LESSON 3
Effects of Forces
Building to the Performance Expectations
The learning experiences in this lesson prepare students for mastery of
HS-PS2-1 Analyze data to support the claim that Newton’s
second law of motion describes the mathematical relationship
among the net force on a macroscopic object, its mass, and its
acceleration.
SEP
Science &
Engineering
Practices
Analyzing and Interpreting Data
Analyze data using tools, technologies,
and/or models (e.g., computational,
mathematical) in order to make valid and
reliable scientific claims or determine an
optimal design solution.
VIDEO Using Data, Mathematical
Thinking, and Computational Thinking
Science Models, Laws, Mechanisms, and
Theories Explain Natural Phenomena
Theories and laws provide explanations in
science.
HS-ETS1-2 Design a solution to a complex real-world problem
by breaking it down into smaller, more manageable problems
that can be solved by engineering.
DCI
Disciplinary
Core Ideas
PS2.A Forces and Motion
Newton’s second law accurately predicts changes in the motion of
macroscopic objects. (HS-PS2-1)
VIDEO Motion and Forces
ETS1.C Optimizing the Design Solution
Criteria may need to be broken down into simpler ones that can be
approached systematically, and decisions about the priority of certain criteria
over others (trade-offs) may be needed. (HS-ETS1-2)
VIDEO Engineering: Physics
Trace Tool to the NGSS
Go online to view the complete
coverage of standards across
lessons, units, and grade levels.
CCC
Crosscutting
Concepts
Cause and Effect
Empirical evidence is required to
differentiate between cause and
correlations and make claims about
specific causes and effects.
Scientific Knowledge Assumes an
Order and Consistency in Natural
Systems
Scientific knowledge is based on the
assumption that natural laws operate
today as they did in the past and they
will continue to do so in the future.
Science Models, Laws, Mechanisms, and
Theories Explain Natural Phenomena
Laws are statements or descriptions of the
relationships among observable phenomena.
MATH STANDARDS
ELA STANDARDS
MP.2 Reason abstractly and quantitatively.
RST.11-12.7 Integrate and evaluate multiple sources of information presented in
diverse formats and media (e.g., quantitative data, video, multimedia) in order to
address a question or solve a problem.
MP.4 Model with mathematics.
HSA-CED.A.2 Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms,
and box plots).
WHST.9-12.9 Draw evidence from informational texts to support analysis, reflection,
and research.
Lesson 3 Effects of Forces 53A
Supporting All Students, All Standards
Professional
Development
Integrating the Three Dimensions
In this lesson, students learn about different examples of forces
(SEP Constructing Explanations and Designing Solutions, DCI
PS2.A, CCC Patterns). Students use graphs and data displays to
model the motion in response to a net force acting on a mass (SEP
Developing and Using Models, DCI PS2.A, CCC Cause and Effect)
and carry out experiments involving net force (SEP Planning and
Carrying Out Investigations, DCI PS2.A, CCC Cause and Effect).
Students relate these to the three laws of motion (SEP Engaging in
Argument from Evidence, DCI PS2.A).
Preassessment
Have students complete the unit pretest, or see the Assessment Guide.
Build on Prior Knowledge
Have students list what they know about force and Newton’s laws of
motion. After they have made a comprehensive list, ask them to share
their list with a partner and discuss any differences. Then create a
classroom list that can be added to over the course of this lesson.
You may want to review the following concepts:
• the pattern of motion observed with no acceleration (such as a ball
rolling across a level table) and with acceleration (such as a ball
falling)
• an object’s change in motion—such as speeding up, slowing
down, or turning—when undergoing acceleration
Go online to view Professional Development videos with strategies
to integrate CCCs and SEPs, including the ones used in this lesson.
Content Background
In everyday experience, objects tend to fall or
to slow to a stop rather than remain at rest or
in steady motion. You may have to push or pull
an object to keep it moving. The formal physical
laws may seem counterintuitive. The intuition
that objects tend to slow to a stop is valid but
incomplete; it doesn’t account for all forces. That
intuition can be developed by noticing forces
such as friction, the normal force, and weight.
Newton’s first two laws of motion describe
the relationship between forces acting on an
object and the motion of that object. Zero net
force produces zero acceleration, and a net
force produces acceleration proportional to the
mass. An object slows to a stop (accelerates)
rather than continuing at constant velocity if the
object is acted on by a net force, such as friction.
The normal force is, by definition, perpendicular
to a surface. It is a reaction force from the
surface and very often equal in magnitude to
an object’s weight. However, it is not a reaction
force to weight; the reaction force to an object’s
weight is a matching gravitational pull on Earth.
Balanced forces, such as a typical weight and
normal force on an object at rest, are different
from an equal but opposite action-reaction force
pair. The latter forces act on different objects.
Newton’s laws do not apply to motion on very
small scales (quantum mechanics) or near the
speed of light (relativity).
Differentiate Instruction
KEY WORDS
ELL SUPPORT
• force
• friction
• weight
• net force
• mass
• stress
• normal force
53B Unit 1 Physics and Engineering
It can be helpful to use net force and its symbol
explicitly in order to avoid confusion with
applied force: Fnet = ma.
Ask students: What does the word force mean in
an everyday sense? Answers may focus on its use
as a verb, causing a change to happen despite
resistance, or as a noun, something that can cause
a change to occur. Both everyday uses carry a sense
of being the cause of a change.
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
ENGAGE: Investigative Phenomenon
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Build on Prior Lessons
1.3
Effects of Forces
In Lesson 2, students learned how to describe accelerated and
unaccelerated motion. Lesson 3 builds on these concepts as students
explore how net force is connected to motion.
Lesson Objective
Students use evidence to develop models of how forces interact and
a mathematical model of the relationships among force, mass, and
acceleration.
Cultivating Student Questions
Have students look at the photo. Prompt them to ask all questions
that come to mind about how an ant might not be harmed by a long
fall. Record the questions on chart paper, and then sort the questions
based on their focus. Have students reflect on this list throughout the
lesson and check off questions as they are answered.
A small creature such as an insect can fall from a great height and walk away unharmed.
Can You Explain the Phenomenon?
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Spike Mafford/Photodisc/
Getty Images
CAN YOU EXPLAIN THE PHENOMENON?
The Investigative Phenomenon is the focus of the lesson. Students are
asked to record their initial thoughts about the relationship between
an object and its motion when it falls. Students will revisit these
inferences at the end of the lesson.
You have studied how objects moving only under the influence of gravity fall with the
same downward acceleration. Yet you know of real-world examples that show more
complex motion, such as the fall of a leaf or a sheet of paper.
Think about an acorn and an ant, each falling from the same high branch of a tree. As
the acorn hits the ground, it produces a sound loud enough to hear. The ant hits almost
silently and walks away unharmed.
1
1 Sample answer: The acorn hits the ground harder, in part
because it is moving faster when it hits. The ant might drift down
more slowly, somewhat like a leaf. (Students may begin to think
about air resistance.)
INFER Use the impact of the ant and the acorn with the ground as a way of comparing
their motion just before impact. Describe a likely way the ant’s motion differs from the
acorn’s motion.
Evidence Notebook
2
Evidence Notebook As you explore the lesson, gather evidence to explain the factors
that can cause the motion of the falling ant and the acorn in the example to differ.
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2 The topic of factors that affect how an object falls will be
revisited throughout this lesson. Help students focus on
the motion rather than the impact by using the impact as
evidence of the motion. Students will learn that forces add
as vectors, that the net force determines the acceleration,
and that some forces, such as friction and air resistance,
depend on factors such as normal force, area, and speed.
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Lesson 3 Effects of Forces 53
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 1 Representing Forces
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3D Learning Objective
EXPLORATION 1
Students use mathematical representations to indicate the forces
acting on an object. They represent phenomena with balanced and
unbalanced forces, compute net force, and understand friction as a
force.
Representing Forces
In everyday language, “to force” can mean to cause something to happen; in science, a
force is a push or a pull exerted by one object on another. In the International System (SI)
2
of Units, the unit for force is the newton (N), which is equal to 1 kg•m/s . Force is a vector
quantity because it has direction as well as magnitude.
Everyday phenomena discussed throughout the Explorations of the
lesson can often be used to connect the science content to students’
personal experiences.
1
Collaborate With a partner, compare and contrast the everyday and scientific meanings of
force. In your discussion, address these questions: Can there be a force if nothing happens?
How might the units (kg•m/s2) be related to the scientific definition?
Analyzing and Interpreting Data
Ask students to explore the everyday phenomenon of moving a
small object, such as a paper clip, around their desktops. Ask: How
did you move the paper clip? How many different ways could you move
the paper clip? Sample responses might include push with a fingertip,
push with a pen, blow on the clip, or jolt the desk. Draw students’
attention to the application of a force.
FIGURE 1: Spring scales are
used to measure force.
Think about the downward pull due to gravity. Scientists distinguish between
weight, the gravitational force acting on an object, and mass, a measure of the
amount of matter. The mass of an object can be measured by comparing it to
known masses using a balance; mass is not a force.
Weight and other forces can be measured—for example, by how much they
push or pull a spring in a spring scale. These tools work because an object’s
weight is balanced by another force. A kitchen or bathroom scale can be used
to measure the downward force (weight) that is balanced by an upward
supporting force, such as from a table or the floor. This supporting force is
perpendicular to a surface and is called the normal force.
Exploring Visuals
Note that the vectors in the Infer illustrations all start from the center
of the object. These diagrams follow a convention of treating forces
as if they act on a point mass at the object’s center of mass. Have a
student support a meter stick on the edges of two hands, and then
slide the hands together. Ask: How can the narrow edge of a hand
support a wide object? It is beneath the center of balance, or center
of mass. Ask: What do you think the dots in the diagram represent? the
box’s center of mass
2
1 Sample answer: In everyday language, force usually applies to
situations where something is happening. You would not use
the term if nothing moves. In science, you can push or pull on an
object without causing motion. That push or pull is still a force.
The units, however, look like mass multiplied by acceleration,
which suggests motion.
2 air resistance—second image, friction—first image, gravitational
force—fourth image, normal force—third image
54 Unit 1 Physics and Engineering
Identifying Forces
54
INFER For each type of force in the table, match the example description with the vector
image of the force.
Force
Description
air resistance
Air exerts a force against the moving
box in a way that increases with the
box’s speed.
friction
Two sliding surfaces produce a force
that acts opposite to the direction of
the relative motion of the surfaces.
gravitational force
Earth exerts a force of attraction on
the box.
normal force
An object exerts a force on the box in a
direction perpendicular to the surfaces
in contact.
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Differentiate Instruction
MTSS/RTI Help students understand that the normal force is a
exerted on an object by another stable object. They might think of
it as a supporting force. When you lean on a wall, the normal force
from the wall on your body prevents you from falling. If you try to
lean against an unstable surface, such as a stack of blocks, the stack
may not provide enough normal force to balance the applied force
as you lean, and the pile will collapse. Encourage students to work in
pairs and experiment with small-scale versions of this phenomenon.
Cause and Effect
Exploring Friction
When an object is pushed or pulled across another object, small
points of the surfaces in contact push against each other and
resist motion. This effect and several other effects, together,
produce friction. Friction is a force that opposes motion between
two surfaces that are in contact. The box in Figure 2 stays in place
because static friction resists the force that would make it slide
down the ramp. Static friction occurs when the two surfaces are
not sliding. When the box slides along the surface, kinetic friction
resists—but does not prevent—the motion. The force of kinetic
friction is less than the maximum value of static friction.
FIGURE 2: The surfaces of the box and
the ramp resist motion between them.
Ask: What is an example of a surface providing enough normal force to
balance the force applied to it? What is an example of one that cannot?
Sample answer: When you stand on a step, it supports your weight;
when you stand on a cardboard box, the cardboard bends and
collapses under you. Follow up by having students reflect on their
modeling in a class discussion during which they share their models.
Unlike air resistance, static and kinetic friction do not typically depend on speed or
on the area of contact. They are each proportional to the force pushing the surfaces
together, which is usually characterized by the normal force. The normal force is in a
direction perpendicular to a surface, so it is not always vertical.
3
Language Arts Connection Use the two types of friction to describe what happens
as you slide a heavy box across a table. You might also research the coefficient of friction.
Prepare an explanation to present to the class.
Collaborate
Jigsaw Divide the class into three groups, and assign each group a
force for the phenomenon in Figure 2: gravitational force, friction, and
normal force. Have each group find out what determines the strength
and direction of the force. Then form groups of one expert in each
force. Have the groups apply their knowledge to a similar everyday
phenomena to determine the minimum information needed to
figure out the strength and direction of all three of the forces.
The normal force and static friction tend to oppose other forces, while forces acting
in the same direction produce a greater force. Forces combine as vectors, in the same
way velocities or accelerations combine. To make calculations, however, you have to
determine which vectors to add together.
4
APPLY Use vector arrows to draw the forces you expect to be present when a car is
parked on flat pavement. Treat the car as a single object.
3 Sample answer: I push on the box gently, then with increasing
force. Static friction keeps the box from moving. When I push
hard enough to overcome static friction, the force of friction
drops suddenly and the box starts to move with a jolt. Then the
motion steadies.
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Houghton Mifflin Harcourt
Using Diagrams to Analyze Force
Compare the vectors you drew with those of a classmate. Each of you may have represented
the car’s weight, for example, in different ways. Perhaps you drew gravitational force pulling
down on the car or the heavy car pressing down on the pavement. Look at the forces on a
single object: the car. You can combine these forces. It is less useful to combine the forces
that act on different objects.
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4 Students should draw the force due to gravity but might
represent it in different ways. (Students may not perceive that the
force of the car pressing on the pavement is a different force than
weight; it is equal to the weight.) They should show the upward
normal force. Students might depict each force in one vector
(acting on the body of the car) or in two vectors (acting on the
tires) but should be consistent.
Lesson 3 Effects of Forces 55
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 1 Representing Forces, continued
PS2.A Forces and Motion
Present students with this everyday phenomenon: A few days
after being filled, a helium balloon floats 2 m above the floor. Ask:
Are the forces on the balloon balanced? How can you tell? Yes; it is at
rest. Someone catches the string and pulls the balloon down so it stays
1 m above the floor. What forces act on the balloon now, and in what
direction? Gravity and the applied force from the person’s hand pull
down, while the buoyant force of the air pushes up.
CCC
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A free-body diagram is a way to model a situation by looking at only one object and the
external forces that act on it. Figure 3a shows some forces on the car and forces on the
pavement. Figure 3b includes the car’s weight but not the forces on the pavement.
FIGURE 3: The first model (a) shows forces on both the car and the ground. The second, freebody diagram (b) shows only forces on the car.
a
b
Patterns
Ask students to give examples of motion they observe in everyday
phenomena such as thrown balls, drifting leaves, coasting on a bike
at constant speed on level ground, coasting to a stop, speeding up in
response to expending more energy, and leaning to turn the bike. Ask
them to group these phenomena into similar patterns.
In a free-body diagram, each force on an object is represented by a vector arrow. This
model treats all forces as if they were acting at a single point, called the center of mass of
the object. The center of mass is usually represented as a dot and may not be exactly at
the center of the object. In Figure 3b, the free-body diagram of the car, the normal force is
shown as a single vector pointing upward from the center of mass. Compare Figure 3a, in
which the normal forces from the ground are represented as two vectors at the tires.
1
Differentiate Instruction
Extension Direct students’ attention to Figure 4 on the facing page.
Fgravity
Demonstrate how tilting the ramp changes the components of force
parallel and perpendicular to the ramp. As the angle increases, the
parallel force also increases. Ask: If the ramp is at angle θ, what is the
normal force on the box in terms of its weight W? W(cos θ) You can
illustrate this by calculating the normal force N at 0° and 90°. If N is one
component of the weight, what is the other? the force down the ramp
What is it equal to? W(sin θ) Again, check that the answer makes sense
for angles of 0° and 90°.
Fnormal
Fspring
Fstring
Determining Net Force
The net force on an object, Fnet, is the vector sum of all external forces acting on it. You may
also see net force written as ΣF, where the capital sigma, Σ, indicates a summation. In
each of the free-body diagrams that you labeled, two forces are balanced. When forces on
an object are balanced, the net force is zero. The forces may be large or small, but if they
balance, the result is as if no force were acting on the object.
1 Top: Fnormal, Fstring, Fspring; bottom: Fgravity for all three. Students might
reasonably use Fnormal for the upward force from the spring.
2 If the object is not moving, each force must be opposed by
another force. The forces must balance, and so the net force must
be zero. If there were an unbalanced force, the object would
move. (It would accelerate, but students are not yet expected to
have that understanding.)
2
56
56 Unit 1 Physics and Engineering
ANALYZE Select the correct label for each vector in the free-body diagrams. A label can
be used more than once.
INFER What can you infer about the net force when an object is unmoving—at rest?
Explain your reasoning.
© Houghton Mifflin Harcourt Publishing Company
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SEP
3
Have students explore opposing forces in one dimension by
dropping nested coffee filters. By nesting the filters, the surface area
remains the same while the weight doubles, triples, and so on. Air
resistance depends on speed as well as surface area but might be
treated as approximately constant in this activity.
PREDICT Next to each diagram, draw a vector to represent the direction and
approximate magnitude of the net force. Then describe what you think will happen
to the motion of the box.
Scenario
Free-body diagram
Planning and Carrying Out Investigations
Predicted motion
box falling in air
Exploring Visuals
box on a spring
Help students understand that in Figure 4, gravity has been broken
into two component vectors, along the ramp and perpendicular to
it. One of these vectors is balanced by the normal force. The other is
balanced by static friction.
If forces act in one dimension—that is, along a single line—they can be represented as
positive and negative numbers. For example, a force of 10 N down and a force 8 N up can
be written as −10 N + 8 N = −2 N, a net force of 2 N downward.
When forces are in two dimensions, you can look separately at the forces
in perpendicular directions, such as vertical and horizontal forces. Because
frictional forces are parallel to surfaces in contact and normal forces are
perpendicular to the surfaces, you might choose a coordinate system oriented
with one axis along the surface. In Figure 4, one axis would be parallel to the
Fnormal
ramp and the other would be perpendicular to the rampFand parallel to
the
friction
normal force on the box.
FIGURE 4: Components of the
force due to gravity
Ffriction
You can often determine the normal force by analyzing the other forces.
Suppose gravitational force is the only force pressing the object to the surface.
Fgravity
For an object at rest on a horizontal surface, the normal force equals
the weight
of the object supported by the surface. For a slanted surface, such as a ramp, the
normal force equals the component of the force due to gravity perpendicular to
the surface.
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
4
3 In each case, gravity pulls downward on the object. A second
force acts upward but is of different magnitude. First scenario:
net force downward; the box will accelerate downward.
Second scenario: net force upward; the box will accelerate
upward. (Students are not yet expected to have the detailed
understanding of force causing acceleration and may reasonably
use “move,” “be pushed,” or similar phrases.)
Fnormal
Fgravity
4 b, d, e, f
Evidence Notebook
5 Sample answer: Diagrams should show weight
(gravitational force) for both objects, with the acorn’s vector
longer than the ant’s. Upward air resistance should be
shown for the ant and possibly for the acorn but should be a
larger fraction of the ant’s weight than the acorn’s weight.
APPLY Suppose you place a coin on a book; the book’s cover acts as a ramp. You open
the cover slowly until static friction is overcome. The coin begins to slide. What happens to
the forces on the coin as the angle of the cover changes? Select all correct answers.
a. A component of the frictional force begins pushing the coin and book together.
b. The frictional force decreases suddenly as the coin starts to slide.
c. The gravitational force increases.
d. The component of gravitational force along the surface increases.
e. The component of gravitational force perpendicular to the surface decreases.
f. The normal force decreases slowly, which produces a slow decrease in static friction.
5
Evidence Notebook Construct a free-body diagram for the falling ant and the falling acorn in
the example, just before each hits the ground. Use the lengths of the vectors to show your estimate
of the relative magnitudes.
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FORMATIVE ASSESSMENT
Card Responses Have students write balanced on one side
of a note card and unbalanced on the other side. Quickly give
students a series of examples (words, images, equations) of
objects at rest (balanced forces) or with changing motion
(unbalanced forces); avoid examples with constant velocity. Ask
students to indicate the type.
Lesson 3 Effects of Forces 57
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 2 Exploring Force and Motion
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3D Learning Objective
EXPLORATION 2
Students analyze data about the pattern of motion observed in
objects acted on by a net force.
Hands-On Lab
Small Groups
Hands-On Lab
Exploring Force and Motion
45 minutes
In this lab, you will explore two ways of producing constant forces and the effects of
constant forces on motion. Then you will use a more formal setup to determine the effects
of constant forces on the motion of objects that are initially at rest and initially moving.
Exploring Force and Motion
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RESEARCH QUESTION How is force related to motion?
Constructing Explanations and Designing
Solutions
1
Students analyze motion in response to a constant force.
MAKE A CLAIM
After completing Part I, use your hypothesis to help you address this question: Suppose
the frictionless system shown in Figure 7 is tested with equal masses. What will happen if
the system is given a small initial motion—one mass moving upward, one downward?
Advance Preparation If probeware or other tools for quickly
determining velocity are available, encourage their use. Students
may wish to use video or photos to record and analyze their results.
They should make a trial run to check the angle of the camera, the
stability of the camera’s location, and how well they can read any ruler,
stopwatch, or other measuring device in the image.
POSSIBLE MATERIALS
• safety goggles
• balance
• box with a flat bottom
Materials Alert Students can use tape to fasten flat strips of material
• dynamics cart
to the work surface or bottom of the box to vary the amount of
friction between surfaces. Strips of tape can also be used for this
purpose.
• elastic cord or rubber
band
• mass set and/or
• ring stand
objects of known mass • spring scale or other force meter
• mass hangers and
• stopwatch or other timing device
slotted mass set
• string
• pulley with clamp for
• surfaces, assorted
table edge
• tape, masking
SAFETY INFORMATION
• Wear safety goggles during the setup, hands-on, and takedown segments of the activity.
• Immediately pick up any items dropped on the floor so that they do not become a
slip/fall hazard.
Planning and Carrying Out Investigations
• Wash your hands with soap and water immediately after completing this activity.
The reasons for testing a high-friction setup first are 1) to make
students aware that the net force (applied force + friction), rather than
the applied force alone, is what affects motion; 2) to give students
experience with a low-velocity system (easier to estimate velocity
using simple tools); and 3) to help students understand the purpose
and design of the more complex, low-friction setup. Qualitative
observations of motion (slow, medium, fast, very fast, etc.) should be
sufficient for Steps 1–3.
FIGURE 5: Use a spring scale to
ensure a steady applied force.
CARRY OUT THE INVESTIGATION
In Part I, you will first explore the relationship between applied force and net
force. Later, you will need to decide which force to use in your hypothesis.
Then you will use a setup in which a gravitational force is approximately the
same as the net force on a system. As you work, you will need to determine
and record details of your procedure based on the materials available, your
ongoing results, and your judgment.
Use three or more values of an independent variable (such as force applied or
mass of the moving object) to make a rough graph as you work. Try to determine whether
the variable has no effect (a horizontal line), a linear effect (a straight line), or a nonlinear
effect (a curved line). If you can’t tell, gather more or better data before you put away the
equipment.
1 Students may initially apply everyday experience and predict that
the system will slow and stop, or they may think that it will speed
up because an object is falling. Some students may understand
that the system will keep moving at constant velocity.
58
PDF
Unit 1 Physics and Engineering
Student Lab Worksheet and complete Teacher Support are available online.
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58 Unit 1 Physics and Engineering
PART I: Testing Constant Forces
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Preconception Alert
Students may try to get a linear relationship of velocity to force. The
effort should not be fruitful, so encourage students to move on after
reasonable attempts.
Procedure
Record details of your procedure and your observations in your Evidence Notebook. You
might design tables to record multiple trials and multiple values of independent variables.
DCI
1. Record the type and mass of the box you use. Tie a loop of string around the box. Place
the box flat on a table or the floor, and hook the force meter to the string loop. Add a
known amount of mass to the box.
Start with a static demonstration of pulling the box. With students,
work out that the net force must be zero, so the frictional force is
balanced by the applied force. Then review that the frictional force
depends on the surfaces and how hard they are pressed together.
2. Gently pull the spring scale with different amounts of force but without moving the
box. Record the range of forces you can apply and the static friction you infer.
3. Gently pull the box along the table using the spring scale. Try to keep the force constant
as the box slides. Optimize the mass in the box and the applied force to find a range for
which you can keep your applied force constant. Then describe the relative velocity and
acceleration for different applied forces, as well as an estimated net force.
If friction is minimal in Step 5, then acceleration should be
proportional to the force divided by the total mass (a + b). Expect
some friction and loss to the pulley.
• You can use the stretch of an elastic cord as another way to estimate the applied force.
• Vary the sliding surfaces or the mass of the box to increase or reduce friction in order
to help you pull the box with a constant force. For example, you can put strips of tape
along the surface or the bottom of the box.
4. Set up a low-friction system as shown in Figure 6. The hanging weight
(b) provides a constant force as it drops. Check that the string’s length
enables the maximum motion. Prevent the cart and hanging weight from
hitting anything at the end of each run.
5. Experiment with different masses in the cart and different hanging weights
to find a range that gives good results. Ignore friction and assume the
hanging weight is the net force. Then test enough values of force to
develop a hypothesis about the effect of force on motion. Record your
measurements or estimates of velocity and acceleration, along with any
qualitative observations of motion for each trial run.
FIGURE 6: Use a hanging
weight (b) to provide a steady
force on the object (a), but
include its mass as part of the
system in motion.
a
CCC
b
ANALYZE
© Houghton Mifflin Harcourt Publishing Company
Patterns
During Part I, you might ask students to enter their data into a
spreadsheet in order to see graphs in real time and make decisions
about additional data to collect. After Part I, you may wish to have
students vary the parameters in a simulation and/or spreadsheets
in order to reinforce and formalize their ideas. Look for simulations
of force and motion, frictional force, static and dynamic (or sliding)
friction, and Newton’s second law. However, be aware that many
simulations state and explain the relationships; you may prefer to
have students develop their understanding independently.
1. List the relationships that were clearly linear or clearly nonlinear.
© Houghton Mifflin Harcourt Publishing Company
PS2.A Forces and Motion
Analyze
2. Do you think the applied force, the frictional force, or the net force has the strongest
relationship to motion? Use a free-body diagram to help you determine your answer.
3. Think about how varying the force you chose affects velocity and acceleration. Write a
hypothesis that summarizes how force affects motion.
Lesson 3 Effects of Forces
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1. Students should rule out a linear relationship between force and
velocity and may find the linear relationship between force and
acceleration for a given mass. They may also find that mass and
acceleration are related inversely (they should not find a linear
relationship). Student data may also suggest other relationships.
2. Experiments with the high-friction box should lead students to
find that the net force has the strongest relationship to motion.
Student data may lead to a variety of hypotheses to be tested.
3. Ideally, students will hypothesize that acceleration is directly
proportional to net force. However, accept any testable hypothesis
at this point.
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Lesson 3 Effects of Forces 59
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 2 Exploring Force and Motion, continued
PS2.A Forces and Motion
To a reasonable approximation, the system with the cart and
hanging weight is affected only by the force from the hanging
weight. Elevators and rising window panes use a similar system. Ask
students to research counterweights and the use of this everyday
phenomenon in industrial design.
PART II: Testing Your Hypothesis
PLAN YOUR INVESTIGATION
Use your hypothesis from Part I to make a claim about the setup shown in Figure 7. Then
use your experiences from Part I to develop a plan to test your hypothesis about force and
motion. Consider these suggestions as you plan your procedure:
Collaborate
• Use or adapt one of the two setups from Part I. Draw a free-body diagram of the system
to help ensure that you will be able to measure or calculate all significant forces.
Discussion Some student hypotheses may lead them to design
• Design a procedure to test and refine your hypothesis about how force affects motion.
investigations that are unlikely to produce useful results, such as those
that fail to determine net force. If so, have the class share hypotheses.
Ask students to design tests to weed out some of the hypotheses.
• Plan to determine whether the effect of force has a linear relationship to an object’s
velocity or acceleration. If not, find a way to describe the relationship.
• Test enough values of force to provide evidence of the relationship. Also test several
values of mass to ensure that the relationship holds for different objects.
• If you can, test a setup in which there is zero net force and a small initial velocity.
Analyze
Make sure your teacher approves your procedure and safety plan. Then carry out your
procedure and record your observations in your Evidence Notebook.
1. Sample answer: The effect of force was more closely related to
acceleration, and the relationship was roughly linear. When the
hanging weight (force) was doubled, acceleration of the system
approximately doubled.
2. Sample answer: Greater mass reduced the acceleration, but the
relationship seems to hold true for any given mass.
1 If students have determined that acceleration is proportional
to net force, then they should use this evidence to predict that
the setup with zero net force will have zero acceleration. The
system should continue moving at the initial velocity until one
of the objects hits the pulley or floor. If students argue for other
relationships, then their claims should be compatible with the
relationships they assert.
ANALYZE
1. Based on your experiment, is the effect of force more closely related to an object’s
velocity or its acceleration? Is the relationship linear? Give details of the relationship.
2. How well does your answer to the first question apply if you use a different mass?
FIGURE 7: A string passing over
a pulley supports two objects.
1
DRAW CONCLUSIONS
Write a conclusion that addresses each of the points below.
Claim Suppose the frictionless system shown in Figure 7 is tested with objects
of equal mass (zero net force). What will happen if the system is given a
small initial motion, such that one mass moves up and the other moves down?
Evidence Present your hypothesis tests and other evidence to support your claim.
Reasoning Explain how your evidence applies to the system in Figure 7.
Evidence Notebook
2 Students may be able to infer that the net force on the ant is
zero or nearly zero for the last part of the fall.
© Houghton Mifflin Harcourt Publishing Company
DCI
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FORMATIVE ASSESSMENT
3-2-1 Have students write three things they found out in the
Exploration, two things they found interesting, and one question
they still have about the concepts presented in Exploration 2.
2
60
a hypothesis about the difference between the falling ant and acorn.
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60 Unit 1 Physics and Engineering
Evidence Notebook Apply what you have learned about the effect of force on motion to form
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LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 3 Connecting Force and Motion
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EXPLORATION 3
3D Learning Objective
Connecting Force and Motion
Students use mathematical representations to analyze the effect of
net force on an object’s motion as summarized by Newton’s second
law of motion.
Collaborate With a partner, choose a scenario such as sliding a table across the floor.
Discuss the effect of the force you apply, such as by pulling or pushing the object. Then discuss
the effect of net force. Which force would you use to predict the object’s motion?
3
DCI
Use a small object resting on a skateboard or similar vehicle to
demonstrate the everyday phenomenon that static friction with a
moving surface can move an object resting on that surface. Ask: Will
the object remain in place as the force used to start the skateboard into
motion or bring it to a stop becomes larger and larger? No, eventually
the force of static friction will not be enough to hold the object in
place against a large force, and the object will slide along the surface
of the skateboard. In which direction will it slide? against the change in
motion—forward if the board abruptly stops, backward if it abruptly
speeds up
Analyzing Force and Motion
4
ANALYZE For each example, describe the car’s motion by determining whether velocity
and acceleration are zero, positive, or negative. Then try to do the same for net force.
Example
Velocity
Acceleration
Net force
A car is parked.
A car moves at a constant speed of 100 km/h
on a straight roadway.
A car slows in a school zone.
A car that was stopped at a red light begins to move
when the light turns green.
Differentiate Instruction
A car turns a corner at a constant speed of 10 km/h.
MTSS/RTI Students may struggle to understand the directions of
motion in the Evaluate activity. Remind them that they can choose
a coordinate system that makes motion easier to model, such as by
focusing on the direction of motion over the top of the pulley. Give
authentic feedback when students persevere, such as “You should be
proud of yourself for not giving up.”
When two balanced forces are exerted on an object, such as an object’s weight and the
normal force from the floor beneath it, the effects of the forces tend to cancel each other.
To predict motion, scientists typically use net force.
© Houghton Mifflin Harcourt Publishing Company
In Figure 8, two objects hang by a single string that runs over a pulley. The device, called
Atwood’s machine, shows how net force affects motion. Each object is pulled down by
gravity and up by the string.
5
FIGURE 8: Atwood’s machine
EVALUATE Select the correct terms to complete the statements about the
forces in Figure 8.
F1,gravity
The forces from the string, F1,string and F2,string, have magnitudes that
are the same | different and directions that are the same | opposite |
perpendicular, whether or not the system is in motion.
If the masses are equal and unmoving, the net force on each object must
be upward | zero | downward.
Suppose the masses of the objects are equal and the masses of the string and
the pulley are small enough to be ignored. If the objects are at rest, they stay
at rest. However, if the system is initially moving, it continues moving steadily
until something stops it. One object moves up and the other moves down,
each at constant velocity, until an object reaches the pulley or the ground.
F1,string
F1,gravity
F
1,string
3 Sample
answer: We apply increasing force until we overcome
F2,string
F2,gravity
static friction and the table starts to move. To keep the table
in motion, our applied force must be at least as great as the
opposing force of sliding friction. We would use the net force,
rather than our applied force, to predict the motion.
4 Parked: v 0, a 0, F 0; constant speed: v +, a 0, F 0; slows: v +, a –,
F –; begins: v +, a +, F +; turns: v changes direction, a sideways
(or +), F sideways (or +). Students may apply past experience to
make reasonable but different inferences. Discuss answers to
ensure that students are considering net force.
F2,string
F2,gravity
Lesson 3 Effects of Forces
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PS2.A Forces and Motion
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5 the same, the same, zero
Lesson 3 Effects of Forces 61
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 3 Connecting Force and Motion, continued
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Nature of Science
Scientific Knowledge is Open to Revision in Light of New
Evidence In Aristotle’s model of motion, an object in motion
Effect of Balanced Forces on Motion
continues in motion only as long as a force acts on it. When the
force stops, so does the motion. To explain things that keep
moving—such as a rolling ball or a shot arrow—Aristotle developed
ideas about forces from the air touching the object. Have students
research Aristotle’s ideas and then defend or dispute his model.
In many everyday experiences, moving objects tend to slow down or stop unless something
keeps them moving. For example, if you tap a pencil to make it slide along a table, it slows
down and comes to a stop. You may not notice that frictional force acts on the pencil; it
represents a net force in the direction opposite to the pencil’s velocity. Gravitational force
and friction are part of most of your everyday experiences. If you have experiences with
objects sliding on ice or other nearly frictionless surfaces, you may have noticed that objects
can move at a constant velocity for a long time without anything pushing on them.
FIGURE 9: Little or no friction is present between a hockey puck and ice.
Collaborate
One Moves Have students work in groups. Each student should
jot down an example of a force, such as weight or friction. Students
should hand the paper to another student, who gives an everyday
example of that force. They then hand the papers off again and ask
the next student to give a force that might balance the first.
1
Explore Online
Hands-On Lab
Small Groups
INFER Draw the free-body diagram for the hockey puck when it is not moving (a),
and when it is moving steadily to the right (b).
45 minutes
SEP
a
Planning and Carrying Out Investigations
Students explore the possible causes of changes in motion. Student
lab worksheet and teacher support available online.
DCI
PS2.A Forces and Motion
You can set up air tracks to demonstrate low-friction motion as a
tabletop experiment.
Explore Online
Not moving, at rest
2 Diagrams should include all apparent forces. Videos made by
astronauts are good examples, but you may need to explain that
the video is taken in a noninertial reference frame. Encourage
students to post links to videos.
62 Unit 1 Physics and Engineering
Exploring Newton’s Laws
Explore the factors that cause a
change in the motion of an object.
2
62
Moving steadily to the right
Apply the idea of net force to everyday experiences in which you exert a force to keep
an object moving. Suppose you pull an object just hard enough to oppose friction, so
Fnet = 0. If you reduce friction, such as by using a slippery surface, less force is needed to keep
the object in motion. If you could reduce friction all the way to zero, an object sliding
across the surface would continue to slide at its initial velocity without any applied force.
You would not have to continue pulling to keep it moving. The same thing happens
with Atwood’s machine and with an ideal hockey puck; an object can move at a constant
velocity when Fnet = 0. When a moving object slows, it is because of a net force, such as
friction, acting on it.
Hands-On Lab
1 In both, the downward force of gravity is balanced by the upward
normal force, shown by equal and opposite vectors. For the
second diagram, students should show a small frictional force to
the left or argue that this is effectively zero (constant speed).
b
You can summarize the two effects of zero net force: An object at rest remains
at rest and an object in motion continues in motion with constant velocity
unless the object is subject to a net external force. This relationship is called
Newton’s first law of motion. Remember that an object at rest has zero velocity.
In other words, when net force is zero, an object remains at constant velocity
(which may be zero); it does not accelerate.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (c) ©francisblack/E+/Getty Images
Exploring Newton’s Laws
Language Arts Connection Find a video, simulation, or physical situation that shows
an example of Newton’s first law of motion. You might instead be able to demonstrate an
example. Describe the example and draw a free-body diagram that represents it.
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Language Arts Connection
Translate Visuals to Words Ask students to write a paragraph
Effect of Unbalanced Forces on Motion
presenting a situation that is qualitatively like the one illustrated in
the table: increasing forces applied to the same mass and the effects
observed. You may want to ask them to adapt the situation to the next
Data Analysis, in which the same force is applied to objects of greater
and greater mass. (RST.9-10.7)
As you may have inferred, an object’s velocity changes when the net force on it is not zero.
The object may slow down, speed up, or turn; the force causes this change in motion.
Data Analysis
Magnitude of Net Force
3
Model
m (kg)
a (m/s2)
Fnet (N)
2
2.5
5
2
5
10
2
10
20
2
15
30
Patterns
In most graphs, the independent variable is plotted on the horizontal
axis. In this case, the axes are arranged so that the slope represents
the mass. Ask: What other phenomena show the same pattern seen
in the graph you made in the Model activity? Any pair of variables
that have a linear relationship. Examples include the displacement
of an object moving at constant velocity and the cost of a group of
items. What is the meaning of the slope? It is the rate of change of one
variable relative to the other. In this case, it represents a mass of 2 kg.
SEP
Developing and Using Models
Have students make graphs of force and acceleration from their
experimental data. Then have students use an online simulation of
force and motion (or Newton’s laws) to produce sets of simulation
data to match the graph in the Model activity and to match their own
data. Challenge students to explain any systematic differences.
Force (N)
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (c) ©francisblack/E+/Getty Images
CCC
MODEL Graph the simulated data from the table, which show the effect of different
forces on a 2 kg object, or make a graph of data from an experiment or a simulation.
Then draw the curve or straight line that best represents the points.
Some have found these simulations useful. They are not necessary for
this program. HMH neither controls nor endorses these simulations.
0
0
Acceleration (m/s2)
4
Math Connection
ANALYZE Select the correct terms to complete the statements.
MP.2 Reason abstractly and quantitatively.
Students graph the data from the table and interpret the pattern. The
axes are arranged so that slope equals mass.
The points lie along a straight line | simple curve | complex path, so the
relationship between acceleration and force is linear | geometric | exponential.
The magnitude of the acceleration a is directly proportional to |
inversely proportional to | the inverse square of the magnitude of the force F.
3 The data should lie along a straight line of slope 2. Units for the
slope are N per m/s2, or kg.
The overall slope represents the velocity | rate of change in acceleration | mass.
4 straight line, linear, directly proportional to, mass
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Lesson 3 Effects of Forces 63
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 3 Connecting Force and Motion, continued
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Differentiate Instruction
ELL Support Translate the motions pictured in the Infer activity
If you push on an object at rest, static friction may prevent it from moving: the net force is
zero. If you push hard enough, the object starts moving—accelerates—in the direction of
the net force. Explore the relationships between net force, velocity, and acceleration when
the object does not start from rest.
into common English descriptions. Example: The first car speeds up
while moving forward, the second speeds up while moving backward,
the third brakes while moving forward, and the last brakes while moving
backward. Remind students that in physics, acceleration is used to
describe any change in motion: speeding up, slowing down, and
turning. The change in motion caused by a net force depends on
whether that net force is in the same direction as the object’s motion
(speeds up), opposite (slows down), or at an angle (turns). Elicit from
students a number of examples of everyday phenomena in which an
object speeds up, slows down, or turns, asking students to identify the
initial direction of motion and the direction of net force in each case.
INFER The dots show the car’s position at equal intervals of time. The vectors show
the car’s initial and final velocities. For each example, first determine whether the car is
speeding up or slowing down, then infer the direction of the net force.
speeding up
slowing down
vf
vi
Cause and Effect
vi
vi
Students may recall that in everyday life, you often have to keep
pushing on an object to keep it moving. You find that pushing
correlates with motion, and less pushing correlates with slowing and
stopping. However, it isn’t the reduction of applied force that causes
the slowing and stopping, despite the correlation. In the everyday
phenomena, other forces, such as friction or gravity, are usually acting
on the object. The cause of any change in velocity is a (nonzero) net
force. Ask students to name and analyze everyday phenomena that
illustrate this cause-effect relationship.
vi
vf
vf
vi
Notice how the direction of net force can be different from the direction of an object’s
motion. For example, when you slide an object across a floor, the force of kinetic friction
is opposite to the velocity and tends to slow the object.
1 first row: speeding up, right; second row: speeding up, left; third
row: slowing down, left; fourth row: slowing down, right
2
2 the same as, speed up, slow down, turn
APPLY Select the correct terms to complete the statements for an object acted upon
by a nonzero net force.
The direction of acceleration is the same as | opposite to the direction of
net force.
A force in the direction of motion causes an object to slow down | speed up | turn.
A force opposite the direction of motion causes an object to slow down |
speed up | turn.
© Houghton Mifflin Harcourt Publishing Company
CCC
1
A force at a 90° angle to the direction of motion causes an object to
slow down | speed up | turn.
64
Unit 1 Physics and Engineering
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Claims, Evidence, and Reasoning
Help students understand how to break down the forces in everyday
phenomena by walking them through the process. Show students
two books, one much larger than the other, and set them on a desk.
Set each book in motion while trying to use the same force—for
example, set the books side by side and use a larger book to strike
both books at the same time. Ask: What claim can you make about
which book will have a larger displacement? Sample answer: The
smaller book has a smaller mass and so will be accelerated more
by the same force. What evidence do you have to support your claim?
Sample answer: The evidence in the data analysis supports an inverse
relationship between mass and acceleration for the same force. How
does the evidence support your claim? Sample answer: The more
massive book came to a stop in a short distance, while the lighter
book traveled a greater distance.
Relating Force, Mass, and Acceleration
You have seen how acceleration is related to the net force, but it also depends on an
object’s mass. Think about how objects of different masses accelerate if pushed with
the same force; imagine the objects on ice or another low-friction surface.
Data Analysis
Effect of Mass on Acceleration
3
MODEL The table shows the results of a simulation in which force is held constant.
Graph the results to find out how an increase in mass affects acceleration.
Model
F (N)
10
1
a (m/s2)
10
10
10
10
2.5
5
10
15
4
2
1
2/3
SEP
0
Students can also use the graph in the Model activity to plot the
results of simulationsor their own experiments. They might plot
acceleration and mass for a given force, or might instead add objects
of different mass (different symbols or color) to the previous graph.
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Mass (kg)
4
Analyzing and Interpreting Data
If students have access to a spreadsheet or graphing application, have
them plot different functions, such as a2 = k×m or a = k×1/m, to try to
match the curve in the graph. They will need to include a constant, k,
and experiment with different values. Students can also use data from
the table to make variations of the graph, such as by plotting1/a or
1/m, until they find a relationship that produces a straight line. Have
them write the equation for the slope of that line.
Acceleration (m/s2)
m (kg)
10
ANALYZE Select the correct terms to complete the statements.
A more massive object acted on by the same net force as a less massive object
has a smaller | the same | a greater acceleration.
The tangent to the curve at each point has positive | zero | negative slope.
Math Connection
There is a direct | an inverse | a complex relationship between the mass of an
MP.2 Reason abstractly and quantitatively.
Students graph data and look for patterns. Remind students that they
can find graphing tips in the online Math Handbook.
object and its acceleration—a is proportional to m | 1/m.
Suppose you gave pushes of equal force to a small child on one swing and an adult on a
second swing. The force has less effect on the adult’s greater mass. To achieve the same
acceleration of the greater mass, you must apply a greater force.
3 The graph should show an inverse proportion, in which
acceleration decreases as mass increases: a is proportional to 1/m.
4 a smaller, negative, an inverse, 1/m
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LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 3 Connecting Force and Motion, continued
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Language Arts Connection
RST.9-10.7 Translate quantitative or technical information expressed in words in a text into visual form.
1
Students make a flow chart to show appropriate uses of the simplified
model. They can learn about diagrams in the “Understanding
Graphics” section of the online English Language Arts Handbook.
a
m
Fnet
=
×
The equation can be rewritten to show how acceleration depends on both force and
mass: a = Fnet/m. This relationship is known as Newton’s second law of motion. Constant
acceleration is the result of a constant net force acting on an object, such as when gravity
alone acts on a falling object near Earth’s surface.
1 Fnet = ma or Fnet = am
2 As the net force increases slightly, the acceleration increases
slightly. When the net force doubles, the acceleration doubles.
As the mass increases slightly, the acceleration decreases slightly.
When the mass doubles, the acceleration halves.
2
APPLY Match the change in the force or mass to the change in the acceleration of an object.
As the net force increases slightly,
the acceleration decreases slightly.
When the net force doubles,
the acceleration doubles.
As the mass increases slightly,
the acceleration halves.
When the mass doubles,
the acceleration increases slightly.
The mass in the equation is the total mass of the system being accelerated. For two
objects connected by a (massless) string over a pulley, both objects contribute to the
system’s mass. If you use a descending weight to provide a constant force, or if you set
up Atwood’s machine with different masses, the net force is the unbalanced part of the
gravitational force.
FIGURE 10: The cart has mass m1 and the
descending weight has mass m2.
3
m1
Evidence Notebook
m2
4 Both start from rest, so the average acceleration of the acorn
must be greater. Air resistance reduces the ant’s acceleration
significantly, possibly to zero for part of the fall. Students
should make any needed corrections to the free-body
diagrams in their Evidence Notebooks. The net downward
force should be greater for the acorn and might be zero for
the ant.
Language Arts Connection When you make calculations
for the system shown in Figure 10, you might assume that the
system is frictionless, that air resistance is zero, and that the
string and pulley have zero mass. List advantages and
disadvantages of using this model. Think about the conditions
under which it is reasonable to use the simplified model. When
might you need to include more detail in your calculations?
Summarize your conclusions in a flow chart.
Think about how this relationship applies to situations with different amounts of friction.
On a frictionless surface or in space, an object accelerates as soon any force is applied.
In contrast, a heavy object on a high-friction surface does not move until the applied
force becomes great enough. It then moves suddenly as the force due to static friction is
exceeded and kinetic friction begins.
On a frictionless surface or in space, a more massive object takes greater force to speed
up, to turn, or to stop. Its mass resists the change in velocity. In situations with significant
friction, the amount of friction often depends on an object’s weight, which is proportional
to its mass. A more massive object takes greater force to accelerate both because its mass
resists acceleration and because its weight produces greater friction.
FORMATIVE ASSESSMENT
Quick Write Ask students to apply the equation to the friction
and net force on a box sliding down a ramp, initially at constant
speed. If the frictional force increases (for example, the box
moves over a rough patch), what happens to the motion of
the box? What if the box hits a smooth patch? What would an
increase in speed indicate?
4
66
Evidence Notebook Think about the motion of the ant and acorn just before each hits the
ground; assume the acorn hits at a greater velocity. Infer the relative accelerations, compare the
net forces on the ant and acorn, and then review the free-body diagrams you made.
Unit 1 Physics and Engineering
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3 Advantage: simpler; disadvantage: less accurate. If the string’s
mass is significant, then the net force changes as its mass shifts
from one side of the pulley to the other. Friction and air resistance
also make the calculations more complicated and possibly
unsolvable. Flow charts should reflect these concepts: if the
hanging masses are large compared with the other components
and the pulley is well designed, the simplified model should give
reasonable results. If the string or pulley has significant mass,
more detailed calculations are needed.
SOLVE The relationships between Fnet, acceleration a, and mass m can be summarized in
an equation. Place each variable in the equation.
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EXPLORATION 4 Analyzing Action and Reaction
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EXPLORATION 4
3D Learning Objective
Analyzing Action and Reaction
Students use representations to analyze forces between objects in a
system as summarized by Newton’s laws of motion.
5
Language Arts Connection Think about a toy that jumps when a spring
is released, as in Figure 11. An upward force causes acceleration at the start of
the jump, yet the spring presses downward on the table. Use a labeled diagram
to identify the unbalanced force that accelerates the toy.
FIGURE 11: A jumping toy
DCI
Help students understand how balanced forces act on a single object
and can be shown in a free-body diagram, while action-reaction force
pairs act on different objects. Ask: If a jumping toy is at rest on a table,
what are the balanced forces? the weight of the toy and the normal
force from the table When the toy jumps, it pushes harder on the table.
What is the reaction force? The normal force from the table on the
toy increases to match. Which force would not be part of a free-body
diagram of the toy? the force of the toy on the table
Analyzing Paired Forces
A free-body diagram models only the forces acting on a single object or
system treated as a point. A different model is needed to analyze the forces
between objects. The car in the visual exerts a forward force as it hits the
wall; this force can be considered an action force. The car’s speed decreases
suddenly, so you can infer that the wall pushes backward on the car. This force
can be considered a reaction force. Unlike the forces in a free-body diagram,
action and reaction forces act on different objects.
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6
PS2.A Forces and Motion
Language Arts Connection
RST.9-10.7 Translate quantitative or technical information expressed in words in a text into visual form.
ANNOTATE Label the action and reaction forces shown. Draw and label vectors for other
forces in this situation, such as the force pairs that include friction.
Students label a diagram to show force. Refer students to the online
English Language Arts Handbook for more information on how to
present information in a visual format.
5 The downward force produced by the spring results in a
matching upward normal force from the table or other surface
beneath the toy. The normal force is exerted on the toy and
produces the acceleration. Prompt students to identify the object
each force is exerted upon.
Forces in the universe occur in pairs. For every action force, there is a reaction force of
equal magnitude in the opposite direction. This relationship is known as Newton’s third
law of motion. Each force in the pair acts on a different object, so these forces cannot
balance one another. The forces are equal even when one or both objects accelerate.
6 Sample answer: On existing arrows—action to the right (from
the car), reaction to the left from the wall. At the tires—action (car
pressing downward), reaction (normal forces) upward; action to
the left (applied force of tires due to engine), reaction to the right
(friction with ground).
Collaborate With a partner, make a list of examples of action-reaction force pairs
you have observed. Compare your list with other groups.
7
The car slows to a stop because of a reaction force to the left, exerted on the car by the
wall. In turn, the wall produces a force to the right on the ground, which produces a
reaction force to the left on the wall. You can also model the wall and ground as if they
were a single object. Think of a swimmer pushing off the wall of a swimming pool; action
and reaction forces are always equal, opposite, and exerted on different objects.
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7 Examples might include weight and normal forces, two people
pushing or pulling against each other, the applied force and
reaction force from an impact (such as a foot kicking a ball),
forces between two surfaces in contact, and many others. Prompt
examples that occur during motion, if needed. Have students
check that the paired forces act on different objects.
Lesson 3 Effects of Forces 67
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 4 Analyzing Action and Reaction, continued
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Scale, Proportion, and Quantity
The femur is the large bone in the thigh or hind leg. Show students
photographs of femurs from animals of different sizes, such as a
squirrel, moose, and elephant. Ask: What pattern do you notice? As the
mass of the animal increases, so does the cross section of the femur
compared with its length. Do muscles exert compression or tension?
Tension; like ropes, muscles can only pull, not push.
Mathematical Models of Newton’s Laws
Math Connection
Second law: An object acted on by a net external force will accelerate in the direction
of that force according to the equation Fnet = ma.
Point out to students that the top and bottom of the tube in the
example are subject to equal forces from two directions, and the
same type of force pairs occur within the material in the form of stress.
Stress also has a second meaning: the force per unit area. Ask: What
happens to stress when the force doubles? It doubles. What happens to
stress when the area doubles? It is cut in half. (MP.4)
Third law: For every action force, there is an equal and opposite reaction force.
Scientific Knowledge Assumes an Order and Consistency
in Natural Systems
The observations about force discussed in this lesson are collectively known as
Newton’s laws of motion.
First law: An object will remain at rest or in uniform straight-line motion unless acted
on by a net external force.
Be careful to distinguish between balanced forces and action-reaction pairs.
Analyzing Internal Forces
Suppose a cardboard tube from a roll of paper towels is lying on a table. The normal force
from the table balances the weight of the tube, and the tube does not accelerate. If you
press down on the tube with your hand, then the tube, in turn, presses down on the table.
The upward normal force from the table, a reaction force, increases as the total downward
force increases. The forces on the cardboard tube remain balanced, and the tube still does
not accelerate.
Biology Connection
Picture the everyday phenomena of running and jumping. Ask:
When force is transmitted through your body, would you expect the
points of failure to be where a small force passes through a large area
or where a large force passes through a small area? Why? A large force
through a small area, such as the connections between tendons and
bones, results in more stress and would be more prone to injury.
However, the downward and upward forces on the tube may cause the cardboard to
deform. The cross-section of the tube may become oval rather than round, or a dent in
the side may form. As the external forces from your hand and the table are transferred
through the tube, they produce internal forces. Action-reaction force pairs occur between
adjacent particles and are, together, called stress. Stress is also the name of a variable, σ,
that has units of force per unit area. Scientists and engineers classify stresses into three
types: compression, tension, and shear stress.
2
Evidence Notebook
1 First law: a net force must have accelerated the ant and
acorn from rest. It is possible that the ant and perhaps the
acorn were moving at constant velocity for part of the fall.
Second law: Acceleration occurred when gravitational force
was greater than air resistance, but acceleration was zero if
the two forces balanced. Third law: The ant pushed against
the air as hard as the air pushed against the ant. The same
was true for the acorn and for the ground as well as the air.
EVALUATE Use your knowledge of root words to label the three types of stress. The
dotted outline shows the shape of an object before the forces were applied. The solid
shapes show the deformation, or strain, resulting from each stress.
tension
shear stress
compression
Aligned forces
push inward
2 left: compression, middle: tension, right: shear stress
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68 Unit 1 Physics and Engineering
Evidence Notebook How do the laws apply to the example of the ant and the acorn?
1
Aligned forces
pull outward
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Nonaligned forces
may push or pull
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Hands-On Lab
Pairs
30 minutes
Model Stresses
Hands-On Lab
SEP
Model Stresses
Students explore the effect of stress on materials.
Advance Preparation Provide flat blocks or molds for students
You will explore the deformation and failure of a material from different types of stress.
who wish to apply forces more uniformly. If the technology is at
hand and permitted, encourage students to record cell-phone
videos or images.
RESEARCH QUESTION How do materials show the effects of balanced external forces?
3
MAKE A CLAIM
Describe how you think the material will respond when subject to different stresses
produced by balanced external forces. Will the deformations or breaks be symmetric?
POSSIBLE MATERIALS
• safety goggles, nonlatex
apron, nonlatex gloves
• sticky sand, compressible
clay, or similar material
3 Sample answer: The material will compress, stretch, or shift
sideways with slow compression, tension, and shear stress. I
expect general but not perfect symmetry.
Students should note whether they compress the block initially.
Large (fast) stresses may cause fracture rather than deformation.
• ruler, metric, or similar tool
SAFETY INFORMATION
4 Sample answer: The first effects of balanced forces were usually
symmetric. Compression, both aligned and shear, was usually
symmetric, but then the material tended to break closer to one
side or the other. Stretching, whether aligned or due to shear
stress, started out evenly but usually failed closer to one side
or the other. It seems as if a small amount of unevenness in the
material can be magnified as the material fails.
• Wear safety goggles, a nonlatex apron, and nonlatex gloves during the setup, hands-on,
and takedown segments of the activity.
• Immediately clean up any water, sand, or clay spilled on the floor so it does not become
a slip/fall hazard.
CARRY OUT THE INVESTIGATION
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Heather Hall/Getty Images
1. Wearing gloves, shape the material into blocks.
2. Use gloved hands to produce moderate amounts of stress of each type within a block;
reshape the material as needed. Try increasing the stress both quickly and gradually.
Record your detailed procedure and observations in your Evidence Notebook.
4
Evidence Notebook
5 At the beginning, air resistance is slight because speed is
relatively small. The ant pushes against the air with equal
force. The two forces increase with speed. Part of the way
down, air resistance matches gravitational force, and
velocity is constant from there on down. The middle and end
diagrams should be similar or the same.
DRAW CONCLUSIONS
Write a conclusion that addresses each of the points below.
© Houghton Mifflin Harcourt Publishing Company
Claim Do materials show symmetry when balanced external forces are applied?
Evidence Give specific evidence from your observations to support your claim.
Reasoning Explain how your evidence supports your claim. Give details of the
connections between the evidence you cited and the argument you are making.
5
FORMATIVE ASSESSMENT
Evidence Notebook Think about the force pair between a falling object and air. Take into
One-Sentence Summary Ask students to read back through
account that air resistance varies with speed. Construct a diagram showing the force pairs for an ant at
the beginning, in the middle, and near the end of its fall.
the Exploration. Have them write a one-sentence summary for
each head and each image.
Lesson 3 Effects of Forces
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Student Lab Worksheet and complete Teacher Support are available online.
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Analyzing and Interpreting Data
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Lesson 3 Effects of Forces 69
LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 5 Forces and Stresses in Engineering
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3D Learning Objective
EXPLORATION 5
Students analyze the forces and stresses that act on structures. They
apply the condition of Fnet = 0 to find the effect of forces on the
stability of structures.
Forces and Stresses in Engineering
Collaborate With a partner, choose an item you can examine, such as a retractable pen.
Discuss how you would evaluate the forces on and within the object.
1
Nature of Science
Science Models, Laws, Mechanisms, and Theories Explain Natural
Phenomena Have students pull gently on the two ends of a thick
rope or rolled fabric. Draw a free-body diagram for the center of
the rope, which should sag. Then have them try to pull the rope
tightly enough to make it straight. They should find that the weight
always causes at least a slight curve; force on the end of the rope is
almost horizontal, so the vertical component is a small fraction of the
magnitude.
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Analyzing Structures
One strategy for analyzing complex systems or structures is to look at one part at a time.
An engineer might make a free-body diagram as if a selected part were a separate object.
For a structure to be stable, there must be a way for the expected forces on each part to
be balanced by reaction forces (Fnet = 0). A supporting column of a bridge must provide an
upward force to match the combined downward weight of the bridge and vehicles.
An engineer may separate the external forces needed to address the design problem—the
load—from the forces due to the structure itself. The weight of vehicles might be a bridge’s
main load. A highway bridge must be designed for a greater load than a pedestrian bridge.
Horizontal forces due to wind are also part of the load on a bridge.
1 Students should be able to propose ways to measure or estimate
at least some of the external forces but should also become aware
of some difficulties in determining forces within a complicated
structure.
Engineering
In a truss—the structure shown—the segments may bend slightly under the weight.
The top is typically compressed and the bottom is typically stretched. You can model
the weight of each segment as a point mass at the center of the segment.
2 Sample answer: Centermost dot: segment weight downward,
tension left and right (balanced) and slightly upward, enough to
balance the weight when combined. Rightmost dot: compression
to right (from the segment to the left), balances horizontal parts
of compression to upper left and tension to lower left. Vertical
components of the last two balance. (Students may assume
different angles, but results should give a net force of zero.)
2
INFER For each of the two locations marked by a dot, draw a free-body diagram
of the forces acting at that point (Fnet = 0). Use the space below the diagram.
© Houghton Mifflin Harcourt Publishing Company
compression
tension
Evidence Notebook
3 This Evidence Notebook question refers to the Unit Project.
The need for upward forces in the center of a segment may
lead students to realize that the beam needs to transfer
the upward forces at the ends into the center of the beam.
Thickness, such as the height of the truss, can be useful. An
open framework is also an option for students to use in their
beam designs. Note: the framework is not just lighter but
also more spread out in a direction perpendicular to tension
or compression. This helps transfer vertical forces.
70 Unit 1 Physics and Engineering
3
70
Evidence Notebook How might you use ideas from the design of a truss to help you test
designs for a beam in your unit project?
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Nature of Science
Scientific Knowledge Assumes an Order and Consistency in
Natural Systems Have students use Newton’s first or second law to
explain why structures are stable when forces are balanced. Have
them use the relationship between force, area, and stress to explain
why a concentrated load is more likely to cause structural failure.
Hands-On Lab
Testing a Bridge
RESEARCH QUESTION How does the distribution of a load affect the forces and stresses
on a structure?
4
Collaborate
MAKE A CLAIM
How might the paper bridge in Figure 12 respond differently to a line of
pennies across the span of paper and to a stack of pennies in the middle?
FIGURE 12: A piece of paper
forms a bridge between books.
Graffiti Use large diagrams of the paper bridge and a truss on
sheets of paper. Students should discuss and then draw free-body
diagrams for several points on a structure. Groups can move to other
papers and discuss or add to the ideas.
POSSIBLE MATERIALS
• safety goggles
• paper, sheets (3)
• books, matching (2)
• pennies or other small
masses (50)
Hands-On Lab
• Wear safety goggles during the setup, hands-on, and takedown segments of the activity.
SEP
• Immediately pick up any items dropped on the floor so they do not become a slip/fall hazard.
• Wash your hands with soap and water immediately after completing this activity.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Houghton Mifflin Harcourt
© Houghton Mifflin Harcourt Publishing Company
5
Advance Preparation Multipurpose printer paper (20–24 pound
sheets) works well for the setup shown. Adapt the folds and space
between books to suit the material. For example, index cards might
be used without folding. Students might make multiple trials or
use a standardized setup and combine results with other groups to
determine the variation in results.
One end of bridge:
DRAW CONCLUSIONS
Write a conclusion that addresses each of the points below.
Claim What load distribution is most likely to cause the model bridge to collapse?
4 The paper is likely to support greater weight if the weight is
spread out, such as pennies in a line across the bridge.
Evidence Give specific evidence from your observations to support your claim.
Reasoning Describe, in detail, how the evidence you cited supports your argument.
5 Students should make a claim that is supported by data. The
configuration that collapsed under the smallest number of
pennies should be the one most likely to cause the bridge to
collapse. Most students should find that a stack of pennies in the
middle of the bridge is most likely to cause a collapse, but a stack
near one end may be a contender.
EXTEND
Test different bridge designs, such as a simple flat sheet or a sheet cut to resemble a truss.
Lesson 3 Effects of Forces
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Student Lab Worksheet and complete Teacher Support are available online.
PHU_CNLESE861794_U01L03EXP5.indd 71
Constructing Explanations and Designing
Solutions
Students construct a simple bridge design and test it under different load
distributions.
CARRY OUT THE INVESTIGATION
Fold a piece of paper to make a bridge, such as in Figure 12, and place it on two books.
Test the bridge by placing pennies, one at a time, and recording the maximum number
before the bridge fails. Make sure that none of the pennies are resting on the books. After
each failure, build a new bridge using fresh paper. Test three distributions of pennies.
Spread along length:
30 minutes
Testing a Bridge
SAFETY INFORMATION
Center of bridge:
Pairs
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LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 5 Forces and Stresses in Engineering, continued
Constructing Explanations and
Designing Solutions
Have students explore the design of several bags, both with and
without handles. Students should apply what they have learned about
forces and stresses to evaluate the designs. For example, they may
infer that a reinforced area or a segment made of a continuous strip of
material is expected to be under relatively great tension. Students can
also look at how a load is concentrated or spread out.
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Using Forces in Designs
For a structure to stay stable or moving as intended, it must withstand the expected
forces. An umbrella, for example, must withstand the weight of precipitation. It must
withstand the forces that cause it to open and close. An umbrella should also withstand
the forces as a person hangs onto the umbrella during a light gust of wind.
FIGURE 13: Use this house design to answer
the question.
1
APPLY Suppose wind blows on the house in Figure 13 from the
left and also produces an upward force on the roof. What reaction
forces are needed to support the weight of the roof and counteract
forces from the wind?
Structure and Function
Ask students to picture a stationary structure, such as the house in
Figure 13. Ask: Does the load constitute a net force on the structure, or is
it balanced by another force? The structure does not move, so the load
must be balanced by another force. How are forces transmitted through
the structure? through points of contact, such as the foundation
against the surrounding dirt and soil, or through screws and nails
holding boards together
A designer may first look at the external forces on a structure, such
as those shown in a free-body diagram. If wind blows on one side
of the house in Figure 13, the reaction force you identified comes
from the structure of the house. The structure pushes on the
ground on the opposite side, which, in turn, opposes the force. The structure of the house
must transfer the force from one side to the other without breaking. A designer might
add stiff braces, rigid triangles, or tight wires to the structure to balance possible forces.
In any building design, many different forces are involved. An engineer uses equations
for balanced forces and action-reaction force pairs to break the problem into solvable parts
and then puts the parts together to find an overall design solution. For example, to reduce
the forces on a support beam or other structure, a designer might choose components
that weigh less. Yet the designer might need to widen a support or add more supports
to provide greater reaction forces, and so may have to make tradeoffs.
1 An upward force is needed to support the roof. In turn, the house
must push downward on the ground (or it would accelerate
downward). A force from the right is needed to counteract the
wind. In turn, the house must push on the ground to the right.
Students may also notice that these nonaligned forces would
produce shear stress. A downward force on the roof is needed
to counteract wind. It might be supplied by the roof’s weight
or by the combined weight with the rest of the building if the
attachments support tension.
2
Calculating Stress
2 Students might propose a broader base, braces or tight wires
between the seat and legs, or supports between the seat and
floor that are wide apart in order to provide reaction forces to
match the extra forces from rocking. Some students might argue
that a center support with a spring or other flexible attachment is
more likely to enable rocking, rather than legs that provide rigid
support to prevent rocking.
External forces produce stress inside a material. The effect depends, in part, on the
area over which the forces act. Think of poking a balloon with a finger and with a pin
using equal forces. The balloon is more likely to break with the pin because the force is
concentrated into a smaller area. As the area decreases, the stress increases. Designers
often seek ways to distribute forces and to reduce stress. They generally avoid having a
large force through one narrow part. They may use larger pieces, use more pieces, change
the angles, or use curved pieces.
3
3 c
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72 Unit 1 Physics and Engineering
Collaborate Analyze the external forces acting on a chair, such as one in which you sit.
Think about how forces are transferred through different parts the chair to the floor. With a
partner, discuss ways to add support for someone who likes to rock from side to side.
SOLVE How does stress (σ) depend on force (F) and area (A)?
1
F
a. σ = F A
b. σ = _
c. σ = _
FA
A
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A
d. σ = _
F
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Claims, Evidence, and Reasoning
Give students items that break easily under tension, such as paper
napkins, threads of different types, thin felt, clay, plant leaves, thin
plastic, and, if suitable in your classroom, food items. (Avoid items that
might injure someone when they snap, such as rubber bands. Have
students take other appropriate precautions.) Have students compare
the approximate amounts of tension needed for the materials to
fail. Avoid twisting, which produces shear stress. Ask: What materials
were stronger under tension given their size? those with a larger crosssectional area, such as heavier thread; those with fibers Based on this,
what would you advise for making a stronger flexible piece in a design?
Make it thicker or incorporate fibers into the material. Have students
support their claims with evidence and reasoning.
Using Stresses in Designs
One measure of a material’s strength is the maximum amount of stress that can be applied
before the material breaks or deforms an unacceptable amount. Tensile, compressive,
and shear strengths describe how a material stands up to tension, compression, and
shear stresses, respectively. The megapascal (MPa) is a unit of strength equal to 106 N/m2,
roughly equal to the weight of a 10 kg object pressing on 1 cm2.
4
SOLVE An engineer is deciding whether to replace a bar made of an aluminum alloy with
steel of tensile strength 500 MPa. A bar of the aluminum alloy 2 cm across (square cross
section) can withstand pulling up to about 120 000 N. What is the tensile strength of the
aluminum alloy, and how would a steel bar of equal tensile strength compare?
a. about 600 MPa; an equivalent steel bar would be thicker
b. about 300 MPa; an equivalent steel bar would be thinner
c. about 60 MPa; an equivalent steel bar would be much thinner
In the example, the steel also has much greater density than the aluminum alloy. A steel
replacement bar would also have a greater mass. Other parts would need to support a
greater weight. Engineers and other designers must consider tradeoffs among strength,
size, and weight as well as other factors such as cost and ease of use.
4 b
5 Sample answer: Concrete—supporting columns; steel—spans.
Students might also reasonably propose wood for either. Point
out, however, that it might not stand up to the concentrated
compression from large vehicles, and the volume of wood
needed would likely result in greater sideways forces from
wind and water currents. Steel might reasonably be proposed
for columns, though the submerged part would need extra
protection against rust. The only unreasonable choice is concrete
for the spans because of its low tensile strength. Students might
know about and recommend steel-reinforced concrete for the
spans.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (cl) ©Li Chengjun/Getty Images
© Houghton Mifflin Harcourt Publishing Company
FIGURE 14: Donghai Bridge near Shanghai and a simplified model of stresses in beam bridges
tension
compression
Think about the tradeoffs for the large beam bridge shown in Figure 14. It has supporting
columns that reduce the lengths of the unsupported horizontal parts, or spans. The
weight causes each span to bend slightly. A material is needed that can support
compression in the top surface and tension in the bottom surface. A choice of material
might be good for longer spans but require stronger columns, while a different choice
might require shorter spans and more columns.
5
EVALUATE Measurements of strength depend on many factors; example values and
ranges are listed in the table. Of the materials listed, recommend a material to use for the
beam bridge’s vertical supporting columns and a material to use for the horizontal spans.
Material
Concrete
Compressive strength (MPa)
Steel (structural)
Wood (pine)
30–50
20–40
300
Tensile strength (MPa)
2–5
400–500
40
Shear strength (MPa)
6–17
300–400
6–10
2400
7900
350–590
3
Approximate density (kg/m )
Recommended use(s) in a
beam bridge
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LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EXPLORATION 5 Forces and Stresses in Engineering, continued
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Cause and Effect
Have students cut one-dimensional models of structures out of thin
plastic, especially PETE (identifiable by the recycling symbol). Have
students wear polarizing sunglasses and hold the model in front of
a white LED screen. They can instead sandwich the model between
two polarizers. Colors show the strain (deformation) of the plastic,
especially if the model is compressed, stretched, or twisted. The strain
is an effect of the stress and can be used as evidence that the material
is or has been under stress. Engineers use a similar technique to test
and improve structural designs, such as by increasing the amount of
material where they detect strain.
DCI
FIGURE 15: Stresses in truss bridges (Astoria Bridge connecting Oregon and Washington)
tension
compression
A truss bridge typically has a framework of triangles, a shape that can resist stress in
different directions. As with a beam bridge, the top is compressed and bottom stretched.
Diagonal pieces support compression or tension, as needed. The height or thickness of
the truss helps provide these extra reaction forces. The open framework results in less
weight and less force from the wind than a solid design.
1
ETS1.B Developing Possible Solutions
EVALUATE Suspension and cable-stayed bridges have cables under tension, as shown
in Figure 16. Study the figure, and select all correct statements.
a. Cables are used where the design calls for both compression and tension.
Point out that a complex structure can be analyzed or designed as
a system of simpler structures. Ask: How might you use a truss in the
design of a suspension bridge? Use it in the horizontal spans or possibly
in the vertical columns.
b. Vertical columns support the weight of the span through compression.
c. Vertical columns are pulled upward by tension from the cables.
d. Tension acts horizontally as well as vertically.
The curved cables of the Golden Gate Bridge (Figure 16a) change the direction of some
forces. A design can be adjusted to produce different stresses. A designer can then make
use of different materials, such as those used in the four bridges in Figures 14, 15, and 16.
1 b, d
2 The forces are likely to produce compression, at least at the
lower surface of the ant’s body. Gravitational force and air
resistance are both spread out, so the relatively large area
reduces the magnitude of the stress.
a
FORMATIVE ASSESSMENT
3-Minute Pause Have students pause to think of the concepts
presented in this Exploration and in the lesson. Have them
respond to the following prompts.
b
I became more aware of . . .
I didn’t realize that . . .
I still don’t understand . . .
2
tension
compression
tension
compression
Golden Gate Bridge, San Francisco
Vasco da Gama Bridge near Lisbon
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (tl) ©Grant Faint/Photolibrary/
Getty Images; (cl) ©Richard Müller/EyeEm/Getty Images; (bl) ©rglinsky/Getty Images
FIGURE 16: Stresses in suspension bridges (a) and cable-stayed bridges (b)
Evidence Notebook
Evidence Notebook Use the forces you have inferred for the ant in the example to evaluate
the stresses. Explain the type(s) of stress you expect as the ant falls.
Have volunteers share their responses with the class.
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TAKE IT FURTHER Guided Research
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TAKE IT FURTHER
Collaborate
Guided Research
You may choose to assign this activity or direct students to the
Interactive Online Student Edition, where they can choose from all
available paths. These activities can be assigned individually, to pairs,
or to small groups.
Accelerometers
FIGURE 17: A micromechanical accelerometer, used in vehicle stability systems
SEP
Designing Solutions
Typical accelerometer designs involve either 1) a mass attached to
an elastic or spring (tension, compression, or shear stress in the form
of bending), with the effect (displacement) measured by a ruler or 2)
a swinging weight with the effect (angle) measured by a protractor.
Students with skills in programming or electronics might wish to
assemble and use more sophisticated devices, but ensure that
students understand the physical change that is being measured.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Volker Steger/Science Photo
Library/Science Source
Earth Science Connection
An accelerometer is a device to measure acceleration.
It may consist of a mass suspended in a casing
on a spring. When the accelerometer is at rest or
moving at constant velocity, the mass doesn’t shift.
When the device accelerates along the axis of the
spring, the mass compresses or stretches the spring.
The displacement of the mass is often measured
electronically, such as by compressing a material that
responds by producing electric current.
Think about your motion when riding in a car, bus, or
other vehicle. When the vehicle accelerates forward
from rest, you are pressed back in your seat briefly and
then move at the velocity of the vehicle. When the
vehicle brakes, you continue forward; when it turns,
your body slides in the opposite direction. However,
from a point of view outside of the car, your body
tends to continue moving in a straight line. Your body
is acting like the mass in an accelerometer.
Accelerometers are used in many fields to determine
changes in motion. For example, they measure the
motion of spacecraft and cars, the orientation of
cell phones, and the motion of artificial limbs.
PULLEYS
TYPES OF FRICTION
Language Arts Connection Research the
design of a simple one-dimensional accelerometer
that you can make with household materials. Build and
calibrate a working prototype. Use it to measure acceleration
in two or more situations, such as the following tests:
Explore Online
• Ride as a passenger in a bus as it speeds up, slows down, and
makes turns.
• Use the device in an elevator or on an amusement park ride.
• Move the device upward or downward quickly, such as by
standing rapidly or jumping off a step.
• Explore circular motion, such as turning or moving the device
in an arc.
Develop an instruction manual.
• Identify the parts of the device.
• Give step-by-step instructions for how to use the device.
• Explain the physical principles behind its function. Why does
it work?
• Compare the device you built to a commercial device, such as
the sensors of a cell phone. How accurate is your device?
MEASURING IN SPACE
Pulleys
Students compare the advantage of a block-and-tackle arrangement
of pulleys to that of a single pulley.
Types of Friction
Students explore static and kinetic friction.
Measuring in Space
Students learn how mass is measured in the absence of gravity.
Go online to choose one
of these other paths.
Lesson 3 Effects of Forces
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Accelerometers are used to detect and measure seismic waves. Ask
students what their device would show if there was a mild tremor.
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LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EVALUATE Lesson Self-Check
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Can You Explain the Phenomenon?
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EVALUATE
Lesson Self-Check
Claims, Evidence, and Reasoning
Have students clearly state their claim—their explanation for the
phenomenon they have been investigating throughout this lesson. They
should present their reasoning for making this claim, along with evidence
such as facts, examples, and statistics that support their claim.
CAN YOU EXPLAIN THE
IT? PHENOMENON?
FIGURE 18: An acorn and an ant fall from a branch at the same time. The insect hits the ground
more gently. Use these details as evidence when you construct your explanation.
You may want to have students present their arguments orally, in
writing, or as a debate. Refer students to the English Language Arts
Handbook for more information on evaluating claims and presenting
arguments.
Cultivating Student Questions
Assessing Student Growth Review the list of questions students
generated at the beginning of the lesson. Have volunteers select any
unanswered questions and suggest how they could be investigated.
After approving student plans, have small groups conduct the
investigations and report back to the class.
In this lesson, you have learned how forces affect motion. You have also learned some
of the factors that affect the magnitudes and directions of different types of forces. For
example, frictional force depends on the normal force but not on area or speed of the
object, while air resistance depends on both the area and the speed of the object moving
through air. Apply your knowledge to the example of an acorn and an ant, each falling
from the same high branch of a tree. Recall that the acorn makes an audible sound as it
hits the ground, while the ant hits almost silently and walks away unharmed.
EVIDENCE NOTEBOOK
1 Sample answer: The ant hits the ground at a lower, constant
or near-constant velocity while the acorn accelerates
through most or all of its fall. Observations include that
the acorn hits at a greater speed, and I know that the ant is
smaller and of lower mass than the acorn. Objects accelerate
because of a net force. The downward force due to gravity
is the weight of the ant or acorn, and the ant’s weight is less
than the acorn’s weight. Air resistance increases with speed,
so the ant’s weight is balanced by the force of air resistance
at a lower speed, giving a net force of zero and resulting in
constant velocity. The acorn’s acceleration is also reduced by
air resistance, but unless it falls a great distance, its weight
is probably not balanced by air resistance, giving a net
downward force and acceleration throughout the fall.
1
that affect the motion of falling objects. Your explanation should include a discussion of
different forces that can act on a falling object, net force, and acceleration due to force.
Claim Explain the factors that can cause the motion of the falling ant and the acorn in
the example to differ. Put your claim in terms of physical quantities such as force, mass,
and acceleration.
Evidence List the information given about the ant and acorn, observations you have made
in labs and other situations, physical laws, and any other information that you are using as evidence
to support your claim.
Reasoning Explain how the evidence supports your claim. Use free-body or force-pair
diagrams to compare the falling ant and acorn. If either or both depart from an acceleration
2
of 9.8 m/s , explain why.
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76 Unit 1 Physics and Engineering
Evidence Notebook Refer to your notes in your Evidence Notebook to explain the factors
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Spike Mafford/Photodisc/
Getty Images
The effect of gravity on a steel ball, a rubber ball, and an iron ball is similar—all fall with
2
a constant acceleration of 9.8 m/s . A leaf is also subject to the force due to gravity, yet it
may fall with a different pattern of motion.
Unit 1 Physics and Engineering
Formal Assessment Go online for student self-checks and other assessments.
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Name
Answers
1. c
2. b
3. b
4. backward, equal to, backward, less than
5. 6, right
6. the same as, m2g
7. d
8. a, b, c
Date
CHECKPOINTS
Check Your Understanding
Use the following description to answer the next
three questions.
A book of mass 0.8 kg is pushed left across a table
with a force of 2.0 N. Kinetic friction provides a force
of magnitude 0.2 N.
Use the diagram to answer the next two questions.
Assume the pulley and string are massless and the
system is frictionless.
FIGURE 19: The cart has mass m1 and the descending
weight has mass m2.
m1
1. Use a free-body diagram to analyze the forces
on the object. In what direction is the net force?
a. Net force is down.
b. Net force is up.
c. Net force is to the left.
d. Net force is to the right.
e. Net force is at a diagonal.
m2
6. Select the correct terms to complete the
statements about the diagram.
2. What is the magnitude of the net force
on the book?
a. 0 N
d. 2.2 N
b. 1.8 N
The tension in the vertical part of the string is
less than | greater than | the same as the tension in
e. 7.8 N
the horizontal part of the same string.
The net force on the cart-string-weight system is
3. What is the magnitude of the acceleration
of the book?
2
2
a. 0 m/s
c. 2.5 m/s
2
2
b. 2.3 m/s
d. 9.8 m/s
4. Select the correct terms to complete the sentence
about force and acceleration. Ignore friction.
When a bowling ball hits a bowling pin of lesser
mass, it exerts a forward force on the pin. The pin
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Spike Mafford/Photodisc/
Getty Images
c. 2.0 N
exerts a forward | backward force on the ball. This
force is less than | more than | equal to the force
of the ball on the pin. The ball accelerates
forward | backward, and the magnitude of the
ball’s acceleration is less than | more than |
equal to the magnitude of the pin’s acceleration.
5. Two ice skaters stand facing each other. The first
skater has a mass of 100 kg and the second has a
mass of 50 kg. They push each other away. During
2
this push, the first skater accelerates at 3 m/s to
the left. The second skater accelerates at
2
m/s to the
m1g | m2 g | (m1 + m2)g | (m2 − m1)g.
7. Suppose that for trial 1, m1 = 0.2 kg and
m2 = 0.5 kg. For trial 2, m1 = 0.4 kg, double the
initial value. How will the acceleration of trial 2
compare to that measured in trial 1?
a. Acceleration will double.
b. Acceleration will be halved.
c. Acceleration will increase by less than
a factor of 2.
d. Acceleration will decrease by less
than a factor of 2.
8. An engineer wants to increase the load that the
legs of a wooden stool can support. Which of the
following changes would meet that goal? Select all
correct answers.
a. Add more legs.
b. Make the legs thicker (larger
diameter).
c. Use stronger wood of the same density.
d. Use taller legs.
e. Make the stool smaller in every dimension.
.
Lesson 3 Effects of Forces
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LESSON 3 Engage • Explore/Explain • Elaborate • Evaluate
EVALUATE Lesson Self-Check, continued
Answers
9.Diagram should show gravity down and normal force
perpendicular, and frictional force parallel to the ramp. The box
is at rest, so the vector sum of the forces on the box is zero. The
normal force is equal to the component of weight perpendicular
to the ramp. If the slope of the ramp is increased, the normal
force is reduced and the surfaces are pressed together less, and
so the maximum static friction is reduced. At the same time,
the component of gravity pointing down the ramp is increased.
Alternatives include decreasing the force of static friction (by
making the surface smoother) or increasing the mass of the box
(so the net force down the ramp is greater, though friction would
also increase).
10.Weight is a force, but mass is a different type of quantity.
The mass of an object resists acceleration but also produces
gravitational force, or weight. An object pushed horizontally
resists the change in its motion according to its mass. The
weight of an object pushes the object and its supporting surface
together and therefore affects the frictional force, which in turn
opposes motion.
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EVALUATE
CHECKPOINTS (continued)
9. A box sits at rest on a ramp. Draw a free-body diagram to model
the forces on the box. Then explain how you could change the
system so that the box would slide down the ramp.
10. What is the distinction between weight and mass? How would each affect the
acceleration of an object pushed horizontally?
Make Your Own Study Guide
MAKE YOUR OWN STUDY GUIDE
In your Evidence Notebook, design a study guide that supports the main ideas from this lesson:
The net force is the vector sum of all external forces acting on an object.
If the net force is zero, the object continues at rest or in straight-line motion at constant velocity.
If the net force is not zero, the object accelerates according to a = Fnet/m.
Forces come in equal and opposite pairs, which act on different bodies.
Engineers balance external forces and design structures that make use of stresses in order to
produce stable structures or desired motion.
Remember to include the following information in your study guide:
• Use examples that model main ideas.
• Record explanations for the phenomena you investigated.
• Use evidence to support your explanations. Your support can include drawings, data, graphs,
laboratory conclusions, and other evidence recorded throughout the lesson.
© Houghton Mifflin Harcourt Publishing Company
Have students create a study guide that helps them organize and
visualize the important information from this lesson. Their study guide
should focus on the main ideas from this lesson and tie multiple ideas
together. Students can create an outline, a concept map, a graphic
organizer, or another representation.
Think about how Newton’s laws explain how force affects motion.
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