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Name
CHAPTER 2
Class
Date
Forces and Motion
3 Momentum
SECTION
BEFORE YOU READ
After you read this section, you should be able to answer
these questions:
• What is momentum?
• How is momentum calculated?
• What is the law of conservation of momentum?
What Is Momentum?
Picture a compact car and a large truck moving at the
same velocity. The drivers of both vehicles put on the
brakes at the same time. Which vehicle will stop first?
You most likely know that it will be the car. But why? The
answer is momentum.
The momentum of an object depends on the object’s
mass and velocity. Momentum is the product of the mass
and velocity of an object. In the figure below, a car and
a truck are shown moving at the same velocity. Because
the truck has a larger mass, it has a larger momentum. A
greater force will be needed to stop the truck.
STUDY TIP
Visualize As you read, try
to picture in your head the
events that are described. If
you have trouble imagining,
draw a sketch to illustrate the
event.
READING CHECK
1. Identify What is the
momentum of an object?
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TAKE A LOOK
2. Predict How could the
momentum of the car be
increased?
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Object
Momentum
Critical Thinking
A train moving at 30 km/h
3. Apply Concepts Fill in
the chart to the left to show
which object has the most
momentum, which object
has a smaller amount of
momentum, and which
objects have no momentum.
A bird sitting on a branch
high in a tree
A truck moving at 30 km/h
A rock sitting on a beach
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Forces and Motion
Name
SECTION 3
Class
Date
Momentum continued
How Can You Calculate Momentum?
READING CHECK
4. Identify What do you
need to know in order to
calculate an object’s
momentum?
Math Focus
5. Calculate A 6 kg
bowling ball is moving at
10 m/s down the alley
toward the pins. What is the
momentum of the bowling
ball? Show your work.
If you know what an object’s mass is and how fast it is
going, you can calculate its momentum. The equation for
momentum is
pmv
In this equation, p is momentum (in kilograms multiplied
by meters per second), m is the mass of the object (in kilograms), and v is the velocity of the object (in meters per
second).
Like velocity, momentum has direction. The direction
of an object’s momentum is always the same as the
direction of the object’s velocity.
Use the following procedure to solve momentum
problems:
Step 1: Write the momentum equation.
Step 2: Replace the letters in the equation with the
values from the problem.
Let’s try a problem. A 120 kg ostrich is running with a
velocity of 16 m/s north. What is the momentum of the
ostrich?
Step 1: The equation is p  m  v.
Step 2: m is 120 kg and v is 16 m/s north. So,
p  (120 kg)  (16 m/s north)  1,920 kg•m/s north
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����������
TAKE A LOOK
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6. Describe Use a metric
ruler to draw an arrow next
to the rocket to show its
momentum. The size of
the rocket’s momentum is
15 kg•m/s. The scale for
the arrow should be
1 cm  10 kg•m/s.
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Forces and Motion
Name
SECTION 3
Class
Date
Momentum continued
What Is the Law of Conservation of Momentum?
When a moving object hits an object at rest, some or
all of the momentum of the first object is transferred
to the second object. This means that the object at rest
gains all or some of the moving object’s momentum.
During a collision, the total momentum of the two objects
remains the same. Total momentum doesn’t change. This
is called the law of conservation of momentum.
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TAKE A LOOK
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The law of conservation of momentum is true for any
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colliding objects as long as there are no outside forces.
For example, if someone holds down the darker ball in
the collision shown above, it will not move. In that case,
the momentum of the lighter ball would be transferred
to the person holding the ball. The person is exerting an
outside force.
The law of conservation of momentum is true for objects
that either stick together or bounce off each other during
a collision. In both cases, the velocities of the objects will
change so that their total momentum stays the same.
7. Identify Draw an
arrow showing the size and
direction of the darker ball’s
momentum after its collision
with the lighter ball.
READING CHECK
8. Identify When is the law
of conservation of momentum not true for two objects
that are interacting?
Say It
When football players tackle another
player, they stick together. The velocity
of each player changes after the collision
because of conservation of momentum.
Although the bowling ball and bowling
pins bounce off each other and move
in different directions after a collision,
momentum is neither gained nor lost.
Explain Words In a group,
discuss how the everyday
use of the word momentum
differs from its use in
science.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Interactive Textbook
39
Forces and Motion
Name
Class
Date
Section 3 Review
SECTION VOCABULARY
momentum a quantity defined as the product of
the mass and velocity of an object
1. Explain A car and a train are moving at the same velocity. Do the two objects
have the same momentum? Explain your answer.
2. Show Relationships Put the following objects in order of increasing momentum: a
parked car, a train moving at 50 km/h, a train moving at 80 km/h, a car moving at
50 km/h.



3. Calculate A 2.5 kg puppy is running with a velocity of 4.8 m/s south. What is the
momentum of the puppy? Show your work.
4. Explain What is the law of conservation of momentum?
5. Calculate A ball has a momentum of 1 kg•m/s north. It hits another ball of equal
mass that is at rest. If the first ball stops, what is the momentum of the other ball
after the collision? (Assume there are no outside forces.) Explain your answer.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Interactive Textbook
40
Forces and Motion
M
Forces, Motion, and Energy Answer Key continued
9. A gravity arrow should be pointing down,
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
8. The groceries have no unbalanced force acting
and an air resistance arrow should be pointing up; arrows should be the same length.
the apple
Never; every object with mass has weight.
The shuttle and astronauts are falling at the
same rate.
orbit farther from Earth
There should be a straight, horizontal line
drawn from the shuttle’s current position to
the right-hand side of the figure.
an unbalanced force
The arrow should point from the moon to
the Earth.
horizontal motion and vertical motion
above the bulls-eye
horizontal, gravity, curved
9.8 m/s2; gravity causes everything to
accelerate by 9.8 m/s2.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Review
1. No, objects in free fall are affected only by
18.
gravity. Parachutists are affected by gravity
and air resistance.
2.
Cause
Effect
Gravity acts on a falling
object.
The object accelerates
toward Earth.
Air resistance equals
gravity and acts in the
opposite direction.
The falling object reaches
terminal velocity.
19.
Review
1. Objects with large masses have large inertia.
2. The arrow should be the same size and
3. final  g  t
final
on them. So they continue moving in a straight
line.
The golf ball has less mass or less inertia.
the pickup truck
Arrows should point from person to cart;
arrows in left-hand and middle figures are
the same length; arrow in right-hand figure
is longer.
newtons (N), or kg•m/s2
10 kg•m/s2, 10 kg•m/s2  1.02 kg, 9.8 m/s2
F  ma
F  (1,250 kg)(40 m/s2)
F  50,000 N
action force  down arrow, reaction
force  up arrow
They are the same size.
The batter is exerting a force on the bat,
which is greater than the force exerted by
the ball.
The “action force” arrow should point from
the ball toward the ground. The “reaction
force” arrow should point from the ground
toward the ball.
Earth is much bigger than the object, so its
acceleration is very small.
m/s  3.5 s  34.3 m/s
 9.8 ____
s
3.
4. centripetal force
5. Gravity affects vertical motion. Gravity
4.
slows upward vertical motion of the projectile and increases downward vertical motion
of the projectile.
5.
SECTION 2 NEWTON’S LAWS OF MOTION
6.
They are the same size.
It will not change speed or direction.
It will stay at rest.
It will continue to move at the same velocity.
The distances would be greater.
Apply an unbalanced force in the direction
opposite to its motion.
7. Friction slows it down.
1.
2.
3.
4.
5.
6.
direction as the arrow in the question.
An arrow should point left. Its length should
be the difference in length of the arrows
shown in the question.
Increase the force on the object; decrease
the mass of the object.
The action force is the push by my foot on
the ball. The reaction force is the push by
the ball on my foot.
F  ma, F  40 kg  4.5 m/s2  180 N
SECTION 3 MOMENTUM
1. the product of the object’s mass and velocity
2. increase in its speed or its mass
3. Object
Momentum
A train moving at 30 km/h
most momentum
A bird sitting on a branch
high in a tree
no momentum
A truck moving at 30 km/h
less momentum
A rock sitting on a beach
no momentum
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Interactive Textbook Answer Key
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Forces, Motion, and Energy
M
Forces, Motion, and Energy Answer Key continued
4. its mass and its velocity
5. p  m  v
11. The pressure inside the lungs is greater than
the pressure outside.
p  6 kg  10 m/s at the pins
p  60 kg•m/s at the pins
6. The arrow should be 1.5 cm long and
pointing up.
7. The arrow should point from the dark ball to
the right-hand side of the figure. It should be
the same size as the arrow in the top image.
8. when outside forces are present
Review
1. The particles of the fluid hit the walls of
the container. The force they exert causes
pressure.
2. Density is the mass of a substance divided
by its volume. Materials that are more dense
will exert more pressure than materials that
are less dense.
force
3. pressure  _____
area
________
pressure  2.5 N 2
0.012 m
pressure  208 Pa
Review
1. No, the train has more momentum because
2.
3.
4.
5.
it has a larger mass. Momentum is velocity
times mass. Because both have the same
velocity, the object with larger mass has
more momentum.
parked car, car moving at 50 km/h, train
moving at 50 km/h, train moving at 80 km/h
pmv
p  2.5 kg  4.8 m/s south  12 kg•m/s south
During a collision, momentum is neither lost
nor gained (as long as no outside forces are
acting).
1 kg•m/s north
4. A muscle in your chest contracts. The
Air
volume of your chest gets larger.
pressure inside your chest is lower than
Air flows into
atmospheric pressure.
The muscle in your chest
your lungs.
relaxes. The volume of your chest gets
smaller.
Air pressure inside your chest
is higher than atmospheric pressure.
Air flows out of your lungs.
SECTION 2 BUOYANT FORCE
1.
2.
3.
4.
5.
Chapter 3 Forces in Fluids
SECTION 1 FLUIDS AND PRESSURE
1. any material that can flow and take the
shape of its container
2. the force exerted on a given area
6.
7.
force
3. pressure  _____
area
3,000 N
pressure  _______
2m2
pressure  1,500 Pa
8.
9.
4. The arrows would still be the same length.
5.
6.
7.
8.
9.
10.
10.
The pressure inside still must equal atmospheric pressure.
It decreases.
about 1/2
The weight of the entire atmosphere is pushing down.
The weight of more and more fluid is pushing on the same area.
201 kPa
When you suck on the straw, you suck air
out of it. Since there is less air in the straw,
the air pressure is lower.
11.
12.
13.
14.
Fluid pressure increases with depth.
differences in pressure
3.6 N
float
Its weight is equal to the buoyant force of
the water it displaces.
more
The buoyant force is greater than the log’s
weight.
the mass of an object divided by its volume
If it is denser than water, it will sink. If it is
less dense than water, it will float.
Greater; air is more dense than helium, so
the same volume has a greater mass.
The volume of the ship is much larger than
the volume of the steel used to make it.
If the shape increases the volume, the
object’s density decreases.
by letting water into its ballast tanks
by letting gases into, or releasing them from,
the swim bladder
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Forces, Motion, and Energy