Minds on Physics

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vector field diagram for air currents in a certain region of space R34 o 3.2. Fields for fundamental forces R35

why we introduce fields for fundamental forces R35 how a fundamental field is defined: in terms of the force exerted on an object R35 what creates what types of fields R35

o 3.3. The electric field R36 force on point charge q due to electric field E R36 definition of the electric field R36

using Coulomb's law to find the electric field created by a point charge R36 finding the direction of the electric field R36 how the mutual forces can be the same even though the fields are different R36

o 3.4. Electric field for multiple point charges R37 an example of how to find the electric field for two point charges R37 vector field diagrams for the "dipole" and "dicharge" distributions of charge R37

o 3.5. Electric field for a spherical shell of charge R38 electric field inside a shell of charge R38 electric field outside a shell of charge R38 finding the direction of the electric field outside a shell of charge R38 an example showing how to find the electric field on a rubber ball R38

o 3.6. The gravitational field R39

why we use the same symbol for "local" and "Universal" gravitation R39 definition of the gravitational field R39 gravitational field created by a point mass R39 how to find the direction of the gravitational field R39

o 3.7. Gravitational field for non-point masses R39,40 using shells to find the gravitational field for a celestial body R39 sketch of gravitational field strength g vs. distance from the center of the Earth R40 finding and verifying the location between the Earth and the Moon where the gravitational

field is zero R40 o 3.8. The magnetic field R41

why we use a compass needle to determine the direction of the magnetic field R41 magnetic field for a long, straight wire R41

magnetic field for a loop of wire R41 o 3.9. Finding the magnetic field for other arrangements of current-carrying wire R42 magnetic field for two parallel wires, with currents moving in opposite directions R42 magnetic field for a coil of wire R42

o 3.10 Force on a point charge moving through a magnetic field R42,43 diagram showing the orientations of the velocity v, magnetic field B , and magnetic

force F m R42 2 mathematical expressions for the magnetic force on charge q R43 finding the direction of the magnetic force R43 why we cannot write an expression for the magnetic field B created by a moving point

charge R43 o 3.11 Limitations of vector field diagrams R43

many reasons why vector field diagrams are sometimes not the best way to represent fields R43

an example using the "dipole" arrangement of charges R43 o 3.12 Field line diagrams R44

what is meant by a field line R44 how to find the direction of the vector field using a field line R44 field line diagrams are 3 dimensional R44 drawing showing the field lines near a positive point charge R44 how to find the comparative strength of the vector field using the density of field lines

R44 why we usually draw field line diagrams in only 2 dimensions R44 limitations of the 2-dimensional field line diagram R44

o 3.13 Interpreting field line diagrams R44,45 an example using a pair of point charges R44,45 description of the field line diagram R44 analysis of the field line diagram R44,45 actual charge distribution used in this example R45

o 3.14 Reasoning with field line diagrams R45 3 conclusions that can be reached through reasoning R45

- Field lines do not cross each other R45 - Field lines are not the paths of objects R45 - The field is not strongest near field lines R45

4. REASONING AND SOLVING PROBLEMS USING PHYSICAL LAWS R46-53 o a list of the useful concepts, principles, and models presented so far R46 o 4.1. Reasoning with Newton's laws R46-48

how this part of the Reader will be different from earlier parts involving forces R46


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an example involving Newton's 2nd and 3rd laws, as well as momentum conservation R47

an example involving our model of materials R47 an example showing how diagrams can be useful R48

o 4.2. Solving problems using Newton's laws R48,49 an example involving the magnetic interaction R48,49

o 4.3. Reasoning with energy ideas R49-51 table showing the major energy principles, with related concepts and their definitions R49

an example involving the Work-Energy Theorem R50 an example involving the Work-Kinetic Energy Theorem R50 o 4.4. Solving problems using energy ideas R51-53

the procedure for determining potential energy R51 some common reference points R51 finding the potential energy stored in the field of two point charges R51 choosing the reference point for two point charges R51 mathematical expression for the potential energy for two point charges R51 mathematical expression for the potential energy for two point masses R52 an example showing how to apply gravitational and electric potential energy R52,53 5 common steps needed to solve problems using energy ideas R53

FF-TG: Teacher's Guide to Fundamental Forces & Fields(ISBN 0-7872-3934-8, 458 pages)Sorry, but we haven't posted the table of contents for this volume (yet). Contact Bill Leonard for assistance.

AT: Advanced Topics in Mechanics

Activities & Reader (ISBN 0-7872-5411-8, 172 pages)How to Use this Book xv Acknowledgments xvii

Activities

AT1 - Exploring Ideas About Circular Motion 1 AT2 - Finding Acceleration for Circular Motion 5 AT3 - Finding Radial Acceleration for Circular Motion 9 AT4 - Finding Tangential Acceleration for Circular Motion 13 AT5 - Reasoning About Circular Motion 15 AT6 - Solving Problems in Circular Motion 19 AT7 - Exploring Ideas About Projectile Motion 23 AT8 - Relating Kinematic Quantities for Two-Dimensional Motion 29 AT9 - Reasoning About Projectile Motion 35 AT10 - Solving Problems in Projectile Motion 39 AT11 - Solving Problems in Two-Dimensional Motion 43 AT12 - Exploring Ideas About Relative Motion 47 AT13 - Exploring Relative Motion in Two Dimensions 51 AT14 - Reasoning About Relative Motion 55 AT15 - Solving Problems in Relative Motion 59 AT16 - Graphing Rotational Motion 63 AT17 - Introducing Rotational Kinematics 67 AT18 - Solving Rotational Kinematics Problems 71 AT19 - Introducing Rotational Dynamics 75 AT20 - Solving Rotational Dynamics Problems 79 AT21 - Identifying Energy in Rotational Systems 83 AT22 - Solving Problems with Energy in Rotational Systems 87 AT23 - Solving Problems in Rotational Motion 91

Reader: Advanced Topics in Mechanics

Chapter 1. Circular, Projectile & Relative Motiono 3 independent sections: circular motion, projectile motion & relative motion R1 o 1.1. CIRCULAR MOTION R1-10

types of situations covered by circular motion R1,2 1.1.1. Uniform circular motion R2-4

what is meant by "uniform" circular motion R2 factors affecting acceleration: speed and radius of circle R2 starting with the definition of acceleration R2 diagram showing the change in velocity [delta]v for a small time period R3
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table showing the average acceleration for smaller and smaller time periods R3 1 effect of doubling the radius of the circular path R3 2 effects of doubling the speed of the ball R3 magnitude of the acceleration for uniform circular motion R4 direction of the acceleration for uniform circular motion R4

1.1.2. Newton's laws and uniform circular motion R4 relationship between net force and acceleration R4

1.1.3. Non-uniform circular motion R5,6

what is meant by "non-uniform" circular motion R5 definition of the radial component of acceleration R5 definition of the tangential component of acceleration R5 magnitude of the radial component of acceleration for motion along any circle

R5 direction of the radial component of acceleration R5 magnitude of the tangential component of acceleration for motion

along any circle R5

direction of the tangential component of acceleration R5 finding the forces responsible for the radial and tangential accelerations R5,6

1.1.4. Motion along a curved path R6,7 importance of finding circles that match the curvature of the path R6

radial acceleration points toward the center of curvature R6 radius of curvature is the radius of the matching circle R7 magnitude of the radial component of acceleration for motion along any path R7

direction of the radial component of acceleration R7 1.1.5. Reasoning with circular motion ideas R7-9

only 2 new "big ideas" in circular motion R7 integrating old ideas into new situations R7 using a free-body diagram to analyze circular motion R8 using energy ideas to analyze circular motion R8,9

1.1.6. Solving problems with circular motion ideas R9,10 table of ideas and principles needed to solve circular motion problems R9 example showing all the ideas that can impact a circular motion problem R10

o 1.2. PROJECTILE MOTION R11-22 what is meant by projectile motion R11

1.2.1. Simple projectile motion R11,12 what is meant by "simple" projectile motion R11 an example using strobe diagram of a ball thrown into the air R11,12 relationship of strobe diagram and plots to Newton's laws and force ideas R12 using plots of v x and v y vs. time to find a x and a y R12

1.2.2. Algebraic representation of simple projectile motion R12,13 using a graph to write an expression for horizontal position vs. time R12 using a graph of velocity vs. time to derive expressions for vertical velocity vs.

time and height vs. time R12,13 1.2.3. Algebraic representation of two-dimensional motion R13

defining symbols for the vectors r , v, and a R13 kinematic expressions for position and velocity as functions of time for constantacceleration R13

1.2.4. Free-fall acceleration R14 difference between g and a g R14 why we use the symbol a g to denote free-fall acceleration R14

1.2.5. Special features of simple projectile motion R14 what is meant by the term trajectory R14 3 special features of a trajectory: time of flight , range , and maximum altitude R14 labeled diagram of trajectory showing special features R14 what the time of flight depends on R14 what the range depends on R14 what the maximum altitude depends on R14

1.2.6. Reasoning about simple projectile motion R15-17 seeing patterns in how the speed and velocity of a projectile change R15 comparing trajectories to understand projectile motion R16 applying Newton's laws to projectile motion R17 applying conservation of energy to projectile motion R17

1.2.7. Solving problems in simple projectile motion R18-20 4 relationships needed to solve problems in simple projectile motion R18 4 keys to solving projectile motion problems R18,19

recognizing that time t is the same in all 4 relationships R18 translating given information properly into equation form R18 focusing on special features of trajectories R18 realizing when you have enough equations to solve for the unknown

R18,19


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2 examples R19,20 how to interpret a negative root R20

1.2.8. Solving problems in two-dimensional motion R21,22 4 relationships needed to solve problems in 2-dimensional motion R21 2 examples R21,22

o 1.3. RELATIVE MOTION R23-35 situations covered by relative motion R23

some goals of studying relative motion R23

1.3.1. Relative motion in one dimension R23,24 4 people at the airport on or near a moving walkway R23 table of velocities as seen from 2 different perspectives R24

1.3.2. Reference frames R24 what is meant by reference frame R24 table of positions as measured in 2 different frames at t = 0.0 s

R24 why some positions change but other positions stay the same R24

1.3.3. Notation and language R25 labeling frames as "primed" and "unprimed" R25 labeling positions and velocities as "primed" and "unprimed" R25 reasons someone's speed can be zero even though everyone agrees he is moving

R25 1.3.4. Relative motion in two dimensions R26 Jamal throws a ball into the air while riding a skateboard R26 to Jamal, motion of the ball is 1-dimensional R26 to Betty, motion of the ball is 2-dimensional R26

1.3.5. Position and velocity transformations R26-29 a boat is crossing a river, while Sue is running along the shore R26 in 2 dimensions, each reference frame has 2 coordinate axes R26 graphical representation of position transformation R26,27 numerical and symbolic representations of position transformation R27 general expressions for transforming positions R27 general expression for transforming velocity R27

3 representations of velocity transformation R27 general expression for transforming acceleration R28 2 examples of velocity transformation R28,29

1.3.6. Newton's laws in different reference frames R29,30 science experiments on a train moving with constant velocity relative to the ground

R29 laws of physics are the same in a frame moving with constant velocity R29 science experiments on a train slowing down relative to the ground R29,30 Newton's laws and empirical laws are different in an accelerating frame R30 small accelerations have only small effects on Newton's laws R30 definition of the phrase inertial frame R30

1.3.7. Conservation of energy in different reference frames R30,31

throwing a ball from the ground and from a moving train R30,31 change in kinetic energy depends on the frame of reference R31 work done by a force depends on the frame of reference R31 table showing how the scenarios look different in different frames R31

1.3.8. Reasoning with relative motion ideas R32,33 only 3 new ideas R32

the reference frame is the key to determining positions, velocities, andenergy R32

when the frames are inertial , forces, masses, and accelerations are thesame in all frames R32

there is no preferred reference frame R32 sometimes, a situation is easier to analyze in one frame than another R32,33

1.3.9. Solving problems with relative motion ideas R33-35 many common problems involve navigation R33,34 definition of the term heading R35

Chapter 2. Rotational Motiono situations covered by rotational motion R36 o how we are going to approach rotational motion R36 o why we are going to always use a fixed axis R36 o 3 main sections: angular kinematics, angular dynamics & energy in rotating systems R36 o 2.1. ANGULAR KINEMATICS R37-42

what is meant by angular kinematics R37 why we need to introduce a new set of kinematic quantities R37

2.1.1. Angular vs. linear kinematics R37,38 description of linear motion R37 description of angular motion R37


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what is meant by "CCW" and "CW" R37 CCW rotations are positive R37 table comparing linear motion and rotational motion (fixed axis) R38

2.1.2. The radian R38,39 why the radian is different from other units of measure R38 why the radian is the preferred unit for angles R38 an example using arc length R38,39 2 examples applying the radian R39

why certain relationships are not proper R39 2.1.3. Reasoning with angular kinematics ideas R40,41 angular velocity and linear velocity are very different quantities R40 linear velocity depends on your location on the spinning object R41 the linear velocity can be zero even though the object is spinning R41

2.1.4. Solving problems in angular kinematics R41,42 relationship between angular speed and angular velocity R41 graphs can help organize information and help solve problems R42

o 2.2. ANGULAR DYNAMICS R43-51 situations covered by angular dynamics R43 2.2.1. Pivots R43

what is meant by pivot R43

an example using a hinged door R43 why we ignore forces parallel to the axis of rotation R43 what is meant by "about the pivot" or "about the point p" R43

2.2.2. Torque R44-46 4 factors affecting the torque R44 2 definitions of torque for rotations about a fixed axis R44 finding the direction of torque R44 SI unit of torque (Nm) R44 2 examples R45 definition of net torque for rotations about a fixed axis R46

2.2.3. Moment of inertia R46,47 3 factors affecting the moment of inertia R46

definition of moment of inertia (point mass) R46 definition of moment of inertia (composite object) R46 2 examples R47

2.2.4. Newton's 2nd law in rotational form R48 mathematical description of Newton's 2nd law for rotations about a fixed axis R48

2.2.5. Angular vs. linear dynamics R48 table comparing linear and angular dynamics R48

2.2.6. Reasoning with angular dynamics ideas R48-50 for static situations, every axis is a fixed axis of rotation R48,49 3 examples R49,50 the gravitational force acts "as though" through the center of gravity or balance point R49

2.2.7. Solving problems in angular dynamics R51

an example R51 relationship between angular acceleration and linear acceleration R51 o 2.3. ENERGY IN ROTATIONAL SYSTEMS R52-56

2.3.1. Kinetic energy of rotating objects R52 rewriting the kinetic energy using rotational quantities R52

2.3.2. Potential energy in rotational systems R52 how energy can be stored in a rotational system R52 torque law for a torsional spring R52 potential energy for a torsional spring R52

2.3.3. Energy for linear vs. rotational motion R53 table comparing energy for linear and rotational motion R53 why we do not refer to "angular energy" R53

2.3.4. Reasoning with energy ideas in rotational systems R53,54 2 examples R53,54 importance of using the center of gravity in energy problems R54

2.3.5. Solving problems with energy ideas in rotational systems R54-56 how conservation of energy and the Work-Kinetic Energy Theorem are applied R54,55 why there is no such thing as "angular" energy R55 2 examples R55,56

o 2.4. SOLVING PROBLEMS IN ROTATIONAL MOTION R56 general guidelines for solving problems in rotational motion R56


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AT-TG: Teacher's Guide to Advanced Topics in Mechanics

(ISBN 0-7872-5412-6)Sorry, but we haven't posted the table of contents for this volume (yet). Contact Bill Leonard for assistance.

CS: Complex Systems

Activities & Reader (ISBN 0-7872-5413-4)Sorry, but we haven't posted the table of contents for this volume (yet). Contact Bill Leonard for assistance.

CS-TG: Teacher's Guide to Complex Systems

(ISBN 0-7872-5414-2)Sorry, but we haven't posted the table of contents for this volume (yet). Contact Bill Leonard for assistance.

Sample MOP Activities

Selected excerpts from the MOP curriculumBelow are links to a few of the "minds-on" activities we have developed, in PDF format. ( Adobe Acrobat Reader orequivalent required.)

1: Motion (core activities 1-35)

1. Looking Ahead

4. Using Graphs of Position vs. Time

11. Translating Graphs of Velocity vs. Time

16. Solving Constant-Velocity Problems Using Different Methods

2: Interactions (core activities 36-70)41. Recognizing Interactions 46. Comparing Magnitudes of Common Forces

50. Recognizing and Interpreting Free-Body Diagrams

59. Reasoning With Newton's Laws

3: Conservation Laws & Concept-Based Problem Solving (core activities71-102)

77. Reasoning with Impulse and Momentum Ideas 86. Recognizing and Comparing Kinetic Energy

91. Computing the Potential Energy

101. Solving More Complex Problems

4FF: Fundamental Forces & Fields (supplemental activities FF1-29)

FF1. Exploring Models of Electromagnetism

FF5. Exploring the Magnetic Interaction

FF9. Exploring the Gravitational Interaction

FF11. Distinguishing Mass and Weight

FF13. Using a Mathematical Model for the Electric Force FF20. Reasoning with Universal Gravitation

FF25. Representing Vector Fields Using Field Line Diagrams FF27. Applying Work and Energy Ideas

4AT: Advanced Topics in Mechanics (supplemental activities AT1-23)

AT1. Exploring Ideas About Circular Motion

AT5. Reasoning About Circular Motion

AT9. Reasoning About Projectile Motion

AT14. Reasoning About Relative Motion

AT16. Graphing Rotational Motion

AT17. Introducing Rotational Kinematics
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AT20. Solving Rotational Dynamics Problems

AT21. Identifying Energy in Rotational Systems

4CS: Complex Systems

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Using MOPAn excerpt from the MOP teacher's guides about how to use MOP effectively

Introduction

This section describes how to get started with MOP. Ideally a teacher would work through all of the studentactivities and read through all of the accompanying materials in the MOP Teacher's Guides . Only then can a teachermake well-informed decisions about how to best use the MOP materials to meet their instructional needs and goals.Our experience, however, is that this ideal is unrealistic for most teachers. Teachers have little disposable time theycan devote to mastering a new curriculum, and so, teachers must "learn as they go." It can take teachers as long asthree years to become thoroughly comfortable and familiar with a new curriculum. We hope the contents of thissection will help make getting started with MOP as efficient and effective as possible.

Getting Started covers the following areas:

MOP Curriculum Materials Components of a MOP Activity About the MOP Reader Contents of the Teacher Aids A Note on Laboratories, Demonstrations, and Hands-On Activities Global Issues: Planning the School Year with MOP Creating a Lesson Plan Around a MOP Activity Formative and Summative Assessment with MOP

To get the most out of this section, it is best to have your copy of the MOP materials handy and refer to it as needed.MOP Curriculum Materials

There are two sets of materials with MOP, a set of four booklets for students and a corresponding set of booklets forteachers. The first three booklets deal with topics in mechanics: Motion , Interactions , and Conservation Laws &Concept-Based Problem Solving . The fourth booklet --- Fields, Complex Systems & Other Advanced Topics ---applies the principles developed in the first three booklets to a wide range of physical phenomena.

Each student booklet is divided into two parts: The Activities form an integrated set of thoughtful engagements for

students, and the Reader organizes and summarizes the ideas of the physics content and is meant to be read afterstudents have engaged in associated activities.

Each corresponding Teacher's Guide also has two parts: Answers and Instructional Aids for Teachers, which provides advice for how to optimize the effectiveness of the activities, as well as brief explanations and commentson each question in the student activities, and Answer Sheets, which may be duplicated and distributed to studentsas desired. Use of the answer sheets is particularly recommended for activities requiring a lot of graphing ordrawing.

The first booklet in the teacher series contains three supplements:

Supplement A: Collaborative Group Techniques provides a short list of ideas for structuring in-class group

activities. Supplement B: Concept-Based Problem Solving gives a more detailed account of the MOP approach. Supplement C: A Comparison of the MindsOn Physics Approach with the NRC's National Science

Education Standards presents a list of the core standards contained in the published 1996 National ResearchCouncil Science Education Standards and a brief description of how MOP addresses each standard.

Components of a MOP Activity

The MOP activities all have the same basic structure:

Purpose and Expected Outcome. In this section, we tell students the specific concepts, principles, and other

ideas that will be raised and addressed during the activity. This section also tells students what they areexpected to learn.
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Prior Experience / Knowledge Needed. We first list for students the concepts and principles they shouldknow or be familiar with before attempting the activity. Then, if necessary, we provide any additional

background needed to do the activity. Main Activity. This section contains the specific questions and problems that probe students' understanding

and prepare them to make sense out of the ideas. Reflection. After finishing the Main Activity, students re-examine their answers to look for patterns. They

are also asked to generalize, abstract, and relate concepts to the situations they have studied.

Occasionally an activity will contain an additional component:

Integration of Ideas. This section is used to get students to bring together different but related ideas --- oftendealt with using separate situations in the activity --- to analyze a single, often more complex, situation.

Although a MOP activity has several components, the Main Activity and Reflection are the most important. Werecommend getting students to the Main Activity as quickly as possible and not overdoing the preparation ofstudents. Students may struggle, but most of their difficulties can be addressed as they proceed through the activity.Students may feel frustrated initially, but with some reassurance from the teacher and a little experience facing andovercoming the inevitable confusion associated with starting something new, students will grow into confident andindependent learners.

Nevertheless, it is worthwhile helping students become aware of the structure of the MOP activities. This can bedone gradually and indirectly by meta-communicating with students. For example, on occasion ask students if theylearned what they were expected to learn --- and how do they know. Sometimes have students consider whetherthey have the knowledge needed to do the upcoming activity. Test their knowledge by asking them some basicquestions. Another good idea is to check whether students understood the directions given in the Main Activity.This can be accomplished by stopping the class (after students have had a reasonable chance to get started) andasking individual students or groups of students to share with the class how they are approaching the activity. Askthe class whether the approach meets all the requirements set forth in the directions. After students finish an activityask students to tell you what is the purpose of the activity from their perspective.

About the MOP Reader

There is no traditional textbook with MOP. There is a Reader, but it serves mostly as a follow-up to the MOPactivities. The intent is that students begin by working the activities with little or no preparation from the teacher orfrom any other source material. Any preparation that might be needed is provided in the Prior Experience /

Knowledge Needed sections of the activities. The appropriate part of the Reader is designed to be read after thestudent finishes the corresponding activity (or set of activities), and is intended to summarize, organize and integratethe ideas and issues raised in the activities. The students can then use the Reader as a resource for later activities.Guidance for reading assignments is provided in the Instructional Aids. Contents of the Teacher Aids

The Answers and Instructional Aids for Teachers are our way of communicating the philosophy behind eachactivity and/or set of activities. We explain our goals and our expectations for each activity, and try to givewarnings about student difficulties, misunderstandings, and common responses. We also suggest ways to interpret

different patterns of students' responses as well as ways to assess student understanding. The Instructional Aids areintended to prepare teachers in their role as coaches of students' learning.

Answers with Short Explanations --- Answers are an invaluable resource. At the very least, they allowteachers to see how we think about a situation or problem. A short explanation or remark is always

provided with an answer. Our intent is to emphasize the process of analyzing each question, being aware ofone's assumptions, and arriving at an answer consistent with those assumptions. When appropriate weindicate how the question might be answered differently under different assumptions. Frequently we alsoindicate how students might answer the question or how they might reason about the situation. Although we

provide answers, we wish to stress that the focus should always be on students' thinking process and neverexclusively on whether an answer is right or wrong.

Goals and Objectives --- Identifies the physics concepts that will be dealt with in the activity and gives a

brief statement of the expected outcomes. Time Needed for Activity --- Provides an estimate of the time needed to complete the activity. Since thereare a number of ways to approach each activity this estimate is very rough. Other factors, such as classability or path through the material, will affect the time required for an activity. We suggest for futurereference that you keep a log of the actual time needed.

Preparation for Students --- Identifies what students need to know before they begin the activity. Typicallyonly two or three major items are mentioned per activity. Our intent here is to assure that the majority of thestudents have been prepared to a certain threshold. Clearly knowledge is cumulative and gaps in students'knowledge/skills are inevitable. Only the teacher can gauge whether or not the class as a whole is ready foran activity. Our advice is not to be unduly timid about moving ahead. However, be prepared to providestudents the support they need.

Link to the Reader --- Indicates which sections of the Reader the students may read after finishing the

activity. Students will often be asked to do several activities in succession with no reading assignment.


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Suggestions for Classroom Use, Organization, etc. --- Contains a variety of information particularlyrelevant to creating a lesson plan for the activity. Suggestions are made regarding which parts of the activityto do in class and which parts to do for homework. Sometimes there are suggestions for introducing theactivity. There are also suggestions on which parts students might do alone, which parts they might do ingroups, and which parts might be done as a class. There are also suggestions for incorporating hands-onmaterials into the activity.

Anticipated Difficulties for Students --- Informs teachers about difficulties students are likely to have withthe activity. We list only a few items --- ones we think many students will share. There are, of course, many

more student difficulties that we do not list, and some of these might actually be more common than theones we have listed. It is useful to keep a log of the most prevalent ones. Probing for Student Understanding --- Contains a list of questions that can be used to assess student

understanding. The questions can be used to gauge student progress on the activity as well as to identifyareas of concern. Many of the items could also be used as exam questions.

Suggested Points for Class Discussion --- Raises some important points for discussion. A class-widediscussion provides a wonderful opportunity for students to hear views of others and get feedback on theirown points of view.

Providing Support to Ensure Student Progress --- Provides some interventions that teachers can try whenstudents get stuck.

A Note on Laboratories, Demonstrations, and Hands-On Activities

The MOP approach stresses the value of building the physical representation for physics concepts and principles,and integrating this with more formal representations. Consequently, some of the activities involve extensive use ofhands-on activities. Clearly, laboratory exercises and demonstrations also serve to develop the physicalrepresentation and a good course will employ these methods as well. We wish here to argue that simple,unstructured explorations of physical ideas in a qualitative, hands-on manner serves an important function not met

by typical demonstrations and formal laboratories.

Traditional formal labs tend to be cook-book in nature, to involve large amounts of data manipulation and analysis,and frequently culminate in time-consuming lab reports. They are often unmotivated from the students' point ofview and do not seem to impact learning of physics. To be sure, there are a multitude of skills to be learned from

good laboratory experiences, but command of the physical representation is not a common result. Many excellentlaboratory materials have already been published and we have elected not to duplicate that effort. In our experiencemost teachers have strong preferences for the laboratory exercises that they use and just about any laboratory iscompatible with MOP.

In many classrooms, demonstrations are used to exemplify a particular concept or principle, with the interpretation,description and explanation provided by the teacher. For a thinking student, however, a demonstration often raisesmany more questions than it answers, and without the opportunity to investigate those questions, students can comeaway with very distorted views about what the demonstration means. To become convinced of this, ask yourstudents what they think they have observed after a demonstration before you tell them what they should haveobserved . We recommend a broader use of demonstrations as a means for students to explore the features relevantfor understanding physical systems and the reasoning used to analyze them. To maximize the effectiveness of

demonstrations, we encourage teachers to use a reason-predict-show-explain sequence of activities, in whichstudents think about the demonstration apparatus, predict what they believe will happen, observe the demonstration,and then describe the reasoning behind their predictions. (This is sometimes called an interactive demonstration.)

In our view, simple commonplace manipulatives, such as balls, marbles, springs, strings, and toy trucks, should bewell integrated into the course. Students should have continuous access to these materials, and they should befrequently asked to employ them to demonstrate physical ideas and principles in a qualitative manner. This is a verydifficult task for students. Perhaps the only thing more difficult for students than translating their ideas into physicalreality is explaining what they are trying to accomplish to another person. For this reason small group or classdiscussions of hands-on activities are particularly fruitful for interrelating the linguistic, formal, and physicalrepresentations. Global Issues: Planning the School Year with MOP

How you implement MOP during your school year depends strongly upon your instructional objectives for yourspecific class. There are many possible objectives, ranging from preparing students for college science courses toexposing students to the broadest possible range of physics phenomena. Faced with a particular class, many teachersfeel that these two objectives are in conflict and they must strike some compromise. Indeed, because time is limited,every teacher is constantly making choices regarding how to spend their class time.

We would argue that your most important objective is to make your students self-aware and self-motivated learners,and that MOP can help you accomplish this. Many students are intimidated by physics, feel inadequate to do

physics and, consequently, disengage. Students spend far too much time looking for the right answer or, evenworse, the answer they think you want. Discussing these issues and your expectations openly will help them focuson the only meaningful outcome, their own learning and development. Obviously, it is important to rewardengagement and effort. Such rewards, however, should not confuse students by creating the impression that all

reasoning is equivalent and just a matter of taste.


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Touching upon many topics and modern phenomena is a desirable goal. Such exposure, however, is only effectiveand long lasting if students have some firm ground of fundamental concepts to which they can relate thisknowledge. Building a solid foundation is what MOP is all about. Depending upon individual goals, the mechanics

portion of MOP (i.e., the first three booklets) should occupy between 1/2 to 3/4 of the school year.

Although the MOP activities are numbered, there is no need to proceed through them in strict order. Nor is there aneed to do every activity or any particular activity in its entirety. While there is no single best path through thematerials, it is best not to invert related activities designed to target different cognitive stages. As mentioned in

the Letter from the Authors and as elaborated in Supplement B: Concept-Based Problem Solving , MOP activitiesdealing with the same topic are sequenced in a cognitive sense. Students are encouraged to (a) explore their currentunderstanding, (b) refine and interrelate their physics concepts, (c) enhance their analyzing and reasoning abilities,(d) develop problem-solving skills, and (e) organize their knowledge into a coherent structure.

Which activities should be used and how much time should be devoted to each of them is something only you candecide. The activities are intended to be a resource, not a recipe. We offer the following general advice for yourconsideration:

Emphasize the need for good communication between students and yourself and among the class as awhole. Students who understand what is being asked of them are usually much more successful. It should

be explained to students that it is not the answer alone that is important, but the relationship between their

reasoning and their answer. Do not let students get bogged down. Even the best of students may not get the desired idea on the first

pass. It often takes students considerable time to accommodate and learn how to use new ideas. Rather thanwait for all students to demonstrate the proficiency with a specific concept that you would like, move on,

but with the intention of returning to the topic at a later time. Keep course topics integrated with each other. Students often perceive an introductory physics course as a

series of unrelated topics. Rarely do teachers ask students to find the velocity or position of a body oncekinematics is over and Newton's laws are being covered. Sometimes this tendency to partition is even morecommon with mathematical topics such as graphs and vectors. Many teachers use graphs extensively whilecovering kinematics and never use them again. Create opportunities for students to interrelate theirknowledge and skills. A spiral, multi-pass approach is more effective for learning and structuringknowledge than a one-pass approach.

As a special case of the above points, consider interweaving motion with interactions. The topics ofkinematics (vectors, algebra, graphs, rates of change, etc.) are among the most difficult for beginningstudents. There is no need to wait for this formal math development to finish before beginning to develop

physical intuition and reasoning skills. The two can be developed in parallel. This has the added advantageof keeping students more interested and motivated because most students consider kinematics a resounding

bore. On the other hand, when they see why one might be concerned about the velocity and position of anobject subject to a net force, they are more motivated to learn kinematics.

Creating a Lesson Plan Around a MOP Activity

Once you decide to use a MOP activity:

1. If possible, invest the time to do the activity yourself. This is the best way to become familiar with theactivity, and you will be in a better position to make decisions. Read over the instructional aids to get ageneral sense of the issues being addressed in the activity.

2. Choose the hands-on materials that will be available.3. Decide how to introduce the activity. Should you let students just jump in, or should you ask a probing

question beforehand, or should you do an interactive demonstration? For instance, you might discuss theGoals and Objectives with your class, or work on the example, or even do part of the activity as a classexercise.

4. Select the portions of the activity you want to do, which parts will be done in class and which parts might be done for homework.

5. Decide how students will engage in the activity. Should it be done as a class, in groups, in pairs, or

individually? When should the class discussion begin? Should students present their answers to the rest ofthe class and, if so, how?6. Think about ways you can support students' progress through the activity.7. Select points for class discussion and/or question(s) to probe student understanding.8. Look at the explanations and comments provided with the answers to get some sense of how students might

respond to the various questions and what these responses might mean.

Formative and Summative Assessment with MOP

Most assessments used by teachers are at the end of a topic and are of a summative nature, that is, they serve toevaluate student progress and assign a grade. Only rarely are tests designed to inform either students or teachers ofthe nature of student difficulties. Assessments of this second type are called formative because the results haveconsequences for subsequent instruction. Generally, it is preferred to identify student problems or


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misunderstandings while there is still time to do something to correct the situation. The MOP approach emphasizesthe need for formative, as opposed to summative, assessment.

We know that the traditional ways of testing students do little to uncover conceptual difficulties or to measureknowledge of physical laws and principles. Traditional exam questions tend to stress answers and be numeric andformulaic in nature. New ways of assessing students' progress must necessarily be developed alongside newapproaches to teaching. These new assessments need to encourage students to focus on those features that areimportant for deep understanding. Without new assessment methods, students will remain largely unwilling to

abandon formulaic approaches. Examples of how new assessments might be structured to probe students' progressand their conceptual understanding can be found in the "Probing for Student Understanding" sections ofthe Answers and Instructional Aids for Teachers . Another suggestion is to reserve part of an activity for a laterassessment. If students are to demonstrate their abilities, it is important that the assessment item resemble the tasksthat they have rehearsed.

Finally, it is our view that tests and exams should serve primarily a pedagogic rather than evaluative function.Students dislike and resent exams because they feel evaluated, i.e. their worth is determined. Failure erodes theirself-confidence and self-esteem. Success on traditional exams does not send a much better message. Successfulstudents come to believe that achievement in the form of grades, rather than intellectual development, is the goal to

be sought. Exams can be designed to be informative to students and can serve as valuable educational experiencesfor students. Students need to go beyond being active, or even engaged learners. They need to become self-invested

in the entire process of education. They need to develop self-evaluation skills and good exams can help themachieve this goal. Frequently asking students to what they attribute their lack of success or inability to do a problemhelps them establish self-reflection as the norm. Teaching self-invested and reflective students is an exciting andrewarding experience.

Where to Get MOP

MindsOn Physics is sold by the Kendall/Hunt Publishing Company .

Kendall/Hunt's listing of MOP books

For MOP Users

If you are a teacher using Minds*On Physics...Are you a teacher who uses MindsOn Physics? If so, we'd love to hear from you. Please don't hesitate tocontact Bill Leonard with any questions, comments, or feedback.You should probably check out the MOP Errata page , too.

MOP Errata

Corrections for errors (gasp!) in the published MOP books

Believe it or not, we have errata lists for the following books. ("TG" means "Teacher's Guide" and "AR" means"Activities & Reader", i.e., the student activities book.) If you think you've found a mistake that we don't list here,

please report it to Bill Leonard .

We'll add errata pages for the other books if/as the need arises.

Errata for Motion AR

Student Reader, p. R4, middle: The components of the position of the ant should be given everywhere in "centimeters" not "meters". [EH,

06Jun04]Student Reader, p. R9, top:

The average velocity from t = 5.0s to t = 6.0s is +10cm/s, not 10cm/s. [AW, 14Jan04] Many thanks to Andrew Wertz of Littlestown HS in Littlestown, PA, and Ed Haley of E.C.O.S. in Springfield, MA,who found these mistakes.

Errata for Motion TG

Activity 4, p. 22, question P8, part (a) answer Add graph D to the list of answers, i.e., "Graphs C, D, and E represent objects that are speeding up."

Activity 8, p. 39, "Link to Reader" Change the ending page of the reading assignment to R9, i.e., "Students may read pages R8-9 (the

beginning of section 1.4, Velocity) after finishing Activity 9."Activity 9, p. 45, "Link to Reader"
http://www.kendallhunt.com/http://www.kendallhunt.com/http://www.kendallhunt.com/http://www.kendallhunt.com/Search.aspx?searchTerm=minds%20on%20physicshttp://www.kendallhunt.com/Search.aspx?searchTerm=minds%20on%20physicshttp://www.srri.umass.edu/leonardhttp://www.srri.umass.edu/leonardhttp://www.srri.umass.edu/leonardhttp://www.srri.umass.edu/mop/MOPErratahttp://www.srri.umass.edu/mop/MOPErratahttp://www.srri.umass.edu/mop/MOPErratahttp://www.srri.umass.edu/leonardhttp://www.srri.umass.edu/leonardhttp://www.srri.umass.edu/leonardhttp://www.srri.umass.edu/leonardhttp://www.srri.umass.edu/mop/MOPErratahttp://www.srri.umass.edu/leonardhttp://www.kendallhunt.com/Search.aspx?searchTerm=minds%20on%20physicshttp://www.kendallhunt.com/


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Change the ending page of the reading assignment to R9, i.e., "Students may read pages R8-9 (the beginning of section 1.4, Velocity) after finishing this activity."

Activity 9, p. 46, "Probing for Student Understanding", question P3 In parts (a) and (c), change the units to cm/s, i.e., " P3. (a) Which object (in part A) reaches a velocity of

1cm/s first? (b) When does this occur? (c) Which object reaches a speed of 1cm/s first? (d) When does thisoccur?"

Activity 12, p. 65, question A4 answer, bullet 1 Change wording to "Students might plot speed vs. time instead of velocity vs. time (as shown below on the

left). In addition, some students might not realize that the speed goes to zero between strobes 4 and 5 (asshown below on the right)."Activity 12, p. 68, question B4 answer

Change answer to " after t = 0.45s ". Add third bullet, " By exa ggerating the curvature of the graph between #4 and #5, you can see that the

marble is at the 1m mark just after the midpoint in time."Activity 13, p. 76, question P1 answer

In part (a), at t = 1s, object X is at x = 7cm .Activity 14, p. 79

question A2 answer, bullet 1, "Object J has the largest displacement..." question A4 answer, bullet 1, "Students might pick only object J, because object I..." question A4 answer, bullet 2, "Students might pick only object I..."

question A6 answer, "... which would correspond to J " question A6 answer, bullet 1, "Students might pick object I because the curves for objects E and I look thesame."

Activity 15, p. 86, question P1 answer The answers to parts (a) and (b) are reversed.

Activity 16, p. 91, question C3 answer Modify paragraph 2: " Yes , this answer agrees..." Fix bullet 1: "Students might have gotten question B2 wrong."

Activity 17, p. 96, question A5 answer Add to the end of paragraph 1, "At 20km/h, the plane travels about 5km before losing contact with the

car." Add to the end of bullet 1, "i.e., after the plane has traveled 20km".

Activity 19, p. 107, question P4 answer The speed is only 1 grid/s, i.e., the answer should read, "... the average velocity is +1 grid/s or 1grid/s, to the right between 2s and 6s."

Activity 23, p. 131, question P8 answer Add bullet, " See table of values for P1 above."

Activity 24, p. 137, question B1 answer, bullet 4 Change A2-A4 to B2-B4, i.e., "Students do not need to make precise calculations to answer questions B2-

B4."Activity 25, p. 145, question A2 answer

In part (i), the Total Area (i.e., column 4) should be 292.5 m.Activity 27, p. 163

question R2 answer is really only the first half of the answer to R2.

question R3 answer is really the second half of the answer to R2. question R4 answer is really the answer to R3. question R5 answer is really the answer to R4.

Many thanks to Lonnie Grimes of Oakmont High School in Roseville, CA, who found almost all of these mistakes.

Errata for Interactions AR

Activity 37, p. 146, "Explanation of Activity and Examples": The page number indicating where to find the map (of King's Court) should be "143", not 134.

Many thanks to Patrick Diehl of Ashley Hall School in Charleston, SC, who found this mistake.

Errata for Interactions TGActivity 36, p. 216, question A4 answer

Quadrant (column 1) should be "2 only", angle relative to horizontal (column 2) should be "27", and anglerelative to East axis (column 3) should be "153".

Activity 36, p. 217 Answer to question B2 should be: 580m @ 149 . Answer to question B3 should be: 500m @ 307 . Answer to question B3, bullet 1: replace -37 with -53.

Activity 37, p.222, "Suggested Points for Class Discussion", bullet 2 The word 'needs' should be 'need', i.e., "... both the origin and the orientation of the coordinate frame need

to be specified..."Activity 38, p. 227, question A5 answer


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All the answers for vector V are wrong. There should be a minus sign in front of each term, and the lengthof the vector is 4.24cm. So, the x-component of V can be written either -(4.24cm) cos(45) or -(4.24cm)sin(45), and the y-component of V can be written either -(4.24cm) sin(45) or -(4.24cm) cos(45).

Activity 38, p. 229, question B5 answer, bullet 2 Change B3 to B2, i.e., "Students might use a rotated coordinate system (as in B2)."

Activity 42, p. 258, question B1 answer, bullet 1 Rephrase third sentence to read, "This is the only situation in this part for which buoyancy is considered

relevant."

Activity 44, p. 267, "Probing for Student Understanding" Change part (b) of question P3 to read, "In part B, how would the readings on scales A, B, and D change ifscale C were removed?"

Activity 45, p. 280 In the answer to question I7, add object E to the list, i.e., " Only objects A, B, D, and E must have friction

forces exerted on them." The answer to question R3 is missing. It should read, "The objects considered in situations A3, A6, and B3

could be accelerating. For the rest, the object has a constant velocity. There are no comments for R3. They are, "Students might not include A3, perhaps because they think the ball is not accelerating at the top of its

trajectory." "Students might include B1, perhaps because the book is accelerating. But the object being considered is the

table, which is not accelerating." "Students might not include B3, perhaps because they think that the ball is at rest when it is touching thewall."

"At this point in the course, students are not expected to know the relationship between force andacceleration. Students should be encouraged to determine which objects definitely have no acceleration.The rest can be considered to possibly be accelerating."

The answer for question R4 is missing. It should read, "(Students indicate any forces other than the sevenintroduced here that they have heard of. They then indicate if any of these other forces behave like any ofthe forces introduced here."

Activity 45, p. 281 The answer to question P5 is wrong. It should read, "If the spring was compressed rather than stretched,

then the strings would be angled inward, rather than outward . In other words, object G would be

hanging to the left of where its string is attached to C, and object H would be hanging to the right of whereits string is attached to C." The comment for the answer to question P5 does not fit any longer. It should read, "Students might not

think it is possible for the spring to remain compressed between objects G and H."Activity 46, p. 284, "(More Ways of) Probing for Student Understanding"

Question P6 is question P4. Question P7 is question P5. Question P8 is question P6.

Activity 47, p. 294, question R2 answer Change 'part B' to 'part A', i.e., "In situation C of part A, the normal force..."

Activity 48, p. 297, "Suggested Points for Class Discussion", bullet 2, last sentence The word 'a' should be 'at', i.e., "(Thus, one can be at rest; the friction is still kinetic.)"

Activity 49, p. 307 The first entry in the table is not the beginning of the answer to question A4, but a continuation of theanswer to question A3.

The answer to question A4 begins with gravitation. There is a force missing from the answer to question A4. The force (i.e., column 1) is "kinetic friction." The

way it will be determined (column 2) is "Multiply the normal force by the coefficient of kinetic friction.Direction is opposite the motion of _m_ 1." The magnitude & direction (column 3) is "(NA)." Comment is "We do not actually know the normal force, so we cannot determine the force of kinetic friction. However,students might think that they know the normal force using common sense."

Activity 49, p. 308, question R1 answer The second bullet for air resistance is wrong. It should read, "At very small speeds, the force law is closer

to Bv.Activity 51, p. 324

The answer to question B1, part (a) is wrong. The x-component of F _N_,left should be F_ _N ,left. The answer to question B1, part (b) is wrong. The x-component of F _N_,right should be - F_ _N ,right. The answer to question B2, part (c) is confusing. Vectors F _g_1 , F _N_2 , and F _T_2 are not part of the answer.

They are simply the other vectors in the situation, which are included because their components are known. The answer to question B2, part (d) is wrong. The x-component of F _g_2 should be - F_ _g_2 cos 60, and its

_y-component should be -_F_ _g_2 sin 60. The word "the" should be removed from the second line of the last bullet for the answer to question B2, i.e.,

"Even if we notate the magnitude of both tension forces as..."Activity 54, p. 350, question P9 answer

Change "velocity" to "velocities", i.e., "(a,b) The forces... Kinetic Friction , which depends on the relativevelocities of the objects in contact, and..."

Activity 55, p. 357, question A5 answer


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In the table showing the time intervals during which the ball is accelerating, change '4.9s' to '4.8s', i.e., thetime interval corresponding to the 2nd time the ball is rolling across the felt should be [4.8s, 6.5s].

In the table showing time intervals during which its velocity is constant (it's part of the 4th bullet of theanswer to question A5), change '4.9s' to '4.8s', i.e., the third time interval during which the ball is rolling atconstant velocity is [3.51s, 4.8s].

Activity 56, p. 370, question C4 answer, bullet 3 Change 'any' to 'a', i.e., "Students might not perceive that there is a net force on them when they walk in a

circle."

Activity 58, p. 384, question A2, part (c) answer Of the three free-body diagrams, the one on the left is for the skydiver, the one in the middle is for the parachute, and the one on the right is for the Earth.

Activity 58, p. 386, question B4 answer Add to the end of the answer to part (b): "But perhaps not as much faster and farther as before, assuming for

example that she does not push as hard as her father did before." Add a bullet: " In other words, her speed might be smaller than it was before, but it is always larger than

her father's."Activity 58, p. 387, question R1 answer, bullet 1

Change to "The action-reaction pair has five features: exerted by different objects, exerted on differentobjects, same type (normal, gravitational, etc.), same magnitude, and opposite direction."

Activity 59, p. 389, "Suggestions for Classroom Use"

Change bullet 2 to: "Focus students' attention on learning the answers and explanations to two questionsusing the following group structure: Divide the class into teams of 3 or 4 students each. Assign each team 2questions from the same part, or put slips of paper with the numbers of 2 questions into a bowl and haveteams choose. Tell students that each of them will be asked to write out the explanation to one of thequestions, and that each student's grade will depend in part on how well the other team members do. As theteams are working, decide which explanation each student will provide. When the working time iscomplete, give students their assignments, to be done either during or after class. When gradingexplanations, give half credit for each individual's contribution and half credit for the contributions of therest of the team. In other words, half of each student's grade will depend on his/her individual explanation,and the other half will depend on his/her team's explanations.

Insert between bullets 2 and 3: " For small classes with only a few teams, do parts B and D first, thenrepeat with parts C and E."

Add bullet: " As a class, compare answers and discuss areas of disagreement."Activity 59, p. 391, question A4 answer

Change 'rope 1' to 'rope 2', i.e., "... then the tension in rope 2 is larger in case II than in case I."Activity 59, p. 392, question C2 answer

Add bullet: " Students might think that the velocity is larger because the net force is larger." Activity 60, p. 402, question R2, part (a) answer

Remove 'of the', i.e., "The mass is much larger for the car ." Many thanks to Lonnie Grimes of Oakmont High School in Roseville, CA, who found almost all of these mistakes.

Errata for Conservation Laws TG

Activity 74, p. 513, question B3, part (c) answer In the second paragraph, the area of each 'box' is wrong. It should be 0.01N-s, i.e., "... and each box has an

area of (2N) x (0.005s) = 0.01N-s..."Activity 76, p. 529, question A3 answer

The parts are not labeled, i.e., the "(a)", "(b)", and "(c)" labels are missing.Activity 76, p. 532

The answers and comments to questions R1, R2, and R3 are missing. The answer for R1 is, "Total momentum is conserved for situations A3 and A6. It is zero initially, and

remains the same throughout the time interval specified. Total momentum is approximately conserved forsituation A1, because the impulse delivered to the system by gravitation is small during the explosion. Atleast one component of the total momentum is conserved for the other 5 situations. We define the x-direction to be the horizontal in the plane of the page (i.e., to the right), the y-direction to be the vertical,and the z -direction to be the horizontal perpendicular to the plane of the page (i.e., directly toward you). Insituations A2, A4, and A7, the net external force is in the y-direction, so total momentum is conserved inthe x- and z -directions. In situation A5, the net external force has y- and z -components, so momentum isconserved only in the x-direction."

The comments for R1 are:o Students might think that momentum is not conserved in situation A6, because the wheel is slowing

down.o Students might consider only the ball in A3, rather than the Earth-ball system.o In situation A3, students might not ignore the gravitational forces exerted on the Earth-ball system

by the Sun, the Moon, and the planets.o Students might not recognize that the total momentum of the Earth-ball system is staying the same

during the motion of the ball.o Students might only consider two directions, i.e., the x- and y-directions.o In situation A5, we are assuming that the bow string exerts a force on the arrow in the yz -plane.


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o Students might think that momentum is not conserved in any direction in situation A7, because the ball's are going in all directions.

The answer for R2 is, "In situations A3 and A6, all forces are internal; the net force on each system is zero." The comments for R2 are:

o If students do not have the correct set of situations here, they are likely to generalize improperly.o Students might not realize that in A3 they are expected to ignore the forces exerted by the Sun, the

Moon, and the other planets.o Students might not realize that in A6 the net force on the wheel is zero, because it is slowing down.

The answer to R3 is, "For those situations in which momentum is not conserved, there are external forceson the specified system. In each case, the direction of the change in momentum is the same as the directionof the net external force. In order to always conserve momentum, it is necessary to choose a system largeenough so that there are no external forces on it. If we include the Earth in each system and ignore thegravitational forces exerted by the Sun, the Moon, and the planets, then momentum is conserved in all thesituations."

(There are no comments for R3 at this time.)Activity 83, p. 584, question A1 answer

The explanation (column 5) should read, "Monkey exerts F_ _N_1 and _F fs. Whatever is holding up the ropeexerts _F_ _N_2 (assuming, e.g., that the rope is tied to a hook in the ceiling). The displacement of the rope iszero."

Activity 87, p. 616, "Anticipated Difficulties for Students", bullet 7 (i.e., last bullet)

The 'clay' should be a 'cart', i.e., "Analyzing the cart in situation R3... because the work done on the cart isdone..."Activity 87, p. 618, "Providing Support to Ensure Student Progress", bullet 6 (i.e., next to last bullet)

Change to: "In situation R3, focus students attention on forces that are applied through a displacement, suchas forces internal to the spring, rather than forces that are applied through zero displacement, such as thenormal force exerted by the wall."

Activity 87, p. 620, question A3(b) answer

The explanation is wrong, because we do not know how to calculate the work done by friction, as describedin the Reader. Therefore, students are expected simply to use common sense to try to answer this question.

Later, the explanation will be that there is a loss of energy from the macroscopic realm to the microscopicrealm, which means that the speed must be smaller after hitting the spring than before.

Activity 87, p. 620, question A3(b) bullet

The comment is inappropriate for the same reason that the explanation is inappropriate, that is we do notknow how to calculate the work done by friction, as described in the Reader. It should read, "The workdone by the friction force on the cart cannot be calculated or even estimated. Further, knowing its valuewould be of no consequence here, because all of the macroscopic kinetic energy lost by the cart

becomes microscopic energy of the cart. In other words, the forces are internal to the cart, so the energyremains with the cart. However, at this point in the course, students are not expected to be able to make thisdistinction between macroscopic and microscopic energy."

Many thanks to Lonnie Grimes of Oakmont High School in Roseville, CA, who found almost all of these mistakes.

Errata for Advanced Topics AR

The following mistakes are in the first 3 printings of Vol. 4AT / Activities & Reader. If you have a 4th printing orhigher, they have been fixed. Please check the copyright page (page iv) to see which printing, or mixture of

printings, you have.Contents, p. v

The correct title of Activity AT13 is "Exploring Relative Motion in One and Two Dimensions".Activity AT4, p. 13, "Prior Experience/Knowledge Needed"

The label of the first equation should read: tangential component of acceleration . The change inspeed can be negative, and when it is, the direction of the tangential component of acceleration is oppositethe direction of motion. And when the change of speed is positive, this component is in the direction ofmotion.

Activity AT8, p. 30, question A3 In the description of the situation, the speed of the marble three seconds later should be

"80cm/s", not "79cm/s".Activity AT8, p. 31, question B2

In the description of the situation, the second sentence should begin: "One second later..."Activity AT8, p. 31, question B3

In the description of the situation, the time at which the toy car stops near the top of the incline should be"t = 0.58s", not "t = 1.8s".

The fourth question in part (d) should be: What is the car's position and velocity at " t = 0.68s", not "t = 2s".Activity AT11, p. 44, question A1


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In the description of the situation, the initial speed of the puck should be "250cm/s", not "25cm/s".Activity AT17, p. 69, questions B1 & B2

A car traveling at 29m/s is moving at "65mi/h", not "60mi/h". This mistake occurs twice in question B1 andonce in question B2.

Activity AT17, p. 69, question B3

The diagram of situation A is not consistent with what is happening.In particular, there is not enough string left hanging to allow the wheel to spin

as many times as it needs before stopping. The following diagram replaces theone accompanying the description. Right-click or command-click and chooseOpen image in new window (or equivalent) to see a full -sized version. Printthat version at 100% for a transparency, or at 33% to replace the figure instudents books. Also note that the diagram on the answer sheet is theTeacher's Guide is the same as that shown below. Finally, the angle of theincline in situation B has been made more shallow to be consistent with theadditional changes listed below.

Many of the values for the given information should be changed. Theinitial speed of the wheel is now 1rev/s , and it is slowing down at a rateof rev/s 2. The ball is now a marble , and it is rolling up the inclineat4m/s and slowing down at a rate of 1m/s 2. (Changes shown in bold type.)

The question for part (b) should read: "Write an expression for the position of the marble ..." (Changeshown in bold type.)

Activity AT18, p. 73, question A5 In part (b), when the car speeds up, its speed in miles per hour should be "65mi/h", not "60mi/h". In other

words, 29m/s = 65mi/h.Activity AT21, p. 86, question R4

The "second" part (b) should be part (c). Part (c) should be part (d).

Errata for Complex Systems AR

The following mistakes are in the first printing of Vol. 4CS / Activities & Reader. If you have a 2nd printing orhigher, they have been fixed. Please check the copyright page (page iv) to see which printing, or mixture of

printings, you have.Activity CS3, p. 13, question A2(c)

The mass of oil (fluid X) should be "16" (grams), not "18".Activity CS11, p. 50, property #4 of idealized fluids (at the very bottom of the page)

The middle of the sentence should read: "... which means that both the pressure and speed are constant...".Activity CS11, p. 51, "Explanation of Activity"

The mass of 10cm 3 of oil should be "8g", not "9g".

Activity CS11, p. 51, figure for problem A3

The following figure should make it clearer to students what is going on here, i.e., the direction in which theglass tube is rotated so that it "rests on its side" in part(a). Right-click or command-click and choose "Openimage in new window" (or equivalent) to see a full-sizedversion. Print that version at 100% for a transparency, orat 33% to replace the figure in students' books. (Theanswer sheet in the Complex Systems TG already has thecorrected figure.)Activity CS12, p. 53, "Purpose and Expected Outcome"

The last sentence should begin: "When you finda system to which you cannot apply..." (Change shown

in bold type.)Activity CS22, p. 106, question A2 Part (a) should read: "Which state(s) has the highest temperature? Explain." Part (b) should read: "Which state(s) has the lowest temperature? Explain." (Changes shown in bold type.)

Activity CS26, p. 127, description for part B

The springs being studied in this part of the activity are said to be "relaxed". This word should be omitted.Instead, the springs should be considered to have zero or very small relaxed length. The need for thischange is that when the springs are relaxed initially, the balls attached to them in situation B1 would tend tomove left and right as well as up and down, which is unnecessarily complicated. By making the relaxedlength very small, the motion of the balls (in B1) becomes purely transverse, i.e., up and down. Note that

this change affects only the results of B1.


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Activity CS30, p. 151, questions D3 and D4

The question in D3 should read: "Will the wave form on the lighter spring move faster or slower than theoriginal wave form on the heavier spring?"

The question in D4 should begin: "Will the wave form on the lighter spring..." (Changes shownin bold type.)

Reader/Chapter 1: Fluids, p. R18, table showing

speeds of water outside holes

The list of speeds in the last column arewrong. The correct table is shown below.(Right-click or command-click andchoose "Open image in new window" orequivalent to see a full-sized version, then

print at 50% to replace in student books.)

Reader/Chapter 1: Fluids, p. R19, table showing speeds of water outside holes and where the water lands

The list of speeds in the thirdcolumn and the list of where thewater lands in the last column arewrong. The correct table isshown below. (Right-click orcommand-click and choose"Open image in new window" orequivalent to see a full-sizedversion, then print at 50% toreplace in student books.)

Many thanks to Prof. Josip Slisko of the Faculty of Physical and Mathematical Sciences at the Benemerita PublicUniversity in Puebla, Mexico, who found many of these mistakes.

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