Download NEWTON`S THIRD LAW OF MOTION

NEWTON'S
THIRD LAW
OF MOTIONACTION
AND REACTION
c
THE BIG
IDEA
.6. Can Jennifer touch lo without lo also touching
Jennifer? Newton's third law says no-you can't touch
without being touched!
For every action there is an equal
and opposite reaction.
hen two classmates running on a
playground collide, do both get
pushed, or only one? When a
heavy truck collides with a small car, which
experiences more force? Or is the force on
each the same? If the heavyweight champion
of the world punches a piece of paper in
W
midair, does the paper hit back? As shown
above, can biology author Jennifer touch
her daughter without her daughter touching
her mom back? In this chapter, we'll see
how Newton's third law of motion guides
our answers to these and other intriguing
questions.
DISCOVER!
This Way and That Way
Observe and Record
1. Gather materials: a basketball and a skateboard
or roller skates.
2. Go outside and stand someplace where you can
roll forward and backward comfortably. Toss the
basketball.
3. What happened when you tossed the ball? Write
down your observations.
Analyze and Conclude
1. Comparing How did the
direction the ball moved
compare to the direction
you moved?
2. Analyzing The ball moved because you applied
a force to it-you pushed it. Why did you move?
What pushed you?
57
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PART ONE
Physics
4.1
FIGURE 4.1 .6.
In the interaction between the
car and the truck, is the force
of impact the same on each?
Why isn't the damage the
same?
,..._
Wt,J
UNIJ:YING
CONCEPT
Friction
SECTION
3.6
;>
FIGURE 4.2 .6.
Forces between the blue and
yellow balls move the yellow
ball and stop the blue ball.
A Force Is Part
of an Interaction
In the previous chapters we've looked at force as a push or a pull. Looking closer, Newton realized that a force is more than just a single push or
pull. A force is part of a mutual action-an interaction-between one
thing and another. We say mutual because the action applies to both.
When a truck crashes into a car, there is an interaction between the
truck and the car. Part of the interaction is the truck exerting a force on
the car. The other part is the car exerting a force on the truck. .I The
forces are equal in strength and opposite in direction, and they occur
at exactly the same time.
In every interaction, forces always occur in pairs. For example, you
interact with the floor when you walk on it-you push backward against
the floor, and at the same time the floor pushes forward on you. Likewise, the tires of a car interact with the road-the tires push against the
road, and the road pushes back on the tires. In swimming you interact
with the water-you push the water backward, and the water pushes you
forward. A pair of forces is acting in each interaction. The interactions in
these examples depend on friction. But a person or car on slippery ice,
by contrast, may not be able to exert a force against the ice to produce
the needed opposite force. Then the ice cannot push back to move the
person or car.
Can things like floors, car tires, and water exert forces? Your friends
(not taking this course) may think that only living things like people and
animals can exert forces. For example, when you push on a wall, how
can the wall push back? It's not alive. It doesn't have muscles. But look at
your fingers as you push on a wall. They're bent a little. Something must
have pushed on them. The wall has pushed back on your fingers as hard
as your fingers have pushed on the wall.
So in this chapter we expand our thinking about forces. We see that
nonliving things can exert them. A force is more than a push or pull. It is
part of a mutual interaction between objects. Look for a force pair in
every interaction.
FIGURE 4.3 .6.
In the interaction between the
hammer and the stake, each
exerts the same amount of
force on the other.
FIGURE 4.4 .6.
You can feel your fingers being pushed by your friend's fingers. You also feel
the same amount of force when you push on a wall and it pushes back on you .
As a point of fact, you can't push on the wall unless it pushes back on you!
CHAPTER 4
NEWTON'S THIRD LAW OF MOTION
Does a speeding baseball have force? The answer is no. Force is not
something an object possesses, like mass. A speeding baseball exerts a
force when it hits something. How much force it exerts depends on
how quickly the ball decelerates. Objects don't possess force as a thing
in itself. As we will see in the following chapters, a speeding object
possesses momentum and kinetic energy-but not force. A force is an
interaction between one object and another.
-it cHECK
YOUWl READINtJ1
For forces that are part of an
interaction: how do their
directions compare? How
do their magnitudes
compare? When do the
forces occur?
CHECK YOUR THINKING
A car accelerates along a horizontal road. Strictly speaking, exactly
what is it that pushes the car?
Answer
It is the road that pushes the car along. Really! Except for some road friction and air drag,
only the road provides a horizontal force on the car. How? The rotating tires push back on
the road (action). At the same time the road pushes forward on the tires (reaction). The
next time you see a car moving along a road, tell your friends that the road pushes the car
along. If at first they don't believe you, convince them that there is more to the physical
world than meets the eye of the casual observer. Turn them on to some integrated science.
4.2
Newton's Third Law-Action
and Reaction
In his investigation of many interactions, Newton discovered an underlying principle called Newton's third law:
Whenever one object exerts a force on a second object, the
second object exerts an equal and opposite force on the first.
UNI~YING
CONCEPT
Newton's Laws of Motion
SECTION
2.5
We can call one force the action force, and the other the reaction
force. Then we can express Newton's third law in the following form:
To every action there is always an opposed equal reaction.
DISCOVER!
Playing with magnets is fun. Applying Newton's
third law to magnets is also fun. Hold a toy
magnet near another magnet. Notice that
when one magnet moves another, it is also
moved by the other. The effect is most noticeable
for equal-mass magnets. That's because the
changes in motion (acceleration) are the same
for each. For different-size magnets, the smaller
59
magnet moves more. Can
you see how this ties into Newton's
second law? (Newton's second law
tells us that the acceleration of
the magnet depends not only on
force, but on mass.)
60
PART ONE
Physics
.I
It doesn't matter which force we call the action or reaction.
The important thing is that they are co-parts of a single interaction
and that neither force exists without the other. Action and reaction
forces are equal in strength and opposite in direction.
FIGURE 4.5 .&.
When you lean against a wall,
you exert a force on the wall.
At the same time, the wall
exerts an equal and opposite
force on you. That's why you
don't topple over.
CHECK YOUR THINKING
1 . Which exerts more force: Earth pulling on the Moon, or the
Moon pulling on Earth?
2. When a heavy football player and a light one run into each other,
does the light player really exert as much force on the heavy
player as the heavy player exerts on the light one?
3. Would the damage to the heavy player be the same as the damage
to the light one?
Answers
Does it matter which force
in an interaction is called
the action and which is
called the reaction?
You can't push or pull on
something that doesn't also
push or pull back on youthat's the law!
1. This is like asking which is greater, the distance between New York and San Francisco,
or the distance between San Francisco and New York. Both distances are the same, but
in opposite directions. Likewise for the pulls between Earth and the Moon.
2. Yes. In the interaction between the two players, the strengths of the forces they exert on
each other are equal.
3. No. Although the forces are the same on each, the effects of these equal forces are quite
unequal! The low-mass player may be knocked unconscious while the heavier one may
be completely unharmed. There is a difference between the force and the effect of the
force.
4.3 A Simple Rule Helps Identify Action
and Reaction
Here's a simple rule for identifying action and reaction forces. First,
identify the interaction: one thing, say object A, interacts with another,
say object B. Then action and reaction forces can be stated in the following form:
Action: Object A exerts a force on object B.
Reaction: Object B exerts a force on object A.
If the action is A on B, what
is the reaction?
This is easy to remember. .I If the action is A on B, the reaction
is B on A. We see that A and B are simply switched around. Consider the
case of your hand pushing on the wall. The inter<,1ction is between your
hand and the wall. We'll say the action is your hand (object A) exerting a
force on the wall (object B). Then the reaction is the wall exerting a force
on the your hand.
CHAPTER 4
f9
NEWTON'S THIRD LAW OF MOTION
61
CHECK YOUR THINKING
In the figure we see two vectors on the sketch of the hand pushing the wall. The wall also pushes back
on the hand. Note that the other sketches show only the action fo rce. Draw appropriate vectors
showing the reaction forces. Can you specify the action-reaction pairs in each case?
Answer
Reaction: road pushes on tire
n-n _
_)->.'~~
Action: rocket pu shes on gas
Reaction: gas pushes on rocket
Action: man pulls on spring
Reaction: ball pulls on Earth
FIGURE 4.6 .A.
Action and reaction forces. Note that when the action is "A exerts force on B, "
the reaction is simply "B exerts force on A."
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PART ONE
Physics
PhysicsPiace.com
Video
Action and Reaction on
Different Masses
4.4 Action and Reaction on Objects
of Different Masses
When a cannon is fired, there is an interaction between the cannon and the
cannonball. The sudden force that the cannon exerts on the cannonball is
exactly equal and opposite to the force the cannonball exerts on the cannon.
This is why the cannon recoils (kicks). But the effects of these equal
forces are very different. This is because the forces act on different
masses. Recall Newton's second law:
F
a=-
m
Let F represent both the action and reaction forces,
m the mass of the cannon, and m the mass of the cannonball. DifFIGURE 4.7 A
INTERACTIVE FIGURE,
The force exerted against the
recoiling cannon is just as great
as the force that drives the
cannonball along the barrel.
Why, then, does the cannonball
undergo more acceleration
than the cannon?
ferent -sized symbols are used to indicate the differences in relative masses
and resulting accelerations. Then the acceleration of the cannonball and
cannon are:
Cannonball:
!_ =
m
a
F
Cannon:- =a
m
Do you see why the change in velocity of the cannonball is so large
compared to the change in velocity of the cannon? .I A given force
exerted on a small mass produces a large acceleration, while the same
force exerted on a large mass produces a small acceleration.
We can extend the idea of a cannon recoiling from the ball it fires to
understanding rocket propulsion. Consider an inflated balloon recoiling
when air is expelled. If the air is expelled downward, the balloon accelerates upward. A rocket accelerates the same way. It continually "recoils"
from the ejected exhaust gas. Each molecule of exhaust gas is like a tiny
cannonball shot from the rocket (Figures 4.8 and 4.9).
A common misconception is that a rocket is propelled by the impact
of exhaust gases against the atmosphere. In fact, before the advent of
rockets, it was commonly thought that sending a rocket to the Moon
was impossible. Why? Because there is no air above Earth's atmosphere
for the rocket to push against. But this is like saying a cannon wouldn't
recoil unless the cannonball had air to push against. Not true! Both the
rocket and recoiling cannon accelerate because of the reaction forces by
the material they fire-not because of any pushes on the air. In fact, a
rocket works better above the atmosphere, where there is no air drag.
FIGURE 4.8 A
The balloon recoils from the
escaping air and climbs
upward.
CHECK YOUR THINKING
A high-speed bus and an innocent bug have a head-on collision.
The force of the bus on the bug splatters the poor bug all over the
windshield. Is the corresponding force of the bug on the bus greater,
less, or the same? Is the resulting deceleration of the bus greater
than, less than, or the same as that of the bug?
CHAPTER 4
£:9.
NEWTON'S THIRD LAW OF MOTION
63
Answer
The magnitudes of both forces are the same, for they constitute an action-reaction
force pair that makes up the interaction between the bus and the bug. The accelerations,
however, are very different because the masses involved are different! The bug undergoes an
enormous and lethal deceleration, while the bus undergoes a very tiny deceleration-so
tiny that the very slight slowing of the bus is unnoticed by its passengers. But if the bug were
more massive, as massive as another bus, for example, the slowing down would be quite
evident.
4.5
In an interaction, the action
and reaction forces are the
same size. Why don't the
objects acted on by these
forces accelerate equally?
Action and Reaction Forces Act
on Different Objects
Because action and reaction forces are equal and opposite, why don't they
cancel to zero? .I They don't cancel out because they act on different
bodies. Consider kicking a football (Figure 4.10). Call the force your
foot exerts action. That's the only horizontal force on the football, so the
football accelerates. Reaction is the football exerting a force on your foot,
which tends to slow your foot down a bit. You can't cancel the force on
the football with a force on your foot. Forces cancel only when they act
on the same body. Now, what would happen if two players kicked the
same football with opposite and equal forces at the same time, as shown
in Figure 4.11? In this case, two interactions occur. Two different forces
act on the football, and these forces together cancel to zero.
I
Defining Your System
A system is defined as any object or collection of objects that you are
studying. In order for a system to accelerate, an external force must act
on it. Consider, for example, a system consisting of a single orange, as
shown in Figure 4.12. The dashed line surrounding the orange encloses
and defines the system. The vector that pokes outside the dashed line
represents an external force on the system. The system accelerates in
accord with Newton's second law. In Figure 4.13, we see that this force is
provided by the apple, which doesn't change our analysis. The apple is
outside the system. The fact that the orange simultaneously exerts a
force on the apple, which is external to the system, may affect the apple
( /i;
v
FIGURE 4.10 A
A acts on B, and B
accelerates.
FIGURE 4.11 A
Both A and C act on B. They
can cancel each other so B
does not accelerate.
FIGURE 4.9 A
The rocket recoils and
rises from the "molecular
cannonballs" it fires.
64
PART ONE
Physics
,.---1
A system may be as tiny as
an atom or as large as the
universe.
I
I
I
I
\ .....
FIGURE 4.12 A.
INTERACTIVE
FIGURE~
A force acts on the
orange, and the orange
accelerates to the right.
------------------,
'
I
I
I
'
FIGURE 4.14
/
A.
INTEIIACTIVE FI~QB~
In the larger system of orange + apple, action
and reaction forces are internal and cancel.
If these are the only horizontal forces, with no
external force, no acceleration of the system
occurs.
------------------~I
'
•I
'
FIGURE 4.15 A.
INTERACTIVE FIGIIII~
An external horizontal force occurs when the
floor pushes on the apple (reaction to the
apple's push on the floor). The orange-apple
system accelerates.
CHECK
YOUR READING
Why don't action and
reaction forces cancel
to zero?
FIGURE 4.13 A.
INTERACTIVE
FIGOR~
The force on the orange, provided by the
apple, is not canceled by the reaction force on
the apple. The orange still accelerates.
(another system), but not the range. You can't cancel a
force on the orange with a force on the apple. So, in this
case, the action-reaction forces don't cancel.
Now let's consider a larger system, enclosing both the
orange and the apple. We see the system bounded by the
dashed line in Figure 4.14. Notice that the force pair is
internal to the orange-apple system. These forces do
cancel each other. They play no role in accelerating the
system. A force external to the system is needed for
acceleration. That's where friction with the floor comes
in (Figure 4.15). When the apple pushes against the floor,
the floor simultaneously pushes on the apple-an
external force on the system. The system accelerates to
the right.
Inside a baseball are trillions and trillions of
interatomic forces at play. They hold the ball together,
but they play no role in accelerating the ball. Although
every one of the interatomic forces is part of an
action-reaction pair within the ball, they combine to
zero, no matter how many of them there are. A force
external to the ball, such as a swinging bat provides, is
needed to accelerate the ball.
If this is confusing, consider that Newton himself had
difficulties with the third law!
CHECK YOUR THINKING
1. On a cold, rainy day, your car battery is dead, and you must push
the car to move it and get it started. Why can't you move the car
by remaining comfortably inside and pushing against the dashboard?
2. Why does a flowerpot sitting on a shelf never accelerate "by
itself" in response to the trillions of interatomic forces acting
within it?
CHAPTER 4
{J;)
NEWTON'S THIRD LAW OF MOTION
65
Answer s
1. In this case, the system to be accelerated is the car. If you remain inside and push on
the dashboard, the force pair you produce acts and reacts within the system. These
forces cancel out, as far as any motion of the car is concerned. To accelerate the car,
there must be an interaction between the car and something external-for example,
you on the outside pushing against the road.
2. Every one of these interatomic forces is part of an action-reaction pair within the
flowerpot. These forces add up to zero, no matter how many there are. This is what
makes Newton's first law apply to the pot. It has zero acceleration unless an external
force acts on it.
4.& The Classic Horse-Cart ProblemA Mind Stumper
A situation similar to the kicked football is shown in the comic strip
"Horse Sense" on page 66. Pretend the horse thinks that its pull on the
cart will be canceled by the opposite and equal pull by the cart on the
horse, making acceleration impossible. This is the classic horse-cart
problem that is a stumper for many students at the university level. By
thinking carefully, you can understand it here.
The horse-cart problem can be looked at from different points of
view. One is the farmer's point of view; his only concern is getting his
cart (the cart system) to market. Then, there is the point of view of the
horse (the horse system). Finally, there is the point of view of the horse
and cart together (the horse-cart system).
First look at the farmer's point of view-the cart system. The net
force on the cart, divided by the mass of the cart, will produce an
acceleration. The farmer doesn't care about the reaction on the horse.
Now look at the horse's point of view-the horse system. It's true
that the opposite reaction force by the cart on the horse restrains
the horse. This force tends to hold the horse back. Without this force
the horse could freely gallop to the market. So how does the horse move
forward? By interacting with the ground. ./ At the same time the
horse pushes backward against the ground, the ground pushes
forward on the horse. If the horse pushes the ground with a greater
force than its pull on the cart, then there will be a net force on the horse.
Acceleration occurs. When the cart is up to speed, the horse needs only
to push against the ground with enough force to offset the friction
between the cart's wheels and the ground.
Finally, look at the horse-cart system as a whole. From this viewpoint, the pull of the horse on the cart and the reaction of the cart on
the horse are internal forces-forces that act and react within the
system. They contribute nothing to the acceleration of the horse-cart
system. The forces cancel and can be neglected. This is similar to
pushing a car while you're sitting in it, as discussed earlier. To get a car
moving you must get outside and make the ground push you and the
car. The horse-cart system is similar. To move the horse and cart across
FIGURE 4.16 .A.
Physics author Paul Hewitt
and wife Lillian show that you
cannot touch without being
touched-Newton's third law.
CHECK
YOUR READING
How does the horse move
forward?
66
PART ONE
Physics
YOU SEE, IF 1 PULL ON THE CART,
THE CARl WILL PULL BACK ON
ME. BY NEWTON'S 3"1 I AW,
THE. FORCES ARE
EQUAL AND OPPOSITE ·
SO THEY'LL CANCEL
OUT. A ZERO NET
FORCE WON'T
6E.T US
MOVIN6 .
FIGURE 4.17 .._
All the pairs of forces that act
on the horse and cart are
shown: (1) the pull P of the
horse and the cart on each
other; (2) the push F of the
horse and the ground on each
other; and (3) the friction f
between the cart wheels and
the ground. Notice that two
forces are applied to the cart
and to the horse. Can you see
that the acceleration of the
horse-cart system is due to
the net force F- f?
the ground, there must be an interaction between the horse-cart system
and the ground. It is the outside reaction by the ground that pushes
the system.
CHECK YOUR THINKING
1 . What is the net force that acts on the cart in Figure 4.17? On the
horse? On the horse-cart system?
2. Once the horse gets the cart moving at the desired speed, must
the horse continue to exert a force on the cart?
Answers
1. The net force on the cart is P- f; on the horse, F- P; on the horse-cart system, F- f
2. Yes, but only enough to counteract wheel friction and air drag. Interestingly, air drag
would be absent if a wind were blowing in the same direction and just as fast as the horse
and cart. If the wind blew fast enough to provide a force to counteract friction, the horse
could wear roller skates and simply coast with the cart all the way to the market.
CHAPTER 4
£[)
NEWTON'S THIRD LAW OF MOTION
4. 'I Action Equals Reaction
When you tie a rope to a wall and pull on it, you produce a tension in
the rope. Your pull on the rope and the pull by the supporting wall are
equal and opposite. Otherwise there would be a net force on the rope
and it would accelerate. The same is true if a friend holds one end of the
rope and you have a tug-of-war. Rope tension when pulled at opposite
ends is the same as the force provided by each end. Both pulls are the
same in magnitude. This leads to a fascinating discovery for people who
play tug-of-war. The team to win is not the team to exert the greatest
force on the rope, but the greatest force against the ground! In this way a
greater net force acts on the winning team.
FIGURE 4.18 .A
Arnold and Suzie pull on opposite ends of the rope. Can Arnold pull any
harder on the rope than Suzie pulls on it? If Suzie lets go, could Arnold
provide tension in the rope?
CHECK YOUR THINKING
1. We said earlier that a car accelerates along a road because the
road pushes it. Can we say that a team wins in a tug-of-war when
the ground pushes harder on them than on the other team?
2. Does the scale read 100 N, 200 N, or zero?
Answers
1. Yes!
2. Although the net force on the system is zero (as evidenced by no acceleration), the
scale reading is 100 N, the tension in the string. Note that the string tension is 100 N
in all the positions shown.
~
->·
~
67
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PART ONE
Physics
DISCOVER!
Perform a tug-of-war between boys and girls. Do
it on a polished floor (that's somewhat slippery).
Have the boys wear socks and the girls wear
rubber-soled shoes . Who will surely win, and why?
FIGURE 4.19 .A
The pair of vectors
represents the force each
wing exerts on the air.
Which forces act on the
bird?
You can't exert a force on
anything unless it also exerts
a force on you!
l
~
FIGURE 4.20 ~
The boxer can hit the massive
bag with considerable force.
But with the same punch he
can exert only a tiny force on
the tissue paper in midair.
CHECK
YOUR READING
Why is it impossible to hit a
piece of paper as hard as
you can hit a solid wall?
Newton's third law tells us how a helicopter gets its lifting force. The
whirling blades are shaped to force air particles down (action), and the
air forces the blades up (reaction). This upward reaction force is called
lift. When lift equals the weight of the craft, the helicopter hovers in
midair. When lift is greater, the helicopter rises. Airplanes also create lift
by deflecting air downward. Birds do the same. The downward push by
the wings on the air is paired with an upward push of the air on the
wings-lift!
Have you ever heard the expression that someone "can't fight their
way out of a paper bag"? There's some interesting physics beneath this
statement. .I According to Newton, you can't hit a piece of paper
any harder than the paper can hit you back. Hold a sheet of paper in
midair and tell your friends that nobody can hit the paper with a force
of 20 N (4.5 lb ). You're correct even if the heavyweight boxing champion
of the world hits the paper. The reason is that a 20-N interaction
between the champ's fist and the sheet of paper in midair isn't
possible-the paper is not capable of exerting a reaction force of 20 N.
You cannot have an action force without its reaction force. Now, if you
hold the paper against a wall, that is a different story. The wall will easily
assist the paper in providing 20 N of reaction force, and more if needed!
'
For every interaction between things, there is always a pair of
oppositely-directed forces that are equal in strength. If you push hard on
the world, for example, the world pushes hard on you. If you touch the
world gently, the world touches you gently in return. The way you touch
others is the way others touch you.
CHAPTER 4
fD.
NEWTON'S THIRD LAW OF MOTION
,..,._ INTEGRATED SCIENCE
Y4J BIOLOGY
Animal Locomotion
The study of how animals move, animal locomotion, is a branch of
biophysics. Biophysics applies concepts from both physics and biology.
It's one of many crossover science disciplines that thrive today.
Biophysicists apply Newton's third law to understand animal
locomotion. When an animal moves forward, it pushes back on something
else. It's the reaction force that pushes the animal forward. A fish swims by
pushing against water-the fish propels water backward with its fins, and
the water propels the fish forward. Likewise, land animals such as humans
push against the ground, and the ground in turn pushes them forward.
When you are standing still, you are not accelerating. The forces
that act on you, gravity and the normal force, balance as shown in
Figure 4.2la. To walk, you must accelerate horizontally-the vertical
forces of gravity and the normal force don't help. The forces involved in
walking are horizontal frictional forces (Figure 4.21 b). Because your feet
are firmly pressed to the floor, there is friction when you push your foot
horizontally against the floor. .I By Newton's third law, the floor
pushes back on you in the opposite direction-forward. (Don't be
confused by all the internal forces within your body that are involved
in walking, such as the rotation of your bones and stretching of your
muscles and tendons. An external force must act on your body to accelerate it. Friction is that force.)
After friction nudges you forward from a standstill, your step is like a
controlled fall. You step forward, and your body drops a short distance
until your front foot becomes planted in front of you. Friction, as shown
in Figure 4.2lc, acts in the opposite direction now as it prevents your
front foot from sliding forward.
kl
weight
(a)
on floor
weight
on floor
(b)
FIGURE 4.21 .A
(a) Standing still, you push against the floor with a force equal to your weight.
The normal force pushes you back equally-action and reaction. (b) Your
lifted foot doesn't accelerate you horizontally; it's your back foot that does
this. When your back foot pushes against the floor, the floor pushes back on
you, supplying the frictional force that pushes you forward. (c) When your
front foot lands, it pushes forward on the floor. Friction acts again, but now it
is directed backward. Friction stops your front foot from slipping forward as
the rest of your body catches up.
UNIPYING
CONCEPT
Friction
SECTION
3.6
69
70
PART ONE
Physics
.tCHECK YOUR
READING
Why does pushing
backward on the floor
enable you to walk?
Locomotion is important for many life functions (eating, finding
mates, escaping predators, and so on). Biophysical research in this area,
therefore, has beneficial applications for countless animals-human and
otherwise-that have impaired locomotion.
CHECK YOUR THINKING
1. In what way is the study of animal locomotion an integrated
science?
2. Why is Newton's third law necessary for understanding animal
locomotion?
3. Why don't the force interactions among your muscles, bones, and
other internal organs-or, for that matter, the forces among the
atoms and molecules in your body-move your body as a whole?
4. Why is walking in a puddle of grease so much more difficult than
walking on carpet?
Answers
1. It combines biology and physics.
2. Animals move forward by pushing back on some medium, which supplies the reaction
force needed to move forward.
3. Forces internal to a system cannot accelerate a system.
4. Grease is so smooth that it offers little friction to your feet and, therefore, insufficient
reaction force to get you walking.
,.....
"'-'
UNIPYING
CONCEPT
Newton's Laws of Motion
SECTION
2.5
Honestly, the wall hit my
hand and sprained my
wrist!
FIGURE 4.22 _..
If you hit the wall, it will hit
you equally hard.
4.8 Summary of Newton's Three Laws
Newton's first law, the law of inertia, is as follows: An object at rest tends
to remain at rest; an object in motion tends to remain in motion at constant speed along a straight-line path. This property by which objects
resist change in motion is called inertia. Mass is a measure of inertia.
Objects undergo changes in motion only in the presence of a net force.
Newton's second law, the law of acceleration, is as follows: When a net
force acts on an object, the object will accelerate. The acceleration is directly
proportional to the net force and inversely proportional to the mass.
Symbolically, a~ F!m. Acceleration is always in the direction of the net
force. When objects fall in a vacuum, the net force is simply the weight, and
the acceleration is g (the symbol g denotes that acceleration is due to gravity alone). When objects fall in air, the net force is equal to the weight
minus the force of air drag, and the acceleration is less than g. If and when
the force of air drag equals the weight of a falling object, acceleration terminates, and the object falls at constant speed (called terminal speed).
Newton's third law, the law of action-reaction, is as follows: Whenever one object exerts a force on a second object, the second object simultaneously exerts an equal and opposite force on the first. Forces come in
pairs, one action and the other reaction, both of which comprise the
interaction between one object and the other. Action and reaction always
act on different objects. Neither force exists without the other.
There has been a lot of new and exciting physics since the time of
Isaac Newton. Nevertheless, it was primarily Newton's laws that got us to
the Moon!
WORDS TO KNOW AND USE
Force pair The action and reaction pair of forces that
occur in an interaction.
Interaction Mutual action between objects in which
each object exerts an equal and opposite force on the
other.
Newton's third law Whenever one object exerts a
force on a second object, the second object exerts an
equal and opposite force on the first. Or put another
way, "To every action there is always an opposed equal
reaction."
System Any object or collection of objects being
studied.
REVIEW QUESTIONS
4.1 A Force Is Part of an Interaction
1. In the simplest sense, a force is a push or a pull.
In a deeper sense, what is a force?
2. How many forces are required for an
interaction?
3. When you push against a wall with your fingers,
they bend because they experience a force. Identify
this force.
4. Why do we say a speeding object doesn't have
force?
4.2 Newton's Third Law-Action
and Reaction
5. State Newton's third law of motion.
6. Consider hitting a baseball with a bat. If we call the
force on the bat against the ball the action force,
identify the reaction force.
7. If a bat hits a ball with 1000 N afforce, with how
much force does the ball hit back on the bat?
4.3 A Simple Rule Helps Identify Action
and Reaction
8. If Earth pulls you downward, what is the reaction
force?
4.4 Action and Reaction on Objects
of Different Masses
9. If the forces that act on a cannonball and the
1 0.
recoiling cannon from which it is fired are equal
in magnitude, why do the cannonball and cannon
have very different accelerations?
Identify the force that propels a rocket.
4.5 Action and Reaction Forces Act
on Different Objects
How can the net force on a ball be zero when you
kick it?
12. Why does a push on the dashboard of a stalled car
not accelerate the car?
11.
4.6 The Classic Horse-Cart ProblemA Mind Stumper
13. Referring to Figure 4.17, how many forces are
exerted on the cart? What is the horizontal net
force on the cart?
14. How many forces are exerted on the horse? What is
the net force on the horse?
15. How many forces are exerted on the horse-cart
system? What is the net force on the horse-cart
system?
4.7 Action Equals Reaction
16. Which is more important in winning in a tug-of-
war: pulling harder on the rope, or pushing harder
on the floor?
17. A boxer can hit a heavy bag with great force. Why
can't he hit a sheet of newspaper in midair with the
same amount of force?
18. Can you physically touch another person without
that person touching you with the same magnitude
of force?
4.8 Summary of Newton's Three Laws
19. Fill in the blanks: Newton's first law is often called
the law of __ ; Newton's second law highlights the
concept of __ ; and Newton's third law is the law
of
and _ _
71
72
PART ONE
Physics
2. For each of the following interactions, identify
3.
4.
s.
6.
,..._ INTEGRATED SCIENCE
.._, THINK AND LINK
Biology-Animal Locomotion
1. Explain how Newton's third law underlies many
forms of animal locomotion-such as those of
fish, birds, and humans.
2. A squid propels itself forward by pushing water
backward. Explain how this works.
3. When you walk, what is the force that pushes you
forward?
4. A duck stuck in an oil spill finds it very difficult to
walk. Why?
7.
8.
9.
THINK AND DO
Hold your hand like a flat wing outside the window
of a moving automobile. Then slightly tilt the front
edge upward and notice the lifting effect. Can you see
Newton's laws at work here?
10.
action and reaction forces.
(a) A hammer hits a nail.
(b) Earth gravity pulls down on you.
(c) A helicopter blade pushes air downward.
Identify the action-reaction pair of forces for each
of the following situations.
(a) You step off a curb.
(b) You pat your tutor on the back.
(c) A wave hits a rocky shore.
Consider a tennis player hitting a ball. Identify
the action-reaction pair of forces for each of the
following situations.
(a) When the ball is being hit
(b) While the ball is in flight
How does a helicopter get its lifting force?
Within a book on a desk, billions of forces are
pushing and pulling on all the molecules. Why is it
that these forces never by chance add up to a net
force in one direction, causing the book to
accelerate "spontaneously" across the desk?
Could a fish swim in a vacuum? Why or why not?
You push a heavy car by hand. The car, in turn,
pushes back with an opposite but equal force on
you. Doesn't this mean the forces cancel one
another, making acceleration impossible? Why or
why not?
A farmer urges his horse to pull a wagon. The
horse refuses, saying that to try would be futile
for it would flout Newton's third law. The horse
concludes that she can't exert a greater force on the
wagon than the wagon exerts on her, and therefore
won't be able to accelerate the wagon. What is your
explanation to persuade the horse to pull?
Suppose two carts, one twice as massive as the
other, fly apart when the compressed spring that
joins them is released. How fast does the heavier
cart roll compared with the lighter cart?
THINK AND EXPLAIN
1 . The photo shows
Steve Hewitt and his
daughter Gretchen.
Is Gretchen
touching her dad, or
is her dad touching
her? Explain.
11. If you exert a horizontal force of 200 N to slide a
crate across a factory floor at constant velocity,
how much friction does the floor exert on the
crate? Is the force of friction equal and oppositely
directed to your 200-N push? If the force of friction isn't the reaction force to your push, what is?
CHAPTER 4
f9
12. If a massive truck and a small sports car have a
head-on collision, on which vehicle is the impact
force greater? Which vehicle experiences the
greater acceleration? Explain your answers.
13. Ken and Joanne are astronauts floating some
distance apart in space. They are joined by a safety
cord whose ends are tied around their waists. If
Ken starts pulling on the cord, will he pull Joanne
toward him, will he pull himself toward Joanne, or
will both astronauts move? Explain.
14. Which team wins in a tug-of-war: the team that
pulls harder on the rope, or the team that pushes
harder against the ground? Explain.
15. In a tug-of-war between two physics types, each
pulls on the rope with a force of 250 N. What is the
tension in the rope? If both remain motionless,
what horizontal force does each exert against the
ground?
16. A stone is shown at rest on the ground.
(a) The vector shows the weight of the stone.
Cm:nplete the vector diagram by showing
another vector that results
in zero net force on the
stone.
(b) What is the conventional
name of the vector you have
drawn?
17. Here a stone is suspended at rest
by a string.
(a) Draw fo~ce vectors for all the
forces that act on the stone.
(b) Should your vectors have a
zero resultant?
(c) Why, or why not?
18. Here the same stone is being accelerated
vertically upward.
(a) Draw force vectors to some suitable
scale showing relative forces acting on
the stone.
(b) Which is the longer vector, and why?
19. Suppose the string in Exercise 18 breaks and the
stone slows in its upward motion. Draw a force
vector diagram of the stone when it reaches the top
of its path.
20. What is the acceleration of the stone in Exercise 19
at the top of its path?
T
NEWTON'S THIRD LAW OF MOTION
73
THINK AND SOLVE
1. If you apply a net force of 5 N on a cart with a
mass of 5 kg, what is the acceleration?
2. If you increase the speed of a 2.0-kg air puck by
3.0 m/s in 4.0 s, show that the force you exert on it
is 1.5 N.
3. A boxer punches a sheet of paper in midair and
brings it from rest up to a speed of 25m/sin
0.05 s. If the mass of the paper is 0.003 kg, show
that the boxer exerts a force of 1.5 N.
4. If you stand next to a wall on a frictionless skateboard and push the wall with a force of 30 N, how
hard does the wall push on you? If your mass is
60 kg, show that your acceleration is 0.5 m/s 2 .
MULTIPLE CHOICE PRACTICE
Choose the best answer to the following questions.
Check your answers with your teacher.
1. When you push a marble with a 0.5-N force, the
marble
(a) accelerates at 10 m/s 2 •
(b) resists being pushed with its own 0.5 N.
(c) will likely not move.
(d) pushes on you with a 0.5-N force.
2. A karate chop delivers a force of 3000 N to a board
that breaks. The force that the board exerts on the
hand during this event is
(a) less than 3000 N .
(b) 3000 N.
(c) greater than 3000 N.
(d) Cannot tell from the given information
3. When you push against a wall, you feel a push on
your hand because
(a) the wall is a hard surface.
(b) the wall pushes back on you.
(c) the muscles in your hand are flexing.
4. When you throw a basketball, your force on the
ball accelerates it. The ball pushes back on you
with an equal and opposite reaction force. Why
don't you accelerate as much as the ball?
(a) The reaction force acts on your hands only.
(b) You would accelerate as much as the basketball if
not for the friction between you and the ground.
(c) Your acceleration is much smaller than the
ball's because of your larger mass.
74
PART ONE
Physics
8. You hold an apple over your head. Identify all
5. A book sits on a table while gravity pulls it downward. The reason that the book doesn't accelerate
is that
(a) it experiences no net force.
(b) the table pushes on the book with a force equal
and opposite to the gravitational force on the
book.
(c) Both (a) and (b)
6. You step off a skateboard and it rolls backward.
What force pairs are involved in this motion?
(a) You push the skateboard backward; the skateboard pushes you forward.
(b) You push on the ground; the ground pushes on
the skateboard.
(c) The skateboard pushes you backward; you push
the skateboard forward.
(d) The skateboard would not roll backward when
you step off it.
7. When you drop a rubber ball on the floor, it
bounces almost to its original height. What causes
the ball to bounce?
(a) The force of the floor on the ball
(b) The force of the air on the ball
(c) The force you apply when you drop the ball
the forces acting on the apple and their reaction
forces.
(a) Earth's pull on the apple and the apple's pull on
Earth
(b) Your hand pushing the apple upward and the
apple pushing your hand downward
(c) Two force pairs act: ( 1) Earth's pull on the apple
and the apple's pull on Earth and (2) your
hand's upward push on the apple and the
apple's downward push on your hand
9. Now you drop the apple you had held over
your head. Identify the main force acting on the
apple as it falls and the corresponding reaction
force.
(a) Earth's pull on the apple and the apple's pull on
Earth
(b) Air pushes up on the apple (air drag) while the
apple pushes down on the air
(c) No force while falling, but when it hits the
ground, the ground in turn hits back on it.
10. The force that moves you forward as you
walk is
(a) the horizontal force of the ground on
your feet.
(b) the reaction to the force of your feet pushing
against the ground.
(c) the frictional force between your feet and the
ground.
(d) All of the above