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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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