The Laws of Motion · PDF file · 2015-09-24SECTION 1 The First Two Laws of Motion 101 Safety BeltsIn Figure 5the crash test dummies are restrained with safety belts. As a result,

96

sections

1 The First Two Laws of Motion

2 GravityLab Gravity and Air Resistance

3 The Third Law of MotionLab The Momentum of Colliding Objects

Virtual Lab How is momentum conservedin a vehicle collision?

Who’s a dummy?Crunch! This test dummy would have someexplaining to do if this were a traffic acci-dent. But in a test crash, the dummy playsan important role. The forces acting on itduring a crash are measured and analyzedin order to learn how to make cars safer.

Explain which would be a safercar—a car with a front that crumples in a crash, or one witha front that doesn’t crumple.

Science Journal

The Laws ofMotion

Tim Wright/CORBIS

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97

The Laws of Motion Make thefollowing Foldable to help youbetter understand Newton’slaws of motion as you read thechapter.

Fold the top of a vertical piece ofpaper down and the bottom up todivide the paper into thirds.

Unfold and label the rows First Law,Second Law, Third Law.

Find Main Ideas As you read the chapter, listthe main ideas in the sections on the laws ofmotion under the appropriate column.

STEP 2

STEP 1

The Force of GravityThe force of Earth’s gravity pulls all objectsdownward. However, objects such as rocksseem to fall faster than feathers or leaves. Doobjects with more mass fall faster?

1. Measure the mass of a softball, a tennisball, and a flat sheet of paper. Copy thedata table below and record the masses.

2. Drop the softball from a height of 2.5 mand use a stopwatch to measure the timeit takes for the softball to hit the floor.Record the time in your data table.

3. Repeat step 2 using the tennis ball andthe flat sheet of paper. Record the timesin your data table.

4. Crumple the flat sheet of paper into a ball,and measure the time for the crumpledpaper to fall 2.5 m. Record the time inyour data table.

5. Think Critically Write a paragraphcomparing the times it took each item tofall 2.5 m. From your data, infer if thespeed of a falling object depends on theobject’s mass.

Start-Up Activities

Preview this chapter’s contentand activities at gpescience.com

Falling Object DataObject Mass Time

Softball

Tennis ball

Flat paper

Crumpled paper

SecondLaw

ThirdLaw

FirstLaw

Tim Wright/CORBIS

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98 CHAPTER 4 The Laws of Motion

The First Two Lawsof Motion

Reading Guide

■ Define Newton’s first law ofmotion.

■ Explain how inertia and mass arerelated.

■ Define Newton’s second law ofmotion.

■ Apply Newton’s second law ofmotion.

Newton’s first two laws of motionexplain how forces cause the motionof objects to change.

Review Vocabularynet force: the combination of allforces acting on an object

New Vocabulary

• first law of motion

• inertia

• second law of motion

Newton’s Laws of MotionWhen you lift a backpack, you exert a force on an object and

cause it to move. The backpack initially was at rest. The forceyou exerted caused its velocity to change. But if you push down-ward on a table, the table doesn’t move. The force you applieddid not cause the velocity of the table to change. How are forcesand motion related?

The British scientist Isaac Newton, who lived from 1642 to1727, published a set of three rules in 1687 that explained howforces and motion are related. These three rules are calledNewton’s laws of motion. They apply to the motion of all objectsyou encounter every day, such as those in Figure 1, as well as tothe motion of planets, stars, and galaxies.

The First Law of MotionNewton’s first law of motion describes how an object

moves when the net force acting on it is zero. According toNewton’s first law of motion, if the net force acting on anobject is zero, the object remains at rest, or if the object is mov-ing, it continues moving in a straight line with constant speed.The first law of motion means that if the forces acting on anobject are balanced, then the velocity of the object doesn’tchange.

Figure 1 Newton’s laws ofmotion apply to all objects, includ-ing the volleyball and the volley-ball players.

David Young-Wolff/PhotoEdit, Inc.

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SECTION 1 The First Two Laws of Motion 99

Only Unbalanced Forces Change Velocity The first lawof motion connects forces with changes in motion. For example,suppose a skateboard is at rest. The skateboard doesn’t moveuntil you give it a push. Then the velocity of the skateboardincreases while you are pushing it. The forces on the skateboardare unbalanced while you are pushing on it. As a result, thevelocity of the skateboard changes as its speed increases.

However, after the skateboard leaves your hand, it slowsdown and stops. It might seem that the skateboard stops mov-ing because there are no forces acting on it. However, there is anunbalanced frictional force that acts on the skateboard as it rolls.This is the force that causes the skateboard to stop. The unbal-anced frictional force causes the velocity of the skateboard tochange as its speed decreases. The velocity of an object changesonly when there are unbalanced forces acting on it.

Inertia and MassAll objects have a property called inertia. Inertia is the ten-

dency of an object to resist a change in its motion. The dirtbike in Figure 2 has inertia that tends to keep it moving with aconstant velocity when its rider tries to steer around a curve.The inertia of an object depends on the object’s mass. Thegreater the mass of an object, the greater its inertia.

For example, a bowling ball has more mass than a volleyball.Which would be harder to stop—a volleyball or a bowling ballrolling at the same speed? You would have to exert a greaterforce on the bowling ball to make it stop. The bowling ball hasmore inertia than the volleyball because it has more mass.

How does the inertia of an object depend on theobject’s mass?

Observing InertiaProcedure1. Create an inclined plane

using a board andtextbooks.

2. Place a small object in acart and let the cart rolldown the plane. Recordthe results.

3. Secure the object in the cartwith rubber bands. Let thecart roll down the plane andrecord your results.

Analysis1. Identify the forces acting

on the object in the cart inboth runs.

2. Explain how safety beltsreduce the risk of injury ina car crash.

Figure 2 Inertia causes the biketo move in a straight line despitethe efforts of the rider to steer thebike around the curve.

Neal Haynes/Rex USA, Ltd.

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Inertia and the First Law of Motion According to thefirst law of motion, the velocity of an object doesn’t changeunless the forces acting on the object are unbalanced. In otherwords, if you observe a change in an object’s velocity, you knowan unbalanced force acted on it. This is similar to the definitionof inertia—an object resists a change in its motion. As a result,the first law of motion sometimes is called the law of inertia.

Inertia and the first law of motion explain why the boxes inFigure 3 slide off the cart when the cart comes to a sudden stop.The student applies an unbalanced force to the cart that makesit stop. However, the inertia of the boxes causes them to keepmoving even after the cart stops.

What happens in a crash?The first law of motion can explain what happens in a car

crash. When a car traveling 50 km/h collides head-on withsomething solid, the car crumples, slowsdown, and stops within about 0.1 s. Anypassenger not wearing a safety belt con-tinues to move forward at the same speedthe car was traveling. Within about 0.02 safter the car stops, unbelted passengersslam into the dashboard, windshield, orsteering wheel, as shown in Figure 4.Passengers in the back seat might slaminto the backs of the front seats. Becauseof their inertia, they are traveling at thecar’s original speed of 50 km/h—aboutthe same speed they would reach fallingfrom a three-story building.

Figure 3 The inertia of theboxes causes them to keep movingafter the cart has been brought toa sudden stop.Describe the velocity of the boxesjust after the cart stops.

Figure 4 This crash test dummyis not restrained in this low-speedcrash. Inertia causes the dummy toslam into the steering wheel.

(tl, tr)Bob Daemmrich, (b)courtesy Insurance Institute for Highway Safety

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Safety Belts In Figure 5 the crash testdummies are restrained with safety belts. Asa result, they slow down at the same ratethat the car slows down. However, theforce exerted on a person that slows from 50km/h to 0 km/h in 0.1 s is about 14 times aslarge as the force of gravity on the person. Tofurther reduce the force acting on a person,the seat belt loosens slightly, increasing thetime it takes to slow the person. Increasingthe time needed to stop reduces the forceexerted on the person. The safety belt alsoprevents the person from being thrown outof the car. Car-safety experts say that abouthalf the people who die in car crashes wouldsurvive if they wore safety belts.

What are two advantages of wearing a safetybelt in a crash?

The Second Law of MotionAccording to Newton’s first law of motion, unbalanced

forces cause the velocity of an object to change. Newton’s sec-ond law of motion describes how the net force on an object, itsmass, and its acceleration are related.

Force and Acceleration What’s different about throwing aball horizontally as hard as you can and tossing it gently? Whenyou throw hard, the net force on the ball is greater than whenyou toss it. Also, the ball has a greater velocity when it leavesyour hand. As a result, the hard-thrown ball has a greater changein velocity, and this change can occur over a shorter period oftime. Recall that acceleration is the change in velocity divided bythe time needed for the change to occur. So, a hard-thrown ballhas a greater acceleration than a gently-thrown ball.

Mass and Acceleration If you throw a baseball and a soft-ball with the same amount of force, why does the baseball movefaster? A softball has more mass than a baseball. Even though thenet force exerted on both balls is the same, the softball has lessvelocity when it leaves your hand than the baseball does. If ittakes the same amount of time to throw both balls, the acceler-ation of the softball is less than that of the baseball. So, the accel-eration of an object depends on its mass, as well as the net forceexerted on it. Net force, mass, and acceleration are related.

Figure 5 These crash test dum-mies were restrained with safetybelts in this crash. This preventedthe dummies from hitting thedashboard or windshield.

Topic: Motion in SportsVisit for Weblinks to information aboutmethods used to analyze themotions of athletes.

Activity Choose a sport andwrite a report on how analyzingthe motions involved in the sportcan improve performance andreduce injuries.

gpescience.com

Donald Johnston/Stone

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The Second Law of MotionNewton’s second law of motion states that the acceleration

of an object is in the same direction as the net force on theobject, and that the acceleration can be calculated from the fol-lowing equation:

Newton’s Second Law of Motion

acceleration (in meters/second2) �net force (in newtons)

mass (in kilograms)

a � Fnet

m

THE ACCELERATION OF A SLED You push a friend on a sled. Your friend and the sled together

have a mass of 70 kg. If the net force on the sled is 35 N, what is the sled’s acceleration?

known values and the unknown value

Identify the known values:

The net force on the sled is 35 N Fnet � 35 N

Your friend and the sled together have a mass of 70 kg m � 70 kg

Identify the unknown value:

What is the sled’s acceleration? a � ? m/s2

the problem

Substitute the known values Fnet � 35 N and m = 70 kg into the equation for Newton’s

second law of motion:

a � �F

mnet� � �

7305

kNg

� � 0.5 �kNg� � 0.5 �

kg

s2m� � �

k1�g

� 0.5 m/s2

your answer

Does your answer seem reasonable? Check your answer by multiplying the acceleration

you calculated by the mass given in the problem. The result should be the net force

given in the problem.

CHECK

SOLVE

means

means

means

IDENTIFY

Solve a Simple Equation

1. If the mass of a helicopter is 4,500 kg, and the net force on it is 18,000 N, what isthe helicopter’s acceleration?

2. What is the net force on a dragster with a mass of 900 kg if its acceleration is 32.0 m/s2?

3. A car is being pulled by a tow truck. What is the car’s mass if the net force on the car is3,000 N and it has an acceleration of 2.0 m/s2?

For more practice problems go to page 879, and visit Math Practice at .gpescience.com

(t)Bob Daemmrich, (b)Peter Fownes/Stock South/PictureQuest

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Calculating Net Force with the Second Law Newton’ssecond law also can be used to calculate the net force if massand acceleration are known. To do this, the equation forNewton’s second law must be solved for the net force, F. To solvefor the net force, multiply both sides of the above equation bythe mass:

The mass, m, on the left side cancels, giving the equation:

For example, when the tennis player in Figure 6 hits a ball, theball might be in contact with the racket for only a few thou-sandths of a second. Because the ball’s velocity changes oversuch a short period of time, the ball’s acceleration could be ashigh as 5,000 m/s2. The ball’s mass is 0.06 kg, so the net forceexerted on the ball would be:

Fnet � ma � (0.06 kg) (5,000 m/s2) � 300 kg m/s2 � 300 N

Fnet � ma

Figure 6 The tennis racketexerts a force on the ball thatcauses it to accelerate.

SummaryInertia and the First Law of Motion

• According to Newton’s first law of motion, thevelocity of an object does not change unlessan unbalanced net force acts on the object.

• The inertia of an object is the tendency of theobject to resist a change in motion.

• The larger the mass of an object, the greaterits inertia.

• In a car crash, inertia causes an unrestrainedpassenger to continue moving at the speed ofthe car before the crash.

The Second Law of Motion

• The acceleration of an object depends on themass of the object and the net force exertedon the object.

• According to Newton’s second law of motion,the acceleration of an object is in the directionof the net force on the object, and can becalculated from this equation:

a � �F

mnet�

6. Calculate Mass You push yourself on a skateboardwith a force of 30 N and accelerate at 0.5 m/s2. Findthe mass of you and the skateboard together.

7. Calculate Net Force You push a book that has a massof 2.0 kg so that it has an acceleration of 1.0 m/s2. What is the net force on the book?

Self Check1. Infer whether the inertia of an object changes as the

object’s velocity changes.

2. Determine whether or not there must be an unbal-anced force acting on any object that is moving.Explain.

3. Determine whether or not there can be forces acting onan object that is at rest. Explain.

4. Infer the net force on a refrigerator if you push on therefrigerator and it doesn’t move.

5. Think Critically Describe three situations in which aforce changes the velocity of an object. Let at least oneof the situations involve the force due to gravity.

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What is gravity?There’s a lot about you that’s attractive. At this moment, you

are exerting an attractive force on everything around you—yourdesk, your classmates, even the planet Jupiter millions of kilo-meters away. It’s the attractive force of gravity.

Anything that has mass is attracted by the force of gravity.Gravity is an attractive force between any two objects thatdepends on the masses of the objects and the distance betweenthem. This force increases as the mass of either object increases,or as the objects move closer, as shown in Figure 7.

You can’t feel any gravitational attraction between you andthis book because the force is weak. Only Earth is both closeenough and has a large enough mass that you can feel its gravi-tational attraction. While the Sun has much more mass thanEarth, the Sun is too far away to exert a noticeable gravitationalattraction on you. And while this book is close, it doesn’t haveenough mass to exert an attraction you can feel.

Gravity—A Basic Force Gravity is one of the four basicforces. The other basic forces are the electromagnetic force, thestrong nuclear force, and the weak nuclear force. The twonuclear forces only act on particles in the nuclei of atoms.Electricity and magnetism are caused by the electromagneticforce. Chemical interactions between atoms and molecules alsoare due to the electromagnetic force.

GravityReading Guide

■ Describe the gravitational force.■ Distinguish between mass and

weight.■ Explain why objects that are

thrown will follow a curved path.■ Compare circular motion with

motion in a straight line.

There is a gravitational forcebetween you and every other objectin the universe.

Review Vocabulary acceleration: the rate of change ofvelocity which occurs when anobject changes speed or direction

New Vocabulary

• gravity

• weight

• centripetal acceleration

• centripetal force

Figure 7 The gravitational forcebetween two objects depends ontheir masses and the distancebetween them.

Increasing the mass of eitherobject increases the gravitationalforce between them.

If the objects are closer together,the gravitational force betweenthem increases.

SECTION 2 Gravity 105

The Law of Universal GravitationFor thousands of years, people have observed the night sky

and collected data on the motions of the stars and planets. IsaacNewton used some of these data on the motions of planets toformulate the law of universal gravitation, which he publishedin 1687. This law can be written as the following equation.

In this equation G is a constant called the universal gravita-tional constant, and d is the distance between the two masses,m1 and m2. The law of universal gravitation enables the force ofgravity to be calculated between any two objects if their massesand the distance between them are known.

The Range of Gravity According to the law of universalgravitation, the gravitational force between two massesdecreases rapidly as the distance between the masses increases.For example, if the distance between two objects increases from1 m to 2 m, the gravitational force between them becomes onefourth as large. If the distance increases from 1 m to 10 m, thegravitational force between the objects is one hundredth aslarge. However, no matter how far apart two objects are, thegravitational force between them never completely disappears.As a result, gravity is called a long-range force.

Why is gravity called a long-range force?

Finding Other Planets Earth’s motionaround the Sun is affected by the gravita-

tional pulls of the other planets in the solar system. In the sameway, the motion of every planet in the solar system is affected bythe gravitational pulls of all the other planets.

In the 1840s the most distant planet known was Uranus. Themotion of Uranus calculated from the law of universal gravitationdisagreed slightly with its observed motion. Some astronomerssuggested that there must be an undiscovered planet affecting themotion of Uranus. Using the law of universal gravitation andNewton’s laws of motion, two astronomers independently calcu-lated the orbit of this planet. As a result of these calculations, theplanet Neptune, shown in Figure 8, was found in 1846.

Topic: Gravity on OtherPlanetsVisit for Weblinks to information about thegravitational acceleration nearthe surface of different planetsin the solar system.

Activity Make a graph with thegravitational acceleration on the y-axis, and the planet’s mass onthe x-axis. Infer from your graphhow the gravitational accelerationdepends on a planet’s mass.

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Figure 8 The location of theplanet Neptune in the night skywas correctly predicted usingNewton’s laws of motion andthe law of universal gravitation.

The Law of Universal Gravitation

gravitational force � (constant) �

F � G �m

d1m

22

�

(mass 1) � (mass 2)��

(distance)2

StockTrek/CORBIS



Earth’s Gravitational AccelerationIf you dropped a bowling ball and a marble at the same time,

which would hit the ground first? Suppose the effects of airresistance are small enough to be ignored. When all forcesexcept gravity acting on an a falling object can be ignored, theobject is said to be in free fall. Then all objects near Earth’s sur-face would fall with the same acceleration, just like the two ballsin Figure 9.

Close to Earth’s surface, the acceleration of an object in freefall is 9.8 m/s2. This acceleration is the gravitational accelerationand is given the symbol g. By the second law of motion, the grav-itational force exerted by Earth on a falling object is the object’smass times the gravitational acceleration. The gravitational forcecan be calculated from this equation:

For example, the gravitational force on a skydiver with a massof 60 kg would be

Weight Even if you are not falling, the force due to Earth’sgravity still is pulling you downward. If you are standing on afloor, the net force on you is zero. The force due to Earth’s grav-ity pulls you downward, but the floor exerts an upward force onyou that balances gravity’s downward pull.

Whether you are standing, jumping, or falling, Earth exerts agravitational force on you. The gravitational force exerted on anobject is called the object’s weight. The weight of an object onEarth is equal to the gravitational force exerted by Earth on theobject. As a result, near Earth’s surface an object’s weight can becalculated from this equation:

On Earth, where g equals 9.8 m/s2, a cassette tape weighsabout 0.5 N, a backpack full of books could weigh 100 N, and ajumbo jet weighs about 3.4 million N.

F � mg � (60 kg) (9.8 m/s2) � 588 N

Figure 9 Time-lapsephotography shows that twoballs of different masses fall atthe same rate.

Weight Equation

weight (N) � mass (kg) � gravitational acceleration (m/s2)

W � mg

Gravitational Force Equation

gravitational force (N)� mass (kg) � gravitational acceleration (m/s2)

F � mg

Peticolas-Megna/Fundamental Photographs


Weight and Mass Weight and mass are not the same. Weightis a force and mass is a measure of the amount of matter anobject contains. However, according to the weight equation onthe previous page, weight and mass are related. Weight increasesas mass increases.

The weight of an object usually is the gravitational forcebetween the object and Earth. But the weight of an object canchange, depending on the gravitational force on the object. Forexample, the acceleration due to gravity on the Moon is1.6 m/s2, about one sixth as large as Earth’s gravitational accel-eration. As a result, a person, like the astronaut in Figure 10,would weigh only about one sixth as much on the Moon as onEarth. Table 1 shows how various weights on Earth would bedifferent on the Moon and some of the planets.

How are weight and mass related?

Weightlessness and Free Fall You’ve probably seen pictures of astronauts and equipment

floating inside the space shuttle. Any item that is not fasteneddown seems to float throughout the cabin. They are said to beexperiencing the sensation of weightlessness.

However, for a typical mission, the shuttle orbits Earth at analtitude of about 400 km. According the law of universal gravi-tation, at 400-km altitude the force of Earth’s gravity is about90 percent as strong as it is at Earth’s surface. So an astronautwith a mass of 80 kg still would weigh about 700 N in orbit,compared with a weight of about 780 N at Earth’s surface.

Figure 10 On the Moon, thegravitational force on the astro-naut is less than it is on Earth. As aresult, the astronaut can takelonger steps and jump higher thanon Earth.Describe how the astronaut’s massand weight on the Moon compareto his mass and weight on Earth.

Table 1 Weight Comparison Table

Weight on Weight on Other Bodies in the Solar System (N) Earth (N) Moon Venus Mars Jupiter Saturn

75 12 68 28 190 87

100 17 90 38 254 116

150 25 135 57 381 174

500 84 450 190 1,270 580

700 119 630 266 1,778 812

2,000 333 1,800 760 5,080 2,320

NASA


Floating in Space Why do objects seem weightless in orbit?Think about measuring your weight. When you stand on a scale,as in Figure 11A, the net force on you is zero. The scale exerts anupward force on you equal to your weight. Now suppose youstand on a scale in an elevator that is in free fall, as shown inFigure 11B. Then the only force acting on you is the gravita-tional force. You and the scale no longer exert forces on eachother. The scale would show zero weight, even though the grav-itational force on you hasn’t changed.

What is the only force on an object in free fall?

A space shuttle in orbit is in free fall, but it is falling aroundEarth, rather than straight downward. Everything in the orbit-ing space shuttle is falling around Earth at the same rate, in thesame way you and the scale were falling in the elevator. Objectsin the shuttle seem to be floating because they are all falling withthe same acceleration.

Projectile MotionIf you’ve tossed a ball to someone, you’ve probably noticed

that thrown objects don’t always travel in straight lines. Theycurve downward. Anything that’s thrown or shot through the airis called a projectile. Earth’s gravity causes projectiles to follow acurved path.

Figure 11 The boy and thescale no longer exert forces oneach other when they both are infree fall. As a result, the boy seemsto be weightless.

When the elevator is stationary,the scale shows the boy’s weight.

If the elevator were in free fall, the scalewould show a zero weight.

Gravity and Earth’sAtmosphere Apart fromsimply keeping your feeton the ground, gravity isimportant for life on Earthfor other reasons, too.Because Earth has a suffi-cient gravitational pull, itcan hold around it theoxygen/nitrogen atmos-phere necessary for sus-taining life. Research otherways in which gravity hasplayed a role in theformation of Earth.


Horizontal and Vertical Motions When you throw a ball,like the pitcher in Figure 12, the force exerted by your handpushes the ball forward. This force gives the ball horizontalmotion. After you let go of the ball, no force accelerates it for-ward, so its horizontal velocity is constant, if you ignore airresistance.

However, when you let go of the ball, gravity can accelerateit downward, giving it vertical motion. Now the ball has con-stant horizontal velocity but increasing vertical velocity. Gravityexerts an unbalanced force on the ball, changing the direction ofits path from only forward to forward and downward. The resultof these two motions is that the ball appears to travel in a curve,even though its horizontal and vertical motions are completelyindependent of each other.

Horizontal and Vertical Distance If you were to throw aball as hard as you could from shoulder height in a perfectly hori-zontal direction, would it take longer to reach the ground than ifyou dropped a ball from the same height? Surprisingly, it won’t.A thrown ball and one dropped will hit the ground at the sametime. Both balls in Figure 13 travel the same vertical distance inthe same amount of time. However, the ball thrown horizontallytravels a greater horizontal distance than the ball that is dropped.

Figure 12 The pitcher gives the ball ahorizontal motion. Gravity, however, ispulling the ball down. The combination ofthese two motions causes the ball to movein a curved path.

Figure 13 Multiflash photogra-phy shows that each ball has thesame acceleration downward,whether it’s thrown or dropped.

Forceofgravity

Force frompitcher's hand

Forceofgravity

(tl)KS Studios, (tr)David Young-Wolff/PhotoEdit, (b)Richard Megna/Fundamental Photographs


Centripetal ForceLook at the path the ball follows as it travels through the

curved tube in Figure 14. The ball may accelerate in the straightsections of the pipe maze if it speeds up or slows down. However,when the ball enters a curve, even if its speed does not change, itis accelerating because its direction is changing. When the ballgoes around a curve, the change in the direction of the velocity istoward the center of the curve. Acceleration toward the center ofa curved or circular path is called centripetal acceleration.

According to the second law of motion, when the ball hascentripetal acceleration, the direction of the net force on the ballalso must be toward the center of the curved path. The net forceexerted toward the center of a curved path is called a centripetalforce. For the ball moving through the tube, the centripetalforce is the force exerted by the walls of the tube on the ball.

Centripetal Force and Traction When a car rounds acurve on a highway, a centripetal force must be acting on the carto keep it moving in a curved path. This centripetal force is thefrictional force, or the traction, between the tires and the roadsurface. If the road is slippery and the frictional force is small,the centripetal force might not be large enough to keep the carmoving around the curve. Then the car will slide in a straightline. Anything that moves in a circle, such as the people on theamusement park ride in Figure 15, is doing so because a cen-tripetal force is accelerating it toward the center.

Figure 15 Centripetal force keeps these riders moving in a circle.

Figure 14 When the ballmoves through the curved portionsof the tube, it is acceleratingbecause its velocity is changing.Identify the forces acting on theball as it falls through the tube.

Observing CentripetalForceProcedure1. Thread a string about 1 m

long through the holes of aplastic, slotted ball.

2. Swing the ball in a verticalcircle.

3. Swing the ball at differentspeeds and observe themotion of the ball and thetension in the string.

Analysis1. What force does the string

exert on the ball when theball is at the top, sides, andbottom of the swing?

2. How does the tensionin the string dependon the speedof the ball?

Pictor

Self Check1. Describe how the gravitational force between two

objects depends on the mass of the objects and thedistance between them.

2. Distinguish between the mass of an object and theobject’s weight.

3. Explain what causes the path of a projectile to becurved.

4. Describe the force that causes the planets to stay inorbit around the Sun.

5. Think Critically Suppose Earth’s mass increased,but its diameter didn’t change. How would the acceler-ation due to gravity near Earth’s surface change?

SummaryGravity

• According to the law of universal gravitation,the gravitational force between two objectsdepends on the masses of the objects and thedistance between them.

• The acceleration due to gravity near Earth’ssurface has the value 9.8 m/s2.

• Near Earth’s surface, the gravitational force onan object with mass, m, is given by:

F � mg

Weight

• The weight of an object is related to its massaccording to the equation:

W � mg

• An object in orbit seems to be weightlessbecause it is falling around Earth.

Projectile Motion and Centripetal Force

• Projectiles follow a curved path because theirhorizontal motion is constant, but gravitycauses the vertical motion to be changing.

• The net force on an object moving in a circularpath is called the centripetal force.

6. Calculate Weight On Earth, what is the weight of alarge-screen TV that has a mass of 75 kg?

7. Calculate Gravity on Mars Find the acceleration dueto gravity on Mars if a person with a mass of 60.0 kgweighs 222 N on Mars.

8. Calculate Force Find the force exerted by a rope on a 10-kg mass that is hanging from the rope.


Gravity Can Be a Centripetal Force Imagine whirlingan object tied to a string above your head. The string exerts acentripetal force on the object that keeps it moving in a circularpath. In the same way, Earth’s gravity exerts a centripetal forceon the Moon that keeps it moving in a nearly circular orbit, asshown in Figure 16.

Figure 16 The Moon wouldmove in a straight line except thatEarth’s gravity keeps pulling ittoward Earth. This gives the Moona nearly circular orbit.

Earth’s gravity keeps the Moon in an orbit.

The Moon would move in a straight linebecause it has inertia.



If you dropped a bowling ball and a feather fromthe same height on the Moon, they would bothhit the surface at the same time. All objectsdropped on Earth are attracted to Earth with thesame acceleration. But on Earth, a bowlingball and a feather will not hit the ground at thesame time. Air resistance slows the feather down.

Real-World ProblemHow does air resistance affect the accelerationof falling objects?

Goals■ Measure the effect of air resistance on

sheets of paper with different shapes. ■ Design and create a shape from a piece of

paper that maximizes air resistance.

Materialspaper (4 sheets of equal size) stopwatchscissors masking tapemeterstick

Safety Precautions

Procedure1. Copy the data table above in your Science

Journal, or create it on a computer.

2. Measure a height of 2.5m on the wall andmark the height with a piece of masking tape.

3. Have one group member drop the flat sheetof paper from the 2.5-m mark. Use the stop-watch to time how long it takes for thepaper to reach the ground. Record your timein your data table.

4. Crumple a sheet of paper into a loose balland repeat step 3.

5. Crumple a sheet of paper into a tight balland repeat step 3.

6. Use scissors to shape a piece of paper so thatit will fall slowly. You may cut, tear, or foldyour paper into any design you choose.

Conclude and Apply1. Compare the falling times of the different

sheets of paper.

2. Explain why the different-shaped papersfell at different speeds.

3. Explain how your design caused the forceof air resistance on the paper to be greaterthan the air resistance on the other papershapes.

GRAVITY AND

AIR RESISTANCE


Effects of Air Resistance

Paper Type Time

Flat paper

Loosely crumpled paper

Tightly crumpled paper

Your paper design

Compare your paper design with thedesigns created by your classmates. As aclass, compile a list of characteristics thatincrease air resistance.

Do not write in this book.

SECTION 3 The Third Law of Motion 113

Newton’s Third LawPush against a wall and what happens? If the wall is sturdy

enough, usually nothing happens. If you pushed against a wallwhile wearing roller skates, you would go rolling backward. Youraction on the wall produced a reaction—movement backward.This is a demonstration of Newton’s third law of motion.

The third law of motion describes action-reaction pairs thisway: When one object exerts a force on a second object, the sec-ond one exerts a force on the first that is equal in strength andopposite in direction. Another way to say this is “to every actionforce there is an equal and opposite reaction force.”

Action and Reaction When a force is applied in nature,a reaction force occurs at the same time. When you jump on atrampoline, for example, you exert adownward force on the trampoline.Simultaneously, the trampoline exertsan equal force upward, sending youhigh into the air.

Action and reaction forces are act-ing on the two skaters in Figure 17.The male skater is pulling upward onthe female skater, while the femaleskater is pulling downward on themale skater. The two forces are equal,but in opposite directions.

The Third Law of MotionReading Guide

■ State Newton’s third law ofmotion.

■ Identify action and reactionforces.

■ Calculate momentum.■ Recognize when momentum is

conserved.

The third law of motion explainshow you affect Earth when youwalk, and how Earth affects you.

Review Vocabularyvelocity: describes the speed anddirection of a moving object

New Vocabulary

• third law of motion

• momentum

• law of conservation of momentum

Figure 17 According toNewton’s third law of motion, thetwo skaters exert forces on eachother. The two forces are equal,but in opposite directions.

Steven Sutton/Duomo


Action and Reaction Forces Don’t Cancel If actionand reaction forces are equal, you might wonder how somethings ever happen. For example, how does a swimmer movethrough the water in a pool if each time she pushes on the water,the water pushes back on her? According to the third law ofmotion, action and reaction forces act on different objects.Thus, even though the forces are equal, they are not balancedbecause they act on different objects. In the case of the swim-mer, as she “acts” on the water, the “reaction” of the waterpushes her forward. Thus, a net force, or unbalanced force, actson her so a change in her motion occurs. As the swimmer movesforward in the water, how does she make the water move?

Why don’t action and reaction forces cancel?

Rocket Propulsion Suppose you are standing on skatesholding a softball. You exert a force on the softball when youthrow the softball. According to Newton’s third law, the softballexerts a force on you. This force pushes you in the directionopposite the softball’s motion. Rockets use the same principle tomove even in the vacuum of outer space. In the rocket engine,burning fuel produces hot gases. The rocket engine exerts aforce on these gases and causes them to escape out the back ofthe rocket. By Newton’s third law, the gases exert a force on therocket and push it forward. The car in Figure 18 uses a rocketengine to propel it forward. Figure 19 shows how rockets wereused to travel to the Moon.

Figure 18 Newton’s third lawenables the rocket engine to pushthe car forward. The rocket enginepushes the hot gases produced byburning fuel backward out of theengine’s nozzle. By the third law,the gases exert a force of equalsize on the engine in the forwarddirection.Infer the direction of the car’sacceleration when the rocket engineis fired.

Space Medicine Astronautswho stay in outer space forextended periods of timemay develop health prob-lems. Their muscles, forexample, may begin toweaken because they don’thave to exert as much forceto get the same reaction asthey do on Earth. A branchof medicine called spacemedicine deals with thepossible health problemsthat astronauts may experi-ence. Research some otherhealth risks that areinvolved in going into outerspace.

Philip Bailey/The Stock Market

NGS TITLE

Figure 19

VISUALIZING ROCKET MOTION

On the afternoon of July 16, 1969, Apollo 11 lifted off from Cape Kennedy, Florida, bound for theMoon. Eight days later, the spacecraft returned to

Earth, splashing down safely in the Pacific Ocean. Themotion of the spacecraft to the Moon and back is governedby Newton’s laws of motion.

Apollo 11 roars toward the Moon.At launch, a rocket’sengines must produceenough force and accel-eration to overcome thepull of Earth’s gravity.A rocket’s liftoff is anillustration of Newton’sthird law: For everyaction there is an equaland opposite reaction.

As Apollo rises, it burns fuel and ejectsits rocket booster engines. This decreases its mass, and helps Apollo move faster.This is Newton’s second law in action: Asmass decreases, acceleration can increase.

The lunar module returns to the Apollo spacecraft, which fires itsengines to start it moving toward Earth. As the spacecraft gets closerto Earth, the gravitational force exerted by Earth becomes larger,continually increasing the acceleration of the spacecraft.

The lunar module usesother engines to slow downand ease into a soft touch-down on the Moon. A day later,the same engines lift the lunarmodule again into outer space.

▼

▼

▼

▼

SECTION 3 The Third Law of Motion 115(l)NASA, (cr)Teledyne Ryan Aeronautical, (others)North American Rockwell


MomentumA moving object has a property called momentum that is

related to how much force is needed to change its motion. Themomentum of an object is the product of its mass and velocity.Momentum is given the symbol p and can be calculated with thefollowing equation:

The unit for momentum is kg�m/s. Notice that momentumhas a direction because velocity has a direction.

THE MOMENTUM OF A SPRINTER At the end of a race, a sprinter with a mass of 80 kg has a

speed of 10 m/s. What is the sprinter’s momentum?

known values and the unknown value

Identify the known values:

a sprinter with a mass of 80 kg m � 80 kg

has a speed of 10 m/s v � 10 m/s

Identify the unknown value:

What is the sprinter’s momentum? p � ? kg•m/s

the problem

Substitute the known values m � 80 kg and v = 10 m/s into the momentum equation:

p � mv � (80 kg) (10 m/s) � 800 kg•m/s

your answer

Does your answer seem reasonable? Check your answer by dividing the momentum you

calculated by the mass given in the problem. The result should be the speed given in the

problem.

CHECK

SOLVE

means

means

means

IDENTIFY

Solve a Simple Equation

1. What is the momentum of a car with a mass of 1,300 kg traveling at a speed of 28 m/s?

2. A baseball thrown by a pitcher has a momentum of 6.0 kg•m/s. If the baseball’s massis 0.15 kg, what is the baseball’s speed?

3. What is the mass of a person walking at a speed of 0.8 m/s if their momentum is52.0 kg•m/s?

For more practice problems go to page 879, and visit Math Practice at .gpescience.com

Momentum Equation

momentum (kg m/s) � mass (kg) � velocity (m/s)

p � mv


SECTION 3 The Third Law of Motion 117

Law of Conservation of Momentum The momentum ofan object doesn’t change unless its mass, velocity, or both change.Momentum, however, can be transferred from one object toanother. Consider the game of pool shown in Figure 20.

When the cue ball hits the group of balls that are motionless,the cue ball slows down and the rest of the balls begin to move.The momentum the group of balls gained is equal to themomentum that the cue ball lost. The total momentum of allthe balls just before and after the collision would be the same. Ifno other forces act on the balls, their total momentum is con-served—it isn’t lost or created. This is the law of conservationof momentum—if a group of objects exerts forces only on eachother, their total momentum doesn’t change.

Figure 20 Momentum is trans-ferred in collisions. Before thecollision, only the cue ball hasmomentum. When the cue ballstrikes the other balls, it transferssome of its momentum to them.

Self Check1. Determine You push against a wall with a force of 50 N.

If the wall doesn’t move, what is the net force on you?

2. Explain how a rocket can move through outer spacewhere there is no matter for it to push on.

3. Compare the momentum of a 6,300-kg elephant walk-ing 0.11 m/s and a 50-kg dolphin swimming 10.4 m/s.

4. Describe what happens to the momentum of twobilliard balls that collide.

5. Think Critically A ballet director assigns slow, gracefulsteps to larger dancers, and quick movements tosmaller dancers. Why is this plan successful?

SummaryNewton’s Third Law

• According to Newton’s third law of motion,for every action force, there is an equal andopposite reaction force.

• Action and reaction forces act on differentobjects.

Momentum

• The momentum of an object is the product ofits mass and velocity:

p � mv

The Law of Conservation of Momentum

• According to the law of conservation ofmomentum, if objects exert forces only on eachother, their total momentum is conserved.

• In a collision, momentum is transferred fromone object to another.

6. Calculate Momentum What is the momentum of a100-kg football player running at a speed of 4 m/s?


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(l)Jeff Smith/Fotosmith, (r)Richard megna/Fundamental Photographs


Momentum of Colliding Balls

Action Time

Velocity

Mass

Momentum Distance Softball

Moved

Racquetballrolled slowly

Racquetball rolled quickly

Tennis ball rolled slowly

Tennis ball rolled quickly

Baseball rolled slowly

Baseball rolledquickly

The Momentum of Colliding Objects

Real-World ProblemMany scientists hypothesize that dinosaurs became extinct 65 millionyears ago when an asteroid collided with Earth. The asteroid’s diameterwas probably no more than 10 km. Earth’s diameter is more than12,700 km. How could an object that size change Earth’s climateenough to cause the extinction of animals that had dominated lifeon Earth for 140 million years? The asteroid could have caused suchdamage because it may have beentraveling at a velocity of 50 m/s,and had a huge amount ofmomentum. The combinationof an object’s velocity and masswill determine how much force itcan exert. How do the mass andvelocity of a moving object affectits momentum?

Goals■ Observe and calculate

the momentum ofdifferent balls.

■ Compare the resultsof collisions involvingdifferent amounts ofmomentum.

Materialsmetersticksoftballracquetballtennis ballbaseballstopwatchmasking tapebalance

Safety Precautions

118 CHAPTER 4 The Laws of MotionMatt Meadows


Procedure1. Copy the data table on the previous page in your Science Journal.

2. Use the balance to measure the mass of the racquetball, tennis ball, and baseball.Record these masses in your data table.

3. Measure a 2-m distance on the floor and mark it with two pieces of masking tape.

4. Place the softball on one piece of tape. Starting from the other piece of tape,slowly roll the racquetball toward the center of the softball.

5. Use a stopwatch to time how long it takes the racquetball to roll the 2-mdistance and hit the softball. Record this time in your data table.

6. Measure and record the distance the racquetball moved the softball.

7. Repeat steps 4–6, rolling the racquetball quickly.

8. Repeat steps 4–6, rolling the tennis ball slowly, thenquickly.

9. Repeat steps 4–6, rolling the baseball slowly, thenquickly.

Analyze Your Data1. Calculate the momentum for each type of ball

and action using the formula p � mv. Record your calculations in the data table.

2. Graph the relationship between the momentum of eachball and the distance the softball was moved using agraph like the one shown.

Conclude and Apply1. Infer from your graph how the distance the

softball moves after each collision depends onthe momentum of the ball that hits it.

2. Explain how the motion of the balls after theycollide can be determined by Newton’s lawsof motion.

Compare your graph with the graphsmade by other students in your class.Discuss why the graphs might lookdifferent.

Distance Softball Moved andMomentum of Colliding Ball

Dis

tan

ce s

oftb

all m

oved

Momentum

119Tim Courlas/Horizons Companies


In 1665, the bubonic plague swept throughEngland and other parts of Europe. IsaacNewton, then a 23-year-old university student,

returned to his family's farm until Cambridgeuniversity reopened. To occupy his time, Newtonmade a list of 22 questions. During the next 18months, Newton buried himself in the search foranswers. And in that brief time, Newton devel-oped calculus, the three laws of motion, and theuniversal law of gravitation!

The Laws of MotionEarlier philosophers thought that force was

necessary to keep an object moving. By analyzingthe data collected by Galileo and others, Newtonrealized that forces did not cause motion. Instead,forces cause a change in motion. Newton came tounderstand that force and acceleration wererelated and that objects exert equal and oppositeforces on each other. Newton’s three laws of

motion were able to explainhow all things moved, froman apple falling from a treeto the motions of the moonand the planets, in termsof force, mass, andacceleration.

What is gravity?Using the calculus and data on the motion of

the planets, Newton deduced the law of universalgravitation. This law enabled the force of gravitybetween any two objects to be calculated, if theirmasses and the distance between them wereknown.

Newton was able to show mathematicallythat the law of universal gravitation predictedthat the planets’ orbits should be ellipses, just asJohannes Kepler had discovered two generationsearlier. The application of Newton’s laws ofmotion and the law of universal gravitation alsowere able to explain phenomena such as tides,the motion of the moon and the planets, and thebulge at the Earth's equator.

A Different View of GravityIn 1916, Albert Einstein proposed a different

model for gravity called the general theory of rela-tivity. In Einstein’s model, objects create distortionsin space-time, like a bowling ball dropped on asheet. What we see as the force of gravity is themotion of an object on distorted space-time. Today,Einstein’s theory is used to help explain the natureof the big bang and the structure of the universe.

Investigate Research how both Newton’s law of gravitation andEinstein’s general theory of relativity have been used to develop thecurrent model of the universe.

Newtonand thePlague

SCIENCE AND

HISTORYSCIENCE

CAN CHANGE THE COURSE OF HISTORY!

Isaac Newton was a university student when he developed the laws of motion.

In Einstein’s theoryof general relativity,gravity is due toa distortion inspace-time.

For more information, visitgpescience.com

(t)Tony Craddock/Photo Researchers, Inc., (b)Bettmann/CORBIS


The First Two Lawsof Motion

1. According to the first law of motion, thevelocity of an object doesn't change unless anunbalanced net force acts on the object.

2. Inertia is the tendency of an object to resist achange in its motion.

3. The second law of motion states that a netforce causes an object to accelerate in thedirection of the net force and that the accel-eration is given by

a � �F

mnet�

Gravity

1. Gravity is an attractive force between anytwo objects with mass. The gravitationalforce depends on the masses of the objectsand the distance between them.

2. The gravitational acceleration, g, nearEarth’s surface equals 9.8 m/s2. The force ofgravity on an object with mass, m, is:

F � mg

3. The weight of an object near Earth’ssurface is:

W � mg

4. Projectiles travel in a curved path becauseof their horizontal motion and verticalacceleration due to gravity.

5. The centripetal force is the net force on anobject in circular motion and is directedtoward the center of the circular path.

The Third Law of Motion

1. Newton’s third law of motion states that forevery action there is an equal and oppositereaction.

2. The momentum of an object can becalculated by the equation p � mv.

3. When two objects collide, momentum canbe conserved. Some of the momentumfrom one object is transferred to the other.

CHAPTER STUDY GUIDE 121

Use the Foldable that you made at thebeginning of this chapter to help you review the laws ofmotion.

Interactive Tutor gpescience.com(l)Neal Haynes/Rex USA, Ltd., (r)Richard Megna/Fundamental Photographs


Complete each statement using a word(s) fromthe vocabulary list above.

1. The way in which objects exert forces oneach other is described by _________.

2. The _________ of an object depends on itsmass and velocity.

3. The _________ of an object is different onother planets in the solar system.

4. When an object moves in a circular path,the net force is called a(n) _________.

5. The attractive force between two objectsthat depends on their masses and the dis-tance between them is _________.

6. _________ relates the net force exerted onan object to its mass and acceleration.

Choose the best answer for each question.

7. What is the gravitational force exerted onan object called? A) centripetal force C) momentumB) friction D) weight

8. Which of the following best describes whyprojectiles move in a curved path?A) They have horizontal velocity and

vertical acceleration.B) They have momentum.C) They have mass.D) They have weight.

9. Which of the following explains whyastronauts seem weightless in orbit?A) Earth’s gravity is much less in orbit.B) The space shuttle is in free fall.C) The gravity of Earth and the Sun cancel.D) The centripetal force on the shuttle

balances Earth’s gravity.

10. Which of the following exerts thestrongest gravitational force on you?A) the Moon C) the SunB) Earth D) this book

Use the graph below to answer question 11.

11. The graph shows the speed of a car mov-ing in a straight line. Over which segmentsare the forces on the car balanced?A) A and C C) C and EB) B and D D) D only

12. Which of the following is true about anobject in free fall?A) Its acceleration depends on its mass.B) It has no inertia.C) It pulls on Earth, and Earth pulls on it.D) Its momentum is constant.

13. The acceleration of an object is in thesame direction as which of the following?A) net force C) static frictionB) air resistance D) gravity

14. Which of the following is NOT a force?A) weight C) momentumB) friction D) air resistance

20

30

10

0Time (s)

Spee

d (m

/s)

10 20 30 40

a

c eb

d

122 CHAPTER REVIEW

centripetal accelerationp. 110

centripetal force p. 110first law of motion p. 98gravity p. 104inertia p. 99

law of conservation ofmomentum p. 117

momentum p. 116second law of motion p.102third law of motion p. 113weight p. 106

Vocabulary PuzzleMaker gpescience.com


CHAPTER REVIEW 123

15. Copy and complete the following conceptmap on forces.

Use the table below to answer questions 16–18.

16. If the objects in the data table above allfell the same distance, which object fellwith the greatest average speed?

17. Describe the forces acting on a softball afterit leaves the pitcher’s hand. Ignore theeffects of air resistance.

18. Determine the direction of the net force ona book sliding on a table if the book isslowing down.

19. Explain whether there can be any forces act-ing on a car moving in a straight line withconstant speed.

20. Explain You pull a door open. If the force thedoor exerts on you is equal to the force youexert on the door, why don’t you move?

21. Predict Suppose you are standing on abathroom scale next to a sink. How doesthe reading on the scale change if youpush down on the sink?

22. Describe the action and reaction force pairsinvolved when an object falls towardEarth. Ignore the effects of air resistance.

Time of Fall for Dropped Objects

Object Mass (g) Time of Fall (s)

A 5.0 2.0

B 5.0 1.0

C 30.0 0.5

D 35.0 1.5

23. Calculate Mass Find your mass if a scale onEarth reads 650 N when you stand on it.

24. Calculate Acceleration of Gravity You weighyourself at the top of a high mountainand the scale reads 720 N. If your massis 75 kg, what is the acceleration ofgravity at your location?

Use the figure below to answer question 25.

25. Calculate Speed The 2-kg metal ball mov-ing at a speed of 3 m/s strikes a 1-kgwooden ball that is at rest. After the colli-sion, the speed of the metal ball is 1 m/s.Assuming momentum is conserved,what is the speed of the wooden ball?

26. Calculate Mass Find the mass of a car thathas a speed of 30 m/s and a momentumof 45,000 kg¸m/s.

27. Calculate Sliding Friction A box beingpushed with a force of 85 N slides alongthe floor with a constant speed. What isthe force of sliding friction on the box?

Metalball

Woodenball

Metalball

Woodenball

Before Collision After Collision

Newton’s 2nd Law

MassAction-reaction

force pairs

Gravitationalattraction

Forces

change motion

relates force to

between two objects

involves

long-rangeforce

depends on

More Chapter Review gpescience.com


1. The net force on an object moving withconstant speed in circular motion is inwhich direction?

A. downward

B. opposite to the object’s motion

C. toward the center of the circle

D. in the direction of the object’s velocity

Use the table below to answer questions 2–4.

2. Over which of the following time intervalsis the acceleration of the object the greatest?

A. 0 s to 1 s

B. 1 s to 2 s

C. 4 s to 5 s

D. The acceleration is constant.

3. Over which of the following time intervalsis the net force on the object the smallest?

A. 0 s to 1 s

B. 1 s to 2 s

C. 4 s to 5 s

D. The force is constant.

4. According to the trend in these data, whichof the following values is most likely thespeed of the object after falling for 6 s?

A. 26.7 m/s

B. 15.1 m/s

C. 20.1 m/s

D. 0 m/s

5. Which of the following would cause thegravitational force between object A andobject B to increase?

A. Decrease the distance between them.

B. Increase the distance between them.

C. Decrease the mass of object A.

D. Decrease the mass of both objects.

Use the graphs below to answer question 6.

Graph 1

Graph 3 Graph 4

Graph 2

Mass

Forc

e

Mass

Forc

e

Mass

Forc

e

Mass

Forc

e

Object in Free Fall with Air Resistance

Time (s) Speed (m/s)

0 0

1 9.1

2 15.1

3 18.1

4 19.3

5 19.9

124 STANDARDIZED TEST PRACTICE

Keep Track of Time If you are taking a timed test, keep trackof time. If you find you are spending too much time on amultiple-choice question, mark your best guess and move on.

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

STANDARDIZED TEST PRACTICE 125

6. Which of the graphs on the previous pageshows how the force on an object changes ifthe mass increases and the acceleration staysconstant?

A. Graph 1

B. Graph 2

C. Graph 3

D. Graph 4

7. You are pushing a 30-kg wooden crateacross the floor. The force of sliding frictionon the crate is 90 N. How much force, innewtons, must you exert on the crate tokeep it moving with a constant velocity?

8. A skydiver with a mass of 60 kg jumps froman airplane. Five seconds after jumping, theforce of air resistance on the skydiver is300 N. What is the skydiver’s accelerationin m/s2 five seconds after jumping?

Use the figure below to answer question 9.

9. Two balls are at the same height. One ballis dropped and the other initially moveshorizontally, as shown in the figure.After 1 s, which ball has fallen the greatestvertical distance?

10. How does the acceleration of gravity5,000 km above Earth’s surface comparewith the acceleration of gravity at Earth’ssurface?

Use the graph below to answer question 11.

11. The graph above shows the how the speedof a book changes as it slides across a table.Over what time interval is the net force onthe book in the opposite direction of thebook’s motion?

12. When the space shuttle is launched fromEarth, the rocket engines burn fuel andapply a constant force on the shuttle untilthey burn out. Explain why the shuttlesacceleration increases while the rocketengines are burning fuel.

Speed of Sliding Book

0.50

0.5

1.0

1.5

1.0 1.5Time (s)

2.0 2.5

Spee

d (m

/s)

Standardized Test Practice gpescience.com


(bkgd)Getty Images, (l)Jack Fields/Photo Researchers, (r)Alfred Pasieka/Photo Researchers


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