billiard ball). Thisequation can be rearranged to findthe billiard ball’s velocity after thecollision:mcvc(initial) � mbvb(final)

vb(final) � mcvc(initial)/mb)

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GENERAL

Historical Perspective Descartes and Huygens The concept ofmomentum was first proposed by the Frenchphilosopher Rene Descartes (1596–1650).Descartes defined momentum as “amount ofmotion,” or “mass times speed.” Descartesthought momentum was a useful quantitybecause it is conserved in some cases.However, according to this definition,momentum would not always be conserved.For example, if two bowling balls both cometo a stop after a head-on collision, momentumwould not be conserved. Descartes wasunable to reconcile this discrepancy.

This was left to the Dutch scientistChristiaan Huygens (1629–1695), who realizedthat momentum would be conserved in allexamples if direction is taken into account.With the example of the two bowling balls, ifthe momentum of one is positive and that ofthe other negative (since the directions areopposite), the total momentum is the samebefore and after the collision. In other words,Huygens realized that in order to be con-served, momentum must be the product ofmass and velocity, rather than of mass andspeed.

Alternative AssessmentApplying Newton’s Laws Ask students tofind examples of forces in their daily lives. Askthem to make a list of at least three examples.For each example, instruct them to write a para-graph explaining how any or all of Newton’slaws can be used to analyze the forces involved.Tell them to be sure to use each law at leastonce in their explanations. Students may wish to use force diagrams to supplement their writ-ten explanations. VerbalLS


Conservation of momentum explains rocket propulsionNewton’s third law and the conservation of momentum are usedin rocketry. Rockets have many different sizes and designs, butthe basic principle remains the same. The push of the hot gasesthrough the nozzle is matched by an equal push in the oppositedirection on the combustion (burning) chamber, which acceler-ates the rocket forward, as shown in Figure 21.

Many people wrongly believe that rockets work because thehot gases flowing out the nozzle push against the atmosphere. Ifthis were true, rockets couldn’t travel in outer space where thereis no atmosphere. What really happens is that momentum is con-served. Together, the rocket and fuel form a system. When thefuel is pushed out the back, they remain a system. The change inthe fuel’s momentum must be matched by a change in therocket’s momentum in the opposite direction for the overallmomentum to stay the same. This example shows the conserva-tion of momentum. Also, the upward force on the rocket and thedownward force on the fuel are an action-reaction pair.

Action and reaction force pairs are everywhereFigure 22 gives more examples of action-reaction pairs. In eachexample, notice which object exerts the action force and whichobject exerts the reaction force. Even though we are concentrat-ing on just the action and reaction force pairs, there are otherforces at work, each of which is also part of an action-reactionpair. For example, when the bat and ball exert action and reac-tion forces, the bat does not fly toward the catcher, because thebatter is exerting yet another force on the bat.

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Gasespushrocketforward

Rocketpushesgasesbackward

Hydrogen

Oxygen

Combustionchamber

Figure 21All forces occur in action-reactionpairs. In this case, the upward pushon the rocket equals the down-ward push on the exhaust gases.

Figure 22Examples of Third Law Forces

The rabbit’s legs exert a force onEarth. Earth exerts an equal forceon the rabbit’s legs, which causesthe rabbit to accelerate upward.

A The bat exerts a force onthe ball, which sends the ballinto the outfield. The ball exertsan equal force on the bat.

B When your hand hits thetable with a force, the table’sforce on your hand is equal insize and opposite in direction.

C

Interpreting Visuals The studenttext discusses rocket propulsion interms of action and reaction forces.Ask students to use Figure 21 toexplain how rocket propulsion isan example of the conservation ofmomentum. (When the rocket is atrest, the momentum of the rocket/fuel system is zero. When combus-tion occurs, the gases move down-ward. The rocket moves in theopposite direction with a velocitythat keeps the total momentumzero.) Visual

Teaching TipForce Pairs To emphasize thataction/reaction force pairs areeverywhere, remind students thatevery action force has a reactionforce. In other words, every forceis part of an action-reaction pair.Since forces are all around us,action-reaction pairs are all aroundus. This is not always obviousbecause in some cases, the effectsof one of the forces in the pair arenot easily visible. This can occurwhen other forces are acting on theobject as well or when the mass ofone of the objects is so large thatthe acceleration produced by theforce is not easily observable.

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1. State Newton’s third law of motion, and give an examplethat shows how this law works.

2. List three examples of action-reaction force pairs that arenot mentioned in the chapter.

3. Define momentum, and explain what the law of conserva-tion of momentum means.

4. Explain why, when a soccer ball is kicked, the action andreaction forces don’t cancel each other. a. The force of the player’s foot on the ball is greater than

the force of the ball on the player’s foot.b. They act on two different objects.c. The reaction force happens after the action force.

5. Critical Thinking The forces exerted by Earth and a skierbecome an action-reaction force pair when the skier pushesthe ski poles against Earth. Explain why the skier acceler-ates while Earth does not seem to move at all. (Hint: Thinkabout the math equation for Newton’s second law of motionfor each of the forces.)

6. Calculate the momentum of a 1.0 kg ball traveling eastwardat 12 m/s.

S U M M A R Y

> When one object exerts anaction force on a secondobject, the second objectexerts a reaction force onthe first object. Forcesalways occur in action-reaction force pairs.

> Action-reaction force pairsare equal in size and oppo-site in direction.

> Every moving object hasmomentum, which is theproduct of the object’smass and velocity.

> Momentum can be trans-ferred in collisions, but thetotal momentum beforeand after a collision is thesame. This is the law ofconservation of momentum.

> Rocket propulsion canbe explained in terms of conservation of momentum.

Materials

How are action and reaction forces related?

✔ 2 spring scales ✔ 2 kg mass

1. Hang the 2 kg mass from one of the springscales.

2. Observe the reading on the spring scale.

3. While keeping the mass connected to the firstspring scale, link the two scales together. Thefirst spring scale and the mass should hang fromthe second spring scale, as shown in the figureat right.

4. Observe the readings on each spring scale.

Analysis1. What are the action and reaction

forces involved in the spring scale—mass system you have constructed?

2. How did the readings on the two spring scales in step 4 compare? Explain how this is an example of Newton’s third law.



1. Newton’s third law states that any time oneobject applies a force to a second object, the second object applies a force on the first objectthat is equal in size and opposite in direction.For example, when you sit in a chair, you pushdown on the chair (action force), and the chairpushes up on you (reaction force).

2. Answers may vary. They can include any action-reaction force pairs, such as fingers and key-board (on computer or piano, etc.), cheese andcheese cutter, person and floor, etc.

3. Momentum is mass � velocity. The law of con-servation of momentum says that in any systemof group of objects, the momentum will not

change if a net outside force does not act on thesystem or group of objects.

4. b5. The forces exerted by Earth and a skier are an

action-reaction force pair because Earth exertsan equal and opposite force on the skier as theskier had exerted on Earth. Since F � ma andF is equal for both, the smaller mass of the skier(when compared to the mass of Earth) willmean the skier’s acceleration away from Earthwill be very much greater than Earth’s unnotice-able acceleration away from the skier.



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How are action and reactionforces related?

Analysis1. If students have difficulty with

item 1, encourage them to listthe forces acting on eachobject separately. For example,the forces acting on the middlespring scale are: its weight, thedownward pull of the 2 kgmass, and the upward pull ofthe top spring scale. See “Continuation of Answers” at the

end of the chapter.

• Quick Lab Datasheet How are action and reaction forces related?

• Concept Review• Quiz

GENERAL

GENERAL


QuizChoose the term that best com-pletes each sentence.

1. Action-reaction forces areequal/unequal in size and opposite in direction. (equal)

2. Momentum is equal to masstimes speed/velocity. (velocity)

3. Momentum is always/sometimesconserved. (always)

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Algebraic RearrangementsA car’s engine exerts a force of 1.5 � 104 N in the forward direction, while friction exerts anopposing force of 9.0 � 103 N. If the car’s mass is 1.5 � 103 kg, what is the magnitude anddirection of the car’s net acceleration?

List all given and unknown values.

Given: forward force, F1 � 1.5 � 104 Nopposing force, F2 � 9.0 � 103 Nmass, m � 1.5 � 103 kg

Unknown: acceleration (m/s2)

Write down the equation for force, and rearrange it for calculating the acceleration.

F � ma

a � �mF

�

Solve for acceleration.

The net acceleration must be obtained from the net force, which is the overall,unbalanced force acting on the car.

Fnet � F1 � F2 , so

manet � F1 � F2

The net acceleration is therefore

anet � �(F1

m� F2)� � ��

16..50

�

�

11003

3

kNg

�� 4.0 m/s2

The net acceleration is 4.0 m/s2, and like the net force, it is in the forward direction.

Following the example above, calculate the following:

1. A car has a mass of 1.50 � 103 kg. If the net force acting on the car is 6.75 � 103 N to the east, what is the car’s acceleration?

2. A bicyclist decelerates with a force of 3.5 � 102 N. If the bicyclist and bicycle have a total mass of 1.0 � 102 kg, what is the acceleration?

3. Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Roberto with a force of 11.0 N straight ahead. If the force of frictionopposing the movement is 8.4 N, what is the magnitude and direction of the book’s acceleration?

(1.5 � 104 N � 9.0 � 103 N)��

1.5 � 103 kg

3

2

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PracticeAlgebraic Rearrangements

Teaching TipNet Forces and AccelerationRemind students that the net accel-eration describes the change in thevelocity of an object due to theunbalanced forces acting on it.While there is an acceleration asso-ciated with each force, these are inthe same direction of the force.Thus, any force in the oppositedirection provides an accelerationthat is also in the opposite direc-tion, and which must cancel withthe original acceleration. The netacceleration is the result of thiscancellation, and accounts for themotion that is actually observed.

Be sure that students understandthat, in problems where more thanone force or acceleration value aregiven, they must determine whetherthese are in the same or oppositedirection to each other, and thusadd or subtract them accordingly.Once the net force or accelerationhas been found, the net accelera-tion or force, respectively, can becalculated.

Answers1. 4.5 m/s2 to the east2. 3.5 m/s2 in a backward direction

(deceleration)3. anet � (F1 � F2)/m �

11.0 N � 8.4 N / 2.2 kg �1.2 m/s2 (using significant figures)LogicalLS


GENERAL

• Science Skills Worksheet OrderingMultiple Operations


6. Any change in an object’s velocity is caused bya. the object’s mass.b. the object’s direction.c. a balanced force.d. an unbalanced force.

7. ____________ is a force that opposes themotion between two objects in contact witheach other.a. Motion c. Accelerationb. Friction d. Velocity

8. An object’s acceleration isa. directly proportional to the net force.b. inversely proportional to the object’s

mass.c. in the same direction as the net force.d. All of the above

9. Suppose you are pushing a car with a cer-tain net force. If you then push with twicethe net force, the car’s accelerationa. becomes four times as much.b. becomes two times as much.c. stays the same.d. becomes half as much.

10. Gravitational force between two masses_____________ as the masses increase andrapidly ____________ as the distance betweenthe masses increases.a. strengthens, strengthensb. weakens, weakensc. weakens, strengthensd. strengthens, weakens

11. According to Newton’s third law, when a450 N teacher stands on the floor, that teacherapplies a force of 450 N on the floor, anda. the floor applies a force of 450 N on the

teacher.b. the floor applies a force of 450 N on the

ground.c. the floor applies a force of 450 N in all

directions.d. the floor applies an undetermined force

on the teacher.

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

1. Newton’s first law of motion states that anobjecta. at rest remains at rest unless it experi-

ences an unbalanced force.b. in motion maintains its velocity unless it

experiences an unbalanced force.c. will tend to maintain its motion unless it

experiences an unbalanced force.d. All of the above

2. The first law of motion applies toa. only objects that are moving.b. only objects that are not moving.c. all objects, whether moving or not.d. no object, whether moving or not.

3. A measure of inertia is an object’sa. mass.b. weight.c. velocity.d. acceleration.

4. Automobile seat belts are necessary forsafety because of a passenger’s a. weight.b. inertia.c. speed.d. gravity.

5. The newton is a measure of a. mass.b. length.c. force.d. acceleration.

UNDERSTANDING CONCEPTSUNDERSTANDING CONCEPTS

368

R E V I E WC H A P T E R 11

Understanding Concepts

1. d2. c3. a4. b5. c6. d7. b8. d9. b

10. d11. a12. d13. c14. c15. b

Using Vocabulary

16. Inertia is the behavior of matterthat defines mass in the laws ofmotion. It is important becauseinertia resists the effects of a netforce. The more mass or inertiaan object has, the smaller theacceleration for a given net force.

17. The newton is the unit of meas-ure for force in the SI system. 1 newton � 1 kg•m/s2


368

18. Free fall literally means falling freely. Fallingstraight down is free fall. An object in orbitfalls freely toward Earth but is also propelledforward. The combination of those twomotions is what keeps the object in orbit.Because we experience our weight by pressingagainst Earth or an object supported byEarth, when we fall freely, we don’t feel ourweight. We feel “weightless.” However,weightless actually means that there is noforce of gravity acting. (Weight is the force ofgravity acting on an object.) So there’s nosuch thing as actual weightlessness. Weight ofobjects that are very far from any otherobjects is very small, but it is not zero.

19. The wrestler will weigh less on the moonthan he does on Earth, because the forceexerted on him will be different at these loca-tions. Since he has the same mass in bothplaces, his weight will depend on the acceler-ation due to gravity at each location. Themoon causes a much smaller acceleration dueto gravity, so the wrestler will weigh lessthere.

C H A P T E R 11

R E V I E W

• Chapter Tests• Test Item Listing for ExamView® Test

Generator

GENERAL


Transparencies

TT Concept Mapping

12. An example of action-reaction forces isa. air escaping from a toy balloon.b. a rocket traveling through the air.c. a ball bouncing off a wall.d. All of the above

13. A baseball player catches a line-drive hit. Ifthe reaction force is the force of the player’sglove stopping the ball, the action force isa. the force of the player’s hand on the glove.b. the force applied by the player’s arm.c. the force of the ball pushing on the glove.d. the force of the player’s shoes on the dirt.

14. Which of the following objects has thesmallest amount of momentum?a. a loaded tractor-trailer driven at highway

speedsb. a track athlete running a racec. a motionless mountaind. a child walking slowly on the playground

15. The force that causes a space shuttle toaccelerate is exerted on the shuttle bya. the exhaust gases pushing against the

atmosphere.b. the exhaust gases pushing against the

shuttle.c. the shuttle’s engines.d. the shuttle’s wings.

16. What is inertia, and why is it important inthe laws of motion?

17. What is the unit of measure of force, andhow is it related to other measurement units?

18. What is the difference between free fall andweightlessness?

19. A wrestler weighs in for the first match onthe moon. Will the athlete weigh more orless on the moon than he does on Earth?Explain your answer by using the termsweight, mass, force, and gravity.

20. Describe a skydiver’s jump from the airplaneto the ground. In your answer, use the termsair resistance, gravity, and terminal velocity.

21. Give an example of projectile motion, andexplain how the example demonstrates thata vertical force does not influence horizontalmotion.

22. Force The net force acting on a 5 kg discus is50 N. What is the acceleration of the discus?

23. Force A 5.5 kg watermelon is pushed acrossa table. If the acceleration of the water-melon is 4.2 m/s2 to the right, what is thenet force exerted on the watermelon?

24. Force A block pushed with a force of 13.5 Naccelerates at 6.5 m/s2 to the left. What isthe mass of the block?

25. Force The net force on a 925 kg car is 37 Nas it pulls away from a stop sign. Find thecar’s acceleration.

26. Force What is the unbalanced force on a boyand his skateboard if the total mass of theboy and skateboard is 58 kg and their accel-eration is 0.26 m/s2 forward?

27. Force A student tests the second law ofmotion by accelerating a block of ice at a rateof 3.5 m/s2. If the ice has a mass of 12.5 kg,what force must the student apply to the ice?

28. Weight A bag of sugar has a mass of2.26 kg. What is its weight in newtons onthe moon, where the acceleration due togravity is one-sixth of that on Earth? (Hint:On Earth, g = 9.8 m/s2.)

29. Weight What would the 2.26 kg bag of sugarfrom the previous problem weigh on Jupiter,where the acceleration due to gravity is 2.36 times that on Earth?

BUILDING MATH SKILLSBUILDING MATH SKILLS

369

USING VOC ABULARYUSING VOC ABULARY

20. As a skydiver jumps from aplane, gravity pulls her down-ward. Air resistance pushesupward against the downwardmotion. The skydiver acceleratesdownward until the force of airresistance equals the downwardforce of gravity. Then the sky-diver stops accelerating and fallsdownward at a constant speed.This is called terminal velocity.

21. A thrown ball or an orbitingobject would be examples.(Accept all reasonable answers.)Projectile motion combines aconstant horizontal velocity withdownward vertical accelerationdue to the force of gravity. Thecurved path of projectiles fits thisassumption, providing proof thatvertical force does not affect hor-izontal motion. The force ofgravity downward cannot changethe horizontal velocity.

Building Math Skills

22. a � �mF

� � �550kNg� � 10 m/s2

23. F � ma � (5.5 kg)(4.2 m/s2) �23 N

24. m � �Fa� � �6

1.35.5m

N/s2� � 2.1 kg

25. a � �mF

� � �93275

Nkg� � 0.040 m/s2

away from the stop sign �4.0 � 10�2 m/s2

26. F � ma � 58 kg � 0.26 m/s2 �15 N

27. F � ma � 12.5 kg � 3.5 m/s2 �44 N

28. w � �m6g

� ��2.26 kg �

69.8 m/s2��

3.7 N

29. w � (mg)(2.36)� (2.26 kg �9.8 m/s2)(2.36) � 52.3 N

30. p � mv � (85 kg)(2.65 m/s) �225 kg•m/s north (or 230 kg•m/snorth using significant figures)

31. p � mv � (9.1 kg)(89 km/hr) �

��1010k0mm

��601

mhin��16

m0

isn

��

225 kg•m/s east (or 220 kg•m/seast using significant figures)


369

Section Questions1 1–9, 16–17, 22–27, 33, 37, 39, 452 10, 18–21, 28–29, 34–36, 38, 41–42,

443 11–15, 30–32, 40, 43

Assignment Guide

34. Critical Thinking What happens to the gravi-tational force between two objects if theirmasses do not change but the distancebetween them becomes four times as much?

35. Critical Thinking What will happen to thegravitational force between two objects ifone of the objects gains 50% in mass whilethe mass of the other object does notchange? Assume that the distance betweenthe two objects does not change.

36. Critical Thinking There is no gravity in outer space. Write a paragraph explaining whether this statement is true or false.

37. Problem Solving How will accelerationchange if the mass being accelerated is multi-plied by three but the net force is cut in half?

38. Problem Solving If Earth’s mass decreasedto half its current mass but its radius (yourdistance to its center) did not change, yourweight would be

a. twice as big as it is now.b. the same as it is now.c. half as big as it is now.d. one-fourth as big as it is now.

39. Applying Knowledge If you doubled the netforce acting on a moving object, how wouldthe object’s acceleration be affected?

40. Applying Knowledge For each pair, deter-mine whether the objects have the samemomentum. If the objects have differentmomentums, determine which object hasmore momentum.

a. a car and train that have the same velocityb. a moving ball and a still batc. two identical balls moving at the same

speed in the same directiond. two identical balls moving at the same

speed in opposite directions

30. Momentum Calculate the momentum of an85 kg man jogging north along the highwayat a rate of 2.65 m/s.

31. Momentum Calculate the momentum of a9.1 kg toddler who is riding in a car movingeast at 89 km/h.

32. Momentum Calculate the momentum of thefollowing objects:

a. a 65 kg skateboarder moving forward atthe rate of 3.0 m/s

b. a 20.0 kg toddler in a car traveling west at the rate of 22 m/s

c. a 16 kg penguin at rest d. a 2.5 kg puppy running to the right at

the rate of 4.8 m/s

33. Graphing An experiment is done with a labcart. Varying forces are applied to the cartand measured while the cart is accelerating.These forces are all in the direction of themovement of the cart, such as pushes tomake the cart accelerate. Each push is madeafter the cart has stopped from the previouspush. The following data were obtained inthe experiment.

Graph the data in the table. Place accelera-tion on the x-axis and applied force on they-axis. Because F � ma and therefore m � �

Fa

�,what does the line on the graph represent?Use your graph to determine the mass of thelab cart.

370

R E V I E WC H A P T E R 11

Trial Acceleration Applied force

1 0.70 m/s2 0.35 N

2 1.70 m/s2 0.85 N

3 2.70 m/s2 1.35 N

4 3.70 m/s2 1.85 N

5 4.70 m/s2 2.35 N

THINKING CR ITIC ALLYTHINKING CR ITIC ALLY

BUILDING GR APHING SKILLSBUILDING GR APHING SKILLS

WRITINGS K I L L

32. p � mva. (65 kg)(3.0 m/s forward) �

195 kg•m/s forwardb. (20.0 kg)(22 m/s west) �

440 kg•m/s westc. (16 kg)(0 m/s) � 0 kg•m/sd. (2.5 kg)(4.8 m/s to the right) �

12 kg•m/s to the right

Building Graphing Skills


370

39. The object’s acceleration would be doubled.40. a. train

b. ballc. equald. equal but opposite

C H A P T E R 11

R E V I E W

1.0 2.00Acceleration (m/s2 )

Forc

e (N

)

4.0 5.0

2.5

1.5

1.0

0.5

0

2.0

3.0

33. The slope of the line representsmass. From F � ma, and usingnumbers from the table, we learnthat mass � 0.50 kg

Thinking Critically

34. The gravitational force betweenthe two objects would become1/16 as much.

35. The gravitational force betweenthe two objects would become1.5 times greater.

36. The statement is false. Even inouter space, objects exert gravita-tional force on each other.

37. The acceleration will be 1/6 whatit was.

38. C is correct. When the masshalves, the mass in the numera-tor on both sides of the equationhalves. So, the gravitational forcewould half.

41. Locating Information Use the library and/orthe Internet to find out about the physiologi-cal effects of free fall. Also find out howastronauts counter the effects of living ina free-fall environment, sometimes calledmicrogravity. Use your information to pro-pose a minimum acceleration for a spaceshuttle to Mars that would minimize physio-logical problems for the crew, both duringflight and upon return to Earth’s atmosphere.

42. Interpreting Data At home, use a gardenhose to investigate the laws of projectilemotion. Design experiments to investigatehow the angle of the hose affects the rangeof the water stream. (Assume that the initialspeed of water is constant.) How can youmake the water reach the maximum range?How can you make the water reach thehighest point? What is the shape of thewater stream at each angle? Present yourresults to the rest of the class, and discussthe conclusions with regard to projectilemotion and its components.

43. Working Cooperatively Read the followingarguments about rocket propulsion. With asmall group, determine which of the follow-ing statements is correct. Use a diagram toexplain your answer.

a. Rockets cannot travel in space because there is nothing for the gas exiting the rocket to push against.

b. Rockets can travel because gas exerts an unbalanced force on the front of the rocket. This net force causes the acceleration.

c. Argument b can not be true. The action and reaction forces will be equal and opposite. Therefore, the forces will balance, and no movement will be possible.

44. Connection to Social Studies ResearchGalileo’s work on falling bodies. What did hewant to demonstrate? What theories did hetry to refute?

45. Concept Mapping Copy the concept mapbelow onto a sheet of paper. Write the cor-rect phrase in each lettered box.

371

DEVELOPING LI FE/WORK SKILLSDEVELOPING LI FE/WORK SKILLS INTEGR ATING CONCEPTSINTEGR ATING CONCEPTS

c.

a.

d. e.

unchanged

b.

which exist(s) in

which is Newton's

remains is changed by

An object'smotion

unless itexperiences

third lawof motion

mass andacceleration

which is Newton's which is Newton's

which isproportional to

www.scilinks.orgTopic: Rocket Technology SciLinks code: HK4123

Art Credits: Fig. 6-7, Stephen Durke/Washington Artists; Fig. 11-12, Craig Attebery/Jeff Lavaty ArtistAgent; Fig. 18, Gary Ferster; Fig. 22, Uhl Studios, Inc.; Lab (scales), Uhl Studios, Inc.

Photo Credits: Chapter Opener image of soccer ball by Japack Company/CORBIS; players collidingby Andy Lyons/Allsport/Getty Images; Fig. 1, SuperStock; Fig. 2, Sam Dudgeon/HRW; “QuickActivity,” Sam Dudgeon/HRW; “Science and the Consumer,” Nicholas Pinturas/Stone; Fig. 3, PeterVan Steen/HRW ; Fig. 4, Sam Dudgeon/HRW; Fig. 5, NASA; Fig. 6, James Sugar/Black Star; Fig. 7,NASA; Fig. 8, Toby Rankin/Masterfile; Fig. 11, Michelle Bridwell/Frontera Fotos; Fig. 12, RichardMegna/Fundamental Photographs; Fig. 16-17, David Madison; Fig. 19, Rene Sheret/Stone; Fig. 20,Yellow Dog Productions/Getty Images/Stone; Fig. 21, Michelle Bridwell/Frontera Fotos; Fig. 23A,Gerard Lacz/Animals Animals/Earth Sciences; Fig. 23B, Image Copyright ©(2004 PhotoDisc,Inc./HRW and Sam Dudgeon/HRW; Fig. 23C, Lance Schriner/HRW; “Design Your Own Lab,” and“Viewpoints,” HRW Photos.

Developing Life/Work Skills

41. Answers may vary. Accept allreasonable answers.

42. Answers may vary. Accept allreasonable answers.

43. a. cannot be correct becauserockets do travel in outerspace

b. is true; The gas in the tank ispushing in all directions. Somegas pushes forward on therocket, and some gas exitsthrough the back of the rocket.This results in an imbalancethat pushes the rocket forward.

c. cannot be true because action-reaction pairs never cancel

Integrating Concepts

44. He wanted to demonstrate thatthe gravitational acceleration isthe same for all objects. He wastrying to disprove the theory that heavier bodies fall faster. He conducted experiments withrolling and dropping balls. Heused logic, observations, andexperiments.

45. a. forceb. unbalanced forcec. action-reaction pairsd. first law of motione. second law of motion


371

Measuring Forces

� Procedure

Testing the Strength of a Human Hair1. Obtain a rubber band and a paper clip.

2. Carefully straighten the paper clip so that it forms adouble hook. Cut the rubber band and tie one end tothe ring stand and the other end to one of the paperclip hooks. Let the paper clip dangle.

3. In your lab report, prepare a table as shown below.

4. Measure the length of the rubber band. Record thislength in Table 1.

5. Hang a hooked mass from the lower paper clip hook.Supporting the mass with your hand, allow the rubberband to stretch downward slowly. Then remove yourhand carefully so the rubber band does not move.

6. Measure the stretched rubber band’s length. Recordthe mass that is attached and the rubber band’slength in Table 1. Calculate the change in length bysubtracting your initial reading of the rubber band’slength from the new length.

7. Repeat steps 5 and 6 three more times using differ-ent masses each time.

8. Convert each mass (in grams) to kilograms using thefollowing equation.

mass (in kg) � mass (in g) � 1000Record your answers in Table 1.

9. Calculate the force (weight) of each mass in newtonsusing the following equation.

force (in N) � mass (in kg) � 9.8 m/s2

Record your answers in Table 1.

How can you use a rubber band tomeasure the force necessary to break ahuman hair?

> Design anexperiment to test a hypothesis.

> Build and calibrate an instrumentthat measures force.

> Use your instrument to measure howmuch force it takes to stretch ahuman hair until it breaks.

comb or hairbrushmetal paper clips, large and smallmetric rulerpen or pencilrubber bands of various sizesstandard hooked masses ranging

from 10 to 200 g

USING SCIENTIFIC METHODS

Introduction

Objectives

Materials

372

Table 1 Calibration

Rubber-band Change in Mass on Mass on Forcelength (cm) length (cm) hook (g) hook (kg) (N)

0 0 0 0

MEASURING FORCES

Teacher’s NotesIn 1660, Robert Hooke(1635–1703) stated that for smalldeformations, the stretching of asolid body is directly proportionalto the applied force. Under theseconditions, the object will return to the original configuration afterthe load is removed. Hooke’s law is given as F=kx, where F is theapplied force; k is a constant, whichdepends on the material, its dimen-sions, and shape; and x is thechange in length.

Time Required 1 lab period

RatingsTEACHER PREPARATION 2STUDENT SETUP 2CONCEPT LEVEL 2CLEANUP 2

Skills Acquired• Collecting data• Communicating• Designing experiments• Experimenting• Identifying/Recognizing patterns• Inferring• Interpreting• Measuring• Organizing and analyzing data

The Scientific MethodIn this lab, students will:• Make observations• Form a hypothesis • Analyze the results • Draw conclusions• Communicate results

Safety CautionsHave students review safety guide-lines before working in the lab.

E A S Y H A R D

1 32 4E A S Y

372


Table 1: Sample Data Table Calibration

Rubber-band Mass on Mass on Forcelength (cm) hook (g) hook (kg) (N)

0 0 0 0

2.1 200 0.200 2.0

7.1 500 0.500 4.9

11.2 1000 1.000 9.8


Designing Your Experiment10. With your lab partner(s), devise a plan to

measure the force required to break ahuman hair using the instrument you justcalibrated. How will you attach the hair toyour instrument? How will you apply forceto the hair?

11. In your lab report, list each step you willperform in your experiment.

12. Have your teacher approve your plan beforeyou carry out your experiment.

Performing Your Experiment13. After your teacher approves your plan, gently

run a comb or brush through a group member’s hair severaltimes until you find a loose hair at least 10 cm long that youcan test.

14. In your lab report, prepare a data table similar to the oneshown at right to record your experimental data.

15. Perform your experiment on three different hairs from thesame person. Record the maximum rubber-band length before the hair snaps for each trial in Table 2.

� Analysis1. Plot your calibration data in your lab

report in the form of a graph like theone shown at right. On your graphdraw the line or smooth curve that fitsthe points best.

2. Use the graph and the length of the rubber band for each trial of your experiment to determine the force that was necessary to break each of the three hairs. Record your answers in Table 2.

� Conclusions3. Suppose someone tells you that your results are flawed because you measured

length and not force. How can you show that your results are valid?

373

Forc

e (N

)

Length (cm)

10 11 12 13 16

1.00

0.80

0.60

0.40

0.20

1514 17

Table 2 Experimentation

Rubber-band ForceTrial length (cm) (N)

Hair 1

Hair 2

Hair 3

Tips and TricksThe rubber bands used in thisexperiment can be compared tospring balances or car shockabsorbers.

Answers to Analysis1. Answers will vary. Sample data is

given in the graph.2. Answers will vary. Sample data is

given in the data table. In the sam-ple data table, length is given asthe change in length. The absolutelength can be used also. The forceis extrapolated from the sampledata graph.

Conclusions3. Although length was measured

and not force, the applied force isproportional to the change inlength. Therefore, length and forceare directly related and to measureone is to have a way to know theother.

373

• Datasheet Measuring Forces

• Observation Lab Observing theConservation of Momentum

• CBL™ Probeware Lab DeterminingYour Acceleration on a Bicycle

GENERAL


Trial Rubber-band Forcelength (cm) (N)

Hair 1 1.1 1

Hair 2 1.1 1

Hair 3 1.2 1

Table 2 Sample Data TableExperimentation

Forc

e (N

)

0 2

109876543210

664 8 10 12

Length (cm)

Sample Data Graph

373A Chapter 11 • Forces

Continuation of Answers

Continuation of Answers from p. 351

Section 1 Review

4. a � �mF

� � �5185

kNg� � 0.26 m/s2 forward

5. F � ma � 1250 kg � 40 m/s2 � 50,000 N � 5.0 � 104 N

6. m � �Fa� � �4

3m4 N

/s2�� 8.5kg

Logical


Section 2 Review

4. Orbital motion has two components—horizontal and vertical.Horizontal motion propels the object forward, and vertical free fall pulls the object downward toward the center of gravity of thelarger mass.

5. Answers may vary, but they should state something similar to thefollowing: Newton’s second law shows that acceleration dependson both force and mass. A heavier object experiences a greatergravitational force than a lighter object (as you can see from thelaw of universal gravitation). But a heavier object is also harder toaccelerate because it has more mass. The extra mass of the heavyobject exactly compensates for the additional gravitational force.Since F � ma (or a � F/m), if F is increased at the same rate as m,then a remains the same.

6. The force of gravity is inversely proportional to the square of dis-tance. Since the distance is made twice as close, the force of gravitywill be four times as great (the square of 2), or 4 million N.


LS



Quick Lab

The reaction forces that correspond with each force are: theupward force on the Earth from the mass of the spring scale, theupward force on the 2 kg mass, and the downward pull on the topspring scale.

The pairs are much easier to identify if students list all forcesacting on each object separately. Scan the lists for pairs like: Apulls down on B, and B lifts up on A.

2. Students should be able to determine that the reading on the topspring scale should be the weight of the 2 kg mass plus the weightof the other spring scale. The reading on the bottom spring scaleshould be the weight of the 2 kg mass. Since the bottom springscale is pulling down on the top spring scale with a force equal toits weight plus the weight of the 2 kg mass, the top scale mustexert an upward force on the bottom scale that is equal to theweight of the bottom scale plus the 2 kg mass.Logical

Section 3 Review

6. p � mv � (1 kg)(12 m/s) � 12 kg•m/s eastward


LS

This page intentionally left blank

374

whether or not to wear a helmet and to sufferany consequences?

But are the consequences limited to therider? Who will pay when the rider gets hurt?Should the rider bear the cost of an injury thatcould have been prevented?

Is this an issue of public health or privaterights? What do you think?

In some communities, bicyclists are re-quired by law to wear a helmet and can beticketed if they do not. Few people dispute

the fact that bicycle helmets can save liveswhen used properly.

But others say that it is a matter of privaterights and that the government should not in-terfere. Should it be up to bicyclists to decide

> FROM: Jocelyn B., Chicago, IL----------------------------------------------They should treat helmets the same way they treat seatbelts. I was in a tragic bike accident when I was 7. I wasjerked off my bike, and I slid on the glass-laden concrete.To make a long story short, I think there should be a hel-met law because people just don’t know the danger.

Should Bicycle HelmetsBe Required by Law?

viewpointsviewpointsviewpoints

> FROM: Chad A., Rochester, MN-------------------------------------------More and more people are getting headinjuries every year because they do notwear a helmet. Now-adays helmets look socool—I wouldn’t beashamed to wear one. > FROM: Laurel R., Coral Springs, FL

---------------------------------------------------I believe that this is a public issue only for

people under the age of 12. Children 12

and under still need guidance and direction

about safety, and they are usually the ones

riding their bicycles out in the road or in

traffic. Often they don’t pay attention to

cars or other motor vehicles around them.

RequireBicycleHelmets

Require Bicycle Helmets

SHOULD BICYCLE HELMETSBE REQUIRED BY LAW?

1. Critiquing ViewpointsStudents’ analyses of a single argu-ment’s weak points may vary. Besure that student responses clearlyidentify a weakness and respondin some way that provides sup-port. Possible responses for eachof the viewpoints in the featureare listed below. (Note that stu-dents should analyze only one ofthe following.)Chad A.: Some objections to hel-met use are more serious thanappearance, such as decreases inperipheral vision and ability tohear.

But bicycle helmets can stillprotect you from serious headinjuries.Laurel R.: Ticketing children isnot likely to change matters.

But children are at greater riskbecause they are more likely to beriding bicycles and have less expe-rience.Jocelyn B.: The unfortunate acci-dent described happened to oneperson. That does not necessarilymean everyone’s at risk.

But this single incident doesshow that accidents that could beless tragic with bicycle helmets dooccur, even when people don’texpect them.

Megan J. and Heather R.: The argument thatindividual rights exceed the public health bene-fits do not take into account the fact that pre-ventable injuries are a waste of money forinsurance companies, hospitals, the govern-ment, and taxpayers.

But laws limiting individual freedom canhave unintended consequences.Melissa F.: If people can’t afford to bicyclesafely and with helmets, perhaps they should-n’t bicycle at all.

But is it right to deny someone access tosuch a simple vehicle because of their financialsituation?

2. Critiquing Viewpoints Students’ analyses of strong points in opposingarguments may vary. Be sure that studentresponses clearly identify the strong points andrespond in some way that provides support forthe opposite point of view. Possible responsesfor each of the viewpoints in the feature arelisted below. (Note that students should ana-lyze only one of the following.)Chad A. and Jocelyn B.: More and moreinjuries that are preventable are occurring.

But the government should not get involvedin every risk someone takes.


374

ViewpointsViewpoints


Your Turn Your Turn >>1. Critiquing Viewpoints Select one of

the statements on this page that youagree with. Identify and explain atleast one weak point in the statement.What would you say to respond tosomeone who brought up this weakpoint as a reason you were wrong?

2. Critiquing Viewpoints Select one ofthe statements on this page that youdisagree with. Identify and explain atleast one strong point in the state-ment. What would you say to respondto someone who brought up thispoint as a reason they were right?

3. Creative Thinking Suppose you live in a community that does not have abicycle helmet law. Design a campaignto persuade people to wear helmets,even though it isn’t required by law.Your campaign could include bro-chures, posters, and newspaper ads.

4. Acquiring and Evaluating Data When arider falls off a bicycle, the rider contin-ues moving at the speed of the bicycleuntil the rider strikes the pavement andslows down rapidly. For bicycle speedsranging from 5.0 m/s to 25.0 m/s, calculate what acceleration would berequired to stop the rider in just 0.50 s.How large is the force that must beapplied to a 50.0 kg rider to cause thisacceleration? Organize your data andresults in a series of charts or graphs.

> FROM: Megan J., Bowling Green, KY-----------------------------------------------------Although wearing a bicycle helmet can be

considered a matter of public health, the

rider is the one at risk. It is a personal

choice, no matter

what the public

says.> FROM: Melissa F., Houston, TX-------------------------------------------Bicycle helmets shouldn’t be requiredby law. Helmets are usually a littleover $20, and if you have five kids,the helmets alone cost $100. You’dstill have to buy the bikes.

> FROM: Heather R., Rochester, MN---------------------------------------------------It has to do with private rights. The police have more serious issues to deal with, like violent crimes.Bicycle riders should choose whether or not theywant to risk their life by riding without a helmet.

Don’t Require bicycle Helmets

Don’t RequireBicycle Helmets

Should helmets be required by law? Why or whynot? Share your views on this issue and learn aboutother viewpoints at the HRW Web site.

TOPIC: Bicycle HelmetsGO TO: go.hrw.comKEYWORD: HK4 Helmet

Laurel R.: Children need to beprotected the most from such acci-dents.

But because they are children,they can’t force their parents toget them helmets anyway.Megan J.: Individual rights areimportant.

But when an individual decidesto risk his life, others do have theright to try to stop him.Melissa F.: Bicycle helmets are notcheap.

But far more money can besaved by preventing a costly acci-dent.Heather R.: This is not likely to bea high-priority for police enforce-ment.

Many other laws are rarelyenforced, but have been institutedso society can go on record infavor of or opposing something.

3. Creative Thinking Student answers will vary.Evaluate students’ plans for cam-paigns using a scale of 1–5 pointsfor each of the following: thoughtbehind the planning of the adver-tising strategy, clarity in the adver-tising message, persuasiveness,creativity, and effort. (25 totalpossible points)

4. Acquiring and Evaluating Data Student answers should indicatethat an acceleration of 10 m/s2

(nearly the same as gravity) and aforce of 500 N would be requiredto stop the slowest bicyclist, andan acceleration of 50 m/s2 and2500 N would be required to stopthe fastest one.

Students should probablychoose a bar graph to displaytheir results if they evaluated spe-cific speeds. Some may choose toshow all values in between themaximum and minimum by plot-ting a line graph.

Evaluate students’ charts orgraphs using a scale of 1–5 pointsfor each of the following: accuracyof calculation, accuracy of graph-ing, neatness of graph, explana-tion of significance of data, andeffort. (25 total possible points)

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