1. Key Term
force
Force
You exert a force on a ball when you throw or kick the ball, and you exert a
force on a chair when you sit in the chair. Forces describe the interactions
between an object and its environment.
Forces can cause accelerations.
In many situations, a force exerted on an object can change the object’s
velocity with respect to time. Some examples of these situations are shown
in Figure 1.1. A force can cause a stationary object to move, as when you
throw a ball. Force also causes moving objects to stop, as when you catch a
ball. A force can also cause a moving object to change direction, such as
when a baseball collides with a bat and flies off in another direction.
Notice that in each of these cases, the force is responsible for a change in
velocity with respect to time—an acceleration.
The SI unit of force is the newton.
The SI unit of force is the newton, named after Sir Isaac Newton (1642–
1727), whose work contributed much to the modern understanding of
force and motion. The newton (N) is defined as the amount of force that,
when acting on a 1 kg mass, produces an acceleration of 1 m/s2.
Therefore, 1 N = 1 kg × 1 m/s2.
The weight of an object is a measure of the magnitude of the gravita-
tional force exerted on the object. It is the result of the interaction of an
Changes in Motion
Objectives
Describe how force affects the
motion of an object.
Interpret and construct
free-body diagrams.
force an action exerted on an object
that may change the object’s state of
rest or motion
Three Ways That Forces Change Motion Force can cause objects to
(a) start moving, (b) stop moving, and/or (c) change direction.
FIGURE 1.1
(b)
(a) (c)
Chapter 4
118
SECTION 1
Untitled-310 118 5/6/2011 12:01:56 PM
Differentiated Instruction
Below Level
Remind students that photographs, such as
those on this page, do not actually show
objects “experiencing force.” This is because
forces cause changes in velocity with respect
to time or direction. Challenge students to
explain what they would need to see in each
photograph if it was a video that showed the
effect of forces.
Preview Vocabulary
Academic Vocabulary In common
usage, the words pressure and force
sometimes are used interchangeably.
In physics, these words are distinctive.
Force is any effect or power that can
change the speed or direction of an
object in motion. Pressure is used only
to define the magnitude of a unit of
force exerted on a unit area. So, the
magnitude of pressure in physics
depends in part on the magnitude of
the force involved.
Teaching Tip
Now that students have studied motion
as complex as projectile motion, explore
their understanding of force. Ask them
what mechanism causes motion and
why some objects accelerate at higher
rates than others do. Point out that
force is attributed to any mechanism
that causes or may cause a change in an
object’s velocity with respect to time.
FIGURE 1.1 Point out to students that
the ball is experiencing force in all three
pictures.
Ask How can you tell that the ball
experiences at least one force in each
picture?
Answer: by changes in the ball’s speed
or direction
Plan and Prepare
Teach
TEACH FROM VISUALS
118 Chapter 4
SECTION 1
2. object’s mass with the gravitational field of another object, such as Earth.
As shown in Figure 1.2, many of the terms and units you use every day to
talk about weight are really units of force that can be converted to new-
tons. For example, a 1
_
4
lb stick of margarine has a weight equivalent to a
force of about 1 N, as shown in the following conversions:
1 lb = 4.448 N
1 N = 0.225 lb
Forces can act through contact or at a distance.
If you pull on a spring, the spring stretches. If you pull on a wagon, the
wagon moves. When a football is caught, its motion is stopped. These
pushes and pulls are examples of contact forces, which are so named
because they result from physical contact between two objects. Contact
forces are usually easy to identify when you analyze a situation.
Another class of forces—called field forces—does not involve physical
contact between two objects. One example of this kind of force is gravita-
tional force. Whenever an object falls to Earth, the object is accelerated
by Earth’s gravity. In other words, Earth exerts a force on the object even
when Earth is not in immediate physical contact with the object.
Another common example of a field force is the attraction or repulsion
between electric charges. You can observe this force by rubbing a balloon
against your hair and then observing how little pieces of paper appear to
jump up and cling to the balloon’s surface, as shown in Figure 1.3. The
paper is pulled by the balloon’s electric field.
The theory of fields was developed as a tool to explain how objects
could exert force on each other without touching. According to this
theory, masses create gravitational fields in the space around them.
An object falls to Earth because of the interaction between the object’s
mass and Earth’s gravitational field. Similarly, charged objects create
electromagnetic fields.
The distinction between contact forces and field forces is useful when
dealing with forces that we observe at the macroscopic level. (Macroscopic
refers to the realm of phenomena that are visible to the naked eye.) As we
will see later, all macroscopic contact forces are actually due to microscopic
field forces. For instance, contact forces in a collision are due to electric
fields between atoms and molecules. In fact, every force can be categorized
as one of four fundamental field forces.
Did YOU Know?
The symbol for the pound, lb, comes
from libra, the Latin word for “pound,”
a unit of measure that has been used
since medieval times to measure
weight.
Electric Force The electric field
around the rubbed balloon exerts an
attractive electric force on the pieces
of paper.
FIGURE 1.3
FIGURE 1.2
UNITS OF MASS, ACCELERATION, AND FORCE
System Mass Acceleration Force
SI kg m/s2 N = kg•m/s2
cgs g cm/s2 dyne = g•cm/s2
Avoirdupois slug ft/s2 lb = slug•ft/s2
Forces and the Laws of Motion 119
Untitled-310 119 5/6/2011 12:01:58 PM
FIGURE 1.3 Tell students that
both contact and field forces are
demonstrated in this picture.
Ask Identify the contact and field force
examples in the picture.
Answer: contact forces: the figure
supporting the pieces of paper, a person
supporting the balloon;
field forces: gravitational force pulling
down on the paper and balloon, electric
force pulling up on the paper
TEACH FROM VISUALS
English Learners
Write the prefixes macro- and micro- on the
board or overhead projector. Explain that the
prefix macro- refers to something large, while
the prefix micro- refers to something small.
Challenge students to come up with a definition
for words such as macroeconomics, microbe
macrobiology, microwave, and micrometer.
Allow students to use a dictionary to confirm
their definitions.
Forces and the Laws of Motion 119
3. PHYSICS
Spec. Number PH 99 PE C04-001-006-A
Boston Graphics, Inc.
617.523.1333
Force Diagrams
When you push a toy car, it accelerates. If you push the car harder, the
acceleration will be greater. In other words, the acceleration of the car
depends on the force’s magnitude. The direction in which the car moves
depends on the direction of the force. For example, if you push the toy car
from the front, the car will move in a different direction than if you push it
from behind.
Force is a vector.
Because the effect of a force depends on both magnitude and direction,
force is a vector quantity. Diagrams that show force vectors as arrows,
such as Figure 1.4(a), are called force diagrams. In this book, the arrows
used to represent forces are blue. The tail of an arrow is attached to the
object on which the force is acting. A force vector points in the direction
of the force, and its length is proportional to the magnitude of the force.
At this point, we will disregard the size and shape of objects and assume
that all forces act at the center of an object. In force diagrams, all forces are
drawn as if they act at that point, no matter where the force is applied.
A free-body diagram helps analyze a situation.
After engineers analyzing a test-car crash have identified all of the forces
involved, they isolate the car from the other objects in its environment.
One of their goals is to determine which forces affect the car and its
passengers. Figure 1.4(b) is a free-body diagram. This diagram represents
the same collision that the force diagram (a) does but shows only the car
and the forces acting on the car. The forces exerted by the car on other
objects are not included in the free-body diagram because they do not
affect the motion of the car.
A free-body diagram is used to analyze only the forces affecting the
motion of a single object. Free-body diagrams are constructed and
analyzed just like other vector diagrams. In Sample Problem A, you will
learn to draw free-body diagrams for some situations described in this
book. Later, you will learn to use free-body diagrams to find component
and resultant forces.
FORCE AND CHANGES
IN MOTION
Use a toy car and a book to
model a car colliding with a
brick wall. Observe the motion
of the car before and after the
crash. Identify as many chang-
es in its motion as you can,
such as changes in speed or
direction. Make a list of all of
the changes, and try to identify
the forces that caused them.
Make a force diagram of the
collision.
MATERIALS
1 toy car
•
1 book
•
Force Diagrams Versus Free-body
Diagrams (a) In a force diagram, vector
arrows represent all the forces acting in a
situation. (b) A free-body diagram shows only
the forces acting on the object of interest—in
this case, the car.
FIGURE 1.4
(b)
(a)
Chapter 4
120
Untitled-310 120 5/6/2011 12:02:00 PM
Differentiated Instruction
Pre-AP
Explain to students that forces acting on a
body at different points can produce transla-
tional movement of the body without
rotation; rotation without translational
movement; or translational movement and
rotation together, depending on exactly where
the forces act on the body. Discuss examples
of each situation. Then explain that the
examples in this chapter are limited to
translational movement without rotation,
so the sum of forces is all that is required.
For this reason, the forces can be drawn as
if they act on the body at a common point.
The concept of torque is discussed in the
chapter “Circular Motion and Gravitation.”
Rotational equilibrium and dynamics are
covered in the Take It Further feature
“Rotational Dynamics.”
Teacher’s Notes
If the toy car is rolled an appreciable
distance before the collision, students
may observe the car slowing down
because of friction. Give students a brief
explanation of friction.
Teach continued
QuickLab
120 Chapter 4
5. PHYSICS
Spec. Number PH 99 PE C04-001-006-A
Boston Graphics, Inc.
617.523.1333
Reviewing Main Ideas
1. List three examples of each of the following:
a. a force causing an object to start moving
b. a force causing an object to stop moving
c. a force causing an object to change its direction of motion
2. Give two examples of field forces described in this section and two ex-
amples of contact forces you observe in everyday life. Explain why you
think that these are forces.
3. What is the SI unit of force? What is this unit equivalent to in terms of
fundamental units?
4. Why is force a vector quantity?
5. Draw a free-body diagram of a football being kicked. Assume that the
only forces acting on the ball are the force due to gravity and the force
exerted by the kicker.
Interpreting Graphics
6. Study the force diagram on the right.
Redraw the diagram, and label each
vector arrow with a description of the
force. In each description, include
the object exerting the force and the
object on which the force is acting.
Drawing Free-Body Diagrams (continued)
1. A truck pulls a trailer on a flat stretch of road. The forces acting on the trailer are
the force due to gravity (250 000 N downward), the force exerted by the road
(250 000 N upward), and the force exerted by the cable connecting the trailer to
the truck (20 000 N to the right). The forces acting on the truck are the force due to
gravity (80 000 N downward), the force exerted by the road (80 000 N upward), the
force exerted by the cable (20 000 N to the left), and the force causing the truck to
move forward (26 400 N to the right).
a. Draw and label a free-body diagram of the trailer.
b. Draw and label a free-body diagram of the truck.
2. A physics book is at rest on a desk. Gravitational force pulls the book down.
The desk exerts an upward force on the book that is equal in magnitude to the
gravitational force. Draw a free-body diagram of the book.
Chapter 4
122
SECTION 1 FORMATIVE ASSESSMENT
Untitled-310 122 5/6/2011 12:02:02 PM
Answers to Section Assessment
1. Answers will vary.
2. gravity and electric force, answers will vary;
because they can cause a change in motion
3. the newton; 1 N = 1 kg•1 m/s2
4. because force has both magnitude and
direction
5. Fg
points down, and Fkicker
points in the
direction of the kick.
6. Each arrow should have a label identifying
the object exerting the force and the
object acted on by the force.
Answers
Practice A
1. Each diagram should include all
forces acting on the object, pointing
in the correct directions and with
the lengths roughly proportional to
the magnitudes of the forces. Be sure
each vector is labeled.
2. Diagrams should include a downward
gravitational force and an upward
force of the desk on the book; both
vectors should have the same length
and should be labeled.
Assess Use the Formative Assessment
on this page to evaluate student
mastery of the section.
Reteach For students who need
additional instruction, download the
Section Study Guide.
Response to Intervention To reassess
students’ mastery, use the Section Quiz,
available to print or to take directly
online at HMDScience.com.
Teach continued
Assess and Reteach
122 Chapter 4
