Laws Governing Motions

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3. Laws Governing MotionMotion is all around uspeople walk, clouds

move, rain falls, and water flows. Things are moving

wherever we look, and motion seems to be associated

with all the changes we observe. Understanding motion

is an important starting point in understanding the

world. Newton helped us to understand motion in terms

of the three laws he published in 1687. Although his

laws of motion appear relatively simple, his perspective

is not intuitively obvious and requires a retraining of the

way we think. We will now describe these laws of

motion and try to understand their meaning, illustratingthem with common experience, but common experience

seen in a new way.

The First Law of Motion

Before dealing with all kinds of motion, we must

first ask: How do objects move if they are left alone?

What is the natural motion of free objects? Only

when we know the answers to these questions do we

know what remains to be explained. If free objects

move in a particular way, objects that move in some

other way are not free and their motions must be

explained by another law. The First Law of Motioncorrectly describes the motion of free objects:

Every object continues in its state of rest, or of

uniform motion in a straight line with unchang-

ing speed, unless compelled to do otherwise by

forces acting upon it.

It seems obvious that an object at rest remains at

rest if it is left alone, yet the consequence can some-

times be startling. A magician depends on this law

when he pulls the tablecloth from a table, leaving the

dinner service undisturbed. The plates and goblets are

at rest and remain at rest unless the tablecloth com-

pels them to do otherwise.

A less entertaining manifestation of the law occurs

when a stopped car with passengers is struck from

behind. The passengers heads momentarily remain at

rest while the car and the rest of their bodies are com-

pelled to move forward by the force of the impact.

This results in stretching and bone dislocation known as

whiplash injury.

This First Law also states that moving objects, if

left to themselves, will continue to move in a straight

line without changing speeduniform motion. At first

this seems contrary to our experience. Moving objects

always seem to slow down and stop if nothing is done

to keep them moving. Is this not a violation of this

statement of the law?

Our problem is that the objects with which we deal

are not free. Friction acts on them and, if it is not

opposed by other forces, compels these objects to

change from their state of uniform motion. We can test

the validity of the First Law, however, by considering themotion of objects in situations where friction is greatly

reduced. One can easily imagine, for example, that an

ice skater could glide on and on without ever slowing

down if friction could be eliminated totally (Fig. 3.1).

Figure 3.1. An ice skater could go on forever without

effort if friction were not present.

Those who drive on icy roads are acutely aware of the

consequences of the law. It is a frightening experience to

approach an intersection, apply the brakes because of a red

light, and then proceed through without slowing down.

Turning is also a problem because, without friction, the car

continues in a straight line no matter how the wheels are

turned. After two or three such experiences, one is easily

convinced that the First Law of Motion is valid.


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Even so, the consequences of the law still catch us

unaware. A common auto injury occurs when a passen-

ger strikes the windshield when the car in which he is

riding suddenly stops. The passenger keeps moving in

accordance with the First Law of Motion (Figure 3.2).

A final example suggests another consequence of

the law. A car makes a left turn at modest speed. A

package next to the driver slides across the seat, away

from the center of the turn, and continues its

straight-line motion in accordance with the First Law of

Motion, while the car turns under it (Fig. 3.3).

Incidentally, none of these examples proves thatthe First Law of Motion is valid, but all suggest that it

might be. Considering other consequences of the law

seems reasonable. As we gain additional experience we

gain increasing confidence in the validity of the law.

Acceleration

Uniform motion in a straight line without changing

speed is the natural motion of free objects. Any object

that is not in uniform motion is said to be accelerating.

An object accelerates if its speed changes, either to

increase or decrease, or if its direction changes. It is

sometimes useful to assign specific words to describe

some simple types of acceleration. Deceleration, for

example, denotes a decrease in speed whereas a direc-

tion change is properly designated as a centripetal (cen-

ter-seeking) acceleration. Any change from uniform

motion, however, is an acceleration (Fig. 3.4 and 3.5).Figure 3.3. Why does the passenger feel thrown to

the outside of a turn?

Figure 3.4. Successive pictures, taken at equal time intervals, of a car in four different kinds of motion. Why do we

say that the car is accelerating in c and d but not in a and b?

Figure 3.2. Both drivers lose their heads in a rear-end

collision. Why?


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Figure 3.5. A coin rests on a moving turntable. How

do you know it is accelerating?

Acceleration may be defined more precisely as the

rate at which speed or direction is changing. The accel-

eration of a car might be designated properly as 5

mi/hr/sec. This car would increase its speed from 30 to

50 mi/hr in 4 sec. It would have the same amount of

acceleration if its speed increased from 10 to 30 mi/hr in

the same amount of time. If it slowed from 50 to 40

mi/hr in 2 sec the acceleration would be 5 mi/hr/sec;the negative sign denotes deceleration.

Force

Your intuitive understanding of force is probably

adequate for our present purposes. Force is simply a

push or pull exerted on one object by another. A more

sophisticated definition of force is implied by the First

Law of Motion: force is anything that causes accelera-

tion. All accelerations are caused by forces. Forces are

acting whenever an object moves faster, moves slower,

changes direction, or experiences any combination of

speed and direction change.

The kind of acceleration caused by a particularforce depends on the direction of the force. If a force

pushes on an object in the same direction as its motion,

the object speeds up. The object slows down if the force

opposes its motion (Fig. 3.6). Lateral forces cause

change in direction with the object turning toward the

direction of the force (Fig. 3.7).

The strength of forces is measured in pounds (lb)

in the English system of units and newtons (N) in the

metric system. The amount of acceleration produced by

a particular force is determined partly by its strength.

Stronger forces produce greater accelerations. If a par-

ticular force causes an object to accelerate from 20 to 30

mi/hr in 10 sec, a force twice as strong would cause the

same change in half the time. A force half as strongwould take 20 sec to produce the same effect.

Most objects we deal with are influenced by more

than one force. These forces may oppose each other so

that the resulting acceleration is reduced, or they may

act in the same direction so that the acceleration is

greater than for either one by itself. The sum of all the

forces acting on an object is called the net force or

resultant force. The strength and direction of the net

force determine the acceleration of the object.

Forces cannot be summed like ordinary numbers,

however. Forces have both a magnitude (strength) and a

direction. Such quantities, called vectors, can be repre-

sented by an arrow whose length has been scaled to rep-

resent the magnitude and whose direction is that of the

pointed arrow. Two vectors can be added by forming a

parallelogram with the two properly scaled and oriented

vectors forming the adjacent sides. The diagonal of the

parallelogram is the resultant force (sum of the two) and

will have both the proper length and direction.

Mass

Not all objects experience the same acceleration

when acted upon by similar forces. An ordinary car, for

example, might be able to provide significant accelerationto a small empty trailer but considerably less when the

trailer is full. If a truck is loaded, the time and distance

required for a safe stop increases significantly (Fig. 3.9).

The property of objects that determines how much

they accelerate in response to applied forces is called

mass. If mass is large, acceleration will be less than if

mass were smaller. The smaller the mass, the greater the

acceleration.Figure 3.6. Both pitcher and catcher exert forces that accel-

erate the baseball. In which direction is each force applied?

Figure 3.7. The puck slides in a circle on an air-hock-

ey table without friction. In what direction is the force

exerted on the puck by the string? (Hint: Have you

ever seen a string that could push on anything?)


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Figure 3.8. Two vectors, A and B, are added to give the

resultant, C. What is the resultant of D and E?

Mass does not depend on location. A particular

force causes the same amount of acceleration no matter

where the object is located: near the earth, in interstel-

lar space, or anyplace else (Fig. 3.10). If the same

object experiences different accelerations at different

places, it is because the forces acting on it are different,

not because its mass has changed.

To be useful, the concept of mass must be made

quantitative. We want to know, for example, whether a

sack of potatoes has a mass of one kilogram or two kilo-

grams. Quantities of mass are defined by comparison to

some arbitrarily defined standard. The standard kilo-

gram is decreed to be the mass of a piece of platinum-

iridium which is kept under the watchful care of the

Bureau Internationals des Poids et Measures at Sevres

near Paris. If you want to know whether you have onekilogram of potatoes, you must directly or indirectly

compare the mass of your potatoes with the mass of this

piece of metal.

To make this process practical, copies of the stan-

dard kilogram are supplied to the bureaus of standards of

the various nations. They, in turn, make copies-some

of which are split in halves, quarters, etc. You may have

seen a box of weights in a chemistry laboratory which

is the result of this process. One way to compare your

potatoes to the standard mass is to place potatoes and

standard mass on opposite sides of a balance (scales) and

let gravity serve as a standard force. Put your potatoes

on one side and keep adding standard masses to the other

until balance is achieved. Now add up the standard

masses you have used and this is equal to the mass of the

potatoes. You have made your comparison (indirectly)

with the standard kilogram near Paris.

Length and time must also be given quantitative

meaning by comparison to standards. For many years

SPACE

EARTH

MOON

Figure 3.9. The same force applied to different objects produces different accelerations. Which of these trucks is

empty? Which has the greater mass?

Figure 3.10. A rocket (or any other object) is just as hard to accelerate no matter where it is. Why?


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the standard meter was a long bar of metal kept along-

side the standard kilogram. The second was defined as

some fraction of the day. Today we have more precise

standards of time and distance which are based on cer-

tain characteristics of atoms. The equations we present

in this book are usually presented in a form which

requires that a certain consistent set of units be adopted

when using the equation. The metric system uses

meters for length, seconds for time, and kilograms formass; the English system uses feet for length, seconds

for time, and slugs for mass. (While almost all civilized

nations have adopted the metric system, the United

States remains an official user of the foot-pound-second

system. This will almost surely change because it

works to our disadvantage in world trade.)

The Second Law of Motion

Perhaps briefly summarizing what we know about

motion so far will help:

1. If an object is left to itself, it will remain at rest

or move with its initial uniform motion.

2. Forces cause objects to accelerate. The stronger

the net force, the greater the acceleration.

3. Accelerations are less if mass is larger.

4. Acceleration is in the same direction as the net

applied force (forward, backward, sideways, or

some combination of these).

The second, third, and fourth of these statements

constitute the Second Law of Motion. In addition, the

law specifies the exact relationship between the mass of

an object, the strength of the net force applied to it, andthe amount of acceleration caused by the force. The

relationship is

acceleration net forcemass

or, equivalently,

net force mass acceleration.

With the First and Second Laws of Motion, you

can begin to study the motion of anything you observe.

Remember, the important question is not why an objectkeeps moving but why its motion changes. This ques-

tion directs our attention to a search for forces and their

causes. An understanding of the forces enables us to

determine if the accelerations we observe are consistent

with the forces and with the objects mass. If they are,

we can go on to other interesting problems; if not, we

have more to learn.

The Third Law of Motion

Forces act on all objects. To understand objects

motion, or lack of motion, we must consider where

forces come from, in what situations they occur, and

what determines their strength and direction.

Otherwise, we can neither explain nor predict motion.

The first important observation about forces is that

they occur only when two things interact with eachother. Nothing can exert a force on itself. For example,

the wheels of a car touch the road. If the interactions

between drive wheels and road do not occur, perhaps

because of ice on the road, there is no force and the car

does not accelerate. A boat propeller touches the water;

an airplane propeller, the air. The forces that accelerate

a rocket result from the contact between the rocket itself

and the fuel that burns inside. No object or system that

can exert a net force on itself has ever been found or

invented. Forces occur only when two objects are asso-

ciated with each other, the most common association

being actual contact.

The next important observation is that two forces

act in every interaction, one on each of the interacting

objects. In some cases, the two forces are both appar-

ent. As a man steps from a small rowboat to a dock, he

is accelerated toward the dock and the boat accelerates

in the opposite direction. A rifle recoils (accelerates)

whenever a bullet is fired.

Sometimes, however, the second force is less obvi-

ous and we may not recognize its presence. When you

start to walk, for example, the force that accelerates you

comes from the interaction between your foot and the

floor. You push backward on the floor (using your leg

muscles), the floor pushes forward on you, and youaccelerate in the direction of this force exerted on your

foot by the floor.

The forward force on your foot in this example is

obvious. It causes your foot and its attachments to

accelerate. The backward force is not quite so apparent.

Nothing seems to accelerate in that direction. We usu-

ally do not notice that the floor is rigidly attached to the

earth, and so its effective mass is quite large. The floor

is, in fact, accelerated backward, but the amount of

acceleration is immeasurably small because of the

floors large mass. The presence of this backward force

would easily be revealed if the floor were covered with

marbles. Their backward acceleration as you walked onthem would make the backward force readily apparent.

By now you should have noticed that the two forces

that interacting objects exert on each other always act in

opposite directions. When a man steps from a rowboat, he

is accelerated one way while the boat moves in the oppo-

site direction. A bullet is fired in a particular direction,

and the gun recoils oppositely. You push backward on the

floor and the floor pushes forward on you. The two forces

in every interaction are always oppositely directed.


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It can be shown by careful measurements that the

two forces in any interaction have the same strengtha

rule always obeyed by nature. For example, if you

forcefully kick a stone, your toe receives the benefit of

a force that has the same bone-breaking strength. If you

kick more gently, the force on your toe is also more gen-

tle by exactly the same amount (Fig. 3.11).

You can probably imagine how this rule might be

tested. Arrange for two objects, whose masses you know

from another experiment, to interact with each other;

measure the accelerations caused by the forces of inter-

action; and use the Second Law of Motion to calculate

the forces. Thousands, perhaps millions, of experiments

of this kind have been performed since Newton first sug-

gested the rule. In every case, the forces the interacting

objects exert on each other have been shown to have

exactly the same strength (Fig. 3.12).

The properties of forces described above are col-

lectively known as the Third Law of Motion, which is

stated as follows:

All forces result from interactions between pairs

of objects, each object exerting a force on the

other. The two resulting forces have the same

strength and act in exactly opposite directions.

As you can see, the Third Law of Motion is a rule

about forces. It is a law of motion only to the extent

that forces and motion are related through the Second

Law of Motion. Nevertheless, the law seems to beobeyed by all the forces in nature that can be studied in

detail. There are apparently no exceptions.

Notice that the Third Law does not tell everything

about forces. It gives no information about how strong

the forces will be for any given interaction. This infor-

mation is expressed by force laws that describe the

kinds of interactions that occur in nature and the result-

ing forces. These are described in the next chapter.

Applications

The First Law of Motion can be used to

explain auto whiplash and windshield injury, the

sensation of being thrown outward during a turn, the

almost effortless motion of an ice skater, and other

common experiences.

The Second Law of Motion can be used to

explain the nearly circular motion of the planets, why

sliding objects slow down, why it is hard to stop or turn

on slick roads, the behavior of electrons in a TV tube,

the operation of electric and gasoline motors, why it is

easier to accelerate a motorcycle than a truck, and

much, much more. Indeed, every mechanical device

involving internal or external motion is based on the

Second Law.The Third Law of Motion can be used to explain

the operation of a rocket engine, the kick of a rifle or

shotgun, the operation of a jet or propeller-driven air-

craft, the motion of a boat when a person steps off it,

and many other phenomena.

In each case, the Third Law of Motion describes

some features of the relevant forces. The resulting

motions are then predicted by the Second Law of Motion.

Figure 3.11. Identify the interaction, the two resulting

forces, and the accelerations that are produced when a

person kicks a rock.

Figure 3.12. Why is gravel thrown backward when a car accelerates? What force accelerates the car?


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What happens to the motion of both the mos-

quito and the truck?

(4) Suppose a man jumps forward toward a

dock from a small boat that is not securely

anchored. What happens to the horizontal

motion of both the man and the boat if the boat

has less mass than the man?

E. EXERCISES

3.1. Suppose you have a friend who does not

believe the First Law of Motion is true. How would you

proceed to convince the friend otherwise?

3.2. If an elephant and an ant are both moving at

the same speed on a level, frictionless surface, which

would stop first? Assume air friction to be unimportant

for both.

3.3. An unrestrained child is standing on the front

seat of a car traveling at 20 mi/hr in a residential neigh-

borhood. A dog runs in front of the car and the driver

quickly and forcefully applies the brakes. The childs

head strikes the windshield.

(a) Explain this result in terms of the First Law of

Motion.

(b) If the car stopped before the child reached the

windshield, with what speed would the childs head

strike the windshield?

3.4. Using the First Law of Motion, explain why a

passenger in a turning car feels thrown away from the

center of the turn.

3.5. State the First Law of Motion in your own

words. Explain its meaning.

3.6. What do the words uniform motion mean as

part of the First Law of Motion?

3.7. A car travels in a large circle (in a parking lot,

for example) without changing speed. Is the car in uni-

form motion? Explain your answer.

3.8. In each of the following situations, describe

(1) what actually happens or would be expected to hap-

pen and (2) how these results can be accounted for bythe First Law of Motion.

(a) A car is struck from behind by a faster moving

vehicle. A passenger later complains of whiplash

injury.

(b) A car experiences a head-on collision with a

lamppost. A front-seat passenger is not wearing a

seat belt.

(c) Aball is placed on a level table fixed to the floor

of a train at rest in a station. The train suddenly

starts moving.

(d) Aball is placed on a level table fixed to the floor

of a train which is moving with uniform motion.

The train suddenly stops.

(e) Same as (d) except the train speeds up.

(f) Same as (d) except the train goes around a curve

in the track.

3.9. The driver of a car has three accelerators (con-trols that can cause the car to accelerate). What are they?

3.10. Suppose you see an object traveling in a cir-

cle with constant speed. What can you say for sure

about the force or forces acting upon it?

3.11. Describe an experiment you could perform

that would determine which of two objects has the larg-

er mass. Be sure that your experiment is consistent with

the definition of mass given in this chapter.

3.12. A constant force is continuously applied to an

object that is initially at rest but free to move without

friction. No other forces act on the object. Describe

what would be observed under these conditions and

explain how the observed results can be accounted for

by the Second Law of Motion. Finally, explain why real

objects-cars for example-do not behave in this

way.

3.13. Describe the three simple types of accelera-

tion which are governed by the Second Law of Motion.

3.14. Does a car accelerate when it goes up a hill

without changing speed? Explain your answer.

3.15. Describe the accelerations which occur as an

elevator rises, starting from rest at the first floor and

stopping at the twentieth floor.

3.16. Imagine an object resting on a horizontal sur-

face where there is no friction (an air-hockey table, for

example). A force is applied to it so that it accelerates,

sliding along the surface. Now imagine that the whole

apparatus is taken to the moon where the same experi-

ment is performed using the same object and the same

force. How would the acceleration of the object near

the moon compare with that near the earth?

3.17. Now suppose that the object in the previous

question is taken to a place, a long way from the earth

or moon, where it is weightless. Again, the same force

is applied to it (using a small rocket engine, for exam-

ple). What does it do?

3.18. State the Second Law of Motion and explain

its meaning.


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3.19. An object is traveling on a smooth horizon-

tal surface where the friction can be ignored. A force is

applied (perhaps by a rocket engine or propeller

attached to the object) in a direction opposite to the

objects velocity. Describe what would happen and

explain how this is consistent with the Second Law of

Motion.

3.20. A rocket in deep space requires less and lessforce to accelerate it at the same rate, even though the

gravitational and frictional forces on it do not change.

What can you conclude?

3.21. A car turns a corner at constant speed. Is

there a force acting on the car? Explain your answer.

3.22. Show how the recoil or kick of a rifle or

shotgun can be accounted for by the Second and Third

Laws of Motion.

3.23. How would the accelerations of a gun and

bullet compare if the gun had 500 times more mass than

the bullet? How would they compare if the gun and bul-

let had the same mass? Explain your answers in terms

of the Second and Third Laws of Motion.

3.24. Describe the force which causes a car to

accelerate as it starts from rest. Identify the important

interaction, describe the two forces in the interaction,

and indicate the directions of both forces. Finally,

describe the resulting accelerations.

3.25. Explain the operation of a rocket engine in

terms of the Second and Third Laws of Motion.

3.26.

(a) Describe what happens when a man jumps

from a small boat if the boat is not securely

anchored.

(b) Explain how the observed result can be

accounted for by the Second and Third Laws

of Motion.

(c) What would be different if he jumped from

a large boat? Why would this situation be

different?

3.27. A balloon is filled with air and then released.(a) What do you imagine the balloon does?

(b) Explain the imagined motion of the bal-

loon by using the Second and Third Laws of

Motion.

3.28. A truck moving at a high speed collides with

a mosquito.

(a) Describe and compare the forces in the

interaction.

(b) If the truck hits the mosquito from the

blind side, so that the mosquito couldnt get

ready, could it exert a greater force on the

mosquito than the mosquito exerts on the

truck? Explain your answer in terms of a

fundamental law.

3.29. Describe the force (or forces) which cause

you to accelerate when you start to walk. That is, iden-tify the interaction, describe the two forces in the inter-

action, and indicate the directions of both forces.

Finally, describe the resulting accelerations.

3.30. Do we arrive at the Third Law of Motion

through an inductive or a deductive process? Can the

law be proved to be true? How could it be proved to be

false?

3.31. Person X stands on a level, frictionless sur-

face. Which is true?

(a) X cannot start moving, but if moving can

stop.

(b) X cannot change horizontal speed or direc-

tion.

(c) X can change speed or direction gradually.

(d) X can change speed, but cant stop.

(e) X can change horizontal motion via verti-

cal motion.

3.32. While riding your bicycle you collide head-on

with a moving car. The acceleration you experience is

(a) the same as that of the car

(b) slightly greater than that of the car

(c) slightly less than that of the car(d) much less than that of the car(e) much greater than that of the car


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