66

Crash! What brought this vehi-cle to its sudden stop? Howdid the impact affect the car

and its driver? Automobile manufac-turers consider factors like mass andacceleration to determine the forceson a driver during a crash. This helpsthem predict whether the driverwould survive or be injured. In thischapter, you will learn how forcessuch as gravity and friction affectmotion.

What do you think?Science Journal Look at the picturebelow with a classmate. Discuss whatthis might be or what is happening.Here’s a hint: Gravity gives this objectits structure. Write your answer orbest guess in your Science Journal.

Forces33

What holds you to Earth, pulls footballs back tothe ground, and keeps the Moon in orbit? The

force of gravity, of course. But did you know that allobjects near Earth’s surface would fall with the sameacceleration due to gravity? If this is true, why do bowl-

ing balls fall faster than feathers? Explore free-falling objects in this activity.

Observe free-falling objects1. Drop a softball from a height of 2.5 m

and use a stopwatch to measure thetime it takes for the softball to fall thegiven distance.

2. Repeat the procedure using a tennisball, a piece of paper crumpled into a ball, and a flat sheet of paper.

ObserveIn your Science Journal, write a para-graph comparing the time it took for thefour items to drop the 2.5 m. Infer whythe crumpled paper fell faster than theflat sheet of paper even though they havethe same mass.

67

EXPLOREACTIVITY

Making a Compare-and-Contrast Study Fold Make the follow-ing Foldable to help you see how the three types of friction aresimilar and different.

1. Place a sheet of paper in front of you so the short sideis at the top. Fold the top of the paper down and thebottom up.

2. Open the paper and label the three rows Static Friction,Sliding Friction, and Rolling Friction.

3. Before you read the chapter, write the definition ofeach type of friction next to it. As you read the chapter,write more information about each type.

FOLDABLESReading & StudySkills

FOLDABLESReading &Study Skills

Rolling Friction

Sliding Friction

Static Friction

68 CHAPTER 3 Forces

Newton’s Second LawS E C T I O N

Force, Mass, and AccelerationNewton’s first law of motion states that the motion of an

object, such as the volleyball in Figure 1, changes only if anunbalanced force acts on it. Force and motion are connected.How does force cause motion to change?

Force and Acceleration What’s different about throwing aball as hard as you can and tossing it gently? When you throwhard, you exert a much greater force on the ball. How is themotion of the ball different in each case?

In both cases, the ball was at rest in your hand before itbegan to move. However, when you throw hard, the ball has agreater velocity when it leaves your hand than it does when youthrow gently. Thus the hard-thrown ball has a greater change invelocity, and the change occurs over a shorter period of time.Recall that acceleration is the change in velocity divided by thetime it takes for the change to occur. So, a hard-thrown ball hasa greater acceleration than a gently thrown ball.

For any object, the greater the force is that’s applied to it, thegreater its acceleration will be. This is true for anything from theblood cells swirling through your body to the galaxies swirlingthrough outer space.

Force and Mass If you throw a soft-ball and a baseball as hard as you can,why don’t they have the same speed?The difference is due to their masses.The softball has a mass of about 0.20 kg,but a baseball’s mass is about 0.14 kg.The softball has less velocity after itleaves your hand than the baseball does,even though you exerted the same force.If it took the same amount of time tothrow both balls, the softball has lessacceleration. The acceleration of anobject depends on its mass as well as theforce exerted on it. Force, mass, andacceleration are connected.

� Explain how force, mass, and acceleration are related.

� Describe the three different typesof friction.

� Observe the effects of air resistance on falling objects.

VocabularyNewton’s second law of motionfriction

Newton’s second law explains whysome objects move and some objects don’t.

Figure 1 The motion of the volleyballchanges when an unbalancedforce is applied to the ball.

Math Skills Activity

You are pushing a friend on a sled. You push with a force of 40 N. Your friend andthe sled together have a mass of 80 kg. Ignoring friction, what is the acceleration

of your friend on the sled?

This is what you know: force: F � 40 Nmass: m � 80 kg

This is what you need to know: acceleration: a

This is the equation you need to use: a � F/m

Substitute the known values: a � 40 N/80 kg � 0.5 m/s2

Check your answer by multiplying it by the mass. Do you calculate the same force that was given?

Calculating Acceleration

For more help, refer to the Math Skill Handbook.

Practice Problem

A student pedaling a bicycle applies a net force of 200 N. The mass of therider and the bicycle is 50 kg. What is the acceleration of the bicycle and the rider?

SECTION 1 Newton’s Second Law 69

Newton’s Second Law Newton’s second law of motion describes how force, mass,

and acceleration are connected. Recall that if more than oneforce acts on an object, the forces combine to form a net force.According to Newton’s second law of motion, the net force act-ing on an object causes the object to accelerate in the directionof the net force. The acceleration of an object is determined bythe size of the net force and the mass of the object according tothe equation:

acceleration �

If a stands for the acceleration, F for the net force, and m for themass, Newton’s second law can be written as follows:

a �

In SI units, the unit of mass is the kilogram (kg), and theunit of acceleration is meters per second squared (m/s2).So, according to the second law of motion, force has the unitskg � m/s2. The unit kg � m/s2 is called the newton (N).

F�m

net force�

mass

Research Visit the Glencoe Science Web site atscience.glencoe.com forinformation about how athletic trainers analyze themotions of athletes so theymake the best use of New-ton’s second law. Select asport and report to yourclass about some of the find-ings in that sport.

Using Newton’s Second Law The second law can be used to calculate the net force on an object if the accleration and mass are known. Suppose a tennis ball like the one in Figure 2 isaccelerated by a tennis racket for five thousandths of a second—the time the racket is in contact with the ball. Because this timeperiod is so short, a ball that leaves the racket at a speed of 100km/h would have undergone an acceleration of about 5,500m/s2. How much force would the tennis racket have to exert togive the ball this acceleration? The ball has a mass of 0.06 kg, soby Newton’s second law the force would have to be:

F � ma � (0.06 kg)(5,500 m/s2) � 330 N

FrictionSuppose you give a skateboard a push with your hand.

According to Newton’s first law of motion, if no forces are actingon a moving object, it continues to move in a straight line withconstant speed. What happens to the motion of the skateboardafter it leaves your hand? Does it continue to move in a straightline with constant speed?

You know the answer. The skateboard gradually slows downand finally stops. Recall that when an object slows down, itsvelocity changes. If its velocity changes, it is accelerating. And ifan object is accelerating, a net force must be acting on it.

The force that slows the skateboard and brings it to a stop isfriction. Friction is the force that opposes motion between twosurfaces that are touching each other. The amount of frictionbetween two surfaces depends on two factors—the kinds of sur-faces and the force pressing the surfaces together.

The amount of friction between two objects depends on what two factors?

What causes friction? Would youbelieve the surface of a highly polishedpiece of metal is rough? Figure 3 shows amicroscopic view of the dips and bumpson the surface of a polished silver teapot.If two surfaces, such as two pieces of sil-ver, are pressed tightly together, welding,or sticking, occurs in those areas wherethe highest bumps come into contactwith each other. These areas where thebumps stick together are called micro-welds and are the source of friction.

Figure 3 While surfaces mightlook and even feelsmooth, they can berough at the micro-scopic level.

Figure 2 The force exerted on the ball bythe tennis racket may be morethan 500 times greater than theforce needed to pick the ball up.

70 CHAPTER 3 Forces

SECTION 1 Newton’s Second Law 71

Sticking Together The stronger the force pushing the twosurfaces together is, the stronger these microwelds will be,because more of the surface bumps will come into contact, asshown in Figure 4. To break these microwelds and move onesurface over the other, a force must be applied.

Static Friction Suppose you have filled a cardboard box, likethe one in Figure 5, with books and want to move it. It’s tooheavy to lift, so you start pushing on it, but it doesn’t budge. Isthat because the mass of the box is too large? If the box doesn’tmove, then it has zero acceleration. According to Newton’s sec-ond law, if the acceleration is zero, then the net force on the boxis zero. Another force that cancels your push must be acting onthe box. That force is friction due to the microwelds that haveformed between the bottom of the box and the floor. This typeof friction is called static friction. Static friction is the frictionbetween two surfaces that are not moving past each other. Inthis case, your push is not large enough to break the microwelds,and the box remains stuck to the floor.

ForceMoreforce

Surfaces Same twosurfaces

Microwelds form where bumps come into contact.

More force presses the bumps closer together.

Figure 4 Friction is due to microweldsformed between two surfaces.The larger the force pushing thetwo surfaces together is, thestronger the microwelds will be.

Figure 5 The box doesn’t move becausestatic friction cancels theapplied force.

Comparing FrictionProcedure1. Position an ice cube, rock,

eraser, wood block, andsquare of aluminum foil atone end of a metal or plastic tray.

2. Slowly lift the end of the traywith the items.

3. Have a partner use a metricruler to measure the heightat which each object slidesto the other end of the tray.Record the heights in yourScience Journal.

Analysis1. List the height at which each

object slid off the tray.2. Why did the objects slide off

at different heights?3. What type of friction acted

on each object?

Static friction

Applied force

Sliding Friction To help youmove the box, you ask a friendto push with you, as in Figure 6.Pushing together, the box startsto move, but it doesn’t moveeasily. Also, if you stop pushing,it quickly comes to a stop. Itmight even seem as if someoneis pushing on it from the oppo-site direction. But, by exertingenough force, you have brokenthe microwelds and started thebox moving. However, as thebox slides across the floor,another force—sliding fric-tion—opposes the motion of

the box. Sliding friction is the force that opposes the motion oftwo surfaces sliding past each other. Sliding friction is caused bymicrowelds constantly breaking and then forming again as thebox slides along the floor. To keep the box moving, you mustcontinually apply a force to overcome sliding friction.

What’s the difference between sliding frictionand static friction?

Rolling Friction You might have watched a car stuck insnow, ice, or mud spinning its wheels. The driver steps on thegas, but the wheels just spin without the car moving. The cardoesn’t move when the wheels are on the slippery surfacebecause there is not enough friction between the tires and thesnow, ice, or mud. One way to make the car move might be to

spread sand or gravel under the wheels. Byspreading sand or gravel, the friction betweenthe tires and the surface is increased. The fric-tion between a rolling object and the surface itrolls on is rolling friction. As you can see inFigure 7, because of rolling friction, the wheelsof the train rotate when they come in contactwith the track rather than sliding over it.Rolling friction is due partly to the microweldsbetween a wheel and the surface it rolls over.Microwelds break and then reform as thewheel rolls over the surface. Rolling friction isusually much less than static or sliding friction.This is why it’s easier to pull a load in a wagonrather than dragging it along the ground.

72 CHAPTER 3 Forces

Figure 7 Rolling friction is what makes atrain’s wheels turn on the tracksor a car’s wheels turn on the road.

Figure 6Sliding friction acts in the direc-tion opposite the motion of thesliding box.

Slidingfriction

Applied force

Air Resistance When an object falls toward Earth,

it is pulled downward by the force ofgravity. However, another force calledair resistance acts on objects that fallthrough the air. Imagine dropping twoidentical plastic bags except that one iscrumpled into a ball and one is spreadout. The crumpled bag falls faster thanthe spread-out bag. So, the accelera-tion of the spread-out bag must beless than that of the crumpled bag.Therefore, the net force acting on thespread-out bag is less. This is becausethe force of air resistance is in theopposite direction to the force of grav-ity for both bags and is greater on thespread-out bag.

Air resistance affects anything thatmoves in Earth’s atmosphere. Likefriction, air resistance acts in thedirection opposite to that of theobject’s motion. In the case of the twofalling bags, air resistance is pushingup as gravity is pulling down, asshown in Figure 8.

The amount of air resistance on an object depends on thespeed, size, and shape of the object. Air resistance, not theamount of mass in the object, is why feathers, leaves, and piecesof paper fall more slowly than pennies, acorns, and apples. If noair resistance is present, then a feather and an apple fall at thesame rate, as shown in Figure 9.

Figure 8Because of its greater surfacearea, the spread-out bag hasmuch more air resistance actingon it as it falls.

Figure 9The apple and feather are fallingin a vacuum. Because there is noair resistance, they both fall atthe same rate.

Force ofgravity

Air resistance

Force ofgravity

Air resistance

SECTION 1 Newton’s Second Law 73

Terminal Velocity The force of air resistance increases withspeed. As an object falls, it accelerates and its speed increases. Sothe force of air resistance increases until it becomes largeenough to cancel the force of gravity. Then the forces on thefalling object are balanced, and the object no longer accelerates.It then falls with a constant speed called the terminal velocity.This terminal velocity is the highest velocity that a falling objectwill reach. A low terminal velocity enables a sky diver, such asthe one shown in Figure 10, to land safely on the ground.

74 CHAPTER 3 Forces

Section Assessment

1. What is Newton’s second law of motion?

2. The same force acts on two objects withdifferent masses.Why does the object withless mass have a larger acceleration?

3. What is the difference between static fric-tion and sliding friction?

4. A squirrel runs across a branch on an oaktree and knocks an acorn and a leaf loose.Why does the acorn hit the ground first?

5. Think Critically To reduce the friction ina metal door hinge, you might try coatingit with oil. Why does oil reduce friction?

6. Drawing Conclusions Boxes of equal size areresting on the floor. Applying the same force oneach box, you find that you can accelerate thefirst one 1 m/s2, the second 4 m/s2, and thethird 6 m/s2. What can you infer about the totalmass of each box? What other factors mighthave influenced your results? For more help,refer to the Science Skill Handbook.

7. Communicating Describe activities in whichfriction would be useful. For more help, refer tothe Science Skill Handbook.

Figure 10The force of air resistance on anopen parachute is large.Thiscauses the sky diver to fall slowly.

SECTION 2 Gravity 75

The Law of GravitationThere’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.According to the law of gravitation, any two masses exert anattractive force on each other. The attractive force depends onthe mass of the two objects and the distance between them.This force increases as the mass of either object increases, asshown in Figure 11A. Also, Figure 11B shows that the force ofgravity increases as the objects move closer.

You can’t feel any gravitational attraction between you andthis book because the force is weak. Only Earth is close enoughand has a large enough mass that you can feel its gravitationalattraction. While the Sun has much more mass than Earth, theSun is too far away to exert a noticeable gravitational attractionon you. And while this book is close, it doesn’t have enoughmass 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 nuclearforces only act on particles in the nuclei of atoms. Electricityand magnetism are caused by the electromagnetic force. Chemi-cal interactions between atoms and molecules also are due tothe electromagnetic force.

� Describe gravitational force.� Distinguish between mass and

weight.� Explain why objects that are

thrown or shot will follow a curved path.

� Compare motion in a straight linewith circular motion.

Vocabularylaw of gravitationweightcentripetal accelerationcentripetal force

No matter where you might be in theuniverse, gravity will affect you.

GravityS E C T I O N

Figure 11The gravitational force betweentwo objects depends on theirmasses and the distancebetween them.

If the mass of either of theobjects increases, the gravitationalforce between them increases.

If the objects are closertogether, the gravitational forcebetween them increases.

The Range of Gravity You might think that a star inanother galaxy is too far away to exert a gravitational force onyou, but you’d be wrong. Despite the distance between twoobjects, the gravitational attraction between them never dis-appears. Gravity is a long-range force. All the stars in a galaxy,such as the one shown in Figure 12, exert a gravitational forceon each other. These forces help give the galaxy its shape. In fact,a gravitational force exists between all matter in the universe.Gravity is the force that gives the universe its structure.

Gravitational AccelerationNear Earth’s surface, the gravitational attraction of Earth

causes all falling objects to have an acceleration of 9.8 m/s2. ByNewton’s second law, the net force, mass, and acceleration arerelated according to the following formula:

F � ma

According to the second law, the force on an object that has anacceleration of 9.8 m/s2 is as follows:

F � m � 9.8 m/s2

This is the force of gravity on an object near Earth’s surface.This force depends only on the object’s mass. A force has adirection associated with it. The force of Earth’s gravity is alwaysdownward.

When an object is influenced only by the force of gravity, itis said to be in free fall. Suppose you were to drop a bowling balland a marble from a bridge at the same time. Which would hitthe water below first? Would it be the bowling ball because it hasmore mass?

76 CHAPTER 3 Forces

Figure 12Gravity is at work in the forma-tion of galaxies like this spiralgalaxy.

Data Update Visit the Glencoe Science Web site atscience.glencoe.com fordata comparing the gravita-tional accelerations objectswould experience on differentplanets. Discuss with yourclass why the gravitationalacceleration is greater onsome planets than on others.

Inertia and Gravity It’s true that the force of gravity wouldbe greater on the bowling ball because of its larger mass. But thelarger mass also means the bowling ball has more inertia, somore force is needed to change its velocity. The gravitationalforce on the marble is smaller because it has less mass, but theinertia of the marble is smaller, too, so less force is needed tochange its velocity. As a result, all objects fall with the sameacceleration, no matter how large or small their mass is.Although the blue ball in Figure 13 is more massive than thegreen one, they fall at the same rate.

Weight If you are standing on the floor of your classroom, your

acceleration is zero. According to Newton’s second law, if youracceleration is zero, the net force on you must be zero. Does thismean Earth’s gravitational attraction for you has disappeared?No. Earth still pulls you downward, but the floor also exerts anupward force that keeps you from falling.

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 symbol W stands for theweight. You can find gravitational force, or weight, using New-ton’s second law, as follows:

gravitational force � mass �

Because the gravitational force is the same as the weight and theacceleration due to gravity on Earth is 9.8 m/s2, this equationcan be written as follows:

W � m � 9.8 m/s2

In other words, a mass of 1 kg weighs 1 kg � 9.8 m/s2, or 9.8N. You could calculate your weight in newtons if you knew yourmass. For example, a person with a mass of 50 kg would have aweight of 490 N. On Earth, a cassette tape weighs about 0.5 N, abackpack full of books weighs about 40 N, and a jumbo jetweighs about 3.4 million N.

How much does a person with a mass of 70 kg weigh on Earth?

Losing Weight What would happen to your weight if youwere far from Earth? Recall that the gravitational attractionbetween two objects becomes weaker as they move farther apart. Soif you were to travel away from Earth, your weight would decrease.

accelerationdue to gravity

SECTION 2 Gravity 77

Figure 13High-speed photography showsthat two balls of different massesfall at the same rate.

Weight and Mass Weight and mass are notthe same. Weight is a force, and mass is a measureof the amount of matter an object contains. How-ever, weight and mass are related. The greater anobject’s mass is, the stronger the gravitationalforce between the object and Earth is. So the moremass an object has, the more it will weigh at thesame location.

The weight of an object usually means thegravitational force between the object and Earth.But objects can have different weights, dependingon what’s pulling on them. For example, a personweighing about 480 N on Earth would weigh onlyabout 80 N on the Moon. Does this mean the

astronaut in Figure 14 would have less mass on the Moon thanon Earth? The answer is no, the mass of the astronaut would beunchanged. His weight is less than on Earth because the Moonhas less mass and exerts a weaker gravitational force. Table 1shows how an object’s weight depends upon the object’s location.

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 in the shuttle floats throughout the cabin. They are said tobe experiencing the sensation of weightlessness.

To be nearly weightless, the astronauts would have to be farfrom Earth to be significantly free from the effects of its gravity.Even while orbiting 400 km above Earth, the force of gravitypulling on the shuttle is still about 90 percent as strong as it is atEarth’s surface, so they are not weightless.

78 CHAPTER 3 Forces

Figure 14The astronaut was able to takelonger steps on the Moonbecause the gravitationalattraction on him there is lessthan 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

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

Floating in Space So what does it mean to say that some-thing is weightless in orbit? Think about how you measure yourweight. When you stand on a scale, as in Figure 15A, you are atrest and the net force on you is zero. So the scale supports youand balances your weight by exerting an upward force. The dialon a scale shows the upward force exerted by the scale, which isyour weight. Now suppose you stand on a scale in an elevatorthat is falling, as in Figure 15B. If you and the scale were in freefall, then you no longer would push down on the scale at all.The scale dial would say you have zero weight, even though theforce of gravity on you hasn’t changed.

Everything in the orbiting space shuttle is falling downwardtoward Earth at the same rate, in the same way you and the scalewere falling in the elevator. Because objects in the shuttle haveno force supporting them, they seem to be floating.

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

thrown objects don’t always travel in straight lines. They tend tocurve downward. That’s why quarterbacks, dart players, andarchers aim above their targets. Anything that’s thrown or shotthrough the air is called a projectile. Because of Earth’s gravita-tional pull and their own inertia, projectiles follow a curvedpath. This is because they have horizontal and vertical velocities.

SECTION 2 Gravity 79

Figure 15The boy pushes down on thescale with less force when he andthe scale are falling at the samerate.

Apart from simply keepingyour feet on the ground,gravity is important for lifeon Earth for other reasons,too. Because Earth has asufficient gravitational pull,for example, it can holdaround it the oxygen/nitro-gen atmosphere necessaryfor sustaining life. Researchother ways in which grav-ity has played a role in theformation of Earth.

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

If the elevator were falling, the scale wouldshow a smaller weight.

Horizontal and Vertical Motions When you throw a ball,like the pitcher in Figure 16, the force from your hand makesthe ball move forward. It gives the ball horizontal motion ormotion parallel to Earth’s surface. After you let go of the ball, noother force accelerates it forward, so its horizontal velocity isconstant, if you ignore air resistance.

However, when you let go of the ball, somethingelse happens. Gravity can now pull it downward, givingit vertical motion, or motion perpendicular to Earth’ssurface. Now the ball has constant horizontal velocitybut increasing vertical velocity. Gravity exerts an unbal-anced force on the ball, changing the direction of itspath from only forward to forward and downward. Theresult of these two motions is that the ball appears totravel in a curve, even though its horizontal and verticalmotions are completely independent of each other.

If you were to throw a ball as hard as you could fromshoulder height in a perfectly horizontal direction, wouldit take longer to reach the ground than if you dropped aball from the same height? Surprisingly, it won’t. Athrown ball and one dropped will hit the ground at the same time. If you have a hard time believing this,Figure 17 might help. The two balls have the same accel-eration due to gravity—9.8 m/s2 downward. Howwould a thrown ball’s path look on the Moon?

80 CHAPTER 3 Forces

Figure 17Time-lapse photography showsthat each ball has the same accel-eration downward, whether it’sthrown or dropped.

Figure 16 The pitcher gives the ball a horizontal motion.Gravity, however, is pulling the ball down. Thecombination of these two motions causes the ballto move in a curved path.

Force ofgravityForce

ofgravity

Force from pitcher's hand

Centripetal ForceRecall that acceleration is the rate of change of

velocity due to a change in speed, direction, or both.Now, look at the path the ball follows as it travelsthrough the pipe maze in Figure 18. The ball mayaccelerate in the straight sections of the pipe maze ifit speeds up or slows down. However, when the ballenters a curve, even if its speed does not change, it isaccelerating because its direction is changing. Whenthe ball goes around a curve, the change in thedirection of the velocity is toward the center of thecurve. Acceleration toward the center of a curved orcircular path is called centripetal acceleration. The wordcentripetal means to “move toward the center.”

For the ball to be accelerating toward the center, an un-balanced force, called centripetal force, must be acting on it in adirection toward the center. The centripetal force acting on theball running through the maze is exerted by the outside wallpushing against it and keeping it from going straight.

When a car rounds a sharp curve on a highway, the centripetal force is the friction between the tires and the roadsurface. If the road is icy or wet and the tires lose their grip, thecentripetal force might not be enough to overcome the car’sinertia. Then the car would keep moving in a straight line in thedirection that it was traveling at the spot where it lost traction.Anything that moves in a circle, such as the people on theamusement park ride in Figure 19, is doing so because a cen-tripetal force is accelerating it toward the center.

SECTION 2 Gravity 81

Figure 19Centripetal force keeps these riders moving in a circle.

Figure 18When the ball moves through thecircular portions of the maze, it isaccelerating because its velocityis changing. Would you expect theball to be traveling faster or slowerif more curves were in the maze?

Observing CentripetalForceProcedure1. Fill a bucket that has a

secure handle with water toa level of about 3 cm.

2. Go outside and stand sev-eral meters away from anyperson or object.

3. Swing the bucket quickly ina circle. It should be upsidedown for just an instant.

Analysis1. Why didn’t you get wet?2. What force did the bottom

of the bucket exert on thewater when you swung thebucket above you?

3. What would happen if youswung the bucket slowly?

82 CHAPTER 3 Forces

Section Assessment

1. What is gravity, and how does the size oftwo objects and the distance betweenthem affect the gravitational force?

2. How is an object’s mass different from itsweight? Do objects always weigh thesame? Explain.

3. What two motions contribute to the pathof a projectile?

4. How do the planets stay in orbit aroundthe Sun?

5. Think Critically Suppose that on a planetyou weigh two-thirds as much as you do onEarth. Is the planet’s mass greater than orless than Earth’s? Explain.

6. Using a Word Processor Use a computer tomake a table showing important characteristicsof projectile motion, circular motion, and freefall. Table headings should include: Kind ofMotion, Shape of Path, and Laws or ForcesInvolved. You can add other headings. For morehelp, refer to the Technology Skill Handbook.

7. Communicating Write a paragraph describinga situation in which you experienced somethingclose to free fall or a feeling of weightlessness.Think about amusement park rides, elevators,athletic events, or even movie scenes. For morehelp, refer to the Science Skill Handbook.

Figure 20 The Moon would move in astraight line except that Earth’sgravity keeps pulling it towardEarth. This gives the Moon itscircular orbit.

The Moon Is Falling A satellite is anything that movesaround another body in a generally circular path called an orbit.Earth and the other planets are satellites because they orbit theSun. The Moon is a natural satellite of Earth. The InternationalSpace Station is another of Earth’s satellites. Because it was madehere on Earth, it is an artificial satellite. Why do satellites movethe way they do?

Imagine whirling an object tied to a string above your head.The string exerts a centripetal force on the object that keeps itmoving in a circular path. In the same way, Earth’s gravity exertsa centripetal force on the Moon that keeps it moving in a circu-lar orbit, as shown in Figure 20.

Earth’s gravity keeps the Moon in an orbit.

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

Figure 21According to Newton’s third lawof motion, the two skaters exertforces on each other. The twoforces are equal, but in oppositedirections.

SECTION 3 The Third Law of Motion 83

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

enough, usually nothing happens. Now, think about what wouldhappen if you pushed against a wall while wearing roller skates.You would go rolling backwards, of course. The harder youpushed, the more you would roll backwards. Your action on thewall produced a reaction—movement backwards. This is ademonstration of Newton’s third law of motion.

Newton’s third law of motion describes action-reactionpairs this way: When one object exerts a force on a secondobject, the second one exerts a force on the first that is equal insize and opposite in direction. Another way to say this is “toevery action force there is an equal and opposite reaction force.”

Action and Reaction When a force is applied in nature, areaction to it occurs. When you jump on a trampoline, forexample, you exert a downward force on the trampoline. Thetrampoline then exerts an equal force upward, sending you highinto the air.

Action and reaction forces are acting on the two skaters inFigure 21. The male skater is pulling upward on the femaleskater, while the female skater is pulling downward on the maleskater. The two forces are equal, but in opposite directions.

� Identify when action and reactionforces occur.

� Calculate momentum.� Demonstrate how momentum

is conserved.

VocabularyNewton’s third law of motionmomentum

From walking across the floor to arocket speeding through space, allmotion occurs because every actionhas a reaction.

The Third Law of MotionS E C T I O N

How You Move If action and reaction forces are equal, youmight wonder how some things ever happen. For example, howdoes a swimmer move through the water in a pool if each timeshe pushes on the water, the water pushes back on her? Animportant point to remember when dealing with Newton’s thirdlaw is that action-reaction forces are acting 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. Why is it harder for aswimmer to swim against a tide?

How is a swimmer able to move in the water?

Rocket Propulsion Suppose you were 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 22 uses a rocketengine to propel it forward. Figure 23 shows how rockets movethrough space.

84 CHAPTER 3 Forces

Astronauts who stay inouter space for extendedperiods of time maydevelop health problems.Their muscles, for example,may begin to weakenbecause they don’t have toexert as much force to getthe same reaction as theydo on Earth. A branch ofmedicine called space med-icine deals with the possi-ble health problems thatastronauts may experience.Research some otherhealth risks that areinvolved in going into outerspace. Do trips into outerspace have any positivehealth benefits?

Figure 22If more gas is ejected from therocket engine, or expelled at agreater velocity, the rocketengine will push the car faster.

Figure 23

VISUALIZING ROCKET MOTION

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

splashing down safely in the Pacific Ocean. The motion ofthe spacecraft to the Moon and back is governed byNewton’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. Thisis Newton’s second law in action: As massdecreases, acceleration can increase.

After the lunar module returns to Apollo, the rocket fires itsengines to set it into motion toward Earth. The rocket then shuts offits engines, moving according to Newton’s first law. As it nears Earth,the rocket accelerates at an increasing rate because of Earth’s gravity.

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.

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SECTION 3 The Third Law of Motion 85

Finding Planets with Newton’s Laws

The gravitationalforce between Earthand the Sun causes

Earth to orbit the Sun. However, Earth’s orbit isalso affected by the gravitational pulls of theother planets in the solar system. Each planetpulls on Earth with a force determined by itsmass and its distance from Earth. In the sameway, the orbit of every planet in the solar systemis affected by the gravitational pulls from all theother planets.

In the 1840s, the most distant planet knownwas Uranus. Astronomers noticed that its orbit

couldn’t be explained by the forces exerted by the Sun and theother known planets. They concluded that there must be anotherplanet affecting the orbit of Uranus that hadn’t been discovered.Using Newton’s laws of motion, Urbain Jean Leverrier and JohnAdams independently calculated where it must be located. Theplanet, shown in Figure 24, was found in 1846 where Leverrierand Adams said it would be, and named it Neptune.

MomentumYou know that a slow-moving bicycle is easier to stop than a

fast-moving one. Also, a slow-moving bicycle is easier to stopthan a car traveling at the same speed. Increasing either thespeed or mass of an object makes it harder to stop.

A moving object has a property called momentum that isrelated 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 withthis equation:

momentum � mass � velocity

p � m � v

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

The two trucks in Figure 25 might have the same velocity,but the bigger truck has more momentum because of its greatermass. An archer’s arrow can have a large momentum because of its high velocity, even though its mass is small. A walkingelephant may have a low velocity, but because of its large mass, ithas a large momentum.

86 CHAPTER 3 Forces

Figure 24The location of the planet Nep-tune was predicted correctlyusing Newton’s laws.

Force and Changing Momentum If you catch a fast-moving baseball, your hand might sting, even if you use a base-ball glove. Your hand stings because the baseball exerted a forceon your hand when it came to a stop, and its momentumchanged.

Recall that acceleration is the difference between the initialand final velocity, divided by the time. Also, from Newton’s sec-ond law, the net force on an object equals its mass times itsacceleration. By combining these two relationships, Newton’ssecond law can be written in this way:

F � (mvf � mvi)/t

In this equation mvf is the final momentum and mv i is theinitial momentum. So the equation says that the net forceexerted on an object can be calculated by dividing its change inmomentum by the time over which the change occurs. Whenyou catch a ball, your hand exerts a force on the ball that stopsit. Here the final velocity is zero. The force depends on the massand speed of the ball and how long it takes to come to a stop.

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 26. Beforethe game starts, all the balls are motionless. The total momen-tum of the balls is, therefore, zero.

What happens when the cue ball hits the group of balls thatare motionless? The cue ball slows down and the rest of the ballsbegin to move. The total momentum of all the balls just beforeand after the collision would be the same. The momentum thegroup of balls gained is equal to the momentum that the cue balllost. If no other forces act on the balls, their total momentum isconserved—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.

87

Figure 25Suppose both trucks have thesame speed. Truck has moremomentum than the smallertruck because the larger truckhas more mass.Under what conditions would thesmaller truck have a momentumgreater than the big truck?

Figure 26Momentum is transferred in collisions.

At the start, the cue ball hasall the momentum. The otherballs have no momentumbecause they are not moving.

When the cue ball strikes theother balls, it transfers some ofits momentum to them.

When Objects Collide Look at the pictures of the air-hockey table in Figure 27. Suppose one of the pucks was movingalong the table in one direction and another struck it frombehind. The puck that was struck would continue to move in thesame direction but more quickly. The second puck has given itadditional momentum in the same direction. What if the twopucks had the same mass and were moving toward each otherwith the same speed? Each would have the same momentum, butin opposite directions. So the total momentum would be zero.After the pucks collided, they would reverse direction, and movewith the same speed. The total momentum would again be zero.

88 CHAPTER 3 Forces

Section Assessment

1. What is Newton’s third law of motion?

2. How can a rocket move through outerspace where no matter exists for it to push on?

3. Compare the momentum of a 50-kg dol-phin swimming 10.4 m/s and a 6,300-kgelephant walking 0.11 m/s.

4. When two pool balls collide, what happensto the momentum of each?

5. Think Critically Some ballet directorsassign larger dancers to perform slow,graceful steps and smaller dancers to perform quick movements. Does this planmake sense? Why?

6. Predicting You are a crane operator using awrecking ball to demolish an old building. Youcan choose to use a 100-kg ball or a 150-kg ball.Which ball would knock the walls down faster?Which ball would be easier for you to control?Explain. For more help, refer to the ScienceSkill Handbook.

7. Communicating In your Science Journal, usethe law of conservation of momentum toexplain the results of a particular collision youhave witnessed. For example, think of games,sports, or amusement park rides or contests. Formore help, refer to the Science Skill Handbook.

Figure 27The results of a collision dependon the momentum of each object.

When the first puck hits thesecond puck from behind, itgives the second puck momen-tum in the same direction.

If the pucks are speedingtoward each other with the samespeed, the total momentum iszero. How will they move afterthey collide?

ACTIVITY 89

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

Measuring the Effects

of Air Resistance

5. Crumple a sheet of paper into a tight ball andrepeat 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. Infer the relationship between the fallingtime and the acceleration of each sheet ofpaper.

3. Explain why the different-shaped papers fellat different speeds.

4. Explain how your design maximized theeffect of air resistance on your paper’s gravi-tational acceleration.

5. Infer why a sky diver will fall in a spread-eagle position before opening her parachute.

If you dropped a bowling ball and a feather fromthe same height on the Moon, they would both

hit the surface at the same time. All objectsdropped on Earth are attracted to the ground withthe same acceleration. But on Earth, a bowlingball and feather will not hit the ground at thesame time. Air resistance slows the feather down.

What You’ll InvestigateHow does air resistance affect the acceleration offalling objects?

Materialspaper (4 sheets of equal size) stopwatchscissors masking tapemeterstick

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.

Safety Precautions

Procedure1. Copy the data table above in your Science

Journal, or create it on a computer.

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

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 the paperto reach the ground. Record your time in yourdata table.

4. Crumple a sheet of paper into a loose ball andrepeat step 3.

Paper Type Time

Flat paper

Loosely crumpled paper

Tightly crumpled paper

Your paper design

Effects of Air Resistance

The Momentum of Colliding Objects

90

Materialsmetersticksoftballracquetballtennis ballbaseballstopwatchmasking tapebalance

Goals� Observe and calculate the

momentum of different balls.� Compare results of collisions

involving different amounts ofmomentum.

Safety Precautions

Many scientists hypothesize that dinosaurs became extinct 65 million years agowhen an asteroid slammed into Earth. The asteroid’s diameter was probably no

more than 10 km. Earth’s diameter is more than 12,700 km. How could an object thatsize change Earth’s climate enough to cause the extinction of animals that haddominated life on Earth for 140 million years? The asteroid could because it may havebeen traveling at a velocity of 50 m/s, and had a huge amount of momentum. Thecombination of an object’s velocity and mass will determine how much force it canexert. Explore how mass and velocity determine an object’s momentum during thisactivity.

What You’ll InvestigateHow do the mass and velocity of a moving object affect its momentum?

Action Time Velocity Mass Momentum Distance ball moved softball

Racquetballrolled slowly

Racquetballrolled quickly

Tennis ballrolled slowly

Tennis ballrolled quickly

Baseball rolledslowly

Baseball rolledquickly

Momentum of Colliding Balls

Procedure

Conclude and Apply

6. Measure the distance the racquet-ball moved the softball. Record thisdistance in your data table.

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

8. Repeat steps 4-6, rolling the tennisball quickly and then slowly.

9. Repeat steps 4-6, rolling the base-ball quickly and then slowly.

1. Copy the data table on the previouspage in your Science Journal.

2. Use the balance to measure themass of the racquetball, tennis ball,and baseball. Record these massesin your data table.

3. Use your meterstick to measure a 2-m distance on the floor. Mark thisdistance with two pieces of mask-ing tape.

4. Place the softball on one piece oftape. Starting from the other pieceof tape, slowly roll the racquetballthe 2-m distance so that it hits thesoftball squarely.

5. Use a stopwatch to time how long ittakes the racquetball to roll the 2-mdistance and hit the softball. Recordthis time in your data table.

5. Explain how you observed New-ton’s third law of motion occurringduring this activity.

1. Using the formula p � mv, calculatethe momentum for each type of balland action. Record your calculationsin the data table.

2. Compare the momentums you cal-culated. Which action had the great-est momentum? Which had thesmallest momentum?

3. Infer the relationship between themomentum of each ball and the dis-tance the softball was moved.

4. Explain why the baseball will have agreater momentum than the tennisball even if both are traveling withan equal velocity.

ACTIVITY 91

Use what you have learned about momentumto discuss the differences between the sportsof softball and baseball.

…The fastestbaseball pitch onrecord was thrown at162.3 km/h. Thissuperfast pitch wasthrown by the Cali-fornia Angels’ NolanRyan during a majorleague game in 1974.

Moving and ForcingDid you know…

…The Sun moves in acircular path around thecenter of the galaxy at about250 km/s. At this rate, theSun could make a trip fromNew York to Los Angeles inabout 18 s.

0 80

(>64)

20 40Wind speed (knots)

60

1 knot � 1.85 kilometers per hour

Tropicaldisturbance

Tropicalcyclone

Tropicaldepression

Gale

Tropicalstorm

Wind Categories

(35–64)

(34–47)

(20–34)

(<20)

92 CHAPTER 3 Forces

Nolan Ryan

Los Angeles

New York

17.58SECONDS

…Ocean waves are powerful. The Atlantichurls an average of 10,000 kg of water per squaremeter at the shore in winter. During one storm, thewaves ripped away a 1,496,880-kg steel-and-concreteportion of a breakwater. During a later storm, its2,358,720-kg replacement met with the same fate.

…The force exerted by the spaceshuttle’s solid rocket booster engineswhen lifting off from Earth equals the forceexerted by the engines of 35 jumbo jets. Toescape Earth’s gravity, a spacecraft must reach aspeed through the atmosphere of more than40,320 km/h. This is about 455 times fasterthan a typical highway speed limit of 88.5 km/h.

1. What is the distance from New York to Los Angeles?2. How far does the Sun travel in 5 min?3. The following is a list of the masses of several types

of balls: volleyball, 280 g; tennis ball, 60 g; baseball,150 g; football, 425 g; basketball, 650 g; and softball,200 g. Make a bar graph that compares the masses of these balls.

Go FurtherWrite Newton’s first, second, and third laws of motion on three separate

sheets of paper. Under each, write a paragraph or make a sketch that showsthat law at work in some common situation.

…The force needed to stop a jumbo jet isequal to the frictional force applied by 1 million auto-mobile brakes. Even so, the airplane has to travel a dis-tance of almost 1 km on the ground before it stops.

Spaceshuttle

747 jumbo jet

SCIENCE STATS 93

94 CHAPTER STUDY GUIDE

3. Weight is the measure of the gravitationalforce exerted on an object by Earth. Weightis expressed in newtons, N. You use the fol-lowing equation to calculate weight

W � m � 9.8 m/s2

where m is the mass of the object.

Section 3 The Third Law of Motion1. Newton’s third law of motion states that for

every action there is an equal and oppositereaction.

2. The momentum of an object can becalculated by the equation p = mv. If theobjects in this photo are moving, whichprobably has the greatest momentum?

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

Section 1 Newton’s Second Law 1. Newton’s second law of motion states that

a net force causes an object to accelerate inthe direction of the net force, with an accel-eration equal to the net force divided by the mass.

2. Friction iscaused by themicroweldsthat developbetween themicroscopicbumps on twosurfaces. Thethree types offriction are static, sliding, and rolling. Whattype of friction is at work in this picture?

3. All objects are attracted to Earth with thesame acceleration. Air resistance exerts an upward force on objects falling through the atmosphere.

Section 2 Gravity1. Gravity is the force of attraction that exists

between any two objects having mass. Thesize of the gravitational force is determinedby the mass of the objects and their distancefrom each other.

2. Projectiles have a horizontal and a verticalmotion that makesthem travel in acurved path. Circu-lar motion is causedby a centripetal, orcenter-seekingforce. What exertsthe center-seekingforce in the photo?

Study GuideChapter 33

Use the information onyour Foldable to compareand contrast the types of

friction. Write similarities and differences onthe back of your Foldable.

After You ReadFOLDABLESReading & StudySkills

FOLDABLESReading & Study Skills

CHAPTER STUDY GUIDE 95

Vocabulary Wordsa. centripetal accelerationb. centripetal forcec. frictiond. law of gravitatione. momentumf. Newton’s second law of motiong. Newton’s third law of motionh. weight

Using VocabularyUsing the vocabulary words list, replace the

underlined words with the correct words.

1. The microwelds that form between the surfaces of two objects sometimes makeobjects hard to move.

2. The Moon’s acceleration toward the center ofits circular path is caused by Earth’s gravity.

3. For every action, there is an equal andopposite reaction.

4. The force of gravity exerted on an object isdifferent on different planets.

5. The combined mass and velocity of therunaway train made it dangerous.

6. The acceleration of an object equals the netforce divided by the mass.

Study GuideChapter 33

Make a note of anything you can’t understandso that you’ll remember to ask your teacherabout it.

Study Tip

Complete the following concept map on forces.

Newton’s 2nd Law

MassAction-reaction

force pairs

Gravitationalattraction

Forces

change motion

relates force to

between two objects

involves

long-rangeforce

depends on

AssessmentChapter 33

Choose the word or phrase that best answers thequestion.

1. What will happen to an object when a netforce acts on it?A) fall C) accelerateB) stop D) go in a circle

2. Which is Newton’s second law?A) F � 1/2ma2 C) p � mvB) F � 2 ma D) a � F/m

3. What is the force of gravity on an objectknown as? A) centripetal force C) momentumB) friction D) weight

4. Which of the following is NOT a type offriction?A) static C) centripetalB) sliding D) rolling

5. What’s true about an object falling towardEarth?A) It falls faster the heavier it is.B) It falls faster the lighter it is.C) Earth pulls on it, and it pulls on Earth.D) It has no weight.

6. Why do projectiles follow a curved path?A) They have a horizontal and a vertical

motion.B) They have centripetal force.C) They have momentum.D) They have inertia.

7. What is the product of mass and velocityknown as?A) gravity C) frictionB) momentum D) weight

8. Which body exerts the weakest gravitationalforce on Earth?A) the Moon C) PlutoB) Mars D) Venus

9. When a leaf falls, what force opposes gravity?A) air resistance C) frictionB) terminal velocity D) weight

10. In circular motion, the centripetal force isin what direction? A) forward C) toward the centerB) backward D) toward the side

11. What is the weight on Earth of a personwith a mass of 65 kg?

12. Some people put chains on their tires in thewinter. Why?

13. List some ways an astronaut could keep hersupplies from floating away from her whileshe is in orbit around Earth.

14. As you in-line skate around the block,what action and reaction forces keep youmoving?

15. Which one ofthe followingwould have themost momen-tum—a charg-ing elephant, ajumbo jet sittingon the runway,or a baseballtraveling at 100 km/h? Explain.

16. Classifying Classify the following as exam-ples of static, sliding, or rolling friction:sledding down a hill, sitting in a chair,pushing a grocery cart, standing on a steepslope, and rowing a boat.

96 CHAPTER ASSESSMENT

CHAPTER ASSESSMENT 97

17. Drawing Conclusions A race car is movingin a circle at a constant speed around atrack. Does a centripetal foce act on the car?

18. Recognizing Cause and Effect Suppose youstand on a scale next to a sink. What hap-pens to the reading on the scale if you pushdown on the sink?

19. Interpreting Data The following tablecontains data about four objects that weredropped to Earth at the same time.a. Which object fell fastest? Slowest?b. Which object has the greatest weight?c. Is air resistance stronger on A or B?d. Why are the times different?

20. Poem Write a poem about a falling leaf.Include the terms gravity, free fall, air resist-ance, and terminal velocity.

21. Oral Presentation Prepare a presentationto explain Newton’s third law of motion toa group of first-grade students.

Tiffany learned that the acceleration ofa free-falling body is 9.8 m/s2. She wantedto find out what speed a sky diver reachesafter several seconds. Her calculations areshown in the table below.

Study the table and answer the following questions.

1. According to these data, about how fast will the speed of a falling sky diverbe after 5 s?A) 39.8 m/s C) 49.0 m/sB) 44.2 m/s D) 54.0 m/s

2. Which of these causes falling sky diversto accelerate?F) gravityG) inertiaH) rotation of Earth on its axisJ) the tilt of Earth on its axis

3. If Tiffany extended her table,what would the sky diver’s speed be after 14 s?A) 107.8 m/s C) 147.0 m/sB) 78.4 m/s D) 137.2 m/s

Test Practice

AssessmentChapter 33

Go to the Glencoe Science Web site at science.glencoe.com or use the Glencoe Science CD-ROM for additional chapter assessment.

TECHNOLOGY

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

Time of Fall for Dropped Objects

Time (s) Speed (m/s)

0 0

1 9.8

2 19.6

3 29.4

4 39.2

5 ?

Speed of a Falling Sky Diver