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CHAPTER 12
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Date
Forces
SECTION
3 Newton’s Third Law
KEY IDEAS
As you read this section keep these questions in mind:
• What happens when one object exerts a force on
another object?
• How can you calculate the momentum of an object?
• How does momentum change after a collision?
What Is Newton’s Third Law of Motion?
Imagine kicking a soccer ball. The ball would move in
a different direction. From Newton’s first law, you know
that the ball’s motion could not have changed unless a
force acted on it. Therefore, there must be a force acting
on the ball. This force came from your foot. However, if
you kicked a soccer ball, you would probably also feel a
force on your foot. Where did this force come from?
When you kick a soccer ball, your foot exerts a force
on the ball. This force is called an action force. At the
same time, the ball exerts a force on your foot. That force
is called a reaction force. Sir Isaac Newton described the
relationship between action forces and reaction forces in
his third law of motion.
Newton’s third law of motion states that action forces
always produce reaction forces. It also states that action
forces and reaction forces are always equal in size, but
act in opposite directions. The figure below shows the
sizes and directions of action and reaction forces when a
person kicks a soccer ball.
READING TOOLBOX
Organize After you read this
section, create a Concept
Map for momentum. Include
the words momentum, mass,
velocity, and direction in your
map.
According to Newton’s third
law, the foot and the soccer
ball exert equal and opposite
forces on each other.
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1. Identify On the figure,
label the action force and the
reaction force.
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Newton’s Third Law continued
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2. Apply Concepts A
student has a weight of
534 N. The student sits in a
chair. When the student sits
in a chair, how much force
does the chair apply to the
student?
FORCE PAIRS
An action force and the reaction force that results are
called a force pair. Newton’s third law states that the
forces in a force pair are equal in size, but opposite in
direction. You may wonder why these forces do not cancel each other out, since they happen at the same time.
The answer is that the forces act on different objects. For
example, in the figure below, the action force acts on the
water. The reaction force acts on the swimmer.
The action force is the swimmer
pushing the water backward.
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3. Explain Why don’t the
action and reaction forces in
the figure cancel each other
out?
The reaction force is the water
pushing the swimmer forward.
EQUAL FORCES, UNEQUAL EFFECTS
READING CHECK
4. Explain Why don’t we
notice Earth moving upward
when an object falls toward
the ground?
Imagine dropping a soccer ball. Earth’s gravitational
force pulls the soccer ball toward the ground. This is the
action force. At the same time, the soccer ball exerts an
equal gravitational force on Earth. This is the reaction
force. The action force and the reaction force are the
same size, but opposite in direction.
It is easy to see the effect of the action force—the ball
falls to the ground. Why don’t you notice the effect of the
reaction force—Earth being pulled upward? The answer
is that these two equal forces act on objects with very different masses.
Recall Newton’s second law of motion: A large mass
will accelerate less than a small mass when you apply the
same amount of force. For example, the same amount of
force acts on the soccer ball and Earth, but Earth’s mass
is much greater than the soccer ball’s. Therefore, Earth’s
acceleration is much smaller than that of the soccer ball.
Earth does move upward, but this acceleration is so small
it is almost impossible to measure.
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Newton’s Third Law continued
SUMMARY OF NEWTON’S THIRD LAW OF MOTION
To summarize, there are four main ideas in Newton’s
third law of motion:
• Forces occur in pairs made up of an action force and a
reaction force.
• Action and reaction forces are equal in size, but opposite in direction.
• Action and reaction forces act on different objects.
• Equal forces acting on different objects may have different effects.
DETERMINING THE EFFECTS OF FORCES
You can use Newton’s third law of motion to determine
how an object will move. For example, think again about
the falling soccer ball. You can measure its weight, which
is equal to the gravitational force on it—the action force.
Once you know the weight of the soccer ball, you know
the size of the reaction force acting on Earth. If you know
Earth’s mass, you can calculate Earth’s acceleration using
Newton’s second law of motion.
What if you do not know the size of the force acting
on an object? You may still be able to predict the object’s
motion using a quantity called momentum.
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Brainstorm Think of 10
examples of force pairs. Describe each action force with
a partner. Ask your partner
to try to think of the reaction force. Then, have your
partner share his or her list of
action forces with you. Try to
think of the reaction force for
each of your partner’s action
forces.
What Is Momentum?
Momentum is a property of all moving objects. The
momentum of an object moving in a straight line is equal
to its mass multiplied by its velocity. Momentum is represented by the variable p.
Momentum Equation
momentum = mass velocity
p = mv
The SI unit of momentum is kilograms times meters
per second (kg • m/s). Like velocity, momentum has both
size and direction. An object’s velocity and momentum
are in the same direction.
READING CHECK
5. Apply Concepts An
object has a velocity of
10 m/s south. In what direction is its momentum?
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Newton’s Third Law continued
EFFECTS OF VELOCITY AND MASS ON MOMENTUM
READING CHECK
6. Identify How does mass
affect momentum?
Look back at the equation for momentum. How does
the velocity of an object affect its momentum? Mass and
velocity are multiplied together to calculate momentum.
Therefore, as an object’s velocity increases, its momentum
also increases. For example, a fast-moving car has more
momentum than a slow-moving car of the same mass.
How does mass affect momentum? If velocity stays
the same, increasing mass also increases momentum. For
example, a tractor-trailer truck has more momentum than
a sports car moving at the same velocity.
CALCULATING MOMENTUM
Imagine a bowling ball rolling toward bowling pins.
The ball has a mass of 6.00 kg. Its velocity is 10.0 m/s
down the alley. What is the ball’s momentum?
Given:
mass,
m = 6.00 kg
velocity,
v = 10.0 m/s down the
alley
Step 2: Write
the equation for
momentum.
p = mv
Step 3: Insert the
known values and solve
for the unknown value.
p = (6.00 kg) × (10.0 m/s down the alley)
p = 60.0 kg • m/s down the alley
Math Skills
7. Calculate An ostrich has a
mass of 135 kg. It is running
with a velocity of 16.2 m/s
north. What is its momentum? Show your work.
Unknown:
momentum, p
Step 1: List the given
and unknown values.
FORCE AND MOMENTUM CHANGES
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8. Infer What is the momentum of a car that has stopped
moving?
Recall Newton’s first law: an object’s motion will not
change until an unbalanced force acts on it. When you
apply a force to a moving object, its motion changes.
If its velocity changes, its momentum also changes.
For example, a moving car has a certain velocity and
momentum. When the driver applies the brakes, the
car slows down. In other words, its velocity changes.
Therefore, its momentum also changes.
If you give an object more time to change its
momentum, you will need to use less force to make
that change. For example, if you move your arm back
when you catch a baseball, the ball’s momentum has
more time to change. Your hand has to use less force to
change the ball’s momentum. This also means your hand
feels less of a sting!
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Newton’s Third Law continued
What Happens to Momentum When Objects
Collide?
You can use the law of conservation of momentum to
predict how objects will move after they collide, or hit.
The law of conservation of momentum states that the
total amount of momentum in an isolated system is conserved. Let’s look at each part of this law to understand
what it means.
An isolated system is a group of objects that does not
gain or lose mass or energy to its environment. Imagine a
cue ball rolling across a table toward other billiard balls.
The cue ball and the other balls are almost an isolated
system. The balls do not gain or lose mass to the environment. They may lose a small amount of energy to friction,
but the amount is generally small enough to ignore.
Conserved means kept the same. The amount of
momentum in an isolated system stays the same, no matter what happens within the system.
Think again about the cue ball rolling across a table.
When the cue ball hits the other balls, they move. Before
the collision, the other balls are not moving; they have no
momentum. Therefore, the total momentum in the system
is equal to the momentum of the cue ball.
When the cue ball hits another ball, it passes some of
its momentum to the other ball. After the collision, all the
balls have a different momentum. However, their total
momentum is the same as it was before the collision.
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9. Rephrase Write the law
of conservation of momentum in your own words.
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10. Explain Why does the
cue ball slow down after it
hits another ball?
When a cue ball hits another ball on the table, the cue ball slows down. The other
ball begins to move. The total momentum of the system stays the same.
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Section 3 Review
SECTION VOCABULARY
momentum a quantity defined as the product of
the mass and velocity of an object
1. Explain How is velocity related to momentum?
2. Identify What is Newton’s third law of motion?
3. Apply Concepts A skier pushes her ski poles against the ground. She begins to
move across the snow. Earth does not seem to move. Identify the action and reaction forces in this example, and explain why the skier moves but Earth does not
seem to.
4. Calculate A baby has a mass of 5.0 kg. The baby is on a train that is traveling east
at 72 m/s. What is the baby’s momentum? Show your work.
5. Calculate A kitten has a mass of 0.8 kg. It is moving forward with a momentum of
0.5 kg • m/s. What is the kitten’s velocity? Show your work.
6. Compare Describe the total momentum of billiard balls before and after the cue
ball collides with another ball.
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