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KEY CONCEPT
Forces transfer
momentum.
BEFORE, you learned
NOW, you will learn
• A force is a push or a pull
• Newton’s laws help to describe
and predict motion
• What momentum is
• How to calculate momentum
• How momentum is affected
by collisions
VOCABULARY
EXPLORE Collisions
momentum p. 64
collision p. 66
conservation of
momentum p. 67
What happens when objects collide?
PROCEDURE
1 Roll the two balls toward each other on a
flat surface. Try to roll them at the same
speed. Observe what happens. Experiment by
changing the speeds of the two balls.
MATERIALS
2 balls of
different masses
2 Leave one ball at rest, and roll the other ball
so that it hits the first ball. Observe what
happens. Then repeat the experiment with the
balls switched.
WHAT DO YOU THINK?
• How did varying the speed of the balls affect the
motion of the balls after the collision?
• What happened when one ball was at rest? Why
did switching the two balls affect the outcome?
Objects in motion have momentum.
If you throw a tennis ball at a wall, it will bounce back toward you.
What would happen if you could throw a wrecking ball at the wall at
the same speed that you threw the tennis ball? The wall would most
likely break apart. Why would a wrecking ball have a different effect
on the wall than the tennis ball?
VOCABULARY
Make a magnet word
diagram for momentum.
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64 Unit: Motion and Forces
A moving object has a property that is called momentum.
Momentum (moh-MEHN-tuhm) is a measure of mass in motion;
the momentum of an object is the product of its mass and its velocity.
At the same velocity, the wrecking ball has more momentum than the
tennis ball because the wrecking ball has more mass. However, you
could increase the momentum of the tennis ball by throwing it faster.
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Momentum is similar to inertia. Like inertia, the momentum of an
object depends on its mass. Unlike inertia, however, momentum takes
into account how fast the object is moving. A wrecking ball that is
moving very slowly, for example, has less momentum than a fastmoving wrecking ball. With less momentum, the slower-moving
wrecking ball would not be able to do as much damage to the wall.
reminder
Inertia is the resistance
of an object to changes
in its motion.
To calculate an object’s momentum, you can use the following
formula:
momentum = mass · velocity
p = mv
In this equation, p stands for momentum, m for mass, and v for
velocity. In standard units, the mass of an object is given in kilograms
(kg), and velocity is given in meters per second (m/s). Therefore, the
unit of momentum is the kilogram-meter per second (kg p m/s).
Notice that the unit of momentum combines mass, length, and time.
RESOURCE CENTER
CLASSZONE.COM
Explore momentum.
Like force, velocity, and acceleration, momentum is a vector—it
has both a size and a direction. The direction of an object’s momentum is the same as the direction of its velocity. You can use speed
instead of velocity in the formula as long as you do not need to know
the direction of motion. As you will read later, it is important to know
the direction of the momentum when you are working with more
than one object.
check your reading
How do an object’s mass and velocity affect its momentum?
Calculating Momentum
Sample Problem
What is the momentum of a 1.5 kg ball moving at 2 m/s?
What do you know? mass = 1.5 kg, velocity = 2 m/s
What do you want to find out? momentum
Write the formula: p = mv
Substitute into the formula: p = 1.5 kg p 2 m/s
Calculate and simplify: p = 3 kg p m/s
Check that your units agree: Unit is kg p m/s.
Unit of momentum is kg p m/s. Units agree.
Answer: p = 3 kg p m/s
Practice the Math
1. A 3 kg ball is moving with a velocity of 1 m/s. What is the ball’s momentum?
2. What is the momentum of a 0.5 kg ball moving 0.5 m/s?
Chapter 2: Forces 65
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Momentum
What happens when objects collide?
SKILL FOCUS
Observing
PROCEDURE
1
Set up two parallel rulers separated by one centimeter. Place a line of five
marbles, each touching the next, in the groove between the rulers.
2 Roll a marble down the groove so that it collides with the line of marbles,
and observe the results.
MATERIALS
• 2 rulers
• 8 marbles
TIME
20 minutes
3 Repeat your experiment by rolling two and then three marbles at the line of
marbles. Observe the results.
WHAT DO YOU THINK?
• What did you observe when you rolled the marbles?
• Why do you think the marbles moved the way they did?
CHALLENGE Use your answers to write a hypothesis explaining
your observations. Design your own marble experiment to test
this hypothesis. Do your results support your hypothesis?
Momentum can be transferred from
one object to another.
If you have ever ridden in a bumper car, you have experienced collisions. A collision is a situation in which two objects in close contact
exchange energy and momentum. As another car bumps into the back
of yours, the force pushes your car forward. Some of the momentum
of the car behind you is transferred to your car. At the same time, the
car behind you slows because of the reaction force from your car. You
gain momentum from the collision, and the other car loses momentum. The action and reaction forces in collisions are one way in which
objects transfer momentum.
If two objects involved in a collision have very different masses,
the one with less mass has a greater change in velocity. For example,
consider what happens if you roll a tennis ball and a bowling ball
toward each other so that they collide. Not only will the speed of the
tennis ball change, but the direction of its motion will change as it
bounces back. The bowling ball, however, will simply slow down. Even
though the forces acting on the two balls are the same, the tennis ball
will be accelerated more during the collision because it has less mass.
check your reading
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66 Unit: Motion and Forces
How can a collision affect the momentum of an object?
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Momentum is conserved.
During a collision between two objects, each object exerts a force on
the other. The colliding objects make up a system—a collection of
objects that affect one another. As the two objects collide, the velocity
and the momentum of each object change. However, as no other
forces are acting on the objects, the total momentum of both objects
is unchanged by the collision. This is due to the conservation of
momentum. The principle of conservation of momentum states that
the total momentum of a system of objects does not change, as long
as no outside forces are acting on that system.
total momentum
momentum 1
A light blue-green arrow
shows the momentum of
an individual object.
A dark blue-green arrow
shows the total momentum.
total momentum
momentum 2
1
reading tip
forces in collision
2
Before the collision The momen-
During the collision The forces
tum of the first car is greater than
the momentum of the second car.
Their combined momentum is the
total momentum of the system.
on the two cars are equal and
opposite, as described by Newton’s
third law. Momentum is transferred
from one car to the other during
the collision.
momentum 1
momentum 2
3
After the collision The momentum
lost by one car was gained by the
other car. The total momentum of
the system remains the same as it
was before the collision.
How much an object’s momentum changes when a force is
applied depends on the size of the force and how long that force is
applied. Remember Newton’s third law—during a collision, two
objects are acted upon by equal and opposite forces for the same
length of time. This means that the objects receive equal and opposite
changes in momentum, and the total momentum does not change.
You can find the total momentum of a system of objects before a
collision by combining the momenta of the objects. Because momentum is a vector, like force, the direction of motion is important. To
find the total momentum of objects moving in the same direction,
add the momenta of the objects. For two objects traveling in opposite
directions, subtract one momentum from the other. Then use the
principle of conservation of momentum and the equation for
momentum to predict how the objects will move after they collide.
check your reading
reading tip
The plural of momentum
is momenta.
What is meant by “conservation of momentum”? What
questions do you have about the application of this principle?
Chapter 2: Forces 67
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Two Types of Collisions
When bumper cars collide, they bounce off each other. Most of the
force goes into changing the motion of the cars. The two bumper cars
travel separately after the collision, just as they did before the collision.
The combined momentum of both cars after the collision is the same
as the combined momentum of both cars before the collision.
In this crash test,
momentum is conserved,
but some of the energy
goes into bending the
metal in these two cars.
When two cars collide during a crash test, momentum is also
conserved during the collision. Unlike the bumper cars, however,
which separate, the two cars shown in the photograph above stick
and move together after the collision. Even in this case, the total
momentum of both cars together is the same as the total momentum
of both cars before the collision. Before the crash shown in the photograph, the yellow car had a certain momentum, and the blue car had
no momentum. After the crash, the two cars move together with a
combined momentum equal to the momentum the yellow car had
before the collision.
check your reading
Compare collisions in which objects separate with collisions in
which objects stick together.
Momentum and Newton’s Third Law
Collisions are not the only events in which momentum is conserved.
In fact, momentum is conserved whenever the only forces acting on
objects are action/reaction force pairs. Conservation of momentum is
really just another way of looking at Newton’s third law.
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68 Unit: Motion and Forces
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When a firefighter turns on a hose, water
comes out of the nozzle in one direction, and the
hose moves back in the opposite direction. You
can explain why by using Newton’s third law. The
water is forced out of the hose. A reaction force
pushes the hose backward. You can also use the
principle of conservation of momentum to
explain why the hose moves backward:
•
•
•
Before the firefighter turns on the water, the
hose and the water are not in motion, so the
hose/water system has no momentum.
Once the water is turned on, the water has
momentum in the forward direction.
For the total momentum of the hose and the water to stay
the same, the hose must have an equal amount of momentum
in the opposite direction. The hose moves backward.
Firefighters must apply a
force to the water hose
to prevent it from flying
backward when the water
comes out.
If the hose and the water are not acted on by any other forces,
momentum is conserved. Water is pushed forward, and the hose is
pushed backward. However, the action and reaction force pair acting
on the hose and the water are not usually the only forces acting on
the hose/water system, as shown in the photograph above. There the
firefighters are holding the hose steady.
The force the firefighters apply is called an outside force because it
is not being applied by the hose or the water. When there is an outside
force on a system, momentum is not conserved. Because the firefighters
hold the hose, the hose does not move backward, even though the
water has a forward momentum.
check your reading
Under what condition is momentum not conserved? What part
of the paragraph above tells you?
KEY CONCEPTS
CRITICAL THINKING
1. How does increasing the
speed of an object change its
momentum?
4. Predict A performing dolphin
speeds through the water and
hits a rubber ball originally at
rest. Describe what happens to
the velocities of the dolphin
and the ball.
2. A car and a truck are traveling
at the same speed. Which has
more momentum? Why?
3. Give two examples showing
the conservation of momentum. Give one example where
momentum is not conserved.
5. Calculate A 50 kg person is
running at 2 m/s. What is the
person’s momentum?
CHALLENGE
6. Apply A moving train car
bumps into another train car
with the same mass. After the
collision, the two cars are coupled and move off together.
How does the final speed of
the two train cars compare
with the initial speed of the
moving train cars before the
collision?
Chapter 2: Forces 69
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