Workbook | 2019
AP Physics 1
®
TEACHER’S EDITION
AP Physics 1
Workbook
Contents
2
About This Workbook
4
Workbook at a Glance
6
Embracing Challenges
7
Learning Physics as Refining Common Sense
8
Unit 1: Kinematics
36
Unit 2: Dynamics
71
Unit 3: Circular Motion and Gravitation
102
Unit 4: Work and Energy
141
Unit 5: Momentum
180
Unit 6: Simple Harmonic Motion
208
Unit 7: Torque and Rotation
241
Unit 8: Electric Charge and Electric Force
269
Unit 9: DC Circuits
300
Unit 10: Mechanical Waves and Sound
335
Unit 11: Review Questions
367
Appendix
368
AP Physics 1 Equation Sheet
370
AP Physics 1 Science Practices
371
AP Physics 1 Task Verbs Used in Free-Response Questions
372
Graphical Methods Summary
373
Writing Tips
AP Physics 1
Workbook
Acknowledgments
The College Board would like to acknowledge the following individuals for their
commitment and dedication toward the completion of this project. All individuals and
their affiliations were current at the time of contribution.
AP Physics Consultants and Reviewers
Angela Benjamin, Woodrow Wilson High School, DC
Brendon Eaton, Rick Reedy High School, TX
Richard Fetzner, McDowell High School, PA
John Frensley, Prosper High School, TX
Kristen Gonzales-Vega, Rick Reedy High School, TX
Peter Harris, Methuen High School, MA
David Maloney, Purdue University Fort Wayne, IN
Joe Mancino, Windsor High School, CT
Terri McMurray, Career Center High School, NC
Rebecca Messer, Northfield High School, MN
John Pinizzotto, Weymouth High School, MA
Jenny Podel, Northampton High School, MA
Gay B. Stewart, West Virginia University, WV
James VanderWeide, Hudsonville High School, MI
Barbara Watson, JJ Pearce High School, TX
College Board Curriculum,
Instruction, and Assessment
Amy Johnson, Director, Instructional Design and PD Resource Development – Physics
Claire Lorenz, Senior Director, Instructional Design and Teacher Resource Development
Michael Robertson, Director, Curriculum, Instruction, and Assessment
Process Management
Tanya Sharpe, Senior Director, Advanced Placement STEM Curriculum,
Instruction and Assessment
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AP Physics 1
Workbook
About This Workbook
Background
The AP Physics 1 course is designed to promote student learning of essential
physics content and foster the development of deep conceptual understanding.
The instructional approaches utilized in this workbook are informed by research
on student learning and knowledge construction, especially with regard to
physics principles.
Contents
This workbook is a compilation of problems written by high school and higher
education physics faculty to help students and teachers master the knowledge and
skills in college-level physics coursework. The AP Physics 1 Exam requires students to
be able to think about physics both conceptually and mathematically as well as to
write about physics. Thinking about physics and defending claims with writing
may be new and challenging for students, and this workbook provides helpful
guidance in supporting students’ development of this skill.
Scaffolding
The units in this workbook are scaffolded so that students can learn the skills such
as argumentation, quantitative analysis, and data analysis, alongside course
content, so that they will be prepared for the AP Exam by May. As you read through
the problems, you will see that the scaffolding slowly decreases as students progress
from unit to unit. By Unit 10, students are expected to be able to demonstrate
all skills without support. Students start their study of physics with their own
unique backgrounds, and it is possible that you will find these questions either too
scaffolded or not scaffolded enough for your students. Teachers are encouraged to
modify the problems in this workbook as necessary, so that they meet students’
needs. If you think some of the questions are too challenging or make too great a leap
for your students, consider supplementing with your own scaffolding to help students
access these scenarios.
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AP Physics 1
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Solutions and Teacher Notes
The answers presented in the teacher version are not inclusive of all possible
solutions—that is, they do not represent the only method of solving these problems.
Teachers may present slightly different methods and/or different symbols and
variables in each topic, but the underlying physics concepts are the same.
It is strongly suggested that teachers support the careful use of language suggested
in the Physics 1 course framework. While the wording in some cases is somewhat
longer than what is traditionally used, this has been done to directly address the
misconceptions that can be supported by using briefer descriptions.
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AP Physics 1
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Workbook at a Glance
Although each unit in this workbook is unique and focuses
on content, skills, and learning objectives for that unit, the
overall formats are similar.
Each page includes a scenario, which acts as the prompt to focus
students’ attention on key elements of the problem.
Each problem is then broken down into several parts, and headers
are added to provide guidance to the students—to key them into the
type of question they’re going to be asked. The major headings are:
▪ Using Representations
▪ Quantitative Analysis
▪ Argumentation
▪ Data Analysis
▪ Experimental Design
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Teacher pages include the Essential Knowledge and
Science Practices that are linked to each scenario.
Teacher pages also include notes about how to
prepare for assigning the page, use it in your
classroom (teach) and assess that your students
have learned key concepts and/or skills. Some of the
teacher notes include quick quizzes, lab ideas, or other
suggestions for extensions.
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AP Physics 1
Workbook
Embracing Challenges
Teachers should consider the noncognitive dimension to teaching and learning when
working with AP Physics 1 students. What a teacher or student believes about how
success is achieved may affect the learning process. As educators, it’s important
to take into account our own perceptions about student success and how we can
empower students as they encounter new academic challenges. A student who
believes that success is possible embraces challenges as new opportunities to learn,
makes concerted efforts to improve, and believes that their ability and potential is not
fixed or static but can grow over time. A teacher who believes that success is possible
measures improvement over time and believes that effort is the linchpin of success.
This way of thinking counters the self-defeating notions that ability is static and
permanent and extra effort has no benefits because success is determined by innate
ability or talent.
The messages that teachers send to students, along with all classroom practices,
can encourage students to take risks, make mistakes, learn, and grow. This culture
is beneficial in an AP class where frustration can short-circuit the learning process.
Teachers who can coach students through such moments, and train them to see
academic setbacks as stepping stones rather than stumbling blocks, can set students
up for success. Students new to AP, or students who seem to be struggling with the
challenges of AP, may benefit from specific strategies such as:
▪
▪▪ Assistance in finding online resources for instruction
▪▪ Assistance in forming study groups to work with other students on developing and
deepening their understanding
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Learning Physics as
Refining Common Sense
There is a quote attributed to Albert Einstein that “science is refined common sense.”
One clear implication of this idea is that students who are taking a course in physics
are bringing to the course their common-sense understanding of how the physical
world works. Physics education research over the last 30 years has identified
many of the ideas students are going to have initially. Since we humans build new
knowledge by using our current understanding (i.e., our current framework), to try
to make sense of what we are being taught, knowing the content of students’ around
“common-sense” frameworks is an important pedagogical tool.
The research has shown that students’ common-sense frameworks contain both
useful ideas and counter productive ideas about the behavior of physical systems.
The task of learning physics can be thought of as helping each student refine his or
her common-sense framework to bring it into closer alignment with the physically
accepted ideas. So, the refinement process involves helping students learn which
components of their framework will help them correctly analyze the behavior of a
physical system, or solve a problem correctly, and which components they need to
modify or replace with new ones.
It is important for instructors to get students to realize that they have useful ideas
that they can use with confidence as well as helping them modify or change other
ideas. One of the primary reasons for paying explicit attention to having the students
use “correct” ideas from their frameworks is motivational. If the focus is always on
problematic ideas in their frameworks (i.e., misconceptions), students can become
discouraged because it can seem like they are “always wrong.” Knowing and using
components that are correct or that can readily be tweaked to be useful can enable
the students to realize that they already have some productive tools available to them.
If the pedagogical focus is to be on refining common-sense frameworks, it is critical
that each student be an active participant of the process since each student will
have a different framework. Consequently, each student needs to have multiple
opportunities to think the ideas through for her- or himself and to test her or
his ideas against the ideas and reasoning of other students as well as actual
empirical evidence.
—David Maloney, TIPERS Co-author;
Professor of Physics Purdue University,
Fort Wayne, IN
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UNIT 1
Kinematics
Misconceptions
Even some of the best students struggle with in-depth conceptual understanding
and resort to using memorized terms to answer conceptual questions. Although
factual misconceptions can often be easily corrected, insisting that students dismiss
their preconceptions or misconceptions is not always effective. If a student already
has a nonscientific model to explain a phenomenon, new concepts, models, and
representations are difficult to learn. Before embracing the concepts held to be
correct by the scientific community, students must confront their own beliefs and
then attempt to reconstruct the knowledge necessary to understand the scientific
model being presented. This process is most effective when the teacher first identifies
students’ misconceptions or preconceptions and then provides a forum for students
to confront them.
It is very important to set the stage for learning by helping students understand that
most of the common ideas that do not align with accepted knowledge are based
on incomplete understanding, not incorrect understanding. Aristotle believed the
same things many of our students believe. Friction is not readily apparent, and if its
presence is neglected when it does exist, your observation would be that you do need
to push something to keep it moving, for example. Helping students understand that
the modifications they need to make are based on better scientific evidence puts them
in the position of real scientists.
In kinematics, it is crucial to help students distinguish among kinematic ideas such
as speed, velocity, distance, displacement, and acceleration. In physics, these ideas
are distinct for important reasons. In everyday contexts, concepts that are physically
distinct are taken as synonyms. For example, students often do not distinguish
between scalar quantities and their vector counterparts (distance and displacement;
speed and velocity) and confuse speed/velocity with acceleration. While students
often know that these terms are distinct, they commonly do not differentiate between
them because the differences are either not important in everyday contexts or will be
acknowledged in another way. It can be useful to have students consider situations
in which they must distinguish such concepts to plant the idea that they will need to
alter their thinking when doing physics. For example, students readily recognize that
if they were to fly at 100 kilometers per hour (km/h) for two hours in a straight line
due east compared to 100 km/h due west for an hour, they would not end at the same
final location. So, there are times when students know that direction is an important
aspect of motion. It can be beneficial to point out that analyzing physics correctly
does not require students to think differently but instead requires them to use
familiar ideas more systematically.
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A related challenge is helping students develop the graphical skills that are used
throughout physics. Part of the challenge here is that many students struggle with the
nature of graphical representation and how to make connections between graphical
and other forms of representation. Some students perceive graphs as a literal picture
of a determined motion. For example, they might interpret a rising line with a steep
slope as a hill or any straight line as representing constant velocity. Before leaving
Unit 1, students should be comfortable graphing position, velocity, and acceleration
as functions of time; moving back and forth between these graphs; and using these
graphs as evidence to support claims or solve problems.
Common misconceptions in Unit 1: Kinematics and the pages that provide students
with the opportunity to confront their misconceptions are summarized in the
table below:
Scenario
Misconception
1.A
Distance and displacement are interchangeable.
1.I
Two objects side by side must have the same speed.
1.A, 1.D
Motion always begins at the origin (0, 0).
1.E
Velocity is absolute and not dependent on frame of reference.
1.H
Acceleration and velocity are always in the same direction.
1.H
If velocity is zero, then acceleration must also be zero.
1.H, 1.J, 1.K
An object that is speeding up has a positive acceleration and an object that
is slowing down has a negative acceleration.
1.J, 1.K
Freely falling bodies can only move downward.
1.C
Average and instantaneous velocities are equivalent.
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AP Physics 1
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Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Plot data on a graph.
Using Representations
1.B, 1.D, 1.F, 1.G, 1.H, 1.I, 1.J, 1.K,
1.L, 1.N, 1.O
1.1
Draw a best-fit line.
Using Representations
1.B, 1.D, 1.G, 1.L, 1.N
1.1
Scale and label axis.
Using Representations
1.E, 1.F, 1.J, 1.K, 1.L, 1.N, 1.O
1.2
Find the area under a curve.
Quantitative Analysis
1.F, 1.G, 1.H
1.2
Find the slope of a best-fit line.
Quantitative Analysis
1.B, 1.D, 1.G, 1.L, 1.N
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
1.B, 1.C, 1.D, 1.E, 1.F, 1.G, 1.H,
1.L, 1.O
1.4
Relate the area under a curve to a physical quantity.
Quantitative Analysis/Data Analysis/
Argumentation
1.F, 1.G, 1.H, 1.I
1.5
Linearize a graph.
Using Representations
1.L, 1.O
1.5
Re-express one type of graph as another.
Using Representations/Argumentation
1.D, 1.H, 1.I, 1.J, 1.K, 1.N
2.1
Defend the use of an equation to solve a specific problem.
Quantitative Analysis
1.K
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
1.L, 1.M, 1.O
2.2
Rearrange an equation to solve a specific problem.
Quantitative Analysis
1.K, 1.M
4.1
Choose correct data to answer a question.
Data Analysis
1.L, 1.M
4.2
Choose equipment to conduct a scientific experiment.
Experimental Design
1.C, 1.L
5.1
Determine if data is reliable.
Data Analysis
1.C
5.3
Use a linearized graph to answer a question about a
physical quantity.
Quantitative Analysis
1.L, 1.O
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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UNIT
1
Kinematics
Displacement
EK
|
3.A.1, 4.A.1
SP
|
1.1, 1.4
Prepare
At first glance, this scenario may seem too introductory for students.
However, it provides a suitable entry point for all students regardless of
their backgrounds or previous experience with physics. Note that more
advanced learners will move through this worksheet quickly.
Teach
In Part C, most of the writing has been done for students so that they know
how to structure responses. Students should see good writing before they
are asked to create good writing on their own.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
The diagram above illustrates a car that, starting from the origin,  x
travels 4 km right, and then 7 km left.
 0
What is the net displacement of the car?
What is the total distance traveled by the car?
Create another diagram with different position labels (i.e., put zero in
a different place) and recalculate the displacement of the car and the
distance traveled on the new coordinate system. Explain how your
answers to the first set of questions are different and/or the same as your
answers to the second set.
What’s the point?
We make up coordinate systems to be able to communicate with each
other. We need a common language to discuss what is happening in a very
precise way. So, choosing zeros and a direction to be positive allows us to
have a common language with which to discuss physical scenarios.
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UNIT
1
Kinematics
Position and Velocity
EK
|
3.A.1, 4.A.1
SP
|
1.1, 2.1
Prepare
Creating, interpreting, and using representations are critical skills for the
AP Physics 1 Exam. While students can be trained to find an equation
and plug in numbers to find an answer, research shows this does not
create a lasting understanding. Creating and then using a representation
as evidence for a claim may seem much more difficult but builds toward
deep conceptual understanding. While using the “big three” kinematic
equations represents one analysis technique, there are many more that
they need to be familiar with including analyzing graphs of position,
velocity, and acceleration vs. time as well as motion maps.
Teach
If your students are using their calculator to calculate the slope, they need
to indicate that they used their calculator to do the linear regression by
stating it on the exam. Students who simply state the slope given to them
by their calculator will receive zero points for this calculation.
In a beginning physics course, it is best to have students determine the
slope of the line without the use of their calculator.
Assess
To further assess student
understanding of the concepts
addressed in this scenario, you
may want to ask students the
questions below:
The position vs. time graph above
represents the motion of two
objects. One object is traveling
at 8 m/s , while the other object
is traveling at 5 m/s . Which line
on the graph represents the
object traveling at 8 m/s? Explain
using evidence.
What’s the point?
Representations come in many forms, including equations! You will
need to be able to create more than one representation for a physical
situation to be able to show that you understand relationships among
physical quantities.
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UNIT
1
Kinematics
Average vs. Instantaneous Speed
EK
|
SP
3.A.1, 4.A.1
|
4.1, 4.2, 4.3, 5.1
Prepare
A foundational concept for students to learn in AP Physics 1 is the
difference between average and instantaneous velocity. Year after year,
the Chief Reader Report on AP Exam performance highlights the fact
that students still—even in May—get confused between average and
instantaneous velocity, how to measure them and how to calculate them.
Just because teachers move on from Unit 1 doesn’t mean students never
have to consider these concepts again. Bring average vs. instantaneous
velocity up every time you talk about velocity. Ask students which one
they need to consider for the physical situation presented to them and
how they could measure it.
§§Students need to be able to differentiate between average velocity,
instantaneous initial velocity, and instantaneous final velocity for an
accelerating object and understand that “delta distance over delta
time” only gives the average velocity.
§§If an object starts from rest and attains some final speed with
constant acceleration, that final speed is DOUBLE the average speed.
If it takes T seconds and D meters to reach the final speed, then it
takes 1 T seconds to reach average speed and 1 D meters to reach
2
4
average speed.
Mistakes Kids Make:
§ Students want to assume that D/T is the final velocity, not just the
average of initial and final.
§§Upon understanding that D/T is the average and not the final speed,
students assume that the object reaches an instantaneous speed
equal to its average speed at half the time (correct) and half the travel
distance (which is wrong).
§§All comments above are only true for CONSTANT accelerations; if
an acceleration is changing (like in AP Physics C, where an object
is subject to air resistance) an object attached to a spring, or an
object going down a ramp with nonconstant incline slope, then
average velocity is still
D
but the object may attain its average
t
speed at a time before or after 1
2
changing acceleration.
T depending on the nature of the
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Teach
Writing a good experimental procedure does not always require the use
of a lot of words. The experimental procedure should be short and to
the point. In later units, there are more scaffolded lab questions where
students can practice designing experiments. Consider doing the
“meeting point challenge” with your students. Each group is given two
constant motion vehicles (one with two batteries and one with a battery
and a “slug” made from aluminum foil), and the students need to design
an experiment to determine the speeds of each vehicle. They are then
given a distance (they will start the cars this distance apart) and a time
(the second car is released after set time), and the students must predict
where the two vehicles will meet. They may use equations, but that should
not be their only representation. (For example, they should have at least
one set of graphs to use as evidence for their claim.)
For Part C, it may be helpful to demonstrate the second claim by setting
up a set of photogates (as suggested in the argument) with a pull-back
car (not constant velocity) to see if this procedure can determine the
instantaneous speed. There are several ways of testing the claim made
by the toy company in Part C. Have the students come up with their
own method!
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
In order to perform an experiment, two students need to determine
the velocity of a cart just as it reaches the bottom of a ramp. Is this the
average or instantaneous velocity that they are looking for? In a few
short sentences, describe an experimental setup that they could use to
determine the needed velocity of the cart at the bottom of the ramp.
What’s the point?
Data is more than just numbers. Every number in physics has meaning,
and we need to analyze that data to determine its meaning.
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UNIT
1
Kinematics
Velocity Is a Vector!
EK
|
3.A.1, 4.A.1
SP
|
1.1, 1.4, 1.5, 2.2, 6.1
Prepare
If students are still unsure about position and velocity with one object,
they may need more scaffolding for this worksheet. The key takeaways
here are that velocity and displacement are vectors and direction matters!
Teach
Follow-Up Questions:
When do Angela and Blake meet? How do you know? What other evidence
could you produce to show that they meet at this time?
What would a position vs. time graph of someone running at 7 m/s look
like? How would that graph show a greater speed than the original 5 m/s
(or −3 m/s )?
What would a graph of position vs. time look like for someone who took a
break in the middle of running?
Suggested Activities: Walking Graphs Lab
Have students act out for themselves the suggested lab in the AP Physics B
question #2 from 2006.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
The above graph represents the position as a function of time for an
object moving in a straight line to the right. Which of the following is true?
A. The object’s velocity increases.
B. The object’s velocity decreases.
C. The object’s velocity remains unchanged.
D. The object stays at rest.
E. More information is required.
Explain.
What’s the point?
The slope relationship between position and velocity is one in a series of
relationships you will discover throughout the course. In math class, the
slope of a line is a number. In physics, it correlates with a physical quantity,
such as velocity.
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AP Physics 1
Workbook
UNIT
1
Kinematics
Relative Velocity
EK
|
3.A.1, 4.A.1
SP
|
2.1, 2.2, 6.1
Prepare
This is relatively easy to replicate in the lab with long sheets of paper and
constant-motion cars. If you have access to these materials, consider
letting your students experiment either before or while they are working
on this worksheet.
Teach
For Part D, we specifically chose numbers so that a student who is not
considering direction will gravitate toward Scenario A.
A related question that always stumps the students because
it involves water instead of a moving train is as follows:
Suppose you and a pair of life preservers are floating
down a swift river as shown. You want to get to either
of the life preservers for safety. One is 3 meters
downstream and one is 3 meters upstream from you.
Which can you swim to in the shortest time?
A. The preserver upstream
B. The preserver downstream
C. Both require the same time.
The Answer is C: Both require the same time. Switch up
the situation so that it is Blake again with Angela 3 meters
in front and Carlos 3 meters behind as the train moves. Which friend can
Blake walk to the fastest? Since Blake, Carlos, and Angela are all traveling
on the train together, they can be considered to be at rest relative to each
other. Therefore, Blake can walk to either friend just as quickly!
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
The motion diagram below represents a cart moving to the right. Is the
cart speeding up? Slowing down? Or moving at a constant speed? Explain.
What’s the point?
Velocity is RELATIVE, meaning that is depends on your reference frame.
When analyzing a physical scenario, the first step is to choose a frame of
reference including a zero position and positive and negative directions.
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AP Physics 1
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UNIT
1
Kinematics
Constant Velocity
EK
|
3.A.1, 4.A.1, 4.A.2
SP
|
1.1, 1.4, 2.2
Prepare
Understanding the meaning of representations is key to understanding
physics. Sometimes students see graphs as busy work they must do
before they can get down to the business of solving the equation for the
“answer.” Encourage students to focus less on finding an answer and
more on what evidence the students can find to back up their claims about
physical situations.
Teach
If you have access to constant-motion vehicles and motion sensors, you
could have students replicate this experiment and collect their own data.
Additional questions: What would the position vs. time graph look like for
this vehicle? What about the acceleration vs. time? What is the relationship
between the velocity graph and the position graph?
The velocity vs. time graph is the most “powerful” graph because in just
one representation, students can find evidence about the displacement
(the area under the curve), the velocity, and the acceleration (the slope of
the curve).
Assess
To further assess student
understanding of the concepts
addressed in this scenario, you
may want to ask students the
questions below:
The position vs. time graph of a
moving object is shown at right.
Sketch the velocity vs. time graph
for the same object during the eight
seconds shown. Explain how you
know what to sketch.
What’s the point?
The area relationship between velocity vs. time graph and position is yet
another relationship you will discover throughout the course. In math
class, the area under a line is a number. In physics, it corresponds to a
physical quantity.
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UNIT
1
Kinematics
Graphs of Velocity
EK
|
3.A.1, 4.A.1, 4.A.2
SP
|
1.1, 1.4, 2.1, 2.2
Prepare
This scenario can be demonstrated by releasing a cart from rest at the top
of an incline with a motion sensor on the track to record the velocity as a
function of time. Students could also use a fan cart and motion sensor to
recreate this graph.
Teach
Problems that are extremely difficult to solve with equations can become
much simpler to analyze with graphs. The better your students become at
using graphs as evidence for claims, the better prepared they will be for
the AP Physics 1 Exam.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Two objects start from the same position at the same time from rest but
with different magnitudes of positive accelerations. Sketch displacement
vs. time, velocity vs. time, and acceleration vs. time graphs for the
two objects. Explain your reasoning in creating the graphs.
What’s the point?
There are so many ways to analyze a graph! The three ways shown here
are 1) reading a quantity directly off the graph, 2) analyzing the slope, and
3) analyzing the area under the curve. When given a graph, think about the
meaning of all the different pieces of information presented there!
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AP Physics 1
Workbook
UNIT
1
Kinematics
Relationships Between Position, Velocity, and Acceleration
EK
|
3.A.1, 4.A.1, 4.A.2
SP
|
1.1, 1.4, 1.5, 2.1, 2.2
Prepare
Have students walk this graph in front of a motion detector, so they have
the opportunity to physically feel that they are not at zero position but at
zero velocity at t = 3 s . If you haven’t already done a “walking the graphs”
lab, you should consider doing it before assigning this worksheet. If
the laboratory equipment is not available, have students use an online
simulator like PhET to recreate motion graphs.
Teach
Part D is very tricky for students. And in fact, many students feel like
deer in the headlights when faced with a blank grid on which to create a
graph. Remind students that they are not expected to know immediately
what shape they should graph. Have them plot the points they know. For
example, for Part D, they should be able to verbalize that the initial position
of the car was x = 10 m (given in the prompt) and that they can find the
position later (at t = 3 seconds) by finding the area under the velocity vs.
time graph from t = 0 to t = 3 s . Now that they have two points plotted,
they have to decide whether there is a line or a curve connecting the
points and if it is a curve, whether it will be concave up or down. However,
even if they only can plot these two points and then guess about the
connection, they will have more points on the AP Exam than if they left the
grid blank or just scribbled nonsense.
Scaffolding for sketching position graphs:
§§Step 1: What are the beginning and end points?
§§Step 2: What is the general shape of the graph? Linear (constant
velocity, even if its zero)? Curvy (accelerating)?
§§Step 3: If accelerating, is the velocity positive and increasing (or
negative and decreasing) or is the velocity positive and decreasing
(or negative and increasing)? A simpler way to think of this is, if
the change in velocity (the acceleration) is negative, the curve of a
position-time graph is concave down (and concave up if it is positive).
An object speeds up when its acceleration and velocity are in the
same direction, so if it is speeding up, the acceleration has the same
sign as the velocity.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
to write a narrative of how they created the two graphs in Part D
(i.e., explain the thoughts they had that helped them create the correct
graphs). For example,
“I first plotted the point ( 0 s , 0 m ) because I knew the object started at
position zero. The object stops at t = 3 because that is where the velocity
changes direction. The area between 0 and 3 is the farthest distance
that the object travels forward, which is 18. So, I then plotted the point
( 3 s , 18 m ). Now I know that the graph before three seconds slopes up
(the velocity is the slope and is positive) and the slope is becoming less
steep as the speed decreases. After time three, the slope is negative and
getting steeper as the object goes faster backward.”
What’s the point?
Moving between representations of the same situation is an important skill
in AP Physics 1. Next time you are asked to create a representation (graph,
sketch, diagram, etc.) challenge yourself to see if you can create a second
representation of the same situation.
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AP Physics 1
Workbook
UNIT
1
Kinematics
The Chase
EK
|
3.A.1, 4.A.1
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 6.1
Prepare
This is very similar to the classic fugitive catching a train problem.
Although in this iteration, the police car doesn’t have a maximum speed, in
real life, the police car would have a maximum speed. Adding that into the
problem (like in the fugitive problem) makes the mathematical approach
much more difficult but doesn’t affect the difficulty of the graphical
solution. Remind your students that the graphical approach for motion
is often simpler and provides clearer evidence for understanding than
just finding a numerical answer. On the AP Physics 1 Exam, it is currently
unlikely that they will be asked to solve for a numerical answer, but it is
extremely likely that they will be asked to create and/or use a graph of
motion to justify a claim.
Teach
Remind students that you cannot catch someone by going the same
speed.
Try this out with your constant-motion vehicles. Start one and then
5 seconds later, start the other from where the first one started. Can the
second car ever catch the first car if it is traveling at the same speed?
For Part C, students might need a graph for a longer time than what they
drew initially. If your students have the time t 1 at the far-right corner of the
grid, encourage them to draw a bigger graph incorporating more time.
Additional Questions:
Determine, using the graph, the approximate time when the car and truck
are in the same location.
Double-check, using another representation, the time at which the car and
truck are in the same location.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
At t = 0 s , two cars are located at the starting line. Car 1 is traveling at
10 m/s , and Car 2 is at rest. Car 1 continues traveling at 10 m/s while Car 2
accelerates at 2 m/s2. Sketch a velocity vs. time graph for each car on the
same axis. (Differentiate the lines and make a key so it is clear which graph
belongs to which car.) Mark on the graph t1 where the two cars have the
same velocity. Mark on the graph t2 the time when Car 2 catches up to
Car 1. How did you know where to mark t1 and t2?
What’s the point?
While position and velocity are related, they are not linked, meaning that
just because two objects are side by side, they are not necessarily going
the same speed, or just because two objects are going the same speed,
they are not necessarily side by side.
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AP Physics 1
Workbook
UNIT
1
Kinematics
Vertical Motion
EK
|
3.A.1, 4.A.1, 4.A.2
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 6.1
Prepare
This worksheet can be paired with the next one for deeper questions
about the motion of the rocket.
Teach
Additional Questions:
What is the relationship between the graphs drawn in Parts A and B?
Are there ways to check that the graphs are self-consistent?
What would the acceleration of the rocket be at 12 seconds?
What would the graph of velocity vs. time look like from the time of launch
until the time the rocket reaches its maximum height?
How would you represent the time when the rocket reaches the maximum
height on the velocity vs. time graph? How could you determine the
maximum height of the rocket only using the velocity vs. time graph?
How could you use a velocity vs. time graph to determine how long it
would take the rocket to land back on Earth? How would you know from
the velocity vs. time graph that the rocket had landed back on Earth?
What would a position vs. time graph look like for the rocket for the first
10 seconds? Until the rocket reaches the maximum height? Until it reaches
the ground?
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A ball is thrown straight up into the air from the ground. It reaches a
maximum height and returns back to the ground. Sketch two vectors that
represent the velocity and the acceleration of the ball on the way up.
Sketch two vectors that represent the velocity and acceleration of the ball
at the maximum height.
Sketch two vectors that represent the velocity and acceleration of the ball
on the way down.
Using the diagrams you just drew, make a claim about the direction
of the acceleration and velocity and when the ball is speeding up or
slowing down.
What’s the point?
In math class, you are used to reaching for an equation to solve a problem.
In physics, representations are often easier and faster to help you
determine an answer or support a claim.
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AP Physics 1
Workbook
UNIT
1
Kinematics
Free Fall
EK
|
3.A.1, 4.A.1, 4.A.2
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 6.1
Prepare
This worksheet can be paired with the one before for deeper understanding.
Teach
Students consistently hunt for equations that look like they can give them
the answer they need without thinking through the meaning of the physical
situation, the variables they are given, or the limitations of the equations.
Finding the time when the rocket lands back on Earth is a classic
AP Physics B “type” problem. It is mathematically a little tricky and requires
two steps to solve correctly. To make this into an AP Physics 1 question,
take out the need for a solution to the question. Ask simply, how could
you find the time? Ask the students for more than one method. Using an
equation is fine, but can they explain how they would use the equation?
Can they then create a graph that they could use to double-check their
solution and/or provide more evidence to justify a claim?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A hot air balloon moving upward at 10 m/s drops a sandbag as the balloon
is 10 meters above the ground. Sketch a velocity vs. time, position vs. time,
and an acceleration vs. time graph for the sandbag. What is the maximum
height reached by the sandbag? Provide evidence for your claim.
(Equations should not be your only evidence!)
How long does it take the sandbag to reach the ground? Provide evidence
for your claim. (Equations should not be your only evidence!)
What’s the point?
Equations are tools. If you try to use a hammer to clean a window, you’ll
make a mess. You must make sure you use the right equation for the job.
Equations include mathematical models of physical behavior and are
another way to communicate relationships among physical variables.
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AP Physics 1
Workbook
UNIT
1
Kinematics
Linearizing Graphs
EK
|
3.A.1, 4.A.1
SP
|
1.1, 1.4, 2.1, 2.2, 5.1, 6.1
Prepare
Consider printing out the table at the bottom right with the most common
relationships used in AP Physics 1 for your students. Being able to
repeatedly reference this will help them see the patterns and feel more
confident in making claims about the relationships between physical
quantities.
Linearization is a tough mathematical concept. Consider doing an activity
to introduce the idea before assigning this worksheet. Give each lab group
a set of paper circles (printed from the internet or cut from craft paper
with a circle cutter). Have each group measure the diameter of each circle
(pre-mark each circle with the area—you can calculate this—it is tedious
to have students determine area by counting boxes and not the point of
this activity). Students will then have data about the area and diameter of a
circle. If they graph area vs. diameter (or radius if that makes it easier), is it
linear? What is the relationship between the two variables? (Compare with
the chart at bottom right). What should they graph to make a linearized
graph? (Students can graph A vs. r 2 and the slope will be π , or if they
graph A vs. D 2, the slope will be π/4.
Teach
You can keep this lesson going by asking students to sketch a graph of
drop height vs. time squared (that they calculated in Part C). Then have
them sketch in a line of best fit. Try to have the line as close as possible to
all points and as many points above the line as below. Next, students can
find the slope of their line of best fit by choosing points on the line (not
data points), marking them on the graph, and using these points with the
point slope equation.
Students can then calculate the acceleration due to gravity by setting the
value of the slope equal to 1 g . Students should be able to explain in a
2
short paragraph or set of sentences how and why they are performing
each of these steps listed above.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Give students a set of data collected about the radius and volume of
a set of spheres. (This can also be done as an activity where students
determine the volume of the spheres by water displacement.) Have the
students graph volume vs. diameter (or radius). Is it linear? What is the
relationship between volume and diameter (or radius)? What should be
graphed to make a linearized graph? What would the slope be? (If students
graph volume vs. r 3, the slope will be 4π/3.)
Ask students for other equations that they may have learned in other
classes in which they could have theoretically collected data. What would
they graph? Would it be linear? How could they linearize the data?
What’s the point?
Not all relationships are linear, but when you manipulate the data so that
the graph is a line, it is easier to get useable information from the graph to
be able to draw conclusions as well as construct equations.
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AP Physics 1
Workbook
UNIT
1
Kinematics
Projectile Motion
EK
|
3.A.1, 4.A.1
SP
|
2.1, 2.2, 6.1
Prepare
This worksheet can be paired with the next one for deeper understanding.
Teach
Students develop personal “theories of motion” by generalizing the
ideas they acquire from the observation of objects in everyday life. Many
student misconceptions result from a pre-Newtonian impetus theory of
motion. This theory attributes motion to an impetus that is given to an
object initially and then is gradually used up over time. (This is the cartoon
theory of motion.) Common misconceptions include:
§§An object moves in the direction it is launched. Only after some
“impetus” has been used up can gravity act, causing the object to fall
to the ground
§§An object that is dropped from a moving object (i.e., a car, train or
airplane) does not receive any impetus, and so falls straight down.
§§Falling objects possess more gravity than stationary objects, which
may possess none at all. (i.e., an object at the top of its path does not
have an acceleration.)
It is important to be both aware of these misconceptions and provide
students with opportunities to confront them.
You can continue this page by asking students the following question:
Part F: If you throw the ball at an angle, it increases the time that the ball
is in the air and decreases the horizontal speed, so will the ball go farther
or not as far if it is thrown at an angle of 20 degrees above the horizontal
rather than being thrown horizontally?
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the question below:
A 0.2-kilogram red ball is thrown horizontally at a speed of 4 m/s from a
height of 3 meters. A 0.4-kilogram green ball is thrown horizontally from
the same height at a speed of 8 m/s . Compared to the time it takes the
red ball to reach the ground, the time it takes the green ball to reach the
ground is
A. half as much.
B. the same.
C. four times as much.
D. one-quarter as much.
E. twice as much.
What’s the point?
When asked to write or derive an equation relating variables, start with an
equation that is already familiar to you. When you are finished, make sure
that you have used ONLY the variables given to you!
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AP Physics 1
Workbook
UNIT
1
Kinematics
Projectile Motion
EK
|
3.A.1, 4.A.1
SP
|
1.1, 1.4, 1.5, 6.1
Prepare
This worksheet can be paired with the one before for deeper
understanding.
Teach
There are many correct answers here. On a question like this, students can
get hung up on what the “correct” answer is. They need to be taught that in
response to an open-ended question, the AP Exam is looking for common
properties that all correct graphs will have in common. For example, for
Part B of this question, all correct vertical velocity vs. time graphs will have
a vertical intercept that is a positive non-zero value and will have the same
slope. Peer grading can be a powerful tool. Students need opportunities
to see that there are other correct responses and to argue the differences
and similarities between correct representations.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A ball of mass m is thrown into the air at an angle of 37 degrees above
the horizontal. What happens to the magnitude of the ball’s vertical
acceleration during the total time interval that the ball is in the air?
A. Acceleration decreases and then increases.
B. Acceleration decreases and then is constant.
C. Acceleration increases and then decreases.
D. Acceleration increases and then is constant.
E. Acceleration stays the same.
What’s the point?
When sketching graphs of velocity vs. time for projectile motion, take
special care to differentiate what is happening in the vertical and horizontal
directions. See AP Physics B 1994 #3 for more practice drawing graphs of
velocity vs. time for objects undergoing projectile motion.
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AP Physics 1
Workbook
UNIT
1
Kinematics
2D Motion
EK
|
3.A.1, 4.A.1
SP
|
1.1, 1.4, 2.1, 2.2, 5.1, 6.1
Prepare
If you have access to projectile launchers and carbon paper, this
experiment can be replicated by your students. Another option is to
purchase a set of dollar-store suction-cup launchers and have your
students replicate. The dollar-store suction-cup launchers may or may
not have a constant launch speed, which will add an interesting spin to the
data analysis! If you use the suction-cup launchers, make sure you do the
experiment before your students so that you are aware of any possible
problems they may have to overcome.
Teach
For more linearization practice, have your students derive an expression
for the distance D to the target in terms of the vertical distance H , the
speed of the dart, and fundamental constants as necessary. Have them
graph D vs. H . Is this linear? What can we say about the relationship
between D and H ? What could we graph instead so that the graph is
linear? If the students graph D 2 vs. H , the slope will be 2v 2/g .
The speed of the dart they calculate should be about 60.5 m/s . Suppose
the “real” speed of the dart is 65 m/s , what could explain the difference?
Have students find the percent error between their speed and the
known value.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
An archer wants to be able to shoot an arrow so that it hits the ground as
far as possible from the point where she shoots it. The ground is level.
The archer reasons that the arrow should be aimed almost horizontally
so its velocity component along the horizontal is as great as possible and
therefore will travel as far as possible in the horizontal direction. Critique
her reasoning.
Is she right?
A. Yes
B. No, because this won’t make the horizontal component of the velocity
bigger.
C. No, because even though this will make the horizontal component of
the velocity bigger, it won’t make the arrow go farther.
In a clear, coherent paragraph-length response, explain your answer above.
What’s the point?
While the rules for significant digits will not be directly tested on the
AP Physics 1 Exam, you will be expected to use a reasonable number of
significant digits in calculations on the free-response section. Significance
is an indication of the quality of the measurement and the given variables
dictate the significance of the answer. Points may be deducted for an
unreasonable number of number of significant digits.
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AP Physics 1
Workbook
UNIT 2
Dynamics
Misconceptions
Students have an instinct about forces as pushes or pulls because of physiological
experience but often have difficulty conceptualizing forces as interactions. If students
are thinking of forces as things in and of themselves or as properties of objects
(which are two common misconceptions about forces), they usually have a difficult
time using Newton’s second and third laws appropriately. Students also tend to
believe that forces are proportional to velocity instead of understanding that net force
is proportional to acceleration.
One approach to helping students envision forces as interactions is to ask them to
explicitly identify the agent exerting the force and the object on which it is exerted
when they work with a force (e.g., in a free-body diagram). Doing this will enable
them to check that any force they think is present actually exists. If they cannot
identify the agent, which has to be Earth, another object or another system, exerting
the force, then they need to reconsider including that force in the analysis. Identifying
the agent and object also enables students to check that forces they are analyzing are
all acting on the same object. It also allows students to check that “action-reaction
pairs” have the same two objects involved, just in opposite roles. For example, is
object A the agent for one force and the object for the other? It is best to avoid using
the common terminology of forces “acting” on objects. The verb acting reinforces
the misconception that forces are independent. Try to always use the term exerted
and ensure that students could complete the sentence: This interaction can be
represented by a force exerted by (object 1) on (object 2), filling in the parentheses as
appropriate for the interaction.
Common challenges that students have regarding Newton’s first law include the idea
that forces are required for motion with constant velocity. When observing classroom
demonstrations of accelerating objects, students often need help recognizing that the
velocity of an object is changing as a result of the net force exerted on the object. It
should be made clear to students that the net force determines an object’s acceleration,
not its velocity. It can be very helpful to discuss friction and air resistance with the
students as you are making this point. They often know you have to push on the
accelerator to keep a car going at constant velocity or keep shoving a box to keep it
sliding at constant velocity, but they have not thought about the forces exerted on the
car or box that they cannot see. Students might not always see the connection between
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AP Physics 1
Workbook
Newton’s laws and kinematics, so it is important for them to recognize Newton’s
second law as “cause and effect.” It is important to present Newton’s second law in its
operational form of a 
F
, as the commonly used F  ma leads some students to believe
m
that the product of mass and acceleration is a force. Scaffolding around the differences
between individual forces and the net force is beneficial, as this often causes students
difficulty. Students often believe that all forces are equal to mass times acceleration,
which further reinforces the misconception that forces are properties of objects.
Scenario
Misconception
2I, 2.J
Velocity is a force.
2.B
Forces are required for motion with constant velocity.
2.B
Inertia deals with the state of motion (at rest or in motion).
2.B
All objects eventually stop moving when the force is removed.
2.B, 2.I, 2.J
Inertia is the force that keeps objects in motion.
2.C, 2.D, 2.E, 2.F
Action-reaction forces are exerted on the same body.
2.I, 2.J
There is no connection between Newton’s laws and kinematics.
2.D, 2.E, 2.F
The product of mass and acceleration, ma, is a force.
2.F, 2.G
Friction can’t be exerted in the direction of motion.
2.G, 2.H, 2.M
The normal force on an object is equal to the weight of the
object by Newton’s third law.
2.H
Equilibrium means that all forces on an object are equal.
2.C, 2.D, 2.E, 2.F
Equilibrium is a consequence of Newton’s third law.
2.C, 2.D, 2.E, 2.F, 2.G, 2.H,
2.I, 2.J, 2.K, 2.M
Only animate things (people, animals) exert forces; passive
objects (tables, floors) do not exert forces.
2.B
A force applied by a hand, for example, is still exerted on an
object after the object leaves the hand.
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AP Physics 1
Workbook
Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Acceleration vs. mass graph
Using Representations
2.A
1.1
Create and use a free-body diagram.
Using Representations
2.C, 2.D. 2.E, 2.F, 2.G, 2.H, 2.I, 2.J,
2.K, 2.M
1.1
Plot data on a graph.
Using Representations
2.A, 2.H, 2.L, 2.N
1.1
Scale and label axis.
Using Representations
2.A, 2.H, 2.L, 2.N
1.1
Velocity vs. time graph
Using Representations
2.B, 2.J
1.4
Identify systems.
Using Representations
2.C, 2.D, 2.E, 2.F, 2.G
1.5
Linearize a graph.
Using Representations
2.H
1.5
Match shapes of graphs to relationship.
Data Analysis
2.A
2.1
Identify an equation that can be used to analyze physical situation.
Quantitative Analysis
2.C, 2.D, 2.E, 2.F, 2.G, 2.H, 2.I, 2.J, 2.K,
2.L, 2.M, 2.N, 2.O
2.2
Derive or calculate including annotations.
Quantitative Analysis
2.C, 2.D, 2.E, 2.F, 2.H, 2.I, 2.M
2.2
Relate slope to a physical quantity.
Data Analysis
2.H, 2.L
4.2
Design an experiment.
Experimental Design
2.L, 2.N, 2.O
5.1
Describe how measurements would be analyzed.
Data Analysis
2.L, 2.N, 2.O
5.1
Sketch a line of best fit.
Data Analysis
2.O
5.2
Error analysis
Data Analysis
2.O
6.1
Justify a claim with evidence.
Argumentation
2.A, 2.E, 2.G, 2.I, 2.K, 2.L, 2.M, 2.N, 2.O
6.4
Use equations to support reasoning.
Using Representations
2.C, 2.D, 2.E, 2.F, 2.G, 2.H, 2.I, 2.J, 2.K,
2.L, 2.M, 2.N, 2.O
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Relationship Between Force and Acceleration
EK
|
SP
3.B.1
|
1.1, 5.1
Prepare
So far, students have seen linear and quadratic relationships. This may be
the first time that they will see a relationship that is inversely proportional.
If your students struggle with determining the functional relationship
between variables, consider with them the equation for average speed
vavg 
d
, which can be rewritten d  vavg
t

  t . For a constant distance,
what happens to the speed and the time? If you increase the speed, the
time decreases. If you want to increase the time, you have to decrease the
speed. Give them some data to graph, see that it is not linear, and decide
what they could graph to make it linear (v avg vs. 1/t ). The slope of that
graph will be the constant distance traveled.
Average Speed
(m/s )
12
Time to Travel Some
Unknown Distance
(seconds)
1
6
2
4
3
3
4
2.4
5
2
6
1.7
7
1.5
8
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Teach
The idea of inverse relationships is powerful and later leads to both Ohm’s
law (V = IR ) and v = λf.
Now that your students know what they should graph to make the graph
linear, have them create the graph. What is the magnitude of the force
exerted on each box?
Can they think of a way to recreate this data themselves, so that they have
a constant net force with varying accelerations based on mass? (One idea
is to use a fan cart that will provide a constant force, and the students can
add masses to the cart. If a motion detector is set up in front of the cart,
it can collect velocity vs. time data and the slope of that line will be the
acceleration of the cart.)
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Data has been collected about the net external force on an object as well
as that object’s acceleration while the net external force is being exerted
on it. What data should be graphed to create a linear graph? What would
be the physical meaning of the slope of the graph?
What’s the point?
Functional relationships will be tested on the AP Physics 1 Exam. You need
to be able to look at a graph and use the data presented as evidence for a
claim of the relationship between the variables graphed.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Force and Acceleration
EK
|
1.C.1
SP
|
1.5, 5.1, 6.1
Prepare
This is a good demonstration for students to get a “feel” for how the
speed changes under the influence of a constant force, and then what
happens to the speed of the object once the force is removed. If you have
access to low-friction carts and motion detectors, you could set up this
experiment for students to try themselves. This worksheet can be their
prediction sheet and then they can test their predictions in the lab.
In this page, we introduce students to a new tool. The “Checklist” will be
provided as a scaffolding tool to help students check their own writing. By
the end of the course, students should be able to ask themselves these
questions without being prompted!
Teach
If you have low-friction skateboards, you can have students pull a box
on the skateboard (to simulate a student) with a spring scale to see for
themselves that if they want to pull with a constant force, their speed and
the speed of the skateboard will increase.
Ask the students here, “What is the relationship between your speed
and the speed of the skateboard?” (They should be equal.) “Why are they
equal?” This will help them understand that systems that are “attached”
must have the same speed at any clock reading. This may help with
misconceptions later about the common speed and acceleration of
systems (i.e., objects connected by strings).
Note that the sample graph provided in Part B suggests that the textbooks
must be VERY massive. This is just to help students visualize that there is a
relationship between net external force, mass, and acceleration. Students
will explore the mathematical relationships in later scenarios.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A box of mass m is pushed for 10 seconds with a force P across a
horizontal floor with negligible friction. After 10 seconds, the person stops
pushing. Sketch a velocity vs. time graph for the box. Sketch in a dotted
vertical line at t = 10 seconds. What is different about the motion of the
box before and after t = 10 seconds?
What’s the point?
In the absence of a net force, an object in motion will continue in the
same motion. All mass has a property called inertia that resists change to
its motion.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Force
EK
|
2.B.1, 3.A.2, 3.A.3, 3.A.4,
3.B.1, 3.B.2, 3.C.4, 4.A.2
SP
|
1.1, 1.5, 2.1, 2.2, 6.1
Prepare
If you have not yet discussed how to break forces into components, you
should do so before assigning this worksheet. If you start from the very
beginning asking students to think about the direction of acceleration
first before breaking forces into components, they will be better prepared
for more difficult physical scenarios like boxes on inclines or conical
pendulums.
Students should decide on the direction of the acceleration (or possible
acceleration)—in this case horizontally—and then they can assign their
axes to be parallel and perpendicular to that direction. (In this case, the
axes should be horizontal and vertical.) Then they can analyze each force,
and any force that is not parallel or perpendicular to the acceleration
must be broken into components. (Part C, the force to be broken into
components is F Pull .)
Teach
There is a very specific way that students will be expected to sketch a
free-body diagram on the AP Physics 1 Exam. All vectors MUST start on,
and point away from, the dot, and each force must be represented by its
own uniquely labeled (or unambiguously labeled) vector. Unless stated
otherwise, students should take special care to make sure that the lengths
of the arrows represent the magnitudes of the forces and they DO NOT
sketch components on the diagram. If at any point during the problem,
they need a free-body diagram with components to help them analyze
the physical scenario, they should feel free to sketch a second diagram
somewhere else on the page that they may mark up as needed.
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Assess
To further assess student understanding of the
concepts addressed in this scenario, you may want to
ask students the questions below:
The diagram shows a block of mass m being slid at a constant speed
across a horizontal concrete floor by a force parallel to the floor. Which
pair of quantities could be used to determine the coefficient of kinetic
friction for the block on the concrete?
A. Mass and speed of the block
B. Mass and normal force on the block
C. Friction force and speed of the block
D. Friction force and normal force on the block
E. Normal force and speed of the block
Explain how your choice of quantities could be used to determine the
coefficient of kinetic friction.
What’s the point?
Drawing a free-body diagram is not just busy work. A carefully sketched
free-body diagram is a key to both understanding a physical scenario AND
demonstrating that understanding.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Newton’s Third Law and Eliminating Internal Forces
EK
|
1.A.1, 1.A.5, 2.B.1, 3.A.2, 3.A.4,
3.B.1, 3.B.2, 3.C.4, 4.A.2
SP
|
1.1, 1.2, 1.5, 2.1, 2.2, 6.1
Prepare
Teaching students to consider the system they are analyzing and to
consciously document the system (by circling the objects) will help them
be prepared to analyze systems by using energy and momentum, which
also depends on the system being analyzed. If the first time they hear
about the idea of a system is in Unit 4, it will be much more difficult for
them to wrap their heads around the concept. A free-body diagram is used
when we can approximate a system as an object (when every point on the
system moves the same way) or when we are only interested in the motion
of the center of mass of the system.
Teach
Have students sketch the system they are analyzing and draw a dotted
box or circle around the object or objects that are part of the system. This
visualization will help them to remember what interactions they can ignore
as being internal to the system.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
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When the frictionless system shown above is accelerated by an applied
force of magnitude F, if friction is negligible, the tension in the string
between the blocks is:
A. F.
B. 2 F.
3
C. 1 F.
2
D. 1 F.
3
What’s the point?
Newton’s second law states that the SUM of all the forces exerted on an
object equals the object’s mass times its acceleration. It is not that ANY
force can equal mass times acceleration or that EVERY force is equal to
mass times acceleration, but it is the net or sum of all forces.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Newton’s Second and Third Laws
EK
|
1.A.1, 1.A.5, 2.B.1, 3.A.2, 3.A.3,
3.A.4, 3.B.1, 3.B.2, 4.A.2
SP
|
1.1, 1.5, 2.1, 2.2, 6.1
Prepare
This is the first complicated derivation in the workbook. If your students
struggle here, you can have them practice by assigning problems from the
text where they are asked to solve for the acceleration (or tension, etc.).
Replace numbers in the problems with variables and ask students to
derive a symbolic solution in terms of given variables and physical
constants as necessary. Have them annotate their derivations and work
on using a clear sequence of thoughts that match from the “math” side
to the “writing” side. (Note: We have tried to give the right number of
spaces for the derivation if they do every step one at a time, but by the
end of the book, this table will disappear—as it will not be given on the
AP Physics 1 Exam.)
Teach
Before the students even try answering the questions—Is the system
accelerating? How do you know? Sketch a dotted circle or box around the
system being analyzed. What are the internal and external forces? Could
the system have a net zero external force?
What is the relationship of the speed of Block 1 to the speed of Block 2?
How do you know? What would it look like if the two blocks had different
accelerations?
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Three blocks of mass m , 2m and 3m sit next to each other on a horizontal
surface where friction between the blocks and the surface can be
neglected. A constant force of magnitude F is applied to the right. Which
of the following statements is true?
A. Each block will have a different acceleration depending on its mass.
The acceleration of each can be calculated by the equation F = ma ,
so a = F/m .
B. The acceleration of each block will be the same a = F/m .
C. The net force exerted on each block is identical and equal to F.
D. The magnitude of the force on block 3m from 2m is greater than the
magnitude of the force back on 2m from 3m .
E. The net force exerted on 3m is three times greater than the net force
exerted on m .
Explain why the answer you chose is correct and the others are incorrect.
What’s the point?
While you are free to choose your own system to analyze a given physical
scenario, the choice of a system can greatly simplify (or greatly complicate)
the analysis.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Direction of Friction
EK
|
1.A.1, 1.A.5, 2.B.1, 3.A.2, 3.A.3,
3.A.4, 3.B.1, 3.B.2, 3.C.4, 4.A.2
SP
|
1.1, 1.3, 1.4, 2.1, 2.2
Prepare
The likelihood that your students will encounter a problem like this, where they
are solving numerically for an answer on the free-response section of the
AP Physics 1 Exam, is extremely low. However, it is possible that they will be
asked to solve numerically for a solution on the multiple-choice exam. So, to
that end, we have included a few problems in this workbook where a numerical
solution is required from the students. Most of your efforts as a teacher should
focus on helping your students to explain and justify results, conclusions, and
ideas. While teaching your students to solve numerically for a solution may not
be the focus, it can still happen—the numeric solution can’t be the “end” of the
analysis. Solutions should be annotated and followed up with questions about
why something happens or what would happen if variables change.
Teach
Students will likely have difficulty understanding why the force from the
ground on the bulldozer is forward. Consider having a discussion with your
students about how they can walk. What is the force that allows them to
walk? If they tried to walk across ice which exerts negligible friction, what
would happen? Which way would their foot slide? Friction prevents this
motion and as you push backwards on Earth, Earth pushes forward on
you. The same is true with the tread of the bulldozer.
The discussions you have about the direction of friction on the rolling
treads of the bulldozer are a good preview of the ideas involved in rolling
that students will see in Unit 7.
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Assess
To further assess student understanding
of the concepts addressed in this
scenario, you may want to ask students
the questions below:
Three boxes of equal mass are being pulled across a smooth table top.
Box 2 is connected to Box 3 by a light cord that is pulled along with a
force F as shown. Block 1 is accelerated at the same rate as Block 2
because of the friction forces between the two blocks. Friction between
the blocks and the table top can be neglected.
Sketch a free-body diagram of Block 1.
What’s the point?
While the force of friction opposes the motion of two surfaces relative to
each other, you have to think hard about what motion is being analyzed. In
a single system, friction can be exerted in more than one direction.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Acceleration in Two Dimensions
EK
|
2.B.1, 3.A.2, 3.B.1, 3.B.2, 3.C.4, 4.A.2
SP
|
1.1, 1.5, 2.1, 2.2, 5.1, 6.1
Prepare
If your students have not yet stood in an elevator on a bathroom scale,
that demonstration might be helpful to perform before this activity.
Why does the scale read more than your “usual” weight when you first
accelerate upward from rest? Why does the scale read less than your
“usual” weight when you accelerate downward slowing to a stop at the
top floor? Discuss the differences in weight and apparent weight with your
students and which one the scale reads.
Teach
Part F can be tricky for some students. The question has given the
answer and students simply need to collect evidence to support the
given statement. However, some students will misunderstand the prompt
and think that they are supposed to collect evidence to determine the
correctness of the given statement. Both kinds of questions are asked
on the AP Physics 1 Exam, and students need to be aware of whether
they are asked to determine the correctness of a statement or support a
statement that has already been determined to be true.
For an extension, you could have students complete the entire FR
question from the AP Physics C 1996 #2, Part G. Derive an equation for
the path of the box that expresses y (the height of the box) as a function
of x (the horizontal position of the box) and not of t , assuming that at
time t = 0, the box has a horizontal position x = 0 and a vertical position
y = 2 meters above the ground with zero velocity.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Multiple Correct
The cart of mass 10 kilograms shown above moves along a smooth
surface on a horizontal table. A 10-newton force pulls on the cart
horizontally to the right. Which of the following describes a manner in
which this cart could be moving? Select two answers.
A. Moving left and speeding up
B. Moving left and slowing down
C. Moving right and speeding up
D. Moving right and slowing down
What’s the point?
Although we don’t often deal with objects accelerating in two directions,
they certainly can. The forces are then modeled using Newton’s laws both
in the horizontal and vertical direction.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Forces on Inclined Planes
EK
|
2.B.1, 3.A.2, 3.B.1, 3.B.2, 3.C.4, 4.A.2
SP
|
1.1, 1.5, 2.1, 2.2, 5.1, 6.1
Prepare
Remember to have students determine the direction of acceleration
first when they encounter a problem where the forces are at angles. In
this case, the box is being held at rest by the friction force and will not
accelerate. However, if we made this a ramp with negligible friction, which
way would the box accelerate? Down the ramp! So, make the “down the
ramp” direction the “x ” direction and make perpendicular to the ramp the
“y ” direction. Which forces are then neither parallel nor perpendicular
to the ramp? The gravitational force—so students should find the
components of the gravitational force.
Teach
This scenario can easily be turned into an experiment that the students
can execute in class. Have them write up the procedure, either individually
or in groups. Once they have collected the data, have them analyze it
according to what they wrote in Part C. This is also a great experiment for
a discussion of errors. Students should know the equation for, and be able
to calculate, both percent error and percent difference.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Derive an equation for the friction force necessary to hold the block
on the incline as a function of the angle of the ramp. Does the derived
quantity make physical sense? Check θ = 0 and θ = 90 degrees. What
would the value of the friction force be in each of these extremes? Does
that make sense?
(For extra linearization practice, have them linearize and determine the
coefficient of static friction from their graph.)
What’s the point?
Practicing the skill of linearization is important and can be done quickly
every time the students do a derivation. “What would we graph, if we had
data, to make this graph linear?”
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AP Physics 1
Workbook
UNIT
2
Dynamics
Stopping Distance
EK
|
2.B.1, 3.A.2, 3.B.1, 3.B.2, 3.C.4,
4.A.1, 4.A.2
SP
|
1.1, 1.5, 2.1, 2.2, 5.1, 6.1
Prepare
The translation between the written argument in Part B and the
Quantitative Analysis in Part C is a critical skill for success on the
AP Physics 1 exam. Again, as with other skills, if your students struggle
with this, you can assign classic textbook questions to them for practice
with slight modifications. First, remove the numbers given in favor of
symbols and ask them to predict the result when one of the variables
changes. Then have them derive a symbolic solution (with annotations)
and show how their derived expression supports their prediction made
from principles of physics. For example, consider a classic Atwood
machine (a pulley of negligible mass over which two objects are
suspended on a string of negligible mass) if the suspended objects have
masses m and M , where M>m , what happens to the acceleration of the
system as M is reduced? Have them predict, using principles of physics to
support their answer. They may reference equations but should not derive
anything. Then have them derive an expression for the magnitude of the
acceleration of the system and use that expression to justify their claim.
Teach
This can be a difficult concept for students to understand if they don’t
have personal experience riding in cars. While nothing can replace
experience, there are ways to simulate this experience in the classroom,
from having the students sit on skateboards and drag their feet to riding
wheeled toys or bicycles, if available.
Students should sketch two velocity vs. time graphs both with the same
initial velocity: one with a gentle stop and one with an emergency stop
(so that the graphs have small or large accelerations). Have students
compare the times to stop as well as the displacement before coming to
rest (the areas under the curves). What would the graphs look like if we
factor in reaction time?
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
What data should be collected if the students wanted to experimentally
determine the coefficient of kinetic friction between the tires and the
road? What would the students graph to determine the coefficient of
kinetic friction?
What’s the point?
Only forces belong on free-body diagrams. While it is often helpful to mark
the direction of the initial velocity on the sketch of the physical situation,
they should never appear on a free-body diagram.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Modified Atwood Machines
EK
|
1.A.1, 2.B.1, 3.A.2, 3.A.3, 3.A.4,
3.B.1, 3.B.2, 3.C.4, 4.A.1, 4.A.2
SP
|
1.1, 1.5, 6.1, 7.1
Prepare
An ideal pulley means that the pulley’s mass is negligible and any friction
in the pulley may also be ignored. Later in the course (Unit 7: Torque and
Rotation), we will introduce the idea of pulleys that have mass and analyze
what that means for the system, but for now, all pulleys will be ideal. You
can challenge your students to think about what would happen to the
acceleration of the system if the pulley is real and not ideal.
Teach
Sketching a graph onto a blank grid can be difficult for students. Rather
than expecting them (or the students expecting themselves) to sketch the
correct shape on the first try, have them focus on plotting the points that
they KNOW to be true. For example, on this graph, v 0 is positive, and at t 1,
the velocity is zero, etc.
For Part B, whenever students are asked to compare two scenarios, they
must talk about the physical quantities of each situation and compare the
similarities and differences.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Is the force of tension in the string the same in both cases? Is t 1 equal to t 2?
Quick Quiz
A massive chain (as opposed to a string of negligible mass) is hung over
1
the length of the chain is over the edge and
the edge of a table, where
10
9
of the length rests on the table. If friction between the chains and the
10
table is negligible, will the chain stay at rest or start to slide off the edge
of the table? Support your answer. Will the acceleration of the chain be
constant or changing? If the acceleration will change, will it increase or
decrease? Support your answer by referencing the net force on the chain
vs. the mass of the system.
What’s the point?
Remembering that friction can change direction depending on the
direction of motion is important. Equally important is remembering that
the direction of forces does not depend on the direction of motion.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Acceleration of Systems
EK
|
1.A.1, 2.B.1, 3.A.2, 3.A.3, 3.A.4,
3.B.1, 3.B.2, 3.C.4, 4.A.1
SP
|
1.1, 1.5, 6.1
Prepare
Students often find this concept difficult to grasp. You can demonstrate
this in class or have them replicate it themselves with low-friction carts
and motion sensors to experience it for themselves.
Teach
Depending on your students, they may find that Part B (i) or (ii) is easier
and more intuitive. It is important that students be pushed to find
explanations beyond their comfort zone and be able to support claims
with multiple lines of evidence.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Ask students to sketch acceleration vs. time and velocity vs. time graphs
for each situation.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Hooke’s Law Springs
EK
|
2.B.1, 3.C.4
SP
|
4.1, 4.2. 5.1, 5.3, 6.1, 6.4, 7.1
Prepare
This can and should be done in class. If this page is sent home as pre-lab
homework, students can meet in small groups at the beginning of the
next class to agree on a procedure before doing the activity themselves
in class.
Since springs and rubber bands change shape when a force is exerted
on them, they cannot be modeled as objects. Remember, in AP Physics 1,
“object” is reserved for something which can be modeled as having no
internal structure. Since a rubber band or a spring can stretch, it has
internal structure that cannot be ignored.
Teach
This is the first workbook page where students are being asked to write
their own procedure from scratch. While we believe the scaffolding
provided to be helpful for students to see visually where they should be
putting their information, most students will need more help in scaffolding
experimental design. Consider introducing your students to the
“SQUARED” method of writing procedures:
S—Setup
Q—Quantities (variables) to be measured
U—Units
A—Apparatus (tools)
R—Repetition (multiple trials)
E—Error reduction (more data points, or more trials of each point)
D—Diagram (labeled)
If you test this experiment with your students be sure to note that
systematic errors can lead to graphs that do not pass directly through the
origin. This is acceptable, but students should be taught not to force their
line through (0, 0).
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A Hookean spring obeys Hooke’s law ( F = −kx ). How could you design a
test for a new kind of plastic spring to see if it can be labeled “Hookean”?
What’s the point?
On lab design questions, there is almost always a point for reducing error
by doing multiple trials! Don’t forget that quick and easy point!
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AP Physics 1
Workbook
UNIT
2
Dynamics
Limiting Cases
EK
|
2.B.1, 3.A.2, 3.B.1, 3.B.2, 3.C.4, 4.A.2
SP
|
1.1, 1.5, 2.1, 2.2, 6.1
Prepare
This problem asks students to think about limiting cases. If you have yet
to discuss this form of analysis with your class, they may find this piece
of the question difficult. Keep circling back to this kind of thinking and ask
students to practice limiting-case analysis often.
Teach
Have students verbalize how they decided which force to break into
components. Although it is straightforward here (break the pulling force
into components because the sled-sister system is accelerating to the
left), the more they practice verbalizing this, the easier it will be later.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A student pulls a wooden box across a rough horizontal floor at a constant
speed by means of a force F P as shown above. Which of the following
must be true?
A. FP > F f and F N < Fg
B. FP > F f and F N = Fg
C. FP = F f and F N > Fg
D. FP = F f and F N = Fg
What’s the point?
Being able to discuss limiting cases is an important skill necessary to
analyze mathematical representations on the AP Physics 1 Exam.
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AP Physics 1
Workbook
UNIT
2
Dynamics
Experimental Procedure Design
EK
|
3.C.4
SP
|
4.1, 4.4, 5.1, 6.1
Prepare
This lab question has a built-in mistake (that the lab group doesn’t take
into account the mass of the blocks is also changing). Most students
will not notice until the end when it is specifically called out, but if your
students notice, be prepared to discuss that this question is designed
to test if lab results support the hypothesis (regardless of the methods)
AND their understanding of good lab procedure. Remind students that it is
not their job to argue with the question. For example, they should not use
Part A to discuss why this lab won’t give the desired results. Go with what
is given. Do not argue with the question.
Teach
Have students determine a way to control for mass and repeat the lab.
(Use the SQUARED method of procedure writing for scaffolding!) Do the
results provide evidence for the reasoning that race cars have wide tires
because the increased area results in a stronger force of friction? Now
may be a good point in the class to discuss that the friction force that
allows a driver to control a car is not simple kinetic or static friction as has
been discussed in the course; it is more complicated.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Sketch a graph of friction force vs. area and friction force vs. mass. Explain in
a few short sentences why these graphs have the shapes they have.
What’s the point?
There are often variables that are linked (like area and mass), and a change
in one results in a change in the other. If students are not careful and
conscious about how variables might be linked, they can invalidate their
results by not controlling their variables.
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UNIT
2
Dynamics
Spring Force and Acceleration
EK
|
2.B.1, 3.B.2, 3.C.4
SP
|
4.1, 4.2, 5.1, 6.1
Prepare
If possible, have students perform experiments in an elevator. Whether
they bring springs and known masses, spring scales, force sensors, or
just simple analog bathroom scales, seeing and feeling the changes in the
normal force (or apparent weight) is powerful for student understanding.
Teach
Remind students that even if they are not specifically asked to sketch
a free-body diagram, drawing one can help them to solidify their ideas
about the magnitudes and the directions of the forces. If they do draw a
free-body diagram and want to reference it in their response, make sure
that they specifically call attention to the free-body diagram. Remember
that anything written or drawn outside the answer area will not be graded
unless the reader is specifically told to do so.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
See Problem #1 on AP Physics B Exam from 1993
for more elevator problems. It is not necessary for
students to even complete the whole question from
1993. Ask them to describe the motion for one or
two of the segments of the motion. For example,
ask, “What is happening to the position, velocity, and
acceleration of the elevator during the segment?”
An object of known mass hangs from a force sensor inside of an elevator.
As the elevator moves from the bottom floor to the top floor, the upward
force exerted on the object as a function of time is recorded in the
following graph. Which of the following questions could NOT be answered
by the data in the graph and the known mass?
A. What is the acceleration of the elevator as it leaves the ground floor?
B. What is the maximum speed attained by the elevator?
C. What is the approximate height of the building?
D. All of these questions could be answered by these data.
What’s the point?
In AP Physics 1, ideas never disappear. Just because you learned
something in the last chapter, doesn’t mean that it won’t pop up again!
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UNIT 3
Circular Motion and
Gravitation
Misconceptions
Unit 3 deals with the idea of centripetal force. Students usually don’t associate any force
or acceleration with objects traveling in circles at constant speed. Many students think
that a centripetal force is exerted on an object when it is in circular motion and this force
is directed outward, not inward to the center of the circle. Students think this because
they are confusing centripetal force with inertia. They often know that if they were in a
car making a fast turn and the door opened, they would be thrown out of the car. Thus,
they believe there is a force related to circular motion directed to the outside of the circle,
instead of realizing that there is a force toward the center needed to keep the object going
in a circle (like the door pushing them inward in the car). It is important to consider
emphasizing that a force is an interaction between two objects to help students identify
the object exerting the force toward the center of another object’s circular motion.
This issue of centripetal force is challenging for several reasons. One is the everyday
association of acceleration as a change in speed rather than a change in velocity.
Asking students if they can make a turn in a car at a constant speed without using the
steering wheel can start them thinking that acceleration can involve just a change in
direction without a change in speed. However, as is true with most of the conceptual
changes we are asking students to make in physics, repeated consideration of the ideas
is needed to change deeply held misconceptions. A second reason students find the
issue of centripetal force challenging is because they tend to think that centripetal force
is a new kind of force. Students want to add it to the list of forces learned in the previous
unit and put it in the same category as the normal force, gravitational force, tension, and
friction forces. Students will also want to, incorrectly, draw the centripetal force as a
separate force on a free-body diagram. It is important to emphasize that the centripetal
force is a net force that causes an acceleration and that net force is a result of one or
more of the previously learned forces. As a result, the centripetal force is not included
as a separate force on a free-body diagram, nor is a new type of force. It is important
to provide students with various opportunities to address this misconception through
identifying the forces acting on objects traveling in circles in a variety of situations.
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Some teachers just tell students that there is no such thing as a centripetal force.
You can remind students that the word “centripetal” refers to a direction and that it
is always some external force, such as the normal force, gravitational force friction, or
tension, exerted centripetally that allows an object to execute circular motion.
Understanding gravitational forces requires the realization that the force of
gravity is an interaction between two objects with mass. We ignore the forces of
gravity between everyday objects because they are so miniscule—but they are
there! Students struggle with Newton’s third law and appropriately applying this
law to physical objects that touch, so they will likely continue to struggle when
thinking about the gravitational force and action-reaction pairs. Another common
misconception that students have is that there is no gravity on the moon because
there is no air. Dispelling the connection between air pressure and gravity takes
careful planning. Consistent practice with identifying the agent and object for each
pair of forces will help students with these misconceptions.
Overcoming contradictions of language is difficult for students. Students commonly
treat mass and weight as synonyms and believe that both are properties of an object.
When an object is transported to the moon, students will tend to believe that either
the mass/weight of an object does not change or both decrease. Consistency of terms
and ideas is often not a matter of concern in everyday discussions, but for a physicist
and other professionals, using terms and ideas in a consistent manner is critical.
Explicitly explaining to students why it is important to be consistent with the terms
and ideas could even be a part of the introduction to the course.
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Scenario
Misconception
3.M, 3.N, 3.O
The force that is exerted on an apple is not the same as the force
that is exerted on the moon.
3.N, 3.O
3.N, 3.O
3.N, 3.O
3.N, 3.O
3.E
3.B, 3.D, 3.E, 3.F, 3.G,
3.H, 3.I, 3.J, 3.K
3.B, 3.D, 3.E, 3.F, 3.G,
3.H, 3.I, 3.J, 3.K
3.B, 3.D, 3.E, 3.F, 3.G,
3.H, 3.I, 3.J, 3.K
3.B, 3.D, 3.E, 3.F, 3.G,
3.H, 3.I, 3.J, 3.K
There are no gravitational forces in space.
The gravitational force exerted on the space shuttle is nearly zero.
The gravitational force acts on one mass at a time.
The moon stays in orbit because the gravitational force is balanced
by the centrifugal force exerted on it.
Weightlessness means there is no gravity.
Centripetal acceleration points inward and centrifugal acceleration
points outward. An object moving in a circle experiences
centrifugal acceleration.
mv 2
Centripetal force Fc 
is a new force (to add to gravity, normal,
R
and friction).
When an object travels in a circle, it is flung toward the outside by a
centrifugal force.
Circular motion does not require a force.
3.A, 3.B, 3.C
Centrifugal forces are real.
3.B, 3.D, 3.E, 3.F, 3.G,
3.H, 3.I, 3.J, 3.K
An object moving in a circle will continue in circular motion when
released.
3.B, 3.D, 3.E, 3.F, 3.G,
3.H, 3.I, 3.J, 3.K
The centripetal force is a new force that needs to be drawn on a
free-body diagram.
3.B, 3.D, 3.E, 3.F, 3.G,
3.H, 3.I, 3.J, 3.K
3.F, 3.G
An object moving in a circle with constant speed has no acceleration.
An object in circular motion will fly out radially when released.
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AP Physics 1
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Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate,
integrated with content knowledge, to reach a goal or complete a learning activity.
While the skills listed below are critical to student success, most of them are
scaffolded skills necessary for students to be successful at the science practice listed
with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Create and use free-body diagrams.
Using Representations
3.D, 3.E, 3.F, 3.G, 3H, 3.I, 3.J
1.1
Plot data on a graph.
Using Representations
3.H, 3.K, 3.N
1.1
Scale and label axis.
Using Representations
3.H, 3.K, 3.N
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
3.H, 3.K, 3.N
1.5
Match shapes of graphs to relationships between variables.
Data Analysis
3.H, 3.K, 3.N
2.1
Identify an equation that can be used to solve a problem.
Create an Equation
3.D, 3.E, 3.I, 3.J, 3.K, 3.M, 3.N, 3.O
2.2
Derive or calculate including annotations.
Create an Equation
3.D, 3.E, 3.I, 3.J, 3.K, 3.M, 3.N, 3.O
4.2
Design an experiment to answer a specific question.
Design an Experiment
3.N
6.1
Identify a claim and evidence that can support that claim.
Argumentation
3.C, 3.E, 3.F, 3.G, 3.M, 3.O
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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UNIT
3
Circular Motion and Gravitation
Inertia and Acceleration
EK
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2.B.1, 4.A.2
SP
|
1.1, 1.4, 5.1, 6.1, 7.2
Prepare
This question can be modified to have students consider riding in a bus,
subway, or train if they don’t have personal experience riding in cars.
If you have access to skateboards, students can take turns sitting on
the skateboard while it is pulled quickly from rest into motion or slowed
quickly to rest.
Teach
Again, these concepts may be difficult for students who don’t have
experience riding in passenger cars, but other experiences (such as riding
in a subway, on a train, or in a bus) should be able to replace the car.
Parts A and B may seem simple and intuitive, but provide a conceptual link
between Newton’s first law and the idea of a centripetal acceleration for
circular motion.
Assess
To further assess student understanding
of the concepts addressed in this scenario,
you may want to ask students the
questions below:
An object shown in the accompanying
figure moves in uniform circular motion.
Which arrow best depicts the net force
acting on the object at the instant shown?
If the force keeping the object in uniform circular motion were to suddenly
and instantaneously disappear, which vector would represent the path of
the object?
What’s the point?
Because of Newton’s first law, the law of inertia, we understand that
objects in motion stay in motion, while objects at rest stay at rest unless
an external force is exerted on them. Therefore, you feel your inertia when
accelerating—you feel pushed in the opposite direction of the net force.
(You feel pushed opposite the direction of the acceleration.)
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UNIT
3
Circular Motion and Gravitation
Direction of Acceleration and Velocity
EK
|
4.A.2
SP
|
1.1, 1.4, 5.1, 6.1, 7.2
Prepare
Review acceleration and velocity with your students before assigning this
page. Emphasize that they don’t have to be in the same direction and the
acceleration is always in the direction of the net force.
Teach
If you have access to constant-motion vehicles, you can have students
fill in this sheet to predict what will happen and then have them test out
their predictions. You could also choose one of the situations and have
them explain their choices of direction and speeding up/slowing down in a
paragraph-length response.
If a and v are in the same direction, an object is speeding up. If they
are in opposite directions, an object is slowing down, and if they are
perpendicular, the object remains at a constant speed.
If the angle between a and v is:
§§Acute → speeding up
§§Obtuse → slowing down
§§Right angle (or no acceleration) → constant speed
Assess
Quick Quiz
A hockey puck is tied to a string that is attached to a stake in the ice. The
puck is given a single push perpendicular to the string causing the puck to
circle the stake at a constant speed.
1) Draw a picture of the physical situation from the top.
2) Sketch a free-body diagram of the puck.
3) What forces are exerted on the puck as it circles the stake?
What’s the point?
An object in uniform circular motion (constant speed) accelerates toward
the center of the circle.
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UNIT
3
Circular Motion and Gravitation
Centrifugal Force
EK
|
3.A.3
SP
|
1.1, 1.4, 5.1, 6.1, 7.2
Prepare
If your students don’t have firsthand experience riding in a passenger car,
this page might be more difficult for them to grasp.
Teach
The concept of Newton’s law of inertia should be discussed here to help
students understand what happens to the two blocks of ice. Review with
the student the difference between static and kinetic friction.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Two bricks are resting on the edge of the lab table. How could you
determine which of the two bricks is most massive without lifting either
brick? What difference will you observe, and how can this observation lead
to the necessary conclusion?
What’s the point?
Inertia is not a force. A person riding in the dump truck would claim that
the two blocks of ice would have the same acceleration toward the outside
of the truck. Real forces cannot accelerate two objects with different
masses with the same acceleration. Centrifugal force is a fictitious force,
a result of the observer watching the motion of objects from a non-inertial
reference frame.
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UNIT
3
Circular Motion and Gravitation
Vertical Circles
EK
|
2.B.1, 3.A.1, 3.A.2, 3.A.3, 3.B.1,
3.B.2, 4.A.2
SP
|
1.1, 1.4, 2.1, 2.2, 5.1, 7.1
Prepare
It is more important that your students understand the conceptual ideas
involved in circular motion than be able to solve single problems for
numeric answers.
Teach
There is almost always a point on the paragraph-length response for
logical flow. Nicknamed the “story point,” we are looking for the response
to be connected to the question and then the evidence that they are
citing has to have a logical flow, connect to the other pieces of evidence,
and make a complete argument. The conclusion needs to be supported by
the flow of ideas.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the question below:
If the string was cut at Point Q (which is a height L above the ground) when
the ball has a speed v, sketch the path the ball takes before it hits the
ground. Derive an expression for the time the ball takes to hit the ground.
What’s the point?
An object swung by a string in a vertical circle, that just barely makes it
around a circular path, has a tension approaching zero at the top of the
path. The tension always is lowest at this point for an object moving in a
circle at constant speed.
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UNIT
3
Circular Motion and Gravitation
Maximum Speed Over the Top
EK
| 2.B.1, 3.A.2, 3.A.3 , 3.B.1, 3.B.2, 4.A.2
SP
|
1.1, 1.4, 2.1, 2.2, 6.1, 7.2
Prepare
When an object is just barely in contact with a surface, the normal force
approaches zero. The normal force will always be perpendicular to the
surface. Students not only need to be able to write force equations but
must also be able to understand what the forces are doing.
Teach
If students choose the direction of the acceleration to be the positive
direction, they won’t have to deal with having a negative acceleration or
negative net force. While this is not necessary to be correct, it does make
the analysis simpler.
Feeling “weightless” does not mean that there are no forces on you.
Astronauts feel weightless when they are in free fall, students at an
amusement park feel weightless when they crest over the top of a
hill, and sky divers feel weightless when they jump out of an airplane.
Weightlessness implies that the person (or object) is in free fall, subject
only to the force of gravity.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A roller coaster approaches the first loop de loop. Draw a free-body
diagram of one of the coaster cars when it is at the top of the first loop.
Starting with Newton’s second law, derive an expression for the minimum
speed of the car without it losing contact with the track. When the car
was on top of the hill, the same expression was derived for the maximum
speed. In a few short sentences, explain how the same expression can
represent both the minimum and maximum speed.
What’s the point?
The speed of an object just barely traveling over a hill is independent
of mass.
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UNIT
3
Circular Motion and Gravitation
Horizontal Circles
EK
|
2.B.1, 3.A.2, 3.A.3, 3.B.1, 3.B.2, 4.A.2
SP
|
1.1, 1.4, 2.2, 5.1, 6.1, 7.2
Prepare
Students might struggle with the friction force being drawn toward the
center of the turn. Commonly included (incorrect) additional forces are a
centripetal or centrifugal force.
Teach
When students are asked to explain their reasoning using physical
principles without manipulating equations, the readers are looking for
students to explain without deriving an equation. They can reference an
equation from the equation sheet but should not rearrange it. A verbal
explanation is preferable to doing algebra.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
An object of mass m moves on a curved path from point X to point Y.
Which of the following diagrams indicates a possible combination of the
net force F, exerted on the object, the velocity v, and the acceleration a of
the object at the location shown.
What’s the point?
The centripetal force is not an additional force to be drawn on a free-body
diagram. The centripetal force is the name we give to the force(s) that
is(are) responsible for making an object move in a circle.
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UNIT
3
Circular Motion and Gravitation
Mass and Frictional Force
EK
|
2.B.1, 3.A.2, 3.A.3, 3.B.1, 3.B.2, 4.A.2
SP
|
1.1, 1.4, 2.1, 2.4, 5.1, 6.1, 7.1
Prepare
If you have a rotating platform, or even a lazy Susan, you can do this
demonstration for your students and/or let them experiment with
it themselves.
Teach
Students will need to know how to solve problems mathematically and
be able to explain what they are doing at each mathematical step. This
can be practiced in class or on homework assignments. The quantitativequalitative translation (QQT) question on the AP Physics 1 Exam requires
students to explain a physical scenario in words and using mathematical
relationships. Also, students will need to dissect statements for
correctness or incorrectness.
This scenario can be demonstrated in class using a turntable and an
object placed on the turntable. Ask students to predict the behavior of the
object depending on the position, mass, etc.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Two objects made of the same material are placed on a rotating table, at
different locations. The object closer to the center is double the mass of
the object farther from the center. If the platform begins to rotate, which
object is more likely to slip? Explain with words and equations.
What’s the point?
Radius and velocity can affect if an object slips while rotating, while mass
does not.
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UNIT
3
Circular Motion and Gravitation
The Rotor Ride
EK
|
2.B.1, 3.A.2, 3.A.3, 3.B.1, 3.B.2, 4.A.2
SP
|
1.1, 1.4, 2.2, 4.1, 5.3, 6.1, 7.1
Prepare
There are videos of this ride than can be found online if your students are
not familiar with the setup.
Teach
Is there a frictional force initially in the direction of motion allowing Carlos
to get up to speed v ? Yes! But once he is at a constant speed, he doesn’t
need that force anymore to keep him moving at a constant speed (ignoring
resistive forces).
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A race car travels along a banked track. Sketch a free-body diagram for the
car as it rounds a banked curve. Which way does the frictional force point?
If the speed of the car were doubled, how would this affect the net force
acting on the car? What change(s) could be made to keep the car on the
track at the higher speed?
What’s the point?
Being able to linearize a graph and from that determine some property of
the physical situation is a critical skill on the AP Physics 1 Exam.
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UNIT
3
Circular Motion and Gravitation
The Conical Pendulum
EK
|
2.B.1, 3.A.2, 3.A.3, 3.B.1, 3.B.2,
3.G.1, 4.A.2
SP
|
1.1, 1.4, 2.1, 2.2, 5.1, 6.1, 7.2
Prepare
Students should never draw a diagram with the
components of the forces drawn in, as shown
at right, on the free-body diagram spot on the
AP Physics Exam. That spot on the exam is for
the forces only (not components). However, this
doesn’t mean that students can’t draw a diagram
with the components to help them with their
analysis; it just can’t be on the free-body diagram
spot on the AP Physics Exam.
Teach
Remember to have students think about the direction of the acceleration
before breaking forces into components. Since this object is rotating
in a circle, the acceleration is directly to the right—toward the center of
the circle. So, in this case, the force of tension is not pointing parallel or
perpendicular to the acceleration and therefore should be broken into
components in order to solve other parts of the problem.
In Part B (ii), students need to refer to the equation sheet to see what
happens to the values of sine and tangent as the angle goes to
90 degrees. If your students struggle mathematically, this could easily be
turned into a paragraph-length response, and the mathematical derivation
could be skipped.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
The students collected the period and the angle of the swing (while the
mass and the length of the string were held constant). Starting with the
equation derived in Part B (i), derive an equation that relates the period to
the angle. What could be graphed so that a linear graph could be created?
What would the slope of the graph be equal to?
A flying pig toy is attached to the ceiling using a string that can spin
about the connection point on the ceiling. Using only a meterstick, what
measurements could be made to calculate the period of the pig’s motion?
Alternately, using only a meterstick and a stopwatch, what measurements
could be made to determine the mass of the pig? how would these
measurements be used in the calculation? If the mass of the pig were
increased, how would this affect the speed of the flying pig? Explain.
What’s the point?
Being able to understand a mathematical expression and make
connections between that representation and the physical scenario is an
important skill for the AP Physics 1 Exam.
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UNIT
3
Circular Motion and Gravitation
Centripetal vs. Linear Acceleration
EK
|
2.B.1, 3.A.2, 3.A.3, 3.B.1, 3.B.2,
3.G.1, 4.A.2
SP
|
1.1, 1.4, 2.2, 5.1, 6.1
Prepare
Before you work this question with your students, make sure that they
have seen a problem involving a conical pendulum (i.e., the flying pig) so
that the students have experience drawing free-body diagrams of objects
in circular motion where one of the forces is at an angle.
Students need practice taking the components parallel and perpendicular
to the acceleration to be able to simplify the analysis of a situation.
Teach
This problem draws the students’ attention once again to the importance
of choosing the direction of acceleration before the free-body diagram
is drawn. This will allow them to sketch the correct vector lengths and
appropriately find components of vectors if needed.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A conical pendulum is formed by attaching a ball of mass m to a string
of length L and then allowing the ball to move in a horizontal circle. If the
string is known to break if the tension exceeds T c , what is the maximum
speed the ball can have without breaking the string?
What’s the point?
Normal forces on a given object are not always equal to the weight of
the object.
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UNIT
3
Circular Motion and Gravitation
Friction as the Centripetal Force
EK
|
2.B.1, 3.A.3, 3.G.1
SP
|
2.2, 4.1, 5.3, 6.1, 7.2
Prepare
This investigation can be prepared by gluing strips of wood to short PVC
pipes. Place the end of the PVC pipe onto the end of a ring stand, and the
whole apparatus should swing freely.
Teach
There are no units for the coefficient of friction, so this is one time where
the students are getting an answer that they can leave unitless!
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Which moves faster in m/s on a merry-go-round: a horse on the inside
or a horse on the outside near the outer rail? Explain using the equation
derived in Part B.
What’s the point?
Remember that in this case, friction is providing the centripetal force!
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AP Physics 1
Workbook
UNIT
3
Circular Motion and Gravitation
Inertia in Space
EK
|
3.A.3, 3.B.2, 4.A.2
SP
|
1.1, 1.4, 4.1, 5.1, 6.1, 7.1
Prepare
Students are familiar with gravity on Earth but may not be aware that you
can create the “feeling” of a gravitational force with circular motion. While
there is gravity “in space,” for example, between Earth and the moon, this
question takes place far far away from massive bodies, so we will ignore
any gravitational forces. Check that students understand that this means
that objects are subject to the law of inertia: An object in motion will
continue in motion. Remind students about the idea of different reference
frames studied in Unit 2.
Teach
The idea of using circular motion to produce artificial gravity has
been used throughout cinema. Finding a clip from a TV show or movie
could help students visualize the idea better. Also, be aware of the
misunderstanding of the “centrifugal” force that some students may
believe is present. Parts C and D may be hard for students to visualize.
Other examples of artificial gravity include twirling a bucket filled with
water in a vertical circle, a salad spinner, a centrifuge with a precipitate
solution, or even a clothes dryer.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
If a person moved closer to the center of the space station, would they
experience an artificial gravity that is greater than, less than, or the same
as 9.8 m/s/s? Why?
What’s the point?
Circular motion can be used to create artificial gravity.
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AP Physics 1
Workbook
UNIT
3
Circular Motion and Gravitation
Gravitational Fields
EK
|
2.A.1, 2.B.1, 2.B.2, 3.C.1, 3.G.1
SP
|
2.1, 2.2, 4.1, 5.1, 6.1, 7.1
Prepare
Before assigning this worksheet, students should have been introduced
to the equation for Newton’s law of universal gravitation. If your students
have already taken chemistry, they may be familiar with the equation for
the electric force, and a discussion about the differences and similarities
would be helpful.
Teach
This is a good place for two things: (1) to practice mathematical
estimation with students and (2) to introduce the idea of fields as a way to
discuss force.
1) For making mathematical estimates, have students estimate
the gravitational force between themselves and Earth without a
calculator. They can round the universal gravitational constant
(6.67 × 10−11 Nm 2/kg 2) to 7 × 10−11. The mass of Earth (5.98 × 1024 kg )
can be rounded to 6 × 1024 , and the distance between themselves and
Earth (the radius of the Earth 6.38 × 106 m ) can be rounded to 6 × 106 .
Then they can multiply and divide easily. (Remind your students if
necessary that when multiplying exponents add, and when dividing
exponents subtract.)
2) While the idea of an electric field is not assessed on the AP Physics 1
Exam, your students will find the idea of electric field extremely difficult
if they haven’t studied the foundational idea of the gravitational field.
Talk to students about how we can measure the gravitational field by
dividing the gravitational force felt by an object by the object’s mass—
allowing us to create a map of how much force per mass an object
would experience at every point around a massive object. Discuss the
size and the direction of the gravitational field. At Earth’s surface, it is
mostly uniform and directed straight down, but then when we consider
Earth as a sphere, the gravitational field points inward, toward the
center of Earth.
Students may not be aware that there is a universal force of gravitation,
and by using Earth’s dimensions, we can calculate the accepted
acceleration due to gravity. This relationship can be applied to any pair
of objects to determine the attractive force between them. When given
a formula, students will be responsible for checking if it makes physical
sense. They need to be taught to check the relationships. For example,
do the variables appear in the numerator or dominator and how does
changing the variables affect the equation as a whole?
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
How does the radial distance away from the center of a planet affect the
acceleration due to gravity? If you were on the top of a mountain and
dropped an object, would that object feel the same force compared to if
you dropped it standing at the surface of the planet?
What’s the point?
When doing derivations, mistakes can happen, but if you check the
units and also check each variable to make sure that what you expect
to happen is represented by your equation, you’ll be more likely to catch
any mistakes!
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AP Physics 1
Workbook
UNIT
3
Circular Motion and Gravitation
Newton’s Law of Universal Gravitation
EK
|
2.B.1, 2.B.2, 3.A.4, 3.C.1, 3.G.1
SP
|
2.1, 2.2, 5.1, 5.3, 6.1, 7.2
Prepare
Geosynchronous means that the object orbits along with the surface of
the moon, staying over one place on the surface and having the same
period of rotation as the surface: T satellite = T surface .
Teach
Have your students finish this activity. They have a linearized graph with
a best-fit line. Have them calculate the slope of the graph. (It should be
about 3 × 10−16 s 2/m 3 .) From that, have them calculate the mass of Jupiter.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
What would happen to the period of the moons if the mass of Jupiter was
increased? What if the mass increased, but the density of the planet did
not change?
What’s the point?
R3/T 2 is a constant value for objects undergoing circular motion around a
particular planet.
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AP Physics 1
Workbook
UNIT
3
Circular Motion and Gravitation
The Gravitational Force
EK
|
2.B.1, 2.B.2, 3.C.1, 3.G.1
SP
|
2.1, 2.2, 5.1, 6.4, 7.2
Prepare
Students often make the same mistake as Angela: They think the mass
of an orbiting object matters when calculating the orbital period. When
looking at the arguments made, students will need to be able to find
both correct and incorrect statements. They also need to be able to
support their arguments mathematically. Students need to be able to see
relationships in equations as well as the effect that changing one variable
has on the other variables in those equations.
Teach
Even though it is not part of the question, you should have the students
think about their responses before they do the analysis—have them think
about the statements and circle correct statements.
Have students go through the arguments and determine whether each
statement (1) correlates to the data table and (2) represents correct
physics. If the statement represents incorrect physics, what is the
correct physics?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Using the correct components of all the arguments and the steps of the
equations made in Part A, write a paragraph describing the relationship
between the period, radius, and gravitational force between the planets
and the sun.
What’s the point?
Period, radius, and gravitational force all influence one another.
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AP Physics 1
Workbook
UNIT 4
Work and Energy
Misconceptions
Force and energy are probably the two most universal concepts in physics.
It has already been mentioned that students have an instinctive physiological
understanding of forces. Unfortunately, they do not have a clear understanding for
energy, which is probably not too surprising since energy is an abstract quantity that
we only use because it is conserved.
One difficulty with energy is that there are many types of energy, and there is also
the process of energy exchange. The most common types of energy are “kinetic”
and “potential.” In AP Physics 1, the only type of transfer students must use
quantitatively is “work.” “Heating” is used conceptually but is primarily a subject
of AP Physics 2. Kinetic energy is a property of objects that are in motion and is
defined by a mathematical relationship. Potential energy is an energy stored in a
system due to its configuration—it is always due to a conservative interaction. Energy
exchanges—work and heating—transfer energy between the system of interest
and its surroundings. Work is a transfer of energy by a mechanical process (a force
exerted on an object or system as it moves through a displacement in the direction
of the force). The amount of energy transferred in this process is referred to as the
work done. Heating is a transfer of energy through a thermal process. The amount
of energy transferred in such a process is referred to as heat. Unlike types of energy,
heat and work are not the property of an object or system but describe interactions
between them. Students often believe that an object can “hold” or “have” potential
energy just because it is “high.” Working with students to define systems will help
students grasp the ideas of energy and energy conservation.
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AP Physics 1
Workbook
Scenario
Misconception
4.B, 4.C, 4.F, 4.H, 4.I, 4.J,
4.K, 4.L, 4.M
Energy gets used up or runs out.
4.F
A force acting on an object does work even if the object
doesn’t move.
4.B, 4.H, 4.I, 4.J, 4.N
Something not moving can’t have any energy.
4.B, 4.C, 4.F, 4.H, 4.I, 4.J,
4.K, 4.L, 4.M
Energy is destroyed in transformations from one type to another.
4.B, 4.C, 4.F, 4.H, 4.I, 4.J,
4.K, 4.L, 4.M
Energy can be recycled.
4.B, 4.I, 4.K
A single object can “hold” gravitational potential energy.
4.D, 4.H, 4.J, 4.K, 4.N
Gravitational potential energy is the only type of potential energy.
4.G, 4.H, 4.I, 4.J
The same types of energy exist, regardless of the system.
4.C, 4.F, 4.G, 4.L, 4.M, 4.O
4.B, 4.E, 4.G, 4.L, 4.M, 4.O
4.A, 4.E
4.B, 4.F, 4.J, 4.K
When an object is released to fall, the gravitational potential
energy immediately becomes all kinetic energy.
Energy is not related to Newton’s laws.
Energy is a force.
The gravitational potential energy lost is always equal to the
kinetic energy gained.
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AP Physics 1
Workbook
Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Create and use force vs. displacement graphs
Using Representations
4.A, 4.I
1.1
Draw a best-fit line through data.
Using Representations
4.A, 4.G
1.1
Create and use energy bar charts.
Using Representations
4.B, 4.G, 4.H, 4.J, 4.K
1.1
Create and use energy vs. position graphs.
Using Representations
4.C
1.1
Create and use energy vs. time graphs.
Using Representations
4.C
1.1
Create and use free-body diagrams.
Using Representations
4.B, 4.G, 4.H
1.1
Identify systems.
Using Representations
4.A, 4.B
1.1
Plot data on a graph.
Using Representations
4.A, 4.B
1.1
Scale and label axes.
Using Representations
4.B
1.4
Relate the area under the curve to a physical quantity.
Quantitative Analysis/Data Analysis
4.A
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
4.A
1.5
Match shapes of graphs to relationships between variables.
Data Analysis
4.A, 4.C, 4.H
1.5
Re-express one type of graph as another.
Using Representations/Argumentation
4.M
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
4.A, 4.E, 4.F, 4.L, 4.M, 4.O
2.2
Derive or calculate including annotations.
Quantitative Analysis
4.E, 4.L, 4.M, 4.O
4.2
Design an experiment to answer a specific question.
Experimental Design
4.D
5.1
Determine if data is reliable.
Data Analysis
4.G, 4.L
6.1
Identify a claim and evidence that can support that claim.
Argumentation
4.D, 4.E, 4.F, 4.G, 4.I, 4.J, 4.K, 4.M,
4.N, 4.O
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Work
EK
|
3.E.1, 4.C.2, 5.A.3, 5.B.1, 5.B.5
SP
|
1.1, 1.4, 1.5, 5.1, 6.1, 7.2
Prepare
It might be helpful to review the relationships between acceleration vs. time,
velocity vs. time, and position vs. time graphs as well as the relationships
of the graphs to the kinematic equations found on the equation sheet.
Up to this point, it has only been clear where the expressions for velocity
and position as functions of time for constant acceleration have come
from. The third equation below has simply been presented as an algebraic
manipulation between the first two to eliminate time:

v v x 0  at
x x0  v x 0t  12 a x t 2
vx 2 
v x20  2a x ( x  x0 )
For a graph of velocity vs. time, the first equation represents the velocity as
a function of time, where the acceleration is the slope, and the y-intercept is
the initial velocity of the object. To help students develop an understanding
of the relationship between velocity and displacement and the relationship
between work and the change in kinetic energy for an object, it is helpful
to carefully go over this derivation and then to discuss the relationship of
acceleration to force (multiply both sides by m). If you then divide through
by 2, you will see that this equation gives that the work done on an object is
equal to its change in kinetic energy. It is important to point out that this is
only true for something for which the object model holds (that all points on
the thing being considered move in the same way—that there is no squeezing
or turning). If the thing being pushed on were, for instance, a spring, which
cannot be modeled as an object since it can be squeezed or stretched, some
of the work would go into changing the potential energy stored in the spring.
Teach
The more different kinds of questions you ask your students, the better
prepared they will be for the kinds of questions they will see on the
AP Physics 1 Exam. Practice asking them about different relationships
besides those you would typically find in a textbook question. For example,
a typical textbook might ask students to calculate the work done by a
person exerting a force up a ramp on a piano while the piano slides down
the ramp at a constant speed. Instead of just asking them to calculate the
work, ask the students to determine if work is being done. How do they
know? What system are they analyzing? What data could they graph to
determine the work done on the piano? Does this representation give the
same value of work as their calculation? Have the students annotate their
calculation, or if they are proficient at annotation, just have them write out
how the work should be calculated without calculating the value.
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Additional questions for this page:
A. The graph shows the force applied to the cart as a function of position
for x = 0m to x = 20m . Explain how you could determine the work
done on the cart for the whole displacement.
B. Explain how you could find the final speed of the cart.
C. Describe the motion of the cart after x = 20m . (Remember that
describing the motion includes a discussion of what happens to the
position, velocity, and acceleration of the cart.)
D. Have the students use the graph given in the prompt to determine
the velocity after every meter and then plot the data. Does this
make a linear graph? What could they graph in order to get a linear
relationship? What should the slope of this graph be? (Hint: 8!)
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
1. How can the results of Part B be used to support the graph in Part E?
2. Suppose you are riding your bike traveling at 5 m/s and apply your
brakes to avoid hitting a dog that has run into your path. Compared
to the stopping distance when traveling at 5 m/s , how much more
distance would it take you to stop if you were traveling at 10 m/s?
Explain.
What’s the point?
Work is done by a force if it changes the energy of the object or system.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Choosing Systems
EK
|
5.A.1, 5.A.2, 5.A.3, 5.A.4, 5.B.1
SP
|
1.1, 1.4, 1.5, 2.1, 4.1, 6.1
Prepare
Energy bar charts are extremely useful in analyzing problems but only
if students see them as a tool and not as busy work. Picking problems
that become simpler when analyzed with bar charts can help convince
reluctant students.
Teach
It is important to remember that when students are asked to sketch a freebody diagram, the force vectors must touch the dot. Vectors that are near
the dot will not be given credit.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
A ball is thrown into the air with initial speed v0 . Sketch the following graphs
from just after the ball is thrown until the ball reaches the highest point:
Position vs. time
Velocity vs. time
Acceleration vs. time
Net external force vs. time
Net external force vs. height
What’s the point?
While students are free to choose their own systems when analyzing a
problem, the choice of system has the ability to make a problem simpler
or more complex. Also, often on the AP Physics 1 Exam, the students will
be given the system they are to analyze, so they need to be comfortable
analyzing different systems.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Energy Graphs
EK
|
4.C.1
SP
|
1.1, 1.4, 2.1, 2.2, 6.4
Prepare
Graphing can be tricky for students. If your students struggle with knowing
how to start a problem that gives them a blank axis, remind them that
they can earn critical points by plotting things they know to be true. For
example, in this problem at the maximum height, the gravitational potential
energy is at its maximum value.
You also may want to consider reviewing the graphs of height, speed, and
acceleration vs. time before starting in on energy graphs. If your students
have yet to consider graphs of velocity vs. height or acceleration vs.
height, now would be a good time because it would help prepare your
students for this page.
Teach
Lines without labels could earn an otherwise perfect graph zero points.
Be sure to have your students label whenever they draw any sort of graph.
Take the y-values at several points on the graph of energy vs. distance
fallen. Have students add the energy values of K and Ug together, point
out that those always sum to the if mechanical energy is conserved.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Discussion question: What about the graphs would change if the ball was
thrown with an initial horizontal velocity?
Quick Quiz
A cart is released from rest at the top of a smooth incline and the Earthcart system has 6 joules of gravitational potential energy at the top of
the incline (relative to the bottom of the incline). When the cart has rolled
halfway down the incline, the cart’s kinetic energy will be:
A. Greater than 3 joules
B. Less than 3 joules
C. Equal to 3 joules
D. Unknown without the cart’s mass
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When the cart has rolled halfway down the incline, the cart’s speed will be:
A. Half its speed at the bottom
B. Greater than half its speed at the bottom
C. Less than half its speed at the bottom
D. Unknown without the cart’s mass
What’s the point?
While graphs of position, velocity, and acceleration vs. time are
the cornerstone of physical representations, students need to feel
comfortable with many more representations.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Spring Potential Energy
EK
|
5.B.4
SP
|
4.1, 4.2, 4.4, 5.1, 6.1, 7.1
Prepare
There are many ways of designing this experiment. You may want to be
prepared with some common equipment so that students can test their
ideas.
Teach
Have students switch papers and critique each other’s procedure for
clarity. Could they follow the procedure as outlined?
Designing a basic experiment is a great way to test for conceptual
understanding.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
“An experiment is made with a spring fixed to a cart that lies on a track that
exerts negligible friction. Students decide to compress the spring and
let the system oscillate. They will use a timer in the center of the motion,
where the speed is highest, to measure how long it takes the cart to travel
a measured distance. From there, they will compare the maximum kinetic
energy to the spring energy.
What sources of error do you see presented here?
How could this error be minimized?
What’s the point?
Just as with gravitational potential energy, the definition of spring potential
energy depends on the difference in stretch lengths from a reference
position. Be careful to differentiate the lengths of the spring for each part
and keep them clear for yourself and the AP graders.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Comparisons of Work by Identical Forces
EK
|
3.E.1
SP
|
1.4, 2.2, 6.4, 7.4
Prepare
In demonstrating this scenario, it may benefit the students to push an
object up a ramp in each one of the manners shown. They will be able to
feel the difference in effectiveness between the two methods.
Teach
The θ in the work equation W = Fdcosθ, is the angle between the force exerted
on an object and the object’s displacement vector. Drawing a free-body
diagram will be extremely helpful in this situation! Students often struggle with
what angle to put in the equation. Starting with a free-body diagram will help.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Extension question: What is the minimum value of F in Case B for the
block to still rise?
Quick Quiz
Shown are graphs of position vs. time for two boxes being pushed across a
rough horizontal surface. A student who is using these graphs to compare the
net work being done on the two boxes between the two marked points says:
“I think that more net work is done on the box in Graph B because the
displacement of Box B is greater than the displacement of Box A.”
What about the student’s argument is correct?
What about the student’s argument is incorrect?
What’s the point?
Work depends on the angle between the applied force and the
displacement of the object, not just on the force and the displacement.
So the same force exerted on an object with the same displacement can
do differing amounts of work.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Energy Transformations
EK
|
5.B.4
SP
|
1.1, 1.4, 2.2, 6.1, 7.2
Prepare
Reflecting back on projectile motion problems can help kids grasp what
will happen in Parts A and C. Having trouble recalling? Take a ball and roll
it off the table while dropping another one at the moment the first leaves
the edge.
Review average vs. instantaneous velocity with students before this page.
Teach
Students can ramble on when answering Part A (i). Make sure to
encourage them to read ahead, so they can pace the argument they are
building to match what the questions are asking.
When you get to rotation, bring this question back and add in a ramp with
a rolling ball.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
In Cases A, B, and C above, rank the boxes by the amount of work done by
the gravitational force from greatest to least. Justify your ranking.
In Cases A, B and C above, rank the boxes by the change in kinetic energy
from greatest to least. Justify your ranking.
What’s the point?
There are times when an object can have a larger final velocity than an
identical object that covers an identical displacement.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Circular Motion, Forces, and Energy
EK
|
5.B.4
SP
|
1.1, 1.4, 2.1, 5.1, 5.3, 6.1, 6.4
Prepare
Students will need to recall from Unit 3 that the car has a minimum velocity
where it can complete the loop. This parameter is set by requiring the
normal force to be greater than zero and pointed inward.
Teach
Students might not even worry about it yet, but it’s worth mentioning that
later students will learn about energy of rotating objects.
If students choose to use a line on the graph to answer Part F, it is
important to have the line as close as possible to all points and as many
points above the line as below for it to be considered a line of best fit.
Assess
To further assess student understanding of the concepts addressed in this
scenario, you may want to assign students the following activity follow up:
Have the students use an online applet to construct a track with a loopde-loop. Have them turn on the bar chart while using a frictionless track
to check their answers to Part B. Have them release the skater lower and
lower until the skater cannot complete the loop.
To challenge students, have them determine the minimum starting height
required for the car to complete the loop-de-loop of radius r.
What’s the point?
Connecting circular motion, forces, and energy is a great way to check
your knowledge and problem-solving skills! On the AP Physics 1 Exam,
you will be expected to make connections between the skills and
understanding from several units to answer a single question.
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AP Physics 1
Workbook
UNIT
4
Work and Energy
Potential Energy and Choice of Zero
EK
|
5.A.4, 5.B.4
SP
|
1.1, 1.4, 2.2, 4.1, 5.1, 6.4
Prepare
Try exploring with oscillating springs using online simulations. While they
aren’t replacements for hands-on inquiry-based laboratory investigations,
adding online simulations can help students gain a conceptual
understanding of concepts that are difficult to envision in the classroom.
Teach
It is important to emphasize that there are two ways to go about a spring
problem. If Earth is included in the system, meaning gravitational potential
energy will be considered during the oscillation process, then the spring
has no gravitational or elastic (spring) energy at its natural rest length. Only
the block’s gravitational potential energy affects the calculations. This is
how this problem is structured. If Earth is not included in the system, we
don’t need to even consider the work done by gravity on the block-spring
system if we consider the equilibrium position of the spring-block system
to be the location where the spring has zero potential energy.
This is a great place to preview simple harmonic motion. You can discuss
simple oscillation and even have students see if the period of the oscillating
mass depends on the amplitude. Have them make a prediction, starting
with fundamental principles of physics and then design an experiment
to test their prediction. Their analysis should end with a graph of their
collected data that can either defend or reject their original hypothesis.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the question below:
How does choosing a different place for gravitational potential energy to
be zero change energy calculations?
Give each student the problem of finding a block’s maximum velocity
when oscillating on a spring. Give all the students the same mass block
and spring constant but predefine different locations to be called h = 0.
Have students compare work and they will see that the supporting work is
different for each h = 0 position, but the final answers are all the same.
What’s the point?
Regardless of where the zero point is chosen for gravitational potential
energy, the analysis yields the same result. In both cases, the KE value
is one joule, leading to the exact same calculation for the velocity of the
block as it passes through equilibrium.
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UNIT
4
Work and Energy
Gravitational Potential Energy
EK
|
5.B.3, 5.B.5
SP
|
1.4, 2.2, 6.4, 7.2
Prepare
Students will need to know Newton’s law of universal gravitation as
well as the equation for the gravitational potential energy of a system
of two objects (not on Earth’s surface). Discuss the implications of
the negative sign, emphasizing that negative energies correspond to
gravitationally bound systems, and the largest Ug value is zero, which is
obtained only at r = infinity.
Teach
“Newton’s cannon” can be a good visual for students to understand orbits
and the concept of escaping a planet’s gravitational pull. A quick internet
search will uncover several good Newton’s cannon applets.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Provide mass and radius data on several astronomical objects, such as
Earth, the moon, the sun, a black hole, etc., and have students find the
energy needed to escape their gravitational pull.
Ask students to write a few sentences on how they could find the escape
velocity for a planet using the ideas of conservation of energy. A challenge
for mathematically talented students would be to calculate the escape
speed for a set of planetary objects, including a black hole. What are the
repercussions of the escape speed for a black hole?
What’s the point?
This problem connects force, work, potential energy, and kinetic energy
without using the constraint that g is constant. Part D can be compared to
a situation close to Earth where g remains constant.
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UNIT
4
Work and Energy
Impact of Mass on Conservation of Energy
EK
|
4.C.2
SP
|
1.1, 1.4, 6.1, 6.4
Prepare
It is important to emphasize that numbers are not always needed on a
bar chart because the ideas and concepts can still be represented with
relative or estimated values. Giving students opportunities to do this
without numbers is a good practice.
Teach
The energy dissipated by friction stays in the defined system as ETherm.
ETherm continues to increase through the entire distance of the slide,
including when the spring is being compressed. If this presents too
much of a challenge for your students, have them do the problem once
where there is negligible friction and then again later, when they feel more
comfortable with energy, with the addition of kinetic friction.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Explain what would happen to the angle necessary to make the box slide,
the speed v, the distance d , and the distance x if the coefficient of static
friction was greater than originally stated.
For students who need a challenge:
Mathematically find the coefficient of friction from the variables given in
the problem (m , d , k , x , θ, g ).
What’s the point?
It is not often that the value of the total mechanical energy of a system
decreases because we often ignore friction when analyzing situations
in AP Physics 1. This is a good problem to highlight what happens when
friction is included using the bar chart.
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UNIT
4
Work and Energy
Energy in Systems
EK
|
4.C.2, 5.B.1, 5.B.2
SP
|
1.2, 1.4, 1.5, 2.2, 6.2, 7.2
Prepare
Before assigning this worksheet, it is important that your students
understand what each of these pieces of a car does, and you’ll want to
have discussed chemical and thermal energy. While not analyzed in-depth
or directly tested in AP Physics 1, chemical and thermal energy are still
forms of energy and conservation rules still apply.
Teach
There are LOTS of different possibilities for correct answers. Have
students switch papers and peer grade—they are looking for common
features—that is, that the total energy remains constant from beginning to
end. Require them to defend their answers to each other.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
How can creating different representations of the same physical scenario
help us better demonstrate our understanding? Give students energy
bar charts and have them write a context for a problem where the given
energy bar chart would be correct.
What’s the point?
Systems with and without Earth are explored in a variety of ways during
this problem.
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UNIT
4
Work and Energy
The Sign of Work
EK
|
5.B.5
SP
|
2.1, 2.2, 4.4, 5.1, 5.3, 6.4
Prepare
Have a discussion on outlying data, how we know what data might be an
outlier, and what should be done about it.
Teach
While free-body diagrams and energy bar charts are not “directly” a part of
this question, students should be sketching both to help them analyze the
situation and provide evidence for claims. While on the AP exam students
are usually asked to draw a free-body diagram if it will be helpful to the
analysis, they are not ALWAYS asked to do so.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
Is there a combination of coefficient of friction and angle such that Block 2
would slide with constant kinetic energy? Draw an energy bar chart of
that situation.
What’s the point?
There is often more than one way to analyze a physical scenario. In
this case, even though this is the energy unit, encourage students to
analyze the way that they feel the most comfortable and then challenge
themselves to look at it a new way.
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UNIT
4
Work and Energy
Energy and Projectile Motion
EK
|
5.B.4
SP
|
1.4, 2.1, 2.2, 6.4, 7.2
Prepare
Projectile motion concepts are in use here. Flight time is only dependent
on vertical components. Review projectile motion before assigning
this worksheet.
Teach
Sketch the drawing at the extremes in the trajectory of the person.
Assess
To further assess student understanding of the concepts addressed
in this scenario, you may want to assign students the following
activity application.
Activity application
Have students set up this ride using thread and a ball with a hole through
it. Cut the string at the bottom of the path (because balls don’t have hands,
so they cannot let go of the string) perhaps using a razor attached to a ring
stand. The ball will enter into a parabolic trajectory, and the students can
predict the ball’s landing location.
Setup tip
Tie the ball up using additional thread and burn that thread to start the “ride.”
What’s the point?
Maximization problems are applicable to many real-life concepts.
Challenge students to find the best length of rope L to maximum
distance D. They should show graphical proof of the answer.
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UNIT
4
Work and Energy
Potential Energy of Systems
EK
|
4.C.1, 5.B.2, 5.B.3, 5.B.4, 5.B.5
SP
|
2.2, 4.1, 5.3, 6.1, 7.1
Prepare
This configuration can be made in the classroom with an embroidery
hoop, springs, and a small object. The students can try moving the object
using a spring scale.
Teach
Address the differences in work done on systems by external forces and
the work done by systems.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Did Spring C do positive work, negative work, or no work on the object in
figure 2?
Positive work
Justify your reasoning.
Negative work
No work
Spring C does do positive work on the mass because the force of just
Spring C is down-left and the mass’s displacement is left, so force and
displacement are acute, which means that positive work is done.
What’s the point?
Potential energy, just like work, is a scalar so when you have a system
with many components contributing to the potential energy, the potential
energies just add. This is similar to a group of several moons: To find the
potential energy of the set of moons, find the potential energy of each pair
and add the energies together.
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UNIT
4
Work and Energy
Conservation of Energy and Circular Motion
EK
|
5.B.4
SP
|
2.2, 4.1, 5.1, 6.1, 7.2
Prepare
Again, although drawing free-body diagrams and energy bar charts are not
expressly part of this question, students who have gotten into the habit of
drawing them will find this question much more accessible.
Teach
The mathematical derivations in this problem are quite lengthy and probably
beyond the scope of the AP Physics 1 Exam. If your students get stuck
in the derivations, give them the derivations and ask them to finish the
question by identifying the steps that could support the engineer’s claims.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
For extra excitement, a new roller-coaster ride is being designed so that
the riders are launched into the air over a moat before landing back on the
track on the other side. Will the maximum height of the cart in the air, be
greater than, less than, or equal to the height where the cart is released?
Justify your answer.
What’s the point?
Often there is more than one factor that leads to a solution, and you have
to take both into consideration to find the solution!
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Workbook
UNIT 5
Momentum
Misconceptions
When it comes to momentum and inertia, students often believe that larger objects
will always have a larger momentum, which is not necessarily the case. In terms of
conservation of momentum, students tend to place a higher value on the velocity of
an object. Students also tend to believe that conservation of momentum is only true
in elastic collisions or (better but still wrong) in isolated systems. The difference
between constant and conserved is often lost. Another challenge with this topic
is that students tend to think that force and impulse are synonymous. They do not
realize that impulse also involves how long the force is exerted on an object.
Students usually have an intuition of one aspect of momentum: its magnitude.
However, they usually do not think of the vector character of the quantity, so it is
particularly helpful to demonstrate the vector nature of change in momentum (e.g., a
ball hitting a wall and bouncing back) to show that the change in direction generates
a much larger change in momentum (and thus larger force) than a ball that hits
the wall and stops. The change in the ball’s momentum is proportional to its final
velocity minus initial velocity. On the other hand, if the ball hits the wall and stops,
the change in momentum of the ball is less than if it bounced off the wall and traveled
back the way it came. Another way to get students to start thinking about the vector
character is to present them with a situation in which two equal mass carts are
moving toward each other at the same speed. Ask them what the total momentum of
the system of two carts is initially, and they are likely to say twice the value for each
cart. Then describe the carts colliding and stopping. Ask what the final momentum of
the system is if neither cart is moving. Then ask them how/why/if the momentum of
the system changed.
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Students often relate the ideas of momentum and force. For example, if two cars of
equal mass are moving at different speeds, students will often say that the car with
the higher speed “has more force.” Try presenting students with the situation of a
car traveling at a certain speed that comes to rest by colliding with either a brick wall
or a haystack. Ask them if the passengers are equally likely to be injured in the two
collisions, and if not, why. The car has the same momentum in either case, but since
it doesn’t “have a force,” which it only experiences during the process of stopping,
the different times when these quantities are present can help students distinguish
between force and momentum. If your students are having this difficulty, it is a good
opportunity to remind them that a force is a way to describe an interaction, so always
requires two objects or systems to define.
Scenario
Misconception
5.D, 5.E, 5.F
Momentum is not a vector.
5.J
Conservation of momentum applies only to collisions.
5.B, 5.C, 5.D, 5.F, 5.H, 5.I
Momentum is the same as force.
5.A
The center of mass of an object must be inside the object.
5.A
The position of the center of mass does not change regardless of what the
objects in a system do.
5.A
The center of mass is always the same as the center of gravity.
5.C
Momentum is not conserved in collisions with “immovable” objects.
5.G, 5.J, 5.K, 5.L, 5.M,
5.N, 5.O
Momentum and kinetic energy are the same.
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AP Physics 1
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Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Create and use energy bar charts.
Using Representations
5.E
1.1
Create and use free-body diagrams.
Using Representations
5.A, 5.B
1.1
Create and use force vs. time graphs.
Using Representations
5.B, 5.D, 5.H, 5.I
1.1
Create and use momentum charts.
Using Representations
5.C, 5.E, 5.F, 5.G, 5.L, 5.M
1.1
Create and use momentum vs. time graphs.
Using Representations
5.D, 5.I
1.1
Create and use velocity vs. time graphs.
Using Representations
5.G, 5.H, 5.I
1.1
Identify systems.
Using Representations
5.A, 5.B, 5.E, 5.F, 5.G
1.1
Plot data on a graph.
Using Representations
5.D
1.1
Scale and label axes.
Using Representations
5.B, 5.C, 5.D, 5.E, 5.F, 5.G, 5.H, 5.I, 5.J
1.4
Relate the area under the curve to a physical quantity.
Quantitative Analysis/Data Analysis
5.B, 5.H, 5.I
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
5.I
1.5
Match shapes of graphs to relationships between variables.
Data Analysis
5.I
1.5
Re-express one type of graph as another.
Using Representations/Argumentation
5.B, 5.D, 5.I
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
5.A, 5.B, 5.D, 5.J, 5.L, 5.M, 5.N
2.2
Derive or calculate including annotations.
Quantitative Analysis
5.D, 5.G, 5.J, 5.L, 5.M, 5.N, 5.O
4.2
Design an experiment to answer a specific question.
Experimental Design
5.H, 5.K, 5.L
5.1
Determine if data is reliable.
Data Analysis
5.H
6.1
Identify a claim and evidence that can support that claim.
Argumentation
5.A, 5.B, 5.C, 5.D, 5.E, 5.F, 5.G, 5.I,
5.J, 5.L, 5.M, 5.N, 5.O
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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UNIT
5
Momentum
Center of Mass
EK
|
5.D.3
SP
|
1.1, 5.3, 6.1, 6.2, 6.4
Prepare
Although the equation for the center of mass will not be tested on the
AP Physics 1 Exam, showing it to your students can allow them to conduct
experiments to determine the center of mass and then justify with a
mathematical representation.
Teach
You can use popsicle sticks, paper clips, and stickers to help students
visualize where the center of mass is when the people are in different
positions. Especially for Part C, where the person moves on the board, the
center of mass won’t move, and so the board must move!
This is also a perfect opportunity to circle back and make sure that
students have internalized Newton’s third law. Ask them, “How do you
know how the board will move?”
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
How far could a person walk out on a long board hanging over the edge
of a building without tipping? This doesn’t have to involve a numerical
solution. Students can move the “person” paper clip along the long board
and see what it does to the center of mass. If you have done center of
mass demonstrations with the students, they will see that the person can
walk out until the center of mass of the system rests on the edge of the
building. While students may or may not have ever heard of a cantilever,
this is the perfect time to introduce the concept, and show them some
real-world examples of physics in action!
What’s the point?
Creating representations is not busy work. Being able to create and use
representations both shows that you understand the physical scenario
and helps you analyze and answer questions about the scenario.
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UNIT
5
Momentum
Impulse
EK
|
3.D.2, 4.B.2
SP
|
2.2, 5.1, 6.4
Prepare
The ideas represented in this worksheet provide a link between Unit 2:
Dynamics and Unit 5: Momentum. Students often forget that in physics
class nothing is taught in segmented units, never to be thought of again.
It is a good reminder to students that they are taught representations and
models so that they can apply them later to situations that might seem
very different!
Teach
Students can be asked to represent this information another way.
Remember that re-expression is a big part of the AP Physics 1 Exam. One
possible re-expression would be to create a momentum vs. time graph for
each of these scenarios. Students could also link the force vs. time graph
to position, velocity, and acceleration vs. time graphs.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
A box of mass M , initially traveling at speed v to the right is slowed to a
stop by a force F.
A. Sketch a free-body diagram for the box.
B. Sketch a momentum diagram for the scenario.
What’s the point?
Impulse is equal to the area under a force vs. time graph.
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UNIT
5
Momentum
Impulse
EK
|
3.D.2, 4.B.2
SP
|
1.1, 1.4, 2.1, 5.1, 6.4
Prepare
Throwing a raw egg at a brick wall vs. a loose hanging sheet provides
an opportunity for students to investigate the relationships between
momentum, force, and impulse.
Teach
Note that there can be many different answers for Part A since no values
were given in the problem and no scale was given on the graph. The
important features to look for when grading are to see if the first area plus
the second area in each set of graphs add to zero and the gentle stop
should have less force over a longer time than the emergency stop.
You should also consider linking this page to the real world. One way to do
that is to ask the students which would be easier to stop, a tractor trailer or
a smart car, if they were both traveling at the same speed. If your students
are of driving age and have experience driving, it is usually eye-opening
for them to think this through and reason through the dangerousness of
“cutting off” a fully loaded tractor trailer.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
Two identical cars travel toward identical barriers at two different speeds:
v1 and v2 , where v1 = 2v2 . When the cars collide with the barrier, the
barriers exert a constant force F on the cars, bringing them to rest.
A. Sketch a momentum vs. time graph for each car.
B. What is the relationship between the slopes of these graphs? Explain.
What’s the point?
Any two objects starting with the same initial momentum being brought to
rest experience the same impulse, regardless of the time it takes to stop
each object. It is the FORCE that changes based on the time over which
the collision happens.
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UNIT
5
Momentum
Change in Momentum
EK
|
4.B.2
SP
|
1.1, 1.5, 2.2, 5.1
Prepare
By this time in the year, students should be comfortable finding the area
under a curve, as well as the slope of a line, and relating them to physical
quantities. However, depending on your student population, they might
still be struggling with these ideas, and especially with Part C. If you feel
that your students will find Part C especially difficult, you can coach them
on creating a table for recording the area of force vs. time graph to help
them in creating their momentum vs. time graph.
Teach
Some parts of the shapes of these graphs should look familiar to
students. How does each graph compare to other graphs? For example,
what would an acceleration vs. time graph look like? What would a velocity
vs. time graph look like? Providing opportunities for students to link what
they are learning now with material from previous units will help them
make connections between the fundamental ideas of physics presented
throughout the course.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
An object of mass M changes its velocity from 3 m/s to the right to 7 m/s
to the left as a force acts on it for time t . Use a momentum diagram to
justify the direction of the force F.
What’s the point?
Representations come in many forms! These momentum charts are similar
to the energy bar charts you created in Unit 4. You will need to be able to
create more than one representation for a physical situation to be able to
show that you understand relationships between physical quantities.
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UNIT
5
Momentum
Conservation of Momentum (Inelastic Collisions)
EK
|
5.D.2
SP
|
1.1, 1.4, 4.1
Prepare
Students will often forget that momentum is a vector, so you will most
likely need to scaffold your instruction so that students are consistently
coached to check their momentum diagrams for consistency. That is, that
the diagrams match on the left and right side of the equal sign, showing
that momentum is conserved.
Teach
The collisions on this page are perfectly inelastic—but they could have
been inelastic without being perfect. To have students consider the
differences between inelastic and perfectly inelastic collisions, have
them sketch a situation where two identical cars collide, first perfectly
inelastically, and then inelastically. Have them write about the differences
that they see in their representations and discuss the consequences of
these differences.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
A toy truck (mass 3 M ) traveling at speed v collides head on and sticks to
a toy car (mass M ) initially at rest.
A. Sketch a momentum diagram for the collision.
B. Sketch an energy bar chart for the collision.
What’s the point?
Drawing momentum and energy charts is helpful (especially in situations
where you don’t have a numerical solution) for deciding the final states of
objects involved in collisions.
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UNIT
5
Momentum
Conservation of Momentum (Elastic Collisions)
EK
|
5.D.1
SP
|
1.1, 1.4, 5.1, 6.1
Prepare
Students often fall into a rut of solving problems using the one tool they
feel most comfortable with regardless of whether it applies or not. Being
able to think about the information given, classify it, and then move on to
solve the problem is a skill that takes practice.
Teach
It is important that you help students to understand that the choice of
system matters and choosing the “correct” system makes the analysis
of a scenario easier. The more you speak aloud your thinking, the more
students will be able to understand the steps that have to be done to solve
a problem. Analyzing a scenario by first choosing an appropriate system
should be scaffolded throughout the course and is especially important in
using energy and/or momentum techniques to analyze a scenario. The more
times that students have the opportunity to identify the system needed to
appropriately analyze, the better and more confident they will become.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Design a problem based on a collision situation that you could observe
in class that requires an understanding of impulse and momentum.
Use experimental design to show what you could do to solve the problem
you created.
What’s the point?
Choosing a system to analyze should be one of the first steps to problem
solving. Choosing a system allows you to determine what physics
principles can or cannot be applied. Choose the easiest system you
can—but watch out—often on the AP Physics 1 Exam, they will choose
for you! Make sure that you read the question and analyze the system
you are given.
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UNIT
5
Momentum
Ballistic Pendulum
EK
|
3.A.1, 5.D.2
SP
|
1.1, 1.4, 2.2, 6.1, 6.2, 7.1
Prepare
The most important step in Part C is when students justify their selection.
When this kind of question is asked on the free-response section, more
often than not, just checking the correct boxes is worth zero points. Your
students need structured scaffolded practice at explaining their thinking
in concise, logical sentences using good physics vocabulary.
Teach
This page gives students a chance to reach back and use representations
they may not have thought about since Unit 1 or 2. Remember that nothing
is off limits in AP Physics 1; just because it was “last unit” doesn’t mean
it can’t come up again. The more cyclical you make the curriculum, the
more students will feel comfortable making connections between the
fundamental physics presented in each distinct unit.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
How is this scenario similar to and different from a dart being shot directly
up into a block of mass M? Sketch momentum bar charts for this new
scenario. Would the maximum height of the dart/block increase, decrease,
or stay the same if the mass of the dart were increased assuming its
launch velocity remained the same?
What’s the point?
To answer this question, you needed to use more than just the ideas you
learned in Unit 5. A good first step when approaching a new problem is
to try and determine what fundamental physics ideas can be applied to
the situation and what representations might help you make sense of the
given information.
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UNIT
5
Momentum
Experimental Design - Impulse
EK
|
3.D.2, 4.B.2
SP
|
1.1, 1.4, 4.2, 4.4, 6.1
Prepare
In other science classes, students may have often been coached to
write a procedure so that “another student could replicate their work.”
The problem with this coaching is that students often get hung up on the
details of organizing a table, finding supplies, and effectively cleaning,
which is where they feel the most comfortable. The more students practice
writing procedures, the more comfortable they will become, and the better
they will be at eliminating the “fluff” and getting down to business.
Teach
When students are creating the graphs in Part B, it is common for them to
forget that the signs of the force and velocity graphs will be related. For
example, in the solution below, the initial velocity is positive, and the final
velocity is negative, meaning that the acceleration (and by extension force)
should be in the negative direction. If the opposite were true, the force
should be in the positive direction.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
How would the velocity vs. time graph be different if the students
performed this experiment on a slight incline? Sketch a possible velocity
vs. time graph if the cart was released from rest and allowed to roll downhill
toward the force sensor. (Have the students consider multiple bounces.)
What’s the point?
Be careful of adding extra details to make your procedure sound good.
The AP graders know and understand the basics. You need to focus on
telling them what you’ll measure, how it will be measured, and what you’ll
do with the data.
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UNIT
5
Momentum
Momentum Representations
EK
|
3.A.1, 3.D.1, 4.A.2, 5.B.4
SP
|
1.1, 7.2
Prepare
Students may struggle with creating these eight graphs—especially since
creating one graph can cause anxiety. Help scaffold the creation of graphs
by coaching students to first plot points that they are confident about.
For example, students might choose to start with the velocity vs. time
graph. They know that the initial speed of the ball is positive v, so they can
plot a point for that. They also know that at some moment (since the ball
is thrown straight up) that the ball will have zero speed, so they can plot
a zero point. They can then be coached to think about the relationships
between the velocity vs. time graph and other graphs. For example, ask,
“What does the slope of the velocity vs. time graph represent? What about
the area under the curve?” This kind of scaffolding will help students to
both more successfully complete this set of graphs and to develop a set
of questions that they can ask themselves when faced with a new set of
graphs to create.
Teach
Being able to sketch graphs of the relationships between physical
quantities as well as being able to discuss these relationships is a critical
skill in AP Physics 1. Students need to be continually challenged to make
connections between material they have studied previously and new
scenarios. If these relationships are second nature for your students, they
are less likely to be tricked by a question that attempts to ask a simple
question in an unfamiliar context.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask give students the assignment below.
Have students make up their own scenario and sketch the same eight
graphs for the situation they created. Have them switch with a partner and
critique the graphs. Are there any inconsistencies between the graphs
that need fixing?
What’s the point?
Linking representations is critically important for success in AP Physics 1.
This is a good exercise to complete throughout the course to make sure
you understand how the ideas you’ve learned so far are tied together and
how one representation can help you to make and analyze others.
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UNIT
5
Momentum
Explosions
EK
|
5.D.2
SP
|
2.2, 5.3, 6.1, 7.2
Prepare
Even though explosions are fundamentally the same as inelastic collisions,
students often struggle with understanding how to analyze them. Being
aware that students might find this page more difficult than previous pages
will help you to better prepare and scaffold your lessons. For example,
you might consider posing a question where two carts are initially at rest
and explode from each other. Ask your students to sketch the momentum
diagram for the explosion as well as energy bar charts and have a discussion
about the relationships between the momentum diagram and energy bar
charts and what is different in this scenario and others they have studied.
Teach
Being able to quantitatively predict the outcome of a situation is a skill
that should be practiced throughout the course. Many classic textbook
problems lend themselves nicely to this kind of analysis. If the problem
asks for a numerical solution, swap out the givens for symbols, and
ask students to predict a result and then solve symbolically to provide
evidence for their claim. If students are uncomfortable with this kind of
analysis, they can start with Part B.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
Two carts are initially at rest on a track with a compressed spring between
them. The spring is released. After the carts are no longer touching, one
cart is found to have more kinetic energy than the other. A student who is
watching makes the following statement: “Since one cart has more kinetic
energy than the other, it also has more momentum, so the spring had to
push harder on that cart than it did on the other.”
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What if anything is wrong with this statement? Justify your answer
with evidence.
Note that the track does not need to have negligible friction to ask this
question. During the collision friction can almost always be neglected
compared to the internal force of the collision.
What’s the point?
Being able to annotate your derivations and calculations will be important
on the AP Physics 1 Exam. Sometimes, you will be asked to simply
calculate, but more likely you will be asked to derive a symbolic expression
or even just explain how a derivation can be done without actually showing
the derivation.
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AP Physics 1
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UNIT
5
Momentum
Conservation of Momentum
EK
|
5.D.1, 5.D.2, 3.A.4
SP
|
1.1, 4.2, 5.1, 6.2
Prepare
This page can easily be turned into an experiment, even with limited
access to equipment. Students can use their phones to capture video that
can be put into a free software program such as Tracker to allow students
to create position vs. time graphs.
One of the best ways to critique student procedures is to have them
switch papers and follow exactly without making assumptions about the
directions given. When the written procedures are unclear, students will be
able to help each other correct them.
Teach
Many procedures could be used to adequately answer the questions
asked here. Goals for this procedure section should be clarity and brevity:
Can students clearly express what will be measured, and how it will be
measured? Can they then clearly relate how the measured quantities will
be used to answer the question?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
How would the procedure change if the carts were able to stick together
after the collision? If the procedure would change, explain the changes,
and if the procedure would remain the same, explain why.
What’s the point?
Remember that there is a difference between inelastic collisions and
perfectly inelastic collisions. In both cases, kinetic energy is lost in the
collision. In inelastic collisions, the two objects do not necessarily have the
same speed after the collision (meaning that they may not stick together),
while in a perfectly inelastic collision, the two objects will have the same
final velocity.
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UNIT
5
Momentum
Inelastic Collisions
EK
|
5.D.2
SP
|
2.2, 4.2, 5.1
Prepare
If you have done a demonstration with the ballistic pendulum in class,
students will probably gravitate toward recreating a ballistic pendulum
for their experiment. There is nothing wrong with this, especially if your
students struggle with thinking of what they should be doing for the
procedure. Giving them an experiment where they already know at least
parts of what they should be doing, allows them the opportunity to focus
on the writing of the procedural paragraph, instead of feeling stuck. If
you have exceptional writers who do not need extra practice, you could
remove the string and hooks from the given equipment, forcing the
students to be a little more creative with their experimental design.
Teach
Again, there are many procedures that could provide data that could
adequately answer the given questions. The most important pieces of any
procedure are a student’s ability to clearly and concisely express what
will be measured, how it will be measured, and how the measured quantity
will help answer the question. In most cases, a clearly drawn sketch of the
experimental setup will go a long way toward helping a student to clearly
outline the procedure.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
Which of the following representations would not allow a calculation of
impulse given to a cart initially at rest?
A. A graph of velocity vs. time
B. A graph of force vs. time
C. A graph of position vs. time
D. A graph of force vs. displacement
Ask for explanations! The explanation is where you’ll learn what the
students understand and misunderstand.
What’s the point?
When asked to create an experimental procedure, make sure to write down
what you need to know AND what needs to be measured. Sometimes, the
thing you need to know can be easily measured, and sometimes, it needs
to be determined. Make sure to note the difference!
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AP Physics 1
Workbook
UNIT
5
Momentum
Collisions
EK
|
5.D.1, 5.D.2
SP
|
1.1, 1.4, 2.2, 6.4, 7.2
Prepare
Momentum charts and energy charts should be easier for most students
at this point in the unit. If your students still struggle, remind them that
starting on the chart will help them get their thinking down on paper. For
example, in each case, the initial momentum of the dart will be equal. Once
they choose a set of squares to represent the initial dart’s momentum for
the first case, it will be the same in the next two cases as well. Then they
can think about how to represent the momentum of the cart before the
collision and what that means for the momentum of the system after the
collision.
Teach
If students have access to colored pencils, crayons, or markers, using
different colors for each object and a third “combined” color for each
momentum chart can be helpful for students to more clearly see where
the momentum goes, how it is transferred, and how the transfer of
momentum affects the velocity of the system.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A dart is launched at a block that is standing vertically on its end. Is the
block more likely to fall over if the dart sticks to the block or bounces
off? Justify first with a momentum chart and then in a clear, coherent,
paragraph-length response (that may also contain figures and/or
equations).
What’s the point?
When writing an argument, it is important that your argument is selfconsistent. You don’t want to write your claim and then argue in the
paragraph that something else is true. To make it easier to keep your
arguments consistent, consider writing the paragraph argument first,
come to a conclusion, and then write the claim.
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AP Physics 1
Workbook
UNIT
5
Momentum
Center of Mass Motion
EK
|
5.D.2
SP
|
2.2, 6.4, 7.2
Prepare
Parts A to C are mostly straightforward momentum calculations that
could have easily come from an AP Physics B Exam. The really tricky part
comes in Part D, which asks students to analyze what they know about
conservation of momentum and the effects of a net external force on the
position and motion of the center of mass. Be careful on Part D. Many
students will mistakenly believe that the accelerations can cancel and
forget that they need to add forces to determine the direction of the net
acceleration of the system.
Teach
Explaining calculations can seem time-consuming, but there are situations
on the AP Physics 1 Exam where students will be asked to simply explain
and not perform a calculation. As the year progresses, you can give them
more opportunities to do each, independently of each other, but at this
point in the year, you should be consistently asking them to do both.
This is also a great place for differentiating instruction. Ask students who
always get the mathematical derivation right to do only the annotations.
Ask students who can explain what is happening but struggle with the
math to only work on the mathematical derivation.
When the force is instantaneous, it means that we don’t deal with the
change from immediately before to immediately after the force, so we’re
not sketching the curvy part of the position vs. time graph where the
velocity changes from zero to positive.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Sketch the position of the center of mass as a function of time if only the
1-kg block encountered a rough patch. Explain the differences between
this graph and the graph given in Part D.
What’s the point?
Momentum, forces, and energy are all linked but have very different
procedures and are better to use in some situations than others. Start
now to practice differentiating between situations that call for energy
applications, momentum, and/or force applications.
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AP Physics 1
Workbook
UNIT
5
Momentum
Conservation of Energy and Momentum
EK
|
5.D.2, 5.B.3
SP
|
2.2, 6.4, 7.2
Prepare
This is a page where again, students will be asked to access their prior
physics knowledge and apply it to a new scenario. If your students had
a difficult time with energy bar charts, you might want to expand this
page and first ask them to draw momentum diagrams and energy bar
charts for this scenario. Those representations will help them to formulate
their responses to Parts A and B. Another option would be to derive the
mathematical relationships first. If they annotate their derivations, they will
find that they already answered Parts A and B. (Just a reminder that on the
AP Exam, if a student answers a question in the wrong spot, they need to
call attention to it. A correct answer in the wrong spot with no marks drawing
the grader’s attention to it cannot be guaranteed to be graded.)
Teach
Students have made their claim and derived a mathematical relationship,
but does it work? Have them test it out! They can design a procedure
individually and then switch papers. They can edit in teams or groups and
settle on one group’s procedure to use in the laboratory. There should
be a discussion of reducing error, and how they will know if the data they
collect support their hypothesis or not.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to challenge students with the ideas below.
Once students have collected data (or if students are not performing the
lab experiment themselves, you may provide them with data, have them
analyze their results. One student may say that because of the equation
they derived in Part C, that M 1 is directly proportional to v f .
Discuss with students the differences between proportional, directly
proportional, inversely proportional, etc. so that they have examples they
can reference when looking at new data to determine relationships.
What’s the point?
Asking questions about a given scenario is a great way to get ready for
the AP Physics 1 Exam. Check out your textbook for standard physics
questions, answer them, and then ask new ones! What would happen if
part of the scenario was removed? Or one of the initial conditions was
doubled? Challenge yourself!
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AP Physics 1
Workbook
UNIT 6
Simple Harmonic Motion
Misconceptions
Students have various levels of familiarity with objects oscillating on springs or
pendulums, but even if they are familiar with such systems, they most likely have
not observed them in any systematic way. Consequently, they have inaccurate ideas
about how those systems actually behave. They understand that such systems are
periodic but often don’t know what factors control the periods. They will normally say
that the amplitude of the motion affects the period. For pendulums, students often
say that the mass of the bob affects the period. One of the best ways to address these
ideas is to have the students experiment with the systems.
Scenario
Misconception
6.C, 6.F, 6.G, 6.J
The period of oscillation depends on the amplitude.
6.A, 6.E, 6.G, 6.J
The restoring force is constant at all points in the oscillation.
6.G
The heavier the pendulum bob, the shorter its period.
6.G, 6.J
All pendulum motion is perfect simple harmonic motion, for any
initial angle.
6.K, 6.L
Harmonic oscillators go on forever.
6.J
A pendulum does not accelerate through the lowest point of its swing.
6.C, 6.E, 6.I, 6.J,
6.K, 6.L
Amplitude of oscillations is measured peak to peak.
6.A, 6.E
The acceleration is zero at the end points of the motion of a pendulum.
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AP Physics 1
Workbook
Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Create and use a motion diagram.
Using Representations
6.A
1.1
Create and use a position vs. time graph.
Using Representations
6.C, 6.E, 6.K
1.1
Create and use energy bar charts.
Using Representations
6.C
1.1
Create and use free-body diagrams.
Using Representations
6.A, 6.E
1.1
Create and use velocity vs. time graphs.
Using Representations
6.F, 6.I
1.1
Identify systems.
Using Representations
6.B, 6.I, 6.J, 6.K
1.1
Plot data on a graph.
Using Representations
6.B, 6.C, 6.E, 6.H, 6.K
1.1
Scale and label axis.
Using Representations
6.B, 6.I, 6.K
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
6.E, 6.F, 6.H
1.5
Match shapes of graphs to relationships between variables.
Data Analysis
6.C, 6.E, 6.I, 6.J
1.5
Re-express one type of graph as another.
Using Representations/Argumentation
6.E
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
6.B, 6.C, 6.D, 6.G, 6.J, 6.L
2.2
Derive or calculate, including annotations.
Quantitative Analysis
6.E, 6.I, 6.K, 6.L
4.2
Design an experiment to answer a specific question.
Experimental Design
6.D, 6.F
6.1
Identify a claim and evidence that can support that claim.
Argumentation
6.A, 6.D, 6.G, 6.I, 6.J, 6.K, 6.L
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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AP Physics 1
Workbook
UNIT
1
6
Simple Harmonic Motion
Forces in Simple Harmonic Motion
EK
|
3.B.3
SP
|
1.1, 1.4, 1.5, 4.1, 5.1, 6.1
Prepare
Drawing free-body diagrams at various points while an object is moving
is a challenge. Most free-body diagrams up to this point in the course
have been drawn at one moment of time, not at several moments of time
in succession. In addition, knowing where the spring force is the greatest
and the least is important.
In Part A, students are asked to create a position diagram. This will be
similar to what would be created from a ticker tape read out. If students
feel comfortable making this diagram, you could challenge them to create
a full motion map, including velocity vectors.
Teach
Students will be challenged by drawing more than one free-body
diagram for an object at various times in succession. They will want to
incorrectly draw arrows that represent the motion of the object. This
shows a significant misunderstanding with what is represented on a free
body diagram. This is not a style preference, it is wrong. Many students
think incorrectly that there is a spring force at equilibrium (point C in the
diagram) that works with or against the motion of the object.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Give students a variety of free-body diagrams and ask them to identify
where the object attached to a spring is located in relation to the
equilibrium position. To add a twist, you could ask them questions about a
vertical object-spring system.
What’s the point?
Restoring forces, like those in springs, always work to return an object
to equilibrium. That’s what makes things that use springs work—like
the springs under your car that help make your ride smoother when the
springs get compressed and stretched as you drive over bumps and
valleys in the road.
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AP Physics 1
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UNIT
1
6
Simple Harmonic Motion
Simple Harmonic Motion and Energy Review
EK
|
5.B.2, 5.B.3, 5.B.4
SP
|
1.1, 1.4, 1.5, 5.1, 7.2
Prepare
If you have not used energy bar charts yet in your course, you may want
to introduce them before this worksheet. If you have used them before, a
quick review would be helpful.
Teach
It will be difficult for students to get the values (number of boxes) on the
bar charts to match correctly as well as add to the same total so that
energy is conserved. This may require some help from you or some
extra time to think about. Parts C and D should help students organize
their thoughts and make corrections if their bar charts do not show the
correct relationships.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to challenge students with the task below:
Give students a variety of energy bar charts and ask them to identify
where the object attached to a spring is located in relation to the
equilibrium position.
What’s the point?
Even with ideal springs, energy is conserved! The transfer of energy from
one form to another using springs is what makes toy dart guns, slinky
springs, and pinball machines work.
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AP Physics 1
Workbook
UNIT
1
6
Simple Harmonic Motion
Equations of Motion for Simple Harmonic Motion
EK
|
3.B.3
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 5.1, 6.1, 7.2
Prepare
Students will need to know about the equations that describe cosine and
sine waves and should have seen them in a prior math class. However,
if they have not, you will need to introduce these equations before this
worksheet or when the equations are introduced. In addition, the topics of
period, frequency, and angular frequency, along with their relationships to
each other, should be discussed.
Teach
Although it is not specifically mentioned, in Parts C and D, there is a shift
of the graph. Students do not need to try and calculate the horizontal
phase shift in these parts, instead, they should be able to recognize that
the graph can now be modeled by a sine curve.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Give students a variety of position vs. time graphs for simple harmonic
motion. Ask them to identify the different components of the graph (like in
Part A) and write equations for them (like in Part B). In addition, you could
have students draw a physical situation that matches the graphs.
What’s the point?
Although this unit might seem unfamiliar, the same relationships between
position, velocity, and acceleration exist for objects undergoing simple
harmonic motion.
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AP Physics 1
Workbook
UNIT
1
6
Simple Harmonic Motion
Measuring Spring Constants
EK
|
3.B.3, 5.B.2, 5.B.3, 5.B.4
SP
|
4.1, 4.2, 5.1, 6.1, 7.2
Prepare
If the equations for the spring constant (Hooke’s law and period of massspring system) have not been covered in class up to this point, you need
to discuss them at some point before assigning this worksheet.
Teach
Having students perform experiments with limited equipment is a good
skill to teach. Many times, scientists are also limited by equipment. It
is also good to figure out the best way to measure/calculate the same
quantity in more than one way to verify results. Giving your students
opportunities to do this in the laboratory setting is a good idea and not
just for test-taking purposes; it is a good science skill.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Sample questions: If the same mass makes two springs stretch different
distances, which spring has the greater spring constant? If two massspring systems have the same mass and are oscillating at different
periods, which spring has the greater spring constant? If two mass-spring
systems are oscillating with the same period but one mass is different
from the other, which spring has the greater spring constant?
What’s the point?
Being able to find the same quantity using more than one method is a very
important skill in science. It helps scientists verify their findings as well as
add confidence to their results.
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AP Physics 1
Workbook
UNIT
1
6
Simple Harmonic Motion
Equilibrium on an Incline
EK
|
3.B.3
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 5.1, 6.1, 7.2
Prepare
It would be helpful to have your students think about a vertically hanging
object before analyzing this problem. Have them sketch a free-body
diagram, determine the spring constant from given data, and write an
expression for the period of oscillation for the object/spring system in
terms of m , x 0 , and physical constants as appropriate.
Teach
Although not specifically requested as a part of the question, students will
need to derive the spring constant for the spring. Students should notice
that they are given information for the spring. Why is it important that the
question gives this information? They should notice that if something
is important enough to take up space on the page, it may be important
enough to think about!
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Give students various algebraic expressions and have them draw the
physical situation that matches the equations. A sample question: If a
spring on an incline stretches a distance x when a mass is attached and
another spring hung vertically with the same mass stretches the same
distance, then which spring has the greater spring constant?
What’s the point?
Being able to move from one situation to another happens a lot in all areas
of science as well as in life in general. Understanding a simpler situation
can help you make sense of a more complicated one.
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UNIT
1
6
Simple Harmonic Motion
Determining if Motion Is SHM
EK
|
3.B.3, 5.B.2, 5.B.3, 5.B.4
SP
|
4.1, 4.2, 4.3, 5.1, 6.1, 7.2
Prepare
It would be good to cover the similarities and differences between
oscillatory motion, periodic motion, and simple harmonic motion before
assigning this worksheet.
Teach
This activity can be done with a long metal yardstick or with a hacksaw
blade. If this worksheet is given as a pre-lab homework assignment,
students can compare procedures in class and perform the experiment
together with classmates.
If you have yet to introduce and discuss gravitational vs. inertial mass,
this is a great place to do so. Discuss the differences with your students
and then discuss how this apparatus could be used to determine the
gravitational and inertial mass placed on the yardstick.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to assign students the following experimental
procedure writing task:
Since there are at least three ways to check simple harmonic motion,
write an experimental procedure to show simple harmonic motion with a
different procedure than what you wrote for your lab experiment.
What’s the point?
Performing experiments to answer questions that people have is exactly
what science is for! If you have ever asked a question about something,
someone has probably already done the experiments to figure out the
answer OR is still working to find the answer. If not, maybe you can design
and carry out an experiment to find the answer and pass it on!
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UNIT
1
6
Simple Harmonic Motion
Period and Amplitude for SHM
EK
|
3.B.3, 5.B.2, 5.B.3, 5.B.4
SP
|
2.1, 2.2, 6.1, 7.2
Prepare
It is very common for students to think that the amplitude will change the
period of an oscillator. You could have some springs or pendulums ready
for demonstrations if your students are not convinced that period and
amplitude are independent.
Teach
The reason the string is really long is that students don’t have to worry
about the ball traveling in a curve on its path—the path is basically a
straight line for this small amplitude. If you have a high ceiling in a gym,
cafeteria, or auditorium where you can fix a pendulum, this can be a very
powerful demonstration.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A box of mass m is attached to an ideal spring (with a spring constant k )
hung from the ceiling. If the spring is displaced a distance x from
equilibrium, the box-spring system oscillates with a period T. If the box is
displaced a distance 2x from equilibrium, is the period more, less, or equal
to T ? Explain.
What’s the point?
The period of oscillation for a simple harmonic oscillator is independent of
the amplitude of oscillation.
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UNIT
1
6
Simple Harmonic Motion
Period and Mass Relationship for Mass-Spring Systems
EK
|
3.B.3, 5.B.2, 5.B.3, 5.B.4
SP
|
1.1, 1.4, 2.2, 5.1, 6.1, 7.2
Prepare
If your students need more practice with linearization, you can give them
the period and mass data before giving them the whole worksheet. Have
the students graph period of oscillation vs. mass and compare the graph
to known relationships (as given in earlier worksheets. Is this a linear
graph? Directly proportional? Indirectly proportional?) Then have the
students determine what they should graph to have a linear graph. Once
students have determined that they should graph period squared vs. mass,
give them the worksheet to finish the analysis.
Teach
It is important to make sure your students can use graphs to obtain
information in various ways, including linearization. In addition, students
should be able to relate variables in equations to different parts of a graph
as done in Part D.
Assess
To further assess student understanding of the concepts addressed in this
scenario, you may want to assign students the following data analysis task.
Have students collect data for period vs. length of a pendulum for a
simple pendulum.
A. Does the amplitude of oscillation matter? Explain.
B. What would the graph of period vs. length look like?
C. What should the students graph to be able to create a linear graph?
D. How could the students use the graph to determine the acceleration
due to gravity?
What’s the point?
Even though, in this case, the amplitude did not affect the data collected
in Part A, it is very important to control all variables in an experiment
to ensure that you are testing how any changes in one tested quantity
affects another.
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AP Physics 1
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UNIT
1
6
Simple Harmonic Motion
Changing Mass and Period of a Mass-Spring System
EK
|
3.B.3, 5.B.2, 5.B.3, 5.B.4
SP
|
1.4, 4.1, 5.1, 6.1, 7.2
Prepare
If it has been a while since students learned about momentum and its
conservation, a quick review may be necessary.
Teach
Students may be able to tell you what happens to the period of a massspring system if the mass is changed, but they will have a difficult time
translating that knowledge into the representations of velocity vs. time
graphs. It will be even more difficult for them to think about what happens
to the velocity graphs when collisions occur at different times.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Why is the maximum speed shown in each case (Part B) different from the
original speed and different between Cases 1 and 2?
What’s the point?
Seeing “real” graphs is important for students. There is a strong possibility
that students will see and be asked to analyze graphs created (e.g., with
motion detectors) that contain “noise.” Even if you don’t have access
to computer technology, graphs can be found on the Internet that
demonstrate “noise” that students can practice analyzing.
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AP Physics 1
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UNIT
1
6
Simple Harmonic Motion
Small Angles, Tensions, and Pendulum Period
EK
|
5.B.2, 5.B.3, 5.B.4
SP
|
5.1, 6.2, 7.2
Prepare
It may help to show students how the small angle approximation works
mathematically. This can be done by taking the cosine of small angles and
showing that they come out to be very close to one or that the sine of very
small angles comes out to be very close to the angle itself.
Teach
Students need to understand how the angle can affect the period of a
pendulum. If this was tested in an experiment or shown in a demonstration
earlier in the class, you can now make the point that as long as the angle
(amplitude) is kept small, the period is not changed. However, if students
used larger angles in their experiment, they may have found some
discrepancies in their data, which would tie in nicely at this point.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
If a grandfather clock was made to swing with a wider arc, would it keep
the same time? If so, why? If not, would the time be longer or shorter, and
why? Where in the swing of the grandfather clock is the net force exerted
on the pendulum bob the greatest? Why?
What’s the point?
As long as the angle of a pendulum is small enough, the period is not
affected. This is why pendulums that are used as timekeepers (like
grandfather clocks) do not swing too far from the lowest point. If they did,
the timing would be inaccurate.
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UNIT
1
6
Simple Harmonic Motion
Mass and Period of Mass-Spring System
EK
|
3.B.3, 5.B.2, 5.B.3, 5.B.4
SP
|
2.1, 2.2, 5.1, 6.1, 7.2
Prepare
Flow rate is not something that is included in the AP Physics 1 curriculum
but being able to use different types of rates is needed. It would be helpful
to review what rates are and that they are not just used for speeds.
Teach
As the sand is added to the cart, students will struggle thinking of this as
a collision even with the hint. Once they understand that it is an inelastic
collision, they will have a difficult time figuring out where the energy went
and what caused it. Your assistance may be needed to lead them to the
correct conclusions.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to challenge students with the scenario below:
Give students another type of dampening graph and ask them to describe
a physical situation, other than the one on the worksheet, that would
match the graph. You could also ask them to explain why the amplitude
decreases while the period increases on the graph.
What’s the point?
Many things can cause springs, as well as other oscillatory devices, to
decrease in amplitude, which is called dampening. This is why shock
absorbers (damped springs) are used on vehicles—to prevent the
vehicle from bouncing over long periods of time, making your ride more
comfortable.
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UNIT
1
6
Simple Harmonic Motion
Sine Function of Simple Harmonic Motion
EK
|
3.B.3, 5.B.2, 5.B.3, 5.B.4
SP
|
1.1, 2.2, 4.1, 5.1, 6.1, 7.2
Prepare
It may be a good idea to show the setup and motion of the cart and bucket
if equipment is available. Also, it would also be fun and interesting to show
students examples of other physical situations that required a scientist to
calculate something that led to an important discovery or measurement.
Teach
It will pose a challenge to students to move from a physical situation to a
numerical solution, which means Part A may need some assistance from
you or some extra time to discuss with a group. Even though all the mass
oscillates, only the gravitational force on the bucket contributes to the net
external force on the system, which determines where equilibrium will be.
The total mass of the system contributes to the period of oscillation.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Students could be given another graph with a different period and
amplitude and asked to find the amount of mass in the bucket and cart.
Also, you could assign them the same graph but tell them what the actual
masses are, which would be less than their calculations, and ask them why
there is a difference (mass of cart and bucket are not negligible).
What’s the point?
Being able to take a physical situation, relate it to a mathematical solution,
and use that to solve for an unknown quantity is exactly what happens in
scientific experiments. The important thing here is that you are able to go
from a physical situation to a numerical calculation.
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AP Physics 1
Workbook
UNIT 7
Torque and Rotation
Misconceptions
When teaching rotational motion, all the misconceptions found in translational
motion have direct analogs. For example, if the angular velocity is zero, students
often believe that the angular acceleration must also be zero. Students also tend
to have less familiarity with rotational motion, so it can be more difficult to find
common-sense ideas to build on.
However, students do usually bring some intuitive understanding of torque. They
know that pushing a door near its hinge makes it hard to open the door, while
pushing on the other side makes it easy to open the door. This means that students
have a useful idea about the importance of the distance between the axis and the line
of action of the force. In addition, if they exert the force so that the line of action is
through the axis, they know that the door will not rotate, so they have some idea that
the angle at which the force is exerted is also a factor.
Students struggle with the role of friction. If objects roll without sliding, the
friction force is necessary to provide the torque to roll the object. Without friction,
an object would not roll but would slide down a ramp. Since they now understand
that objects of different mass fall at the same rate with no air resistance and those
same objects will slide down an incline at the same rate if there is no friction,
students may predict that all the objects will roll down the incline and reach the
bottom at the same time and with the same speed. And although different shapes will
roll/rotate differently, the final speed of an object at the bottom of an incline does not
depend on the mass or radius of the rolling object, which may be surprising to many
students. It is often helpful to bring the discussion around to what causes objects to
roll and ask students to justify whether what they have learned, in the case of a ramp
for which friction is negligible, is still valid.
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Scenario
Misconception
7.B, 7.D, 7.E, 7.F,
7.G, 7.H, 7.J, 7.K,
7.L, 7.M, 7.N
Any force exerted on an object will produce a torque.
7.I
Objects moving in a straight line cannot have angular momentum.
7.B, 7.D, 7.E, 7.F, 7.G
Torque is the same as force and in the same direction.
7.I, 7.L
Angular momentum is not a vector.
7.I, 7.L
The direction of angular momentum is in the direction of the linear
momentum.
7.C, 7.H, 7.I, 7.J, 7.O
There is only one kind of kinetic energy.
7.K
v = Rω is always true.
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AP Physics 1
Workbook
Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Create and use acceleration vs. time graphs.
Using Representations
7.D
1.1
Create and use energy bar charts.
Using Representations
7.C, 7.H
1.1
Create and use free-body diagrams.
Using Representations
7.D, 7.G
1.1
Create and use force diagrams.
Using Representations
7.A, 7.B, 7.D, 7.E, 7.F, 7.G, 7.H, 7.K
1.1
Create and use velocity vs. time graphs.
Using Representations
7.D, 7.K
1.1
Identify systems.
Using Representations
7.H, 7.I
1.1
Plot data on a graph.
Using Representations
7.A, 7.D, 7.K, 7.L
1.1
Scale and label axis.
Using Representations
7.A, 7.L
1.4
Relate the area under the curve to a physical quantity.
Quantitative Analysis/Data Analysis
7.D
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
7.A, 7.D, 7.K
1.5
Match shapes of graphs to relationships between variables.
Data Analysis
7.A, 7.K
1.5
Re-express one type of graph as another.
Using Representations/Argumentation
7.A, 7.K, 7.L
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
7.A, 7.E
2.2
Derive or calculate, including annotations.
Quantitative Analysis
7.E, 7.G, 7.H, 7.M
4.2
Design an experiment to answer a specific question.
Experimental Design
7.N, 7.O
6.1
Identify a claim and evidence that can support that claim.
Argumentation
7.A, 7.B, 7.C, 7.F, 7.G, 7.H, 7.I,
7.J, 7.M
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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AP Physics 1
Workbook
UNIT
7
Torque and Rotation
Relationship Between Arc Length and Angle of Rotation
EK
|
3.A.1
SP
|
1.1, 1.4, 5.1, 6.1
Prepare
Students should have some background knowledge on conversions
between degrees and radians but may need a refresher. Also, at this point
in the class, they should have a good grasp on how to graph data and use
the slope of the graph to their advantage. Students will need to be familiar
with the equation of a line to complete this problem.
Teach
When having students look at data, make sure they note what quantities
are changing and how that affects the data. You could give students more
data examples, so they know what data should be used and what data
should not be used.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
If the turntable’s radius were doubled, how would that affect the graph?
How would changing the radius affect the arc length and the angle?
What’s the point?
The slope of a graph can be used to find an unknown quantity.
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UNIT
7
Torque and Rotation
Torque
EK
|
3.F.1, 4.D.1
SP
|
1.1, 1.4, 6.1, 7.1
Prepare
If the net force on a system is zero, the system is not accelerating.
Forces create torques when they are a perpendicular distance away
from the pivot point. There can be both vertical and horizontal forces at
pivot points.
Teach
You can demonstrate in class that when a force is applied at different
distances from a pivot point, the torque is different. Using a meterstick,
you could create a scenario where the boxes are placed at different
distances away from a pivot point in order to create equilibrium. You could
also show that if a force is applied at different distances from the hinge
on a door, the rotation about the hinges will change.
Have your students try this experiment at their desks. They can use one
of their fingers pushing downward on a pen to symbolize the box and
then have a partner apply a force F at each of the points in Cases A to F.
Which way does the table have to push on the pen to create a situation
in equilibrium?
Assess
To further assess student understanding
of the concepts addressed in this
scenario, you may want to ask students
the questions below:
A uniform block has mass m . Resting on
it is half of an identical block as shown
at right. The blocks are supported
by two legs as shown above. Which table leg, if either, should provide a
larger force on the bottom block? In terms of L , m , and g , determine the
magnitude of the force each leg applies to the block.
What’s the point?
Torque depends not only on the force but also the perpendicular distance
of the force from the pivot point.
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UNIT
7
Torque and Rotation
Rotational Energy
EK
|
5.E.2, 4.C.1, 5.A.1, 4.C.2, 5.B.1, 5.B.3
SP
|
1.1, 1.4, 6.1, 7.2
Prepare
Explain to students that when an object is rolling, it has both translational
and rotational kinetic energy. Velocity and angular velocity can be related
to each other through the formula ω = v/r AS LONG AS THE OBJECT IS
ROLLING WITHOUT SLIPPING. This formula can be used with the moment
of inertia to relate both kinetic energies in terms of mass and velocity.
Teach
Remind students that if the object leaves the track at point C, it undergoes
two-dimensional motion. Therefore, it will have velocity both in the vertical
and horizontal directions.
Students need to be shown that, in the absence of friction, there is no
torque to create rotation. Therefore, there will be no rotational kinetic
energy in Part D. When dealing with energy conservation, students may
not know how rotational and translational kinetic energies can be related
to each other.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Draw a bar chart for both the friction case and the case neglecting friction
when the sphere is at its highest point.
What’s the point?
Potential energies can be transferred into both translational and
rotational energies.
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UNIT
7
Torque and Rotation
Forces vs. Torques
EK
|
3.A.1, 3.F.1, 3.F.2, 4.D.1
SP
|
1.1, 1.4, 1.5, 5.1, 7.2
Prepare
When tension is applied a perpendicular distance away from a pivot point,
it causes a torque. If there is a net torque, an extended object will have an
angular acceleration.
Teach
With a pulley, a string, and a box, you can show students that the falling
box will cause the pulley to rotate. Also show students how an angular
velocity vs. time and an angular acceleration vs. time graph can be used
together. Lastly, show students that the slope of an angular velocity vs.
time graph is angular acceleration, and the area can also help you find
angular displacement.
Create T shapes out of PVC piping (available at local home improvement
stores). Place a PVC T over a ring stand so that it will rotate freely. Wrap a
string around the bottom of the T shape, hang it over a pulley, and attach
the end of the string to a hanging object. When the object is released,
the T-shaped PVC pipe will rotate. How is this situation the same as and
different from the scenario given in this problem?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
How would the graphs change in Parts C and D if the radius of the pulley
were doubled? How would the graphs change if the mass of the box were
doubled?
What’s the point?
A net torque creates an angular acceleration and hence a changing
angular velocity.
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UNIT
7
Torque and Rotation
Rotation
EK
|
3.F.1, 3.F.2, 4.D.1, 5.E.2
SP
|
1.1, 1.4, 2.1, 2.2, 5.1, 6.1, 7.2
Prepare
Remind students that there is a difference between a free-body diagram
and a force diagram. For a free-body diagram, the forces are drawn as if
they are all exerted at the center of mass (and the vector arrows MUST
touch and start from the dot). For a force diagram, the force’s vector
arrows are drawn from the point of application of the force. For this page,
there is a normal force exerted on the meterstick from the table’s edge so
that force should be drawn in on the left end, while the force of gravity is
always exerted at the center of mass and should be drawn in the middle
of the meterstick.
Teach
This scenario can be demonstrated in your class very easily. You can
change the amount of the meterstick that hangs over the edge and show
how that affects how the meterstick will fall. Explain to your class that
when a rotational inertia is given, it is for a specific point of rotation of that
object. Lastly, you can ask your class how much mass would need to be
added to the end on the table in order for the meterstick not to rotate.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
What would the acceleration of the meterstick be if the 25-centimeter
mark was placed precisely at the edge of the table? If the meterstick was
balanced on the edge of the table, would placing an object on the hanging
edge cause any motion?
What’s the point?
Not only the force but also the perpendicular distance away from a pivot
point affects the angular acceleration.
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UNIT
7
Torque and Rotation
Rotation
EK
|
3.F.1, 4.D.1
SP
|
1.1, 1.4, 6.1, 7.2
Prepare
Even though intuition may not tell someone to look at torques when a ladder
is placed up against a wall, the torque equation is needed mathematically
because of the number of unknowns. Because the ladder is in contact with
two surfaces, there are two different normal forces, and the force of friction
is related only to the normal force at the point where the friction is exerted.
Summing forces will not be enough to model this situation!
Teach
Although it will be hard to eliminate friction from a surface, this scenario
can be approximated in class by using a meterstick. Students will be
able to visually see what happens to the “ladder.” Show students why it is
important mathematically that they have three equations. Show students
how the torque equation changes depending on their choice of pivot point
although the solution remains the same.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
If the mass of the ladder was m and had a length of l , what would the
angular acceleration of the ladder be in terms of m , l , and θ. What would
the acceleration of the center of mass of the ladder be?
What’s the point?
Linear acceleration is caused by a nonzero net force, and angular
acceleration is caused by a nonzero net torque.
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UNIT
7
Torque and Rotation
Rotation vs. Translation
EK
|
3.A.1, 3.F.1, 3.F.2, 4.D.1, 5.E.2
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 6.1
Prepare
This can be demonstrated in class with rolls of toilet paper. Alternately,
students can derive an equation to determine the heights from which the
two rolls should be dropped so that they land at the same time.
Teach
You can easily demonstrate this scenario with your students to show that
they will have different accelerations. You could then look at how different
types of yo-yos (solid or hollow disks) accelerate. Students may have the
misunderstanding that because both yo-yos are falling through the air,
they are both undergoing free-fall acceleration.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Sketch an energy bar chart for both yo-yos at the time just before they are
dropped and then the instant right before they hit the ground.
What’s the point?
Time of fall is dependent on acceleration, and acceleration is dependent
on the net forces acting on the object.
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AP Physics 1
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UNIT
7
Torque and Rotation
Rotational Kinetic Energy
EK
|
5.E.2, 4.C.1, 5.A.1, 4.C.2, 5.B.1, 5.B.3
SP
|
1.1, 1.4, 1.5, 2.2, 6.1, 7.2
Prepare
Just like when nonrotating objects are dropped, potential energy will be
converted into kinetic energy. When the object is rotating, there is both
translational and rotational kinetic energy. When looking at the rotating
extended objects, it is essential that forces are drawn directly where they
are exerted on the extended object.
Teach
When teaching rotational kinetic energy, show students that if the
rotational inertia of a rigid body is known, both rotational and translational
kinetic energies can be written in terms of the mass and the translational
velocity. You can show students that if the rotational inertia changes
(if the extended object is not rigid), the speed at the bottom of the incline
will also change. Try having a soup can race. If you can get soup cans
with approximately the same diameter and mass but different viscosity
(soup thickness), will they all reach the bottom of the incline at the same
time and with the same speed? Which soup can will win and why?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
If there was no friction between the object and incline, would the distance
found in Part D change?
What’s the point?
The rotational inertia will affect the acceleration of an object rolling down
an incline.
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UNIT
7
Torque and Rotation
Collisions
EK
|
3.F.3, 4.D.1, 4.D.2, 4.D.3, 5.E.1, 5.D.2
SP
|
5.1, 6.1, 7.2
Prepare
If there is a net external force on a system, momentum will not be
constant. Likewise, if there is a net external torque on a system,
angular momentum is not constant. Objects moving linearly can have
angular momentum, and the magnitude of that momentum will be the
linear momentum multiplied by the perpendicular distance from the pivot
point. Reviewing collisions and conservation of energy before assigning
this page is helpful for students.
Teach
Students may incorrectly make the assumption that in all collisions, linear
momentum is constant. They can be shown that there is a force between
the rod and the point where it is fixed to the table. Students may also be
confused as to why a linearly moving object has angular momentum. As
an extension, you can ask students what would change if the puck didn’t
stick but instead bounced backward in each case.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
If the mass of the puck is given as m 1 and the mass of the rod is given
as m 2 and has a length of l , calculate the final angular speed of the
puck-rod system in Cases A and D. Which case has the most kinetic
energy after the collision?
What’s the point?
Conservation of linear momentum and angular momentum are not
mutually dependent on each other.
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UNIT
7
Torque and Rotation
Translation vs. Rotation
EK
|
3.F.1, 3.F.2, 4.D.1
SP
|
1.4, 6.1, 7.2
Prepare
Without the presence of friction, objects will not roll on a surface. Also,
there must be a torque in order to create an angular acceleration and
hence a change in angular velocity. When an object is rotating and moving
linearly, it has both translational and rotational kinetic energy.
Teach
Explain how, in both cases, there is a downward force that is parallel to the
inclined plane. You can have students draw energy charts for both objects
to help them identify the transfer of energies and the type of energy
each has.
What would happen to the sphere if it rolled along the rough horizontal
surface and approached a smooth incline?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Write the force and torque equations for the wheel as it is rolls up the
incline. In terms of mass, angle, and radius of the wheel, what is the
acceleration of its center of mass?
What’s the point?
An object’s rotational motion can influence its translational motion.
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UNIT
7
Torque and Rotation
Rolling/Sliding/Both
EK
|
3.A.1, 3.F.1, 3.F.2, 4.D.1
SP
|
1.1, 1.4, 1.5, 2.2, 5.1, 7.2
Prepare
Every point on a rotating object has the same angular speed, yet different
points have different linear speeds. The linear speed is defined as v   r.
The linear speed increases as the radius increases.
Teach
Before teaching Part A, have students investigate the relationship
between the angular speed of points on a rotating object. Do
two horses at different radial locations on a carousel have the same
rotational speed? What about linear speed? All points on a rotating
object have the same angular speed, yet different linear speeds if
they’re at different radii. Students should be familiar with looking at given
expressions at this point and checking their plausibility. Make sure that
they know to look for direct or indirect relationships and think of the
physical aspects of each equation.
Before doing Part C, you may be able to track the rotational speed of
rotating objects in this scenario using a rotary motion sensor. Students
can then be shown how to create an angular velocity vs. time graph based
on the linear velocity vs. time graph.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A student states that the radius will not affect T. Explain in a few sentences
why the student’s conclusion is not correct. You may include equations
but not solely use equations.
What’s the point?
All points on a rotating object have a constant angular speed, but linear
velocity depends on distance from the axis of rotation.
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AP Physics 1
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UNIT
7
Torque and Rotation
Angular Momentum
EK
|
3.F.1, 3.F.3, 4.D.1, 4.D.2, 4.D.3, 5.E.1
SP
|
1.1, 1.4, 5.1, 6.1, 7.2
Prepare
When objects undergo elliptical orbits, the total energy and the angular
momentum stay constant. Because the radius changes, the potential
energy, kinetic energy, and speed will also change, keeping the total energy
and angular momentum constant. It is still a gravitational force that keeps
the object in the elliptical orbits, just like circular orbits. Even though the
angle between the radius and the velocity changes with the location in
the orbit, the gravitational force between the planet and the star is always
along the radius, so it can never cause a torque.
Teach
Show students how at every point, the distance between the planet and
the star changes. Therefore, either by using the conservation of angular
momentum or the conservation of energy, the speed must also change.
You can also use Kepler’s laws to show how the speed has to change in
order for the orbiting object to cover the same amount of area in the same
amount of time for different points in the orbit. You may want to go over
the graph given with this problem in detail and map out where the planet is
located throughout the graph.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A planet is undergoing an elliptical orbit around a star. At one point, it is a
distance R A from the star with a speed of vA and an angular momentum
of L A . At some other point R B , the radius increases. What does this do to
the speed of the planet and its angular momentum?
What’s the point?
Energy and angular momentum are constant during elliptical orbits.
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UNIT
7
Torque and Rotation
Massive Pulley
EK
|
3.A.1, 3.F.1, 3.F.2, 4.D.1, 5.E.2
SP
|
2.1, 2.2, 5.1, 6.1, 7.2
Prepare
The slope of a speed vs. time graph will give the magnitude of the average
acceleration, even if the slope changes as it does in this problem. Because
the radius at which the tension is exerted on the axle changes, the torque
provided by the tension will also change.
Teach
Show students that even though the slope of a graph doesn’t remain
constant, as long as they take the slope between two points (on a line
tangent to the curve), they can estimate what the slope is. You can
demonstrate an example of this problem by placing a thick cord around a
rotary motion sensor and showing example graphs or even by tracking the
motion of the hanging mass using a motion sensor placed on the ground.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Assume that you had a second string that was the same length but much
thicker. How would that change the graph? Would the acceleration change?
What’s the point?
Torques can change in magnitude if the distance from the pivot to the
point of application of force changes.
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UNIT
7
Torque and Rotation
Frictional Torque
EK
|
3.F.1, 3.F.2, 4.D.1
SP
|
4.1, 4.2, 5.1, 7.2
Prepare
When a rotating object slows down, it is usually the force of friction that
applies a torque to decrease the rotational motion. Every object also has
a specific rotational inertia, which describes how easily that object can
change its rotational motion about a particular pivot point.
Teach
Students will be responsible for designing experiments to find different
quantities. In every experiment, a student can choose from multiple routes
to arrive at a feasible answer. Therefore, be sure to let students know that
there is no “one right way.” Show and explain to students the different
equipment that they could potentially see in a lab setting (even if your
school does not have the equipment). They will also need to know what
measurements can be taken from the lab equipment, so familiarize them
with taking data and using that data.
A main focus of this page is to assess that students understand the
difference between average and instantaneous velocity. A common
incorrect lab procedure involves students timing a number of rotations to
find the initial speed of the wheel, neglecting to include that the wheel is
slowing during that time.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A solid cylinder of mass m and radius R has a string wound around it.
A person holding the string pulls it vertically upward, such that the cylinder
is suspended in midair for a brief time interval Δt and its center of mass
does not move. The tension in the string is T, and the rotational inertia of
the cylinder around the axis is I =
during the time interval Δt is:
1
MR2 . The net force on the cylinder
2
A. mg
B. T  mgR
C. mgR  T
D. zero
What’s the point?
Multiple experimental methods can be used to correctly solve a problem.
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UNIT
7
Torque and Rotation
Rotational Inertia
EK
|
5.E.2, 4.C.1, 5.A.1, 4.C.2, 5.B.1, 5.B.3
SP
|
4.1, 4.2, 5.1, 7.2
Prepare
When a rigid body has a uniform density, we assume that the center of
mass is in the center of the rigid body. When a rigid body does not have a
uniform density, the center of mass can be anywhere. Using a fulcrum is
the easiest way to find the center of mass of a rigid body.
Teach
Demonstrate to the class how to find the center of mass of uniform and
nonuniform rigid bodies by balancing them on your finger.
Once again, students will be asked to design experiments, so make sure to
expose them to as much physics data collection equipment as possible.
Assess
To further assess student understanding
of the concepts addressed in this scenario,
you may want to ask students the
questions below:
A fisherman balances his rod on his finger
as shown. If he were to cut the rod along the
dashed line, would the weight of the piece on the left-hand side be greater
than, less than, or equal to the weight of the piece on the right?
What’s the point?
The center of mass is not always in the center!
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AP Physics 1
Workbook
UNIT 8
Electric Charge and
Electric Force
Misconceptions
Students usually come into AP Physics with a number of misconceptions about
electric phenomena, and many of them can be difficult for the students to wrestle
with. For one, students tend to think about “electricity” as a vague, general term that
can be used as a reasonable description of charge, force, current, and other ideas.
When it comes to electric charge, students often think that there are three kinds:
positive, negative, and neutral. This idea can be addressed by initially spending time
experimenting with charge and helping them to come to their own understanding.
Students may also know “likes repel and opposites attract” but may use this phrase
to mean that there are repulsive and attractive forces. Helping students understand
Coulomb’s law involves coaching students to conceptualize forces as interactions.
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AP Physics 1
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Scenario
Misconception
8.B, 8.E, 8.H, 8.I, 8.J
The electrical force is the same as the gravitational force.
8.B, 8.F, 8.H
Coulomb’s law applies to charge systems consisting of something other than point charges.
8.A
A charged body has only one type of charge.
8.H
Forces at a point exist without a charge there.
8.I
Acceleration and velocity are always in the same direction.
8.I
Acceleration is the same as velocity.
8.K
There is no gravity in a vacuum.
8.D, 8.K
Gravity only acts on things when they are falling.
8.F
An object that is speeding up has a positive acceleration, and an object that is slowing down has a negative
acceleration.
8.C, 8.E
Action-reaction forces act on the same body.
8.G, 8.H, 8.J
Equilibrium means that all forces on an object are equal.
8.K
There are no gravitational forces in space.
8.K
The moon stays in orbit because the gravitational force is balanced by the centrifugal force acting on it.
8.K
Centripetal force Fc 
mv 2
is a new force (to add to gravity, normal, and friction)
R
8.D, 8.K
Gravitational potential energy is the only type of potential energy.
8.K
Momentum and kinetic energy are the same.
8.L
The restoring force is constant at all points in the oscillation.
8.G
Torque is the same as force and in the same direction.
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AP Physics 1
Workbook
Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Draw a best-fit line through data.
Using Representations
8.H, 8.J
1.1
Plot data on a graph.
Using Representations
8.H
1.1
Scale and label axis.
Using Representations
8.H
1.1
Create and use free-body diagrams.
Using Representations
8.B, 8.C, 8.E, 8.H, 8.I, 8.J
1.1
Sketch a sample charge distribution.
Using Representations
8.A
1.1
Create and use a force diagram.
Using Representations
8.G
1.1
Sketch force, velocity, and/or acceleration vectors.
Using Representations
8.K
1.4
Relate the slope to a physical quantity.
Use an Equation/Data Analysis
8.I, 8.J, 8.L
1.4
Relate the area under the curve to a physical quantity.
Use an Equation/Data Analysis
8.I, 8.L
1.4
Use representations to answer questions.
Data Analysis
8.E, 8.F
1.5
Match shapes of graphs to relationships between variables.
Data Analysis
8.I
1.5
Re-express one type of graph as another.
Using Representations/Argumentation
8.I
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
8.B
2.2
Derive or calculate, including annotations.
Quantitative Analysis
8.B, 8.G, 8.H, 8.J, 8.K
5.3
Match graphs to equations.
Data Analysis
8.D
6.1
Identify a claim and evidence that can support that claim.
Argumentation
8.C, 8.D, 8.E, 8.F, 8.G, 8.J, 8.K, 8.L
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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UNIT
8
Electric Charge and Electric Force
Conservation of Electric Charge
EK
|
5.A.2, 1.B.1, 1.B.2
SP
|
1.1, 1.4, 6.1
Prepare
Before beginning this lesson, students will need to know that like-charged
objects or systems repel and unlike-charged objects or systems attract.
Teach
This is a difficult topic for students to understand conceptually. You can
give students pieces of clear tape and have them charge the tape by
putting the tape together and then pulling them apart. Have students
play with the charged tape, noticing how the charged tape interacts with
other pieces of tape, both charged and uncharged. Have students collect
evidence to support their claims.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Discussion
What evidence is there that has helped scientists to construct the two
charge model of electric charge? How does this evidence help us better
understand the world around us?
What’s the point?
An object can exhibit charge separation by the proximity of another
charged object.
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UNIT
8
Electric Charge and Electric Force
Electric Force
EK
|
3.C.2, 2.A.3
SP
|
1.1, 1.4, 2.2, 5.1, 6.1
Prepare
It is important to emphasize that Newton’s third law still applies to
electrostatic problems. In cases where the charges are different sizes, the
students can get confused about how the charges can differ in size, yet
the forces that they apply on each other are still equal in magnitude.
Teach
It is helpful for students to recap this type of problem in terms of planets
and gravity.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
Two charges of value Q and 2Q are separated by a distance D and exert a
force F on one another. The separation distance will now be increased to 2D.
How will the value of the force change in terms of the original force F ?
What’s the point?
Just because this is Unit 8 doesn’t mean that Newton’s third law isn’t
fair game!
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AP Physics 1
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UNIT
8
Electric Charge and Electric Force
Internal Forces
EK
|
3.C.2, 3.A.3
SP
|
1.1, 1.4, 6.1
Prepare
Remind students that free-body diagrams need to have the force vectors
begin on the object and point away. All forces must have unambiguous
labels to earn credit.
Teach
In earlier problems, students were asked to circle the system in question.
It is a good idea to have them start this problem by identifying the system.
This way, they can see what is considered internal.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap the Discussion Question
If Sphere A were to be removed from the cart and fixed in place, how would
the parts of this problem change?
What’s the point?
Remember the full definition of Newton’s second law: It is the SUM of the
forces on an object or a system that is equal to ma. If the net force is zero,
there will be zero acceleration.
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UNIT
8
Electric Charge and Electric Force
Conservation of Energy
EK
|
3.C.2, 5.B.4
SP
|
2.2, 4.1, 5.1, 5.3, 6.1, 6.2, 6.4, 7.2
Prepare
If students struggle with identifying graphing relationships, it is helpful to
do some basic review on the shapes of common graphs.
Teach
It is worth discussing what the sign of the potential energy function
means. For example, if the electric potential energy function is negative,
the two charges have the same sign and will spontaneously spread apart.
If the potential energy function is positive, the two charges are of opposite
sign, and it would take work to separate them. They are a bound system.
It is also worth reminding students about work and change in energy of
systems. Even though the electric force is not constant so work cannot be
directly calculated, since the electric force is toward the sphere, the work
done by the electric force on the point charge will be positive as the point
charge moves toward the sphere. This positive work increases the kinetic
energy of the point charge. It the force were bigger (e.g., a bigger charge),
the change in energy will be greater, so the final kinetic energy of the point
charge would be greater. Since kinetic energy depends on mass as well as
speed, mass also has to be considered.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Discussion Question
How would the motion of the point charge be different if it carried a
positive charge? Describe how the point charge’s velocity, acceleration,
and position changes with time.
What’s the point?
Predicting a quantity’s relationship with respect to others is a good skill to
evaluate the correctness of your answers.
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UNIT
8
Electric Charge and Electric Force
Equilibrium with Electric Force
EK
|
3.C.3, 3.B.1, 2.B.1, 3.A.2, 3.A.4, 3.B.2
SP
|
1.1, 1.4, 6.1, 7.1
Prepare
It can be helpful to remind students that the force of tension is always
exerted in the direction along the string but the length of the string itself is
unrelated to the magnitude of the tension.
Teach
A great problem-solving hint for students is to connect the word
“equilibrium” with the concept of forces. If they connect seeing that word
with using forces, they can have a strategy for solving the problem.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Discussion Question
Balloons 1 and 2 were determined to each carry a Charge Q and 2Q,
respectively. They now are rubbed again with fur so that the charge
distribution is the same on each. Will this change the angles at which
they hang?
What’s the point?
When an object or a system is in static equilibrium, remember that
all forces exerted on the object or system must balance. So be extra
careful of the lengths of vectors drawn in free-body diagrams.
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UNIT
8
Electric Charge and Electric Force
Forces and Acceleration (Motion Review)
EK
|
3.C.2, 4.A.2
SP
|
5.1, 6.1, 7.1, 7.2
Prepare
Have students read the opening paragraph and look at the cases before
jumping into the questions being asked. From the content of the prompt,
students can predict some things they might be asked, which will help
them get into the mindset of the question.
Teach
Have students sketch free-body diagrams for the sphere if they initially
struggle with the ideas presented in this question.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Discussion Question
Pick a case and describe what happens to position, velocity, and
acceleration of the sphere as time goes on.
What’s the point?
The AP Physics 1 curriculum is spiral in nature—things you learned very
early in the course are still fair game! Try and review a little bit of one unit
every night to prepare for the AP Physics 1 Exam.
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AP Physics 1
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UNIT
8
Electric Charge and Electric Force
Forces and Torques in Equilibrium
EK
|
3.C.2, 3.A.2, 3.B.1, 3.B.2, 3.F.1, 3.F.2
Prepare
Review of τ
SP
|
1.1, 1.2, 2.2, 6.1, 6.4, 7.2
= R ⊥F is needed to be able to work through Case 2.
Teach
Students should predict the magnitude of the torque on the rod caused
by the electric force on puck A compared to B before they begin the
derivation.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Question Design
Create a scenario like this one containing a rod with charged end
caps. Draw a series of charge configurations, one where the rod only
accelerates, one where it only rotates, one where it does both of these,
and the last having it in equilibrium.
Let students switch papers to check their work.
What’s the point?
Content integration is a key part of AP Physics 1 questions. Here, you are
exploring three different units in one question. Can you name them?
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AP Physics 1
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UNIT
8
Electric Charge and Electric Force
Equilibrium
EK
|
1.B.3, 3.C.2, 3.A.2, 3.B.1, 3.B.2
SP
|
1.1, 1.4, 2.2, 5.1, 5.3, 6.1, 6.3, 7.2
Prepare
If your students have never graphed really large or really small numbers
on a graph by hand, it will be useful to have a discussion about how it can
be done. Remind them that they can place the units (i.e., × 10−9C ) on the
axis, and then they can just label their scale 1, 2, 3, etc. See AP Physics C
2005 #2 for a review question about gravitation and circular motion that
requires students to graph large numbers.
It is also important to know here that although this is presented as a
scenario that could be completed in a laboratory, the magnitude of the
charge Q is large enough that the electric field due to the charge Q will
cause the dielectric breakdown of air out to about 5 cm . While a similar
experiment could theoretically be conducted with similar results, the
experiment explained here is fictional.
Teach
Students do NOT need to consider the electric or the gravitational forces
between particles. Why is this true? Because the magnitudes of the
masses of the grains and the charges of the grains are so small compared
to the mass of Earth and the charge of the sphere at the bottom that the
other intergrain forces can be ignored.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Make a claim about the sign of the charge on the sphere at the bottom. Is
it negatively or positively charged? How do you know? Justify your claim
with evidence.
Quick Quiz
If the sign of the bottom charge were reversed, determine the initial
acceleration of the grains of pollen. Have the students sketch a
free-body diagram and use it to support their claim.
What’s the point?
It is important for you to practice applications where charge is changed by
a fundamental unit. This is a reminder that electrons are the smallest value
of charge we can have.
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AP Physics 1
Workbook
UNIT
8
Electric Charge and Electric Force
Electric Force and Motion Review
EK
|
3.C.2, 3.A.2, 3.B.1, 3.B.2, 4.A.2
SP
|
1.1, 1.4, 1.5, 5.1, 5.3, 6.1, 6.4, 7.2
Prepare
To get the most out of this question, the relationship between a vs. t , v vs.
t , and x vs. t should be revisited.
Teach
Encourage students to label the charges with +/− so that they can refer
to the diagram later rather than having to reread the whole paragraph to
find the information they may need. Alternately, students can be coached
to make a table of information that is filled in as they read the paragraph to
keep track of all the information they are given.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Discussion
How would the motion of the cart change if the cart and the fixed charge
were of opposite signs?
What’s the point?
Three different representations of the problem are being connected:
graphing, creating free-body diagrams, and writing paragraph-length
explanations. This will help you enhance the meaning you get out of each
individual representation.
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AP Physics 1
Workbook
UNIT
8
Electric Charge and Electric Force
Oscillation
EK
|
3.C.2, 3.B.1, 3.B.3
SP
|
1.4, 2.2, 4.4, 5.1, 5.3, 6.1, 7.2
Prepare
Students should be able to estimate slopes at specific points and use
graphs to gather enough data to solve problems.
Teach
The magnitude of charge needed to balance a laboratory cart on an
incline is massive. The electric field due to this much charge would cause
the dielectric breakdown of air—and dangerous lightning! This scenario is
fictitious.
Extension question: Have students use the slope of the tangent line
around the equilibrium position to determine the spring constant of the
effective spring. Once students have discussed how to find the effective
spring constant for this system, you could have them determine the slope
and then use it to determine the period of the cart’s oscillation around the
equilibrium position.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Quick Quiz
If the angle of the ramp was increased, what, if anything, about the graph
would change?
What’s the point?
On the AP Physics 1 Exam, you will be asked to extract information you
need to analyze situations from graphs. The more you practice, the better
you will get!
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AP Physics 1
Workbook
UNIT
8
Electric Charge and Electric Force
Electric Force and Orbits
EK
|
3.C.1, 3.C.2, 3.B.1, 5.B.1
SP
|
1.1, 1.4, 2.2, 6.1, 7.2
Prepare
While looking at orbits, gravitational force, and electric force, the
opportunity arises to compare the strengths of these forces. Have
students calculate the value of the electrical force and the gravitational
force for an electron in orbit around a proton in a standard atom.
Be prepared to discuss the feasibility of this problem with your students.
The final answer for the charge needed to keep the two stars in orbits (in
part C) are catastrophically large. Reference LO 3.C.2.2. where students
are asked to connect the concepts of gravitational and electric force and
compare similarities and differences. Students need to think about how
they know when to include each force and when one can be appropriately
neglected from a calculation.
Teach
While the answer for Part C (ii) is written out all the way from first
principles, it is also important that students be able to think about
relationships. An alternate solution includes realizing that the net force
is now four times larger, which means that the electric force has to be
three times the gravitational force (so that the electric force plus the
gravitational force is four times larger than the gravitational force alone).
kQ 2
This means that 2 
R
fewer steps.
3GMm
, which gets you to the correct answer in
R2
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Question
What about our answers would be different if the kinetic energy of the star
was to become one-fourth of what it was calculated to be in Part B?
What’s the point?
What common mistake do you think the AP readers are looking for on
Part A (i)? If you can look at a problem and guess the common mistakes,
you can avoid making them!
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AP Physics 1
Workbook
UNIT
8
Electric Charge and Electric Force
Collisions Review/Electric Force
EK
|
5.A.2, 1.B.1, 3.C.2, 5.D.1
SP
|
2.2, 4.1, 4.4, 5.1, 5.3, 6.1, 7.2
Prepare
Students will need to remember the three types of collisions they learned
when studying momentum: elastic, inelastic, and perfectly inelastic.
Teach
A great testing strategy that can be taught in this problem is skipping a part
and moving on. During the test, students might feel tight on time. Rather
than scratching their heads in confusion, make sure they know to move
on to answer other parts and questions, so they can earn the maximum
number of points.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Is momentum constant during this collision? One student claims that it
is impossible for us to know if momentum is constant because we are
unaware of the mass of the pucks. Another student says that it should
be obvious that momentum is constant regardless of the pucks’ mass.
What do you think?
What’s the point?
This problem connects graphing, collisions, electrostatics, and energy.
Connecting concepts makes your understanding deeper.
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AP Physics 1
Workbook
UNIT 9
DC CIRCUITS
Misconceptions
Students may have several major, and deeply held, misconceptions about DC circuits.
One of the most common and most persistent is that the current is used up going
around a series circuit. There is a legitimate intuition here—energy is transferred
from the battery to the circuit elements—however, current is not used up. Asking
students a few probing questions about why current values are the same around a
series circuit should help dispel this misconception.
Another misconception students often have is that the battery is the source of the
current rather than the source of the energy and the charges that flow through the
circuit all start at the battery. Students also incorrectly believe that batteries are
constant current sources.
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AP Physics 1
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Scenario
Misconception
9.H, 9.I
Current is the flow of energy.
9.B, 9.D
The battery is the source of current.
9.C
The circuit is initially “empty” of the “stuff” that flows through conductors.
9.B, 9.C, 9.D,
9.E, 9.F
The battery releases the same, fixed amount of current to every circuit.
9.B
Resistors consume charge.
9.H
Charge carriers slow down as they go through a resistor.
9.B, 9.D, 9.E, 9.F
Current is the same as potential difference.
9.G
There is no current between the terminals of a battery.
9.A
A circuit does not have to form a closed loop for current to flow.
9.B
Current gets “used up” as it flows through a circuit.
9.K, 9.N
A conductor has no resistance.
9.C
The bigger the battery, the more potential difference.
9.J, 9.L, 9.M, 9.O
Power and energy are the same thing.
9.C, 9.M
Batteries create energy out of nothing.
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AP Physics 1
Workbook
Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Draw a best-fit line.
Using Representations
9.G, 9.O
1.1
Plot data on a graph.
Using Representations
9.C, 9.M, 9.O
1.1
Scale and label axis.
Using Representations
9.C, 9.M, 9.O
1.2
Find the area under a curve.
Quantitative Analysis
9.E
1.2
Find the slope of a best-fit line.
Quantitative Analysis
9.G, 9.O
1.4
Create and use a circuit schematic.
Using Representations
9.C, 9.D, 9.I, 9.J, 9.K
1.4
Create and use a potential vs. position graph.
(Kirchhoff’s Loop Rule)
Using Representations
9.C
1.4
Relate the area under a curve to a physical quantity.
Quantitative Analysis/Data Analysis/
Argumentation
9.E
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
9.G, 9.O
1.5
Linearize a graph.
Using Representations
9.O
2.1
Defend the use of an equation to solve a specific problem.
Quantitative Analysis
9.I, 9.J, 9.M, 9.N
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
9.B, 9.D, 9.E, 9.F, 9.G, 9.H, 9.I, 9.J,
9.K, 9.L, 9.M, 9.N, 9.O
2.2
Rearrange an equation to solve a specific problem.
Quantitative Analysis
9.H, 9.I, 9.K, 9.N, 9.O
4.1
Choosing correct data to answer a question.
Data Analysis
9.C, 9.F, 9.G, 9.J, 9.M, 9.O
4.2
Choose equipment to conduct a scientific experiment.
Experimental Design
9.K
5.3
Use a linearized graph to answer a question about a
physical quantity.
Quantitative Analysis
9.G, 9.O
6.4
Identify a claim and evidence that can support that claim.
Argumentation
9.C, 9.E, 9.G, 9.J, 9.L, 9.N, 9.O
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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UNIT
9
DC Circuits
Open and Short Circuits
EK
|
1.B.1
SP
|
4.1, 5.1, 6.1
Prepare
By definition, a circuit is a closed loop of electrical current. An open circuit
is simply not closed. Understanding these vocabulary terms is vital to a
student’s chances of having success with questions about DC circuits.
Strong vocabulary not only helps the student figure out the correct
response but also helps with the justification.
Teach
Students may have no experience using circuits and cannot see
interactions on the level of an electron. Creating tangible, simple
experiences for them is an excellent way to lay the framework for
understanding. A simple “Can you find ways to make the light bulb light?”
investigation using small low-voltage light bulbs, wire, and batteries allows
students to discover the basic elements of circuits. Provide chances for
students to see what works and what does not. Lead them through a
discussion about open vs. closed circuits. One of the characteristics they
can see is that a closed loop is necessary for the current to go through
the bulb.
For such an activity, the instructor should warn students against setups
that yield short circuits. Have students hold the wire by hand on the circuit
elements (bulb and low-voltage battery). The wire rapidly heats up if there
is a short circuit. If the wire gets hot, remove it from the circuit element
and try and different placement!
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Which of the following light bulbs will be on and which will be off? Why?
(Use images of simple circuits with various open branches, closed
branches, and/or shorts.)
What’s the point?
Whether it is an open circuit or a short that destroys the circuit, the
behavior can be explained through properties (i.e., conductivity, resistivity)
of the material. Air is not a great conductor, so an open circuit that has a
separation of air may prevent electron flow. However, humid air or small
distances of air may yield sparks as electric charge carriers will ultimately
try to seek a lower state of potential energy.
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UNIT
9
DC Circuits
Series Circuits
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
4.1, 5.1, 6.1
Prepare
The main idea here is that the geometry of the resistive material affects
its resistance. While dealing in the realm of the nonvisible, think of tangible
real-world experiences whose properties depend similarly on geometry
such as the length of a traffic backup and its effect on travel time (or the
lunch line), the number of open lanes at the grocery checkout, etc.
Teach
This concept could be taught in combination with resistance in parallel.
In large-group discussions, consider advantages and disadvantages of
arranging light bulbs in series vs. parallel.
A laboratory opportunity could be made using a long cylindrical conductor
such as a ring stand bar or other available metals. Students can adjust
where along the bar they connect an alligator clip to complete a circuit
and take measurements of current with an ammeter. Students may
evaluate how the effective length (the material between alligator clips or
connection points) relates to current as an indication of resistance. This
may also be a good lead into Ohm’s law.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Check for understanding with an array of cylindrical resistors of simple
geometries.
Cylindrical resistors can be made of the same material but have different
dimensions for radius r and length L .
Rank the resistors in order of their resistance.
A. r, L
B. 2r, 2L
C. 1 r, L
2
D. 2r, 4L
What’s the point?
Since we understand that resistance is dependent on the geometry of
resistive material, engineers are able to create specific resistance values
out of raw materials by manipulating their shape. How cool?!
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Qualitative Electric Potential Diagram
EK
|
1.B.1, 5.B.9
SP
|
1.1, 1.4, 1.5, 5.1, 6.1
Prepare
Graphing skills, such as sketching and interpreting, are an important part
of the course. Prepare students to investigate the axes and ask themselves
“Is the product of the quantities on the axes the unit of another physical
quantity? If so, the area under a graph drawn on these axes can be used
to evaluate the value of this quantity.” and “If the quotient of the units
on the vertical to horizontal axes has a physical meaning, then this
quantity can be found from a slope of a graph on these axes.” Sometimes,
there are physical concepts such as energy or momentum as a result of
the multiplication or division. Sometimes, the area or the slope can have
no meaningful associated term. In Part D, the product of the axes has a
physical meaning of charge (coulombs per second times seconds). The
area under a graph of current versus time can be used to determine the
total charge.
When sketching a trend, one may think about what is happening to a value
while another value changes. Is there a relation? Is the relation linear?
Quadratic? etc. In Part B, between points C and D, the student must
evaluate how electric potential decreases (linearly, inversely, etc.). Since
V is directly proportional to R by Ohm’s law, and R is directly proportional
to length by the resistance formula, V will be directly proportional to L ,
meaning that electric potential is lost proportionally to the additional
length as your position progresses down the resistor. This direct relation
(and a negative change) yields a linear trend.
Teach
Graph bingo is an idea to get students comfortable evaluating
combinations of variables and graphing them.
In graph bingo, print the standard AP equation sheet and a set of variable
cutouts (literally every variable on the sheet: mu , F, t , etc.). Students
draw cards (variables) until they can make a meaningful graph using
three variables: one for each axis and one for a graph property.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
A variable resistor is connected to a 12V power supply in a simple
circuit. An ammeter is connected to measure current, and a voltmeter is
connected to either end of the resistor to measure potential difference
across the resistor. The resistor is adjusted and values of current as well
as potential difference are recorded.
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Identify the trend of:
1. Resistance vs. current
A. Linear
B. Inverse
C. Quadratic (polynomial of second order)
D. No relation
2. Potential difference vs. resistance
A. Linear positive
B. Linear negative
C. Linear horizontal (no change)
D. Quadratic (polynomial of second order)
E. Not given
What’s the point?
Familiarity can be a crutch that some students use to gain confidence in
certain areas. However, when presented with unfamiliar scenarios, these
students can experience a lack of confidence. There may be a graph on
the AP Exam that a student has never seen before, and this can be a blow
to their confidence. By focusing less on remembering graphs and adopting
the process of evaluating axes for meaning, a student can feel confident
that they can interpret any AP Physics 1 graph presented to them.
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AP Physics 1
Workbook
UNIT
9
DC Circuits
Parallel Circuits
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
2.2, 4.1, 5.1, 6.1
Prepare
Adding resistors in parallel is a geometric manipulation of resistive
material by widening the cross-sectional area available for travel. Parallel
branches provide more pathways for electron flow, reducing total
resistance.
A difficult concept for students to grasp is that when adding resistors
in parallel, even those with very large resistance, total resistance is
always reduced. It is important for students to conceptualize how this is
happening.
Teach
While this is still in the microscopic realm and students may be lacking
tangible experiences to picture electron behavior, modeling can be helpful.
Have students volunteer to “resist” flow and line them up in a straight line
with the objective of passing tennis balls or any plentiful object forward.
Give each student a resistive task such as performing three jumping jacks
or reciting the alphabet before passing the ball on to the next person.
Have students observe the rate at which the “electrons” flow through the
medium. Then manipulate the circuit by adding another parallel branch of
student resistors/wires. Have the class predict if the flow will increase or
decrease and discuss why.
Real-world models include opening up multiple lanes at the checkout
to get more customers through the store, opening more gates at
stadium entrances . . .
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Resistors A, B, and C are made of the exact same material. The geometries
are drawn to scale with lengths B and C twice that of length A and
cross-sectional area of A and C one quarter that of B.
Draw an arrangement of resistors B and C that would yield the same
resistance as resistor A. Use as many resistors and as much wire as needed.
What’s the point?
The total resistance of a set of resistors in parallel is smaller than the
smallest resistance.
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Workbook
UNIT
9
DC Circuits
Kirchhoff’s Loop Rule and Ohm’s Law
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
4.1, 5.1, 6.1
Prepare
Reasoning is a skill that is valuable both in and out of the classroom.
Students must be able to go beyond simply choosing a correct answer
from a limited set of choices. They should also be able to use valid lines
of reasoning to support why a statement or a claim is true or false. One
can expect to see plenty of reasoning prompts all over the free-response
portion of the AP Exam, including but not limited to the paragraph-length
response. The paragraph-length response is one you want to encourage
students not to skip or cut short because it is a high point-density prompt.
Teach
Students may encounter many types of reasoning prompts on the
AP Physics 1 Exam. The paragraph-length response is perhaps the most
thorough, yet the requisite reasoning skills needed does not differ much
from the typical “justify your answer” or “evaluate person A’s reasoning
when they said X.”
In each case, encourage students to use firmly established laws/principles
to support their claims. For example, consider the voltage across resistors
in the parallel circuit. To say “the voltage drop across r p is equal to the
voltage drop across R p ” is a correct statement. However, it may not score
points until students support the statement with “each resistor makes a
loop with only the battery, so they have the same voltage by the loop rule.”
The main idea is to get students to reason their claims by supporting their
writing using the laws/principles of physics.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Angela observes both circuits (same diagram from this page) and states,
“The number of electrons per second leaving Rp is less than the number
of electrons per second moving away from the battery.”
What physical law do you think can be used to support her claim (or refute
it if incorrect)? Why/How?
What’s the point?
There is rarely a physics prompt that cannot be answered without citing a
valid principle. Just make sure you provide evidence for your citation!
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AP Physics 1
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UNIT
9
DC Circuits
Reasoning with Ammeters and Voltmeters
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
1.1, 1.4, 1.5
Prepare
Major concepts culminate here to make it possible to predict voltmeter
and ammeter readings. Ohm’s law and Kirchhoff’s rules (loop and junction)
are all needed to successfully resolve the unknown values. Having
students attempt this problem has the added benefit of reinforcing the
correct placement of ammeters and voltmeters.
Teach
A laboratory investigation of Kirchhoff’s rules is highly recommended
before attempting applications like this. Allow students to measure the
potential difference and current at points or across elements of simple
circuits (if materials available).
Use variations of simple diagrams with labeled points like the figure below.
Prompts could ask students for current at particular points (A, B, C, or D)
or potential differences (i.e., determine ΔVab , ΔV ac , ΔV bd , ΔV ad . . . )
and as many combinations as necessary for students to solidify their
understanding, including the switch on or the switch off.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Another student connects each of the circuits below, using the same
resistors, batteries, and meters.
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A. The student draws the reading on the ammeter for Circuit X as shown
below. Draw what the other two ammeters should read. In the other
two diagrams, the reading for Circuit X is shown for reference.
B. The student draws the reading on the voltmeter for Circuit X as shown
below. Draw what the other two voltmeters should read. In the other
two diagrams, the reading for Circuit X is shown for reference.
C. Complete the following two sentences:
If the power delivered to one resistor in Circuit X is P, the power
delivered to one resistor in Circuit Y is __________.
If the power delivered to one resistor in Circuit X is P, the power
delivered to one resistor in Circuit Z is ___________.
Determine the resistance of the identical resistors.
What’s the point?
Ultimately in AP Physics 1, the circuits to evaluate will not be very complex,
and a student should feel confident they can find current at any point and
potential difference across any two points.
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AP Physics 1
Workbook
UNIT
9
DC Circuits
Internal Resistance
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
1.1, 1.4, 2.1, 2.2, 4.1, 5.1, 6.1
Prepare
The key concept is that batteries have internal resistance that can be
evaluated as a separate resistor within the power supply. The internal
resistance is subject to the same circuit rules as external resistors.
Graphing skills, including evaluating the meaning of slope, are also
important for this question. (See previous remarks regarding graphing.)
Teach
Prior to this conceptual step, students have been thinking of a battery as
one object. Now, they unpack more detail and need to distinguish interior
elements and properties. This is an excellent time to ensure that they
have a firm grasp of the vocabulary. At this point, they have done potential
difference measurements and some problem solving with regard to the
loop rule. However, the terms voltage and/or potential difference may still
give them trouble. Check if they understand the word “potential” and can
distinguish it from “potential difference.” Throwing the term emf into the
mix before they can successfully define the others may not go over well. It
is worth the class time to do a short writing prompt and group discussion
on the topic. Ask “What does the word voltage mean?” See what they
write. If they hinge their reply on “potential difference,” press that and ask
them what potential difference means.
Assess
To further assess student understanding
of the concepts addressed in this scenario,
you may want to ask students the
questions below:
Using colored pencils or highlighters, label
branches with a unique color to represent
electric potential. Any two points that have
a potential difference between them is to be
drawn a different color (as shown in figure).
What’s the point?
If you can become comfortable with the terms voltage, potential
difference, and emf, the payout will show in your writings. Misconceptions
such as “voltage splitting at a junction” can be easily thwarted.
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UNIT
9
DC Circuits
Power
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
4.1, 5.1, 6.1
Prepare
The key idea is that power is the rate of energy transfer (power = work/
time). An exercise in algebra can connect the concepts of power, energy,
time, charge, potential difference, current, and electrical resistance to
reveal several different ways to express power with other variables.
Another key concept/skill needed for this page is reasoning. (See the
previous remarks regarding justification/reasoning.)
Teach
Put the challenge of making these connections on the students as a way
of not only sharpening their algebra skills but also giving them the chance
to take ownership of the equations.
Begin with the definitions (expressions):
Power = change in energy per unit time
Electric potential difference = energy/unit charge
Current = the amount of charge that passes a point in a circuit
per unit time.
and Ohm’s law: ΔV = IR
Ask your students how many ways they can write a simple expression for
power and see what they generate.
Assess
To further assess student understanding of the concepts addressed in this
scenario, you may want to challenge students with the scenario below:
Using various simple circuits, ask students to determine values for power
for resistors and/or prompt them to rank brightness of bulbs.
What’s the point?
As in other chapters, there are equations that are always true and others
that are established for specific conditions such as a net force expression.
In this unit, students become familiar creating their own Kirchhoff loop
expressions and understanding universal formulas for potential difference,
power, current, and resistance.
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AP Physics 1
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UNIT
9
DC Circuits
Building a Lightbulb
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
1.1, 1.4, 2.2, 4.1, 5.1, 6.1
Prepare
Kirchhoff’s loop and junction rules are critically important for student
success on the AP Physics 1 Exam. Students need to feel comfortable
using Kirchhoff’s rules as evidence for claims and need to be comfortable
rearranging the equations as necessary to match the given situation.
Students who memorize a loop or junction rule for a specific circuit will
not have the skills necessary to analyze any given situation. It is important
to note here again, that all batteries on the P1 exam are “ideal” batteries,
meaning that they will not have internal resistance. If your students
struggle with this question, its okay to skip it and spend more time on
the basics!
Teach
Have students practice using Kirchhoff’s rules as evidence for claims
about current, voltage drop, and power. There are only a handful of circuits
that are likely to show up on the AP Physics 1 Exam. Making sure students
are able to think through the functions, behaviors, and interactions
between circuit elements is very important.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Design an experiment to determine the internal resistance of a battery.
Does the internal resistance change throughout the life of the battery?
Quick Quiz
Kirchhoff’s loop rule for circuit analysis is an expression of which of
the following?
A. Conservation of charge
B. Conservation of energy
C. Ampere’s law
D. Ohm’s law
What’s the point?
Kirchhoff’s loop and junction rules will help you analyze and understand
circuits. Ask for help if you are struggling with writing these equations for
various circuits!
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UNIT
9
DC Circuits
Non-Ohmic Resistors
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
1.1, 1.4, 4.1, 5.1, 6.1
Prepare
It is important to introduce your students to the many possible vocabulary
words they could expect to see on the AP Physics 1 Exam. Although
students have heard of Ohm’s law, many students are stumped when
asked to design a lab around a non-ohmic resistor on the AP Physics 1
Exam. Non-ohmic resistors do not follow Ohm’s law. Students should be
able to determine whether or not a resistor is non-ohmic if they measure
the potential difference across and the current through a resistor. If the
result isn’t a linear graph, then it is a non-ohmic resistor.
Teach
Consider giving students the opportunity to create potential difference vs.
current graphs for traditional resistors and then for light bulbs. What is the
difference? Why do light bulbs behave as they do?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Design a laboratory experiment to determine if a certain circuit element
is ohmic.
What’s the point?
It is important to recognize that the graphs you may see on the AP Physics
1 Exam may include “real-life” graphs including errors and scatter. The
graphs shown in textbooks are often perfect and clean, so you want to
make sure that you are comfortable looking through the scatter and issues
with the data to see the patterns underneath.
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AP Physics 1
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UNIT
9
DC Circuits
Resistivity
EK
|
SP
1.B.1, 1.E.2, 5.C.3
|
4.1, 4.2, 4.3, 5.1, 6.1
Prepare
It will be helpful if you have students not only design this lab but also
conduct it. You can use store-bought or homemade modeling compound
for the clay and then either batteries or power sources as available.
Teach
Again, on this page, the word ohmic appears. If your students completed
the previous page, they should feel more comfortable with this word, what
it means, and how to test for it.
If students are completing this lab in class, be sure that they have the
ammeter and voltmeter connected correctly before closing the circuit, as
incorrect placement can damage the meters.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Students collect the following data about the current flowing through long
cylinders of conductive clay. All the clay cylinders have the same crosssectional area of 1 cm 2 and are each connected to a brand new 9-volt
battery. Use the following data to create a linearized graph with which you
can determine the resistivity of the clay.
Length (m)
Current (A)
0.1
1.40
0.3
0.36
0.2
0.4
0.5
0.6
0.7
0.63
0.27
0.22
0.19
0.17
What’s the point?
Resistivity is a property of the material and will not change even if the
shape of the resistor changes. The resistance of a resistor depends on the
resistivty and also on the shape of the resistor.
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UNIT
9
DC Circuits
Brightness vs. Labeled Wattage
EK
|
1.E.1, 5.B.9, 5.C.3
SP
|
4.1, 5.1, 6.1
Prepare
This is a difficult topic, and it is helpful for students to be able to see this
for themselves. You can set this up by getting two different wattage bulbs
(e.g., 25W and 100W ) and connecting them in parallel. When both receive
the same potential difference, the 100W bulb is brighter. Then connecting
the two bulbs in series. When both receive the same current, the 25W bulb
is brighter.
Teach
When going to the store to buy light bulbs, we buy them based on
wattage—the bigger the wattage, the brighter the bulb. This takes into
account a very specific assumption that the consumer is using the bulb
correctly and plugging the bulb in so that it gets 120V from the outlet.
Why do you think that bulbs are rated this way?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
The four resistors shown below have the lengths and cross-sectional
areas indicated and are made of material with the same resistivity. Which
resistor has the least resistance?
What’s the point?
Is a higher wattage bulb always brighter regardless of the circuit it is in?
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AP Physics 1
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UNIT
9
DC Circuits
Current and Power vs. Time
EK
|
1.B.1, 5.B.9, 5.C.3
SP
|
1.1, 1.4, 1.5, 2.2, 5.1, 6.1
Prepare
These are idealized graphs of current and power as functions of time.
Discussions of what these graphs would look like in real life would help
students make the connections between what they are seeing here and
what they might see in the laboratory.
Teach
How would these graphs be different for a circuit that consists of
three resistors? All in series? All in parallel? As connected below?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
The batteries in each circuit shown below are identical, and the wires have
negligible resistance. Which circuit dissipates the LEAST power?
What’s the point?
You are likely to see graphs on the AP Physics 1 Exam that you have never
seen before. Take a deep breath and take a minute to carefully read the
axes and think about what the graph is telling you. What relationships exist
between the variables that are being graphed? Is there an equation that
already exists to help you understand the relationship?
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UNIT
9
DC Circuits
Resistivity vs. Resistance
EK
|
1.B.1, 1.E.2, 5.B.9
SP
|
2.2, 5.1, 6.1
Prepare
This activity can be done in class with an immersion heater and water.
Teach
Connections to chemistry: What if this experiment was done with a
different liquid? How would that affect the experiment?
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
You are given a constant source of potential difference V0 and three
resistors R 1, R 2 , R 3 , with R 1 > R 2 > R 3 . If you want to heat the water in a
pail, which of the following combinations of resistors will give you the
most rapid heating?
What’s the point?
Even if you are not asked to annotate your derivations, doing so will help
the AP readers understand your logic and your answer.
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UNIT
9
DC Circuits
Resistivity and Real Batteries
EK
|
1.B.1, 1.E.2, 5.B.9
SP
|
1.1, 1.4, 4.1, 5.1, 6.1
Prepare
Students can calculate the slope using a calculator if given data that they
can plug in. However, if they make a mistake, there is no work on the paper
to back them up and show that they understand what they are doing.
When calculating the slope on the paper, it is important that students
show which points they are using and that they are not using data points
in their calculation. For help on how to scaffold finding the slope, look in
Unit 1 of this workbook.
Teach
When connected to a sufficiently high source of potential difference, a piece
of graphite pencil lead will glow. Have students create a “light bulb” by putting
the pencil lead inside a mason jar.
Is the pencil lead ohmic? How can you tell? Support your claim
with evidence.
Note that Part D relies on students understanding internal resistance in a
battery which is not a part of the AP Physics 1 curriculum. This part can be
made optional.
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Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
The circuit shown above contains two resistors of resistance R and 2R .
The graph shows the total energy E dissipated by the smaller resistance
as a function of time. Which of the following shows the corresponding
graph for the larger resistance?
What’s the point?
The occasions for you to solve for a numerical answer on the AP Physics 1
Exam will be few and far between. Don’t forget that when solving for a
number, that number needs units!
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AP Physics 1
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UNIT 10
Mechanical Waves
and Sound
Misconceptions
Most students have limited experience with waves, so they have fewer long-standing
misconceptions getting in the way of conceptual understanding. One of the most
widely held student misconceptions about mechanical waves is that changing one
wave characteristic (amplitude, frequency, etc.) changes the speed of the wave.
Telling students repeatedly that this is not the case is not as effective at dispelling
this misconception as giving them opportunities to experiment with these variables
and solidify their understanding through inquiry.
Another primary misconception comes once you introduce transverse and
longitudinal waves. Students will have experience seeing what they consider water
waves, even if only in the bathtub, without considering that this clearly transverse
motion comes at a boundary. It can help to have them do some simple physical
models, such as having students stand next to each other and propagating a wave
down the line of students by each lifting their right hand in turn. If the students are
holding hands (or holding onto a string), then they can tell when the person next to
them lifts their hand. If they are not somehow connected and they close their eyes,
the wave does not propagate. The string or held hands makes the connection between
students stronger, like the connection between molecules in a solid. Disconnected
molecules, unable to exert a shear force, are more like fluids or gases. Then you can
have them try to propagate a wave of shifting slightly to the right (without moving
their feet). If they are standing close enough together, this wave will propagate
even if their eyes are closed because each student bumps into the next. This is why
longitudinal waves can propagate in solids, liquids, or gases.
Sound waves can vibrate objects. Oscillating pressure from a sound wave causes
our eardrums to vibrate, which ultimately leads to our perception of sound. Students,
however, may also think that sound waves can move objects. Students may have seen
commercials showing a man listening to a set of speakers with the scarf around his
neck flying out away from the speakers and believe that sound waves can cause an
object not only to vibrate but to physically move. Challenge students to confront this
misconception and provide evidence for why this cannot be true.
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Lastly, students often have trouble understanding that there are two speeds
associated with mechanical waves: the speed of the wave itself moving through the
medium and the variable speed of the particles of the medium.
Scenario
Misconception
10.E
Waves transport matter.
10.A, 10.F
All waves travel the same way.
10.L
Frequency is connected to loudness for all amplitudes.
10.I, 10.L
Big waves travel faster than small waves in the same medium.
10.F, 10.G, 10.I
Pitch is related to intensity.
10.C, 10.D
Waves bounce off each other.
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AP Physics 1
Workbook
Skills
The design of the AP Physics 1 course and exam focuses on seven overarching
practices that capture important aspects of the work of scientists. Science practices
describe the skills and abilities that students should learn and demonstrate, integrated
with content knowledge, to reach a goal or complete a learning activity. While the
skills listed below are critical to student success, most of them are scaffolded skills
necessary for students to be successful at the science practice listed with each skill.
Science Practice
Related Skill
Prompt Heading
Scenario
1.1
Create and use standing wave diagrams.
(Open-Open and Open-Closed)
Using Representations
10.F, 10.G, 10.J
1.1
Demonstrate superposition of pulses.
Using Representations
10.D, 10.G, 10.K, 10.L, 10.O
1.1
Draw a best-fit line through data.
Using Representations
10.B
1.1
Plot data on a graph.
Using Representations
10.B
1.1
Scale and label axis.
Using Representations
10.B
1.1
Sketch force, velocity, and/or acceleration vectors.
Using Representations
10.E
1.4
Create and use diagrams showing beats.
Using Representations
10.G, 10.O
1.4
Demonstrate what pulses do at barriers.
Using Representations
10.C, 10.K
1.4
Relate the slope to a physical quantity.
Quantitative Analysis/Data Analysis
10.B
1.4
Use representations to answer questions.
Using Representations
10.A, 10.B, 10.C, 10.D, 10.E, 10.F,
10.G, 10.H, 10.J, 10.K, 10.L, 10.O
1.5
Re-express one type of graph as another.
Using Representations/
Building an Argument
10.F
2.1
Identify an equation that can be used to solve a problem.
Quantitative Analysis
10.B, 10.E, 10.F, 10.G, 10.I,
10.J, 10.M
6.1
Identify a claim and evidence that can support that claim.
Building an Argument
10.B, 10.C, 10.D, 10.E, 10.I,
10.N, 10.O
A full list of the Science Practices can be found on page 370 in the Appendix of this workbook.
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UNIT
10
Mechanical Waves and Sound
Properties of a Wave
EK
|
6.A.1, 6.A.2, 6.A.3, 6.A.4, 6.B.1,
6.B.2, 6.B.4
SP
|
1.1, 1.4, 1.5, 6.1
Prepare
Show students both graphs of waves where the x-axis is position and
where it is time. Talk about the differences in those graphs and the
advantages of each.
Teach
Using a simple slinky, students can recreate the waves in this problem with
a partner. Set the students up in a hallway or the gym where they have
room to create these waves. If students have access to cameras, they
can document the waves they create and label their own pictures with
amplitude, wavelength, etc.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to challenge students with the task below.
Print out graphs where there are wavelengths displayed in different ways
(crest-crest, trough-trough . . . ). Some labels should be incorrect, and
students can try to pick out which ones are truly one wavelength.
What’s the point?
Linking the motion of the source to the attributes of the wave will help you
better understand the physical meaning of wave attributes.
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UNIT
10
Mechanical Waves and Sound
Relationship Between Wave Speed, Frequency, and Wavelength
EK
|
6.A.1, 6.A.2, 6.B.1, 6.B.2, 6.B.4,
6.D.2, 6.D.3, 6.D.4
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 6.1
Prepare
Remind students how to linearize data. Write down an equation relating
the variables, then manipulate the equation to isolate what should be on
the y -axis. This will help students map the variables to the basic linear
expression y = mx + b. Look for old AP Physics 1 or Physics B questions
that ask students to linearize data. You don’t have to do the whole
question—simply focusing on the linearization part and asking students
to write down how they would manipulate the data to be able to create a
linearized graph is good practice.
Teach
This lab setup is a great demo to do in class. The students will have
something to constantly reference when thinking about waves.
If you have the equipment, tilt the experiment 90 degrees and replicate
question #5 from the 2016 AP Physics 1 Exam. Why does the wavelength
of the wave change?
Assess
To further assess student understanding of the concepts addressed in this
scenario, you may want to challenge students with the scenario below:
Have students draw four graphs of their own, like in Part F. They can be
triangle, square, or sine waves. Students can trade with a partner and pick
out the graphs with the largest amplitude, frequency, and wavelength.
What’s the point?
Linearization an important skill for the AP Exam. Any lab question
that asks about data analysis may require linearization or at minimum
graphical interpretation.
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AP Physics 1
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UNIT
10
Mechanical Waves and Sound
Superposition of Wave Pulses
EK
|
6.A.1, 6.A.2, 6.A.3, 6.A.4, 6.D.1
SP
|
1.1, 1.4, 5.1, 6.1, 6.4
Prepare
There are several online simulations that can be helpful for students
to visualize the interactions between waves. Look for one that allows
students to change the amplitude, wavelength, and frequency as well as
the end boundary from fixed to free.
Teach
This is an exercise best reinforced with a long slinky, snakey spring, or
string. An easy way to create an open end is by tying a string into a loop at
the end and sliding the loop over a pole. Another option is to put a metal
keychain on the end of the slinky and letting that slide along a horizontal
ring stand pole.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Complete Part C again but have one of the students send an
upside-down pulse.
What’s the point?
Reflection at a boundary is important for students to understand if they
are going to work with standing waves later. Wave superposition is also a
fundamental aspect of waves.
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AP Physics 1
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UNIT
10
Mechanical Waves and Sound
Superposition of Wave Pulses
EK
|
6.A.1, 6.A.2, 6.A.3, 6.A.4, 6.D.1
SP
|
1.1, 1.4, 5.1, 6.1, 6.4
Prepare
Playing with online simulations one way to help students think through
how pulses interact. Students can access online simulations for free that
allow students to select different-shaped pulses on a string and see the
unique shapes created when the waves interact.
Teach
As students work through these, you can give them several tips. The first
is to lightly sketch in each individual pulse and then highlight over the
region where there is no overlap. (As that string position is just along the
pulse.) Then add the values of each pulse for the squares where the pulses
do overlap and plot that value. Connect, with a highlighter, each side
through the points to the far side.
Assess
To further assess student understanding of the concepts addressed in this
scenario, you may want to challenge students with the scenario below:
Have students repeat this exercise using a square and triangle pulse. Make
them set up the pulses two ways. In one case, they add to be higher, while
in the other, they act destructively. With only instructions about using the
shapes of a triangle and a square, the students should come up with a
variety of graphs that then can be shown to the class.
What’s the point?
The principle of superposition is simple at its core but can be tricky!
Make sure you get plenty of practice adding and subtracting waves!
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Displacement of Wave vs. Displacement of Medium
EK
|
6.A.1, 6.A.2, 6.A.3, 6.A.4, 6.B.1,
6.B.2, 6.B.4
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 5.1, 6.1, 6.4
Prepare
It is important for students to understand that the wave propagates
through the material. The particles move up and down while the wave
travels horizontally. The best way for students to get that is to have them
do “the wave.” The student on the left side of the room will raise their
hands, the next student to their right will follow by raising their hands, and
so on. The wave travels right but the student’s hands only go up and down.
Although students do not need to memorize the equation for the speed of
a wave on a string as a function of mass, length, and tension, they should
be familiar with it and understand why it makes sense that if you increase
the tension, the speed increases.
Teach
Particles “ride the wave.” This is analogous to a leaf floating on the
surface of a pool. If you toss a rock into the pool, a wave pulse is caused
by the rock. The wave pulse travels outward, moving away from the
disturbance, but the leaf bobs up and down. If you imagine instead using
your finger to dip in and out of the water repeatedly, your motion would
cause a series of wave fronts that look similar to the wave on the cord
in this scenario. The wave on the cord had to be caused by someone or
something moving the end up and down repeatedly. It’s the pulse that
is traveling in both cases. The string (or the water) oscillates up and
down. To discuss wave travel, it is helpful to refer students to when they
made “the wave” with their hands. They had to look in the direction of the
source to see what to do next but their hands only ever go up or down.
Assess
Take the same picture as in Part C and have the students label the
acceleration of points.
Released AP Physics 1 exam of 2018 Question 4 is a great follow-up to
this content.
So What
This question is a really great way to emphasize the propagation of a
wave through a medium without focusing on the source. It emphasizes
using different representations to describe the wave properties.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Standing Sound Waves in Tubes
EK
|
6.A.1, 6.A.2, 6.B.1, 6.B.2, 6.B.4,
6.D.2, 6.D.3, 6.D.4
SP
|
1.1, 1.4, 1.5, 2.1, 2.2, 5.1
Prepare
In these pictures, the air moves in a longitudinal manner and the amplitude
of the oscillation of the particles is represented by a transverse pattern,
but it is important to understand that the particles in the air are not moving
up and down like this picture shows.
Teach
Several free online interactive simulations allow students to look at the
patterns in different tubes. Provide students time to play with these
simulations to get familiar with the effects of changing the end or the
speed of sound, etc.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Quick Quiz
If you had a 1.5 m long tube with two removable caps in a room where the
air speed is 340 m/s , what would be the lowest note (frequency) that you
could make in the tube? What would be the second lowest note? Draw
the wave pattern for each of your answers including the calculation of the
wave’s frequency. Include how you chose to cap the tubes in your picture.
What’s the point?
Resonance is a key feature of waves and an important application of
superposition and boundary conditions.
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UNIT
10
Mechanical Waves and Sound
Beats
EK
|
6.A.1, 6.A.2, 6.B.1, 6.B.2, 6.B.4,
6.D.2, 6.D.3, 6.D.4, 6.D.5
SP
|
1.1, 1.4, 2.1, 2.2, 5.1, 6.1
Prepare
Have a demo of this ready to go. A middle C (524 Hz ) fork is common
laboratory equipment. You also might be able to acquire tuning forks from
a local music store. (A fun investigation for your students—If the tuning
forks are old, do they still vibrate with the frequency printed on the fork?)
This investigation will require about 17 cm of air space (v = 345 m/s ).
What if you do not have a tuning fork? Make the 17 cm air column in the
bottle, blow across the top, and you have made yourself a C note.
Teach
Use real-time graphing to look at the super position of sine waves. Here is
a way to get started: https://www.desmos.com/calculator/hzy8ta2zhg.
AP Physics 1 only requires a qualitative understanding of beat frequency.
You can make part E and F optional.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Questions
1. If the experiment was done outside in the winter, what would be
different and why?
2. A tuning fork of frequency f = 343 Hz is observed to create
resonance in the tube when the distance between the water and the
top of the tube is 25 cm . Is it possible for other tuning forks to achieve
resonance from the exact same water level? Justify your answer.
Yes, if a higher frequency fork is used
Yes, if a lower frequency fork is used
Yes, both higher and lower frequency forks will create
resonance
No
What’s the point?
Resonance is an important phenomenon in physics and engineering.
Research the Tacoma Narrows Bridge for a real-life example.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
The Doppler Effect
EK
|
6.A.1, 6.A.2, 6.B.1
SP
|
5.1, 5.3, 6.1
Prepare
Let students listen to a video of a noise moving with respect to the
observer. Fire engines, police cars, or ambulance videos are good sources
of this. There are several great videos on YouTube showing the Doppler
effect. You could also put a buzzer inside a football and let students throw
it around and listen to the sound change as the football goes away from
them and then returns.
Teach
The Doppler shift is a difficult topic to imagine—help students by
assigning one of the free online Doppler shift applets. Playing with one (or
more) of these applets will give students the chance to see what happens
to the wavelength of waves emitted by a moving source. Students can
then make connections between this and examples of the Doppler shift in
their own lives.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Question
Describe the pitch of a police siren in the following situation: You are
driving past a stopped cop car. The cop then turned on his sirens and
accelerated out onto the road behind you. He cruised at constant velocity
behind you until, in a panic, you pulled over. To your amazement, he
whizzed by you.
What’s the point?
Doppler shift is a key component of waves with relative velocities used in
many branches of physics including astrophysics.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Relationship Between Speed, Frequency, and Wavelength
EK
|
6.A.1, 6.A.2, 6.B.1, 6.B.2, 6.B.4,
6.D.2, 6.D.2, 6.D.4
SP
|
5.1, 6.1, 6.4
Prepare
Students need to know that when waves switch the medium of
propagation, the frequency remains unchanged.
Teach
Using a slinky to demonstrate, send a wave pulse when the slinky is
loose. Pull in some coils, increasing the tension, so students can see the
pulse will travel faster. Reference that in high-tension situations, pulses
travel quicker.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Discussion Question
What would it sound like if you went to a concert with an ice theme? The
musicians all tuned their instruments while on their chilly ice-covered
stage, but you are in the audience where it is several degrees warmer.
Include justification of your thoughts.
What’s the point?
Understanding what is constant in a situation shows an understanding of
wave fundamentals. Emphasize that if length is constant, the fundamental
wavelength must also be constant.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Standing Waves in Tubes
EK
|
6.A.1, 6.A.2, 6.B.1, 6.B.2, 6.B.4,
6.D.2, 6.D.3, 6.D.4
SP
|
1.1, 1.4, 2.1, 2.2, 5.1
Prepare
Students benefit from drawing these diagrams many times. Create
cards with different-sized tubes (open and closed) drawn on them. Have
students play a version of the card game war, where the students compare
the wavelength of the standing wave formed in the tube based on a
specific set of initial conditions.
Teach
The best accompaniment for this lesson is a set of “Boomwhackers.”
These are plastic tubes cut to a length that corresponds to a musical note.
When you hit them, they resonate at their fundamental frequency and you
hear the note they correspond to. (You may make your own out of PVC
tubing.) With a set of tuning forks, you can force a higher resonance (like a
high C note in a low C-note tube). Additionally, you can cap one end of the
tube and that will drop the note down an octave. (A higher C tube can play
a lower C note.)
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Have the students draw out one more condition for each tube type.
To challenge them, don’t make it the next frequency. For example, for the
open-open tube, have them sketch the 6th frequency.
What’s the point?
Fundamental wave harmonics are common on the AP Exam and in real life
are applicable to music.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Pulse Interference and Superposition
EK
|
6.A.1, 6.A.2, 6.D.1
SP
|
1.1, 1.4, 5.1, 6.1
Prepare
Students will need practice with boundary conditions and the principle of
superposition of waves.
Teach
It would be helpful for students to draw the wave form at a few more
instances in time. Drawing t = 6, 7, 8, and 9 will help them answer Part B.
Recap Question
Revisit this question with an open end. What does the interference pattern
look like? What does the graph of point P look like?
Assess
Multiple Correct MC
One end of a horizontal string is fixed to a wall. A transverse wave pulse
is generated at the other end, moves toward the wall, and is reflected at
the wall. Properties of the reflected pulse include which of the following?
Select two answers:
A. It has a greater speed than that of the incident pulse.
B. It has a greater amplitude than that of the incident pulse.
C. It is on the opposite side of the string from the incident pulse.
D. It has a smaller amplitude than that of the incident pulse.
What’s the point?
This question is ideal for connecting multiple aspects of this unit:
boundary conditions, motion of the medium, and the principle
of superposition.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Interference of Sound
EK
|
6.A.1, 6.A.2, 6.A.3, 6.A.4, 6.B.1,
6.B.2, 6.B.4, 6.D.2, 6.D.3, 6.D.4
SP
|
1.1, 1.4, 5.1, 6.1
Prepare
Students need to understand ways to model longitudinal waves.
Many times, transverse waves are drawn to represent them.
Teach
Constructive and destructive interference happens when forming
standing waves. It is good to remind students of this connection.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Recap Discussion Question
How would this graph look different if the speaker was moving at a
nontrivial speed?
What’s the point?
This problem enforces connecting graphical data to a real-life situation.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
The Speed of Sound
EK
|
6.A.1, 6.A.2, 6.B.1, 6.B.2, 6.B.4,
6.D.2, 6.D.3, 6.D.4
SP
|
4.1, 4.2, 4.3
Prepare
When writing a procedure, remind students that it is the physics that
matters most. Emphasis should be put on having students address what
will be measured and what can be done with it.
Teach
There is no difference if a student picks a tuning fork or a speaker.
The idea is simple—the frequency needs to be known.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Provide a sample graph of data (frequency of tuning fork and length of
tube sticking out of the water) and ask the students to find the velocity.
Several different data sets can be given. Students will find different
answers and can be asked to discuss why they think the answers vary.
They should postulate that the temperature of the air was different in
each case.
What’s the point?
Experimental design is a key aspect of the AP Exam.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Conditions that Affect Waves
EK
|
6.A.1, 6.A.2, 6.B.1, 6.B.2, 6.B.4
SP
|
4.1, 4.2, 5.1, 6.1, 6.4
Prepare
Students need to know which parameters stay constant when looking
at frequency, wavelength, and wave speed in different mediums
and conditions.
Teach
Encourage students to model a situation on physics that they know.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Multiple Correct MC
A standing wave pattern is created on a guitar string as a person tunes
the guitar by changing the tension in the string. Which of the following
properties of the waves on the string will change as a result of adjusting
only the tension in the string? Select two answers.
A. The speed of the traveling wave that creates the pattern
B. The wavelength of the standing wave
C. The frequency of the standing wave
D. The density of the string
What’s the point?
Knowing which aspects remain constant reflects understanding of
wave fundamentals.
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AP Physics 1
Workbook
UNIT
10
Mechanical Waves and Sound
Doppler Shift and Beats
EK
|
6.A.1, 6.A.2, 6.A.3, 6.A.4, 6.B.1,
6.D.3, 6.D.4, 6.D.5
SP
|
5.1, 5.3, 6.1, 6.4
Prepare
Students need to know about beat frequencies and how relative velocity
affects frequency in order to answer this question.
Teach
Here is a way to show the addition of sine waves in real time:
https://www.desmos.com/calculator/hzy8ta2zhg.
Recap Discussion Question
What would this graph look like if the car was approaching the student
instead of away from the student?
Students in AP Physics 1 need only a qualitative understanding of beats.
Parts B and C can be optional.
Assess
To further assess student understanding of the concepts addressed in
this scenario, you may want to ask students the questions below:
Multiple Correct MC
Two fire trucks have sirens that emit waves of the same frequency. As the
fire trucks approach a person, the person hears a higher frequency from
Truck X than from Truck Y. Which of the following statements about Truck X
can be correctly inferred from this information? Select two answers.
A. It is traveling faster than Truck Y.
B. It is closer to the person than Truck Y.
C. It is speeding up, and Truck Y is slowing down.
D. Its wavefronts are closer together than Truck Y.
What’s the point?
Graphical analysis of a complex situation helps you integrate concepts
within the unit such as Doppler shift; principle of superposition; amplitude
as volume; and beats.
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Unit 11 Review
Questions
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AP Physics 1
Workbook
UNIT
11
Review Questions
Average vs. Instantaneous Speed
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AP Physics 1
Workbook
UNIT
11
Review Questions
Relative Velocity
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AP Physics 1
Workbook
UNIT
11
Review Questions
Lab Experiment: Force vs. Distance
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AP Physics 1
Workbook
UNIT
11
Review Questions
Make the Rope Horizontal
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AP Physics 1
Workbook
UNIT
11
Review Questions
Motion in an Elevator
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AP Physics 1
Workbook
UNIT
11
Review Questions
Will the String Break?
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AP Physics 1
Workbook
UNIT
11
Review Questions
Magnitude of Friction Paragraph
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AP Physics 1
Workbook
UNIT
11
Review Questions
Gravitational Force and Newton’s Third Law
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AP Physics 1
Workbook
UNIT
11
Review Questions
Energy Graphs for Systems
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AP Physics 1
Workbook
UNIT
11
Review Questions
Momentum and Energy in Collisions
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AP Physics 1
Workbook
UNIT
11
Review Questions
Velocity and Energy Graphs for a Vertical Collision
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AP Physics 1
Workbook
UNIT
11
Review Questions
Simple Harmonic Motion on an Incline
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AP Physics 1
Workbook
UNIT
11
Review Questions
Rotational Motion Experimental Design
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AP Physics 1
Workbook
UNIT
11
Review Questions
Circuits Experimental Design
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AP Physics 1
Workbook
UNIT
11
Review Questions
Using Data to Determine the Speed of Sound
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Appendix
|
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AP® PHYSICS 1 TABLE OF INFORMATION
CONSTANTS AND CONVERSION FACTORS
Proton mass, =
mp 1.67 ¥ 10-27 kg
e 1.60 ¥ 10 -19 C
Electron charge magnitude, =
Neutron mass, =
mn 1.67 ¥ 10 -27 kg
Coulomb’s law constant, =
k 1 4 pe
=
9.0 ¥ 10 9 N  m 2 C 2
0
Universal gravitational
=
G 6.67 ¥ 10 -11 m 3 kgs2
constant,
Acceleration due to gravity
g = 9.8 m s2
at Earth’s surface,
Electron mass, =
me 9.11 ¥ 10 -31 kg
Speed of light, =
c 3.00 ¥ 108 m s
UNIT
SYMBOLS
Factor
10
12
meter,
kilogram,
second,
ampere,
PREFIXES
Prefix
Symbol
tera
T
m
kg
s
A
kelvin,
hertz,
newton,
joule,
K
Hz
N
J
watt,
coulomb,
volt,
ohm,
W
C
V
W
∞C
degree Celsius,
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES


q
0
30
sinq
0
12




37
45
53
60
90
35
2 2
45
32
1

10 9
giga
G
10 6
mega
M
cosq
1
32
45
2 2
35
12
0
10 3
kilo
k
tanq
0
3 3
34
1
43
3
-2
•
centi
c
10 -3
milli
m
-6
micro
m
10 -9
nano
n
10-12
pico
p
10
10
The following conventions are used in this exam.
I. The frame of reference of any problem is assumed to be inertial unless
otherwise stated.
II. Assume air resistance is negligible unless otherwise stated.
III. In all situations, positive work is defined as work done on a system.
IV. The direction of current is conventional current: the direction in which
positive charge would drift.
V. Assume all batteries and meters are ideal unless otherwise stated.
-2-
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AP® PHYSICS 1 EQUATIONS
MECHANICS
=
Ãx Ãx 0 + a x t
x =x0 + Ãx 0 t +
1 2
at
2 x
Ãx2 =
Ãx20 + 2 a x ( x - x 0 )


Fnet
 ÂF
=
a =
m
m


F f £ m Fn
Ã2
r
ac =


p = mv
 
Dp = F Dt
1 2
mv
2
K=
DE
= W
= F=
d Fd cos q
DE
P=
Dt
q =q0 + w0t +
1 2
at
2
=
w w0 + at
x = A cos ( 2 p ft )


t net
 Ât
=
a =
I
I
=
t r=
rF sin q
^F
L = Iw
DL = t Dt
1 2
Iw
2
K =


Fs = k x
Us =
r=
1 2
kx
2
m
V
ELECTRICITY
a
A
d
E
f
F
I
K
k
L

m
P
p
r
T
t
U
V
v
W
x
y
a
m
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
acceleration
amplitude
distance
energy
frequency
force
rotational inertia
kinetic energy
spring constant
angular momentum
length
mass
power
momentum
radius or separation
period
time
potential energy
volume
speed
work done on a system
position
height
angular acceleration
coefficient of friction
q
r
t
w
=
=
=
=
angle
density
torque
angular speed

qq
FE = k 1 22
r
A
F
I

P
q
R
r
t
V
r
Dq
Dt
r
R=
A
DV
I =
R
I =
P = I DV
Rs =
 Ri
1
=
Rp
1
 Ri
i
WAVES
v
f
l =
f = frequency
v = speed
l = wavelength
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
A=
1
bh
2
Circle
=
T
2p
=
w
A = pr 2
C = 2 pr
1
f
Ts = 2 p
m
k
Tp = 2 p

g
A = area
C = circumference
V = volume
S = surface area
b = base
h = height
 = length
w = width
r = radius
Right triangle
Rectangular solid
V = wh
Cylinder
V = pr 2
=
S 2 pr  + 2 pr 2

mm
Fg = G 1 2 2
r

 Fg
g =
m
UG = -
area
force
current
length
power
charge
resistance
separation
time
electric potential
resistivity
i
Triangle
DUg = mg Dy
=
=
=
=
=
=
=
=
=
=
=
2
c=
a2 + b2
a
sin q =
c
b
cos q =
c
a
tan q =
b
Sphere
4
V = pr 3
3
Gm1m2
r
S = 4pr 2
-3-
c
q
a
90
b
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1.5 The student can reexpress key elements of
natural phenomena across
multiple representations in
the domain.
1.4
The student can
use representations
and models to analyze
situations or solve
problems qualitatively
and quantitatively.
1.1 The student can
2.1 The student can
create representations and justify the selection of a
models of natural or manmathematical routine to
made phenomena and
solve problems.
systems in the domain.
2.2 The student can
1.2 The student can
apply mathematical
describe representations
routines to quantities
that describe natural
and models of natural or
man-made phenomena
phenomena.
and systems in the domain.
2.3 The student can
1.3 The student can
estimate quantities
refine representations and that describe
models of natural or mannatural phenomena.
made phenomena and
systems in the domain.
3.3 The student can
evaluate scientific
questions.
3.2 The student
can refine scientific
questions.
3.1 The student
can pose scientific
questions.
The student can engage
in scientific questioning to
extend thinking or to guide
investigations within the
context of the AP course
(not assessed on the AP Exam).
The student can use
representations and models
to communicate scientific
phenomena and solve
scientific problems.
The student can use
mathematics appropriately.
3
Scientific
Questioning
Mathematical
Routines 2
1
Modeling
Practice 3
Practice 2
Practice 1
Science Practices
AP PHYSICS 1
4.4 The student can
evaluate sources of data
to answer a particular
scientific question.
4.3
The student can
collect data to answer
a particular scientific
question.
4.2
The student
can design a plan for
collecting data to answer
a particular scientific
question.
4.1 The student can
justify the selection of
the kind of data needed
to answer a particular
scientific question.
The student can plan
and implement datacollection strategies in
relation to a particular
scientific question.
Experimental
Methods 4
Practice 4
5
5.3 The student can
evaluate the evidence
provided by data sets in
relation to a particular
scientific question.
5.2 The student can
refine observations and
measurements based on
data analysis.
5.1 The student can
analyze data to identify
patterns or relationships.
The student can perform
data analysis and evaluation
of evidence.
Data Analysis
Practice 5
6
6.5 The student can
evaluate alternative
scientific explanations.
6.4 The student
can make claims and
predictions about natural
phenomena based
on scientific theories
and models.
6.3 The student
can articulate the
reasons that scientific
explanations and
theories are refined
or replaced.
6.2 The student can
construct explanations
of phenomena based
on evidence produced
through scientific
practices.
6.1 The student can
justify claims with
evidence.
The student can work with
scientific explanations
and theories.
Argumentation
Practice 6
7
7.2 The student can
connect concepts in
and across domain(s) to
generalize or extrapolate
in and/or across
enduring understandings
and/or big ideas.
7.1 The student can
connect phenomena and
models across spatial
and temporal scales.
The student is able to connect
and relate knowledge across
various scales, concepts,
and representations in and
across domains.
Making
Connections
Practice 7
Task Verbs Used in
Free-Response
Questions
The following task verbs are commonly used in the free-response questions.
Calculate: Perform mathematical steps to arrive at a final answer, including
algebraic expressions, properly substituted numbers, and correct labeling of
units and significant figures. Also phrased as “What is?”
Compare: Provide a description or explanation of similarities and/or differences.
Derive: Perform a series of mathematical steps using equations or laws to
arrive at a final answer.
Describe: Provide the relevant characteristics of a specified topic.
Determine: Make a decision or arrive at a conclusion after reasoning,
observation, or applying mathematical routines (calculations).
Evaluate: Roughly calculate numerical quantities, values (greater than, equal
to, less than), or signs (negative, positive) of quantities based on experimental
evidence or provided data. When making estimations, showing steps in
calculations are not required.
Explain: Provide information about how or why a relationship, pattern, position,
situation, or outcome occurs, using evidence and/or reasoning to support
or qualify a claim. Explain “how” typically requires analyzing the relationship,
process, pattern, position, situation, or outcome, whereas, explain “why”
typically requires analysis of motivations or reasons for the relationship,
process, pattern, position, situation, or outcome.
Justify: Provide evidence to support, qualify, or defend a claim and/or provide
reasoning to explain how that evidence supports or qualifies the claim.
Label: Provide labels indicating unit, scale, and/or components in a diagram,
graph, model, or representation.
Plot: Draw data points in a graph using a given scale or indicating the scale and
units, demonstrating consistency between different types of representations.
Sketch/Draw: Create a diagram, graph, representation, or model that illustrates
or explains relationships or phenomena, demonstrating consistency between
different types of representations. Labels may or may not be required.
State/Indicate/Circle: Indicate or provide information about a specified topic,
without elaboration or explanation. Also phrased as “What . . . ?” or ”Would . . . ?”
interrogatory questions.
Verify: Confirm that the conditions of a scientific definition, law, theorem, or test are
met in order to explain why it applies in a given situation. Also, use empirical data,
observations, tests, or experiments to prove, confirm, and/or justify a hypothesis.
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AP Physics 1: Algebra-Based Course and Exam Description
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Exam Information
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Graphical Methods Summary
Mathematical
Model
Graph Shape
Written
Relationship
How to
Linearize
Constant
y is constant
Proportional
y is directly
proportional to x
Linear
y is proportional to x
Inversely
Proportional
y is inversely
proportional to x
y vs.
Power Law
y is proportional
to xn
y vs. x n
Square Root
y is proportional to
the square root of x
y 2 vs. x
1
x
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Writing Tips
(Adapted from J. Frensley Lab Manual)
Drawing Conclusions from Laboratory Data
Your conclusion(s) must be written as one or more paragraphs after your data and
graphs/calculations. The conclusion paragraph(s) must accomplish each of
the following:
§ ƒ Directly connect to and answer the purpose of the lab.
§ ƒ State the evidence clearly.
The conclusion will sound different depending on the purpose of the lab:
Purpose
Conclusion
“Establish a relationship
between two quantities”
You will have a graph of the two quantities plotted. In the
conclusion, clearly state the type of relationship. Clearly
explain how you determined the type of relationship.
“Determine a single quantity”
“Demonstrate or Test or
show a law of physics”
“Make something happen”
“Observe a phenomenon”
“Answer a scientific question”
You will have a graph OR a set of calculations. In the
conclusion, clearly state the value of the quantity you
determined with units.
You will have measurements of all quantities that have
to do with the law of physics you are testing. In the
conclusion, state the equation that relates to the law of
physics. Show your measurements being plugged into the
left-hand side of the equation and the result. Show your
measurements being plugged into the right-hand side of
the equation and the result. Then compare the two results
to determine if they are close enough to be equal.
State whether you were able to accomplish the challenge
for the lab. Show evidence, such as a target or a
measurement. If you failed to accomplish the challenge
for the lab, state how close you came.
State whether you made the phenomenon occur and
what you observed as a result. Your observations will
likely be qualitative. Using appropriate physical principles,
explain why the phenomenon occurred.
Answer the question clearly with no vagueness.
Use whatever graphs, analysis, or measurements you
have as evidence. Clearly state the evidence and explain
how it answers the question.
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Justifying a Response
On AP Physics free-response questions, you are often required to answer a question
and then either “justify your answer” or “explain your reasoning.” Your ability to write a
coherent and easy-to-read justification is key. When you are asked to justify or explain,
do the following:
§ ƒ First, answer the question directly and clearly so that there is no ambiguity in the
position you are taking. Some questions ask you to mark an answer before your
justification, so that counts as answering the question. Otherwise, answer the question!
§ ƒ The next one or two sentences need to state laws of physics that are always true and
pertain to this particular question. If you don’t remember the name of the law of
physics (i.e., you can’t remember to say “Newton’s first law”), then just recite the law
of physics (“if the net force on an object is zero, then it moves with constant velocity”).
Saying an “if-then” statement at this point is usually a good sign.
§ ƒ Next, you have to connect the laws of physics you cited or recited to the situation at
hand. If you find yourself using the words “in this situation,” you’re probably in good
shape. These sentences need to flow logically from one point of your argument to the
next so that you can do the last bullet point.
§ ƒ Answer the question again. If you did the third bullet point correctly, then it should feel
natural to put the word “therefore” in front of your answer.
EXAMPLE PARAGRAPH LENGTH RESPONSE (AP Physics 1 Question 5, 2018)
§ The amplitude of block PQ is less than that of block P.
§ The law of conservation of momentum applies to the collision between blocks P
and Q. Once the two blocks collide and stick, energy is lost even though momentum
is conserved.
§ The second block (Q) adds mass without changing the horizontal momentum of
the two-block system. In effect, block P (mass m) becomes block PQ (mass 3m).
v
This reduces the speed at equilibrium from vmax to max according to
3
conservation of momentum. To see how this affects amplitude, we must analyze
what happens to the maximum kinetic energy (K ) of the oscillating mass:

KP
2
1
mvmax
K PQ
2
1
2
2
 vmax 
(3m )  

 3 
2
1
mvmax
6
1
3
KP
Because the maximum K is reduced, this means the maximum potential energy in the
spring is also reduced (to 13 of its former value).
§ Because amplitude is related to maximum potential energy U max  12 kA2,
the amplitude of block PQ is less than that of block P.
Additional Pointers from AP Readers:
§ ƒ Make sure you answer the question clearly first.
§ ƒ Read the entire question and take a couple of minutes to organize your thoughts before
beginning to write.
§ ƒ Write legibly. If your answer is difficult to read, then it might as well be blank.
§ ƒ Underline key words or phrases like “increases,” “decreases,” “remains the same,”
“is proportional to,” etc.
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§ ƒ Use simple sentence structure. “Noun-verb-direct object”. You are not being graded for
advanced grammatical constructions.
§ ƒ Use the nouns of physics in your answer (“velocity,” “acceleration,” “kinetic
energy,” “force,” etc.). All other words (particularly verbs) can be simple first- or
second-grade vocabulary.
The Following Practices Will Not Earn Points:
Steer clear of the words “it” and “they”. If “it” isn’t a noun that appears five words
before the word “it” or less, then “it” is squirrels.
Don’t restate the question in your answer. Don’t just restate the information given in
the problem unless you’re about to use the words “because” or “therefore” or “meaning
(interpret the information given to you).” Restating the question or given information in
your answer means that you don’t know what you’re talking about.
Lots of words won’t necessarily result in lots of points. You may believe that your
grade is proportional to the length of your writing. This is NOT the case in science.
On the AP Physics 1 exam, use the fewest number of words necessary to get all the
information across.
If you are going to talk about force, specifically state which force you are talking about.
Are you talking about weight, normal, tension, friction, buoyancy, or electric force? Be clear.
If you are going to talk about energy, specifically state what type of energy
you are talking about. “Energy” may not be clear enough. Try “kinetic energy,”
“gravitational potential energy,” “elastic (or spring) potential energy,” “electric
potential energy,” “thermal energy.” For kinetic energy, say which object has the kinetic
energy. For potential energy, say what system has the potential energy. For internal
energy, say what holds the internal energy.
Don’t argue with the question. If the question states that X will happen and asks you to
explain why X happens, don’t write a paragraph about why X WON’T happen.
Don’t just say that something “moves.” That is not clear enough because everything
moves. You need to be more precise than that. If you’re asked, “What will happen when
the object is released?” try these answers rather than “it moves”:
§ ƒ “The object moves with constant speed in a straight line.” or “The object moves with
constant velocity.”
§ ƒ “The object moves with a constant acceleration.” or “The object accelerates.”
(But the first one is better.)
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§ ƒ “The object has an acceleration that (increases/decreases).”
§ ƒ “The object travels as a projectile.”
§ ƒ “The object is in free fall.”
§ ƒ “The object exhibits uniform circular motion.”
§ ƒ “The object exhibits simple harmonic motion.”
Beware of other nonspecific words like “rate” or “components.” Say which rate you
are referring to (velocity or acceleration) and say what you are breaking into components.
The Paragraph-Length Response
Each AP Physics Exam has at least one problem where you must compose an answer to
a complex question in the form of a paragraph. In essence, this is just a longer version
of “justifying your answer.” All of the above guidelines apply to your paragraph-length
response (answer the question, laws of physics that apply, connect laws to this situation,
logically make arguments until you answer the question again). All of the above
warnings also apply (don’t say “it”)! However, there are a few extra hints:
§ ƒ If drawing a diagram helps your paragraph, then draw a diagram! Make sure you refer
to the diagram in your words so that the diagram connects to your words.
§ ƒ If citing an equation helps your argument, then cite the equation! Students have this
(wrong) idea that “paragraph” means “math-free zone.” But remember that your words
are needed to connect the equation(s) to your overall explanation.
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