Unformatted text preview: Course
Description H PHYSICS
Physics B, Physics C PH
MAY 2004, MAY 2005 The College Board is a national nonproﬁt membership association whose mission
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Sincerely, Gaston Caperton
President
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2004, 2005 Course Description for AP Physics. Copyright © 2003
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ii Contents
Welcome to the AP Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
AP Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
AP Exams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Introduction to AP Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
What We Are About . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
A Message from the Development Committee . . . . . . . . . . . . . . . . . 3
The Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Course Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Instructional Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Laboratory Experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Documenting Laboratory Experience . . . . . . . . . . . . . . . . . . . . . 12
Physics B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Physics C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Comparison of Topics in Physics B and Physics C . . . . . . . . . . . . . 15
Content Outline for Physics B and Physics C . . . . . . . . . . . . . . . . . . . 16
The Examinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
The FreeResponse Sections–Student Presentation . . . . . . . . . . . . 22
Calculators and Equation Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Physics B: Sample MultipleChoice Questions . . . . . . . . . . . . . . . . 26
Answers to Physics B MultipleChoice Questions . . . . . . . . . . . 35
Physics B: Sample FreeResponse Questions . . . . . . . . . . . . . . . . . 36
Physics C Mechanics: Sample MultipleChoice Questions . . . . . . . 44
Answers to Physics C Mechanics MultipleChoice Questions . . 48
Physics C Mechanics: Sample FreeResponse Questions . . . . . . . . 49
Physics C Electricity and Magnetism: Sample MultipleChoice
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Answers to Physics C Electricity and Magnetism
MultipleChoice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Physics C Electricity and Magnetism: Sample FreeResponse
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
AP Program Essentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
The AP Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
AP Grades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Grade Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Earning College Credit and/or Placement . . . . . . . . . . . . . . . . . . . . 64
Why Colleges Grant Credit and/or Placement for AP Grades . . . . 65
Guidelines on Granting Credit and/or Placement for AP Grades . . 65
Finding Colleges That Accept AP Grades . . . . . . . . . . . . . . . . . . . . 66
apcentral.collegeboard.com iii AP Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
AP Calendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Test Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Teacher Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
PreAP ® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
PreAP Professional Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
AP Publications and Other Resources . . . . . . . . . . . . . . . . . . . . . . . . . 69
Ordering Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Print . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Multimedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 iv apcentral.collegeboard.com Welcome to the AP® Program
The Advanced Placement Program® (AP®) is a collaborative effort
between motivated students, dedicated teachers, and committed high
schools, colleges, and universities. Since its inception in 1955, the Program
has allowed millions of students to take collegelevel courses and exams,
and to earn college credit or placement while still in high school.
Most colleges and universities in the U.S., as well as colleges and universities in 21 other countries, have an AP policy granting incoming students credit, placement, or both on the basis of their AP Exam grades.
Many of these institutions grant up to a full year of college credit (sophomore standing) to students who earn a sufﬁcient number of qualifying
AP grades.
Each year, an increasing number of parents, students, teachers, high
schools, and colleges and universities turn to AP as a model of educational excellence.
More information about the AP Program is available at the back of this
Course Description and at AP Central™, the College Board’s online home
for AP professionals (apcentral.collegeboard.com). Students can ﬁnd more
information at the AP student site (www.collegeboard.com/apstudents). AP Courses
Thirtyfour AP courses in a wide variety of subject areas are currently
available. Developed by a committee of college faculty and AP teachers,
each AP course covers the breadth of information, skills, and assignments
found in the corresponding college course. See page 2 for a list of the AP
courses and exams that are currently offered. AP Exams
Each AP course has a corresponding exam that participating schools
worldwide administer in May. Except for Studio Art, which is a portfolio
assessment, AP Exams contain multiplechoice questions and a freeresponse section (either essay or problemsolving).
AP Exams represent the culmination of AP courses, and are thus an
integral part of the Program. As a result, many schools foster the expectation that students who enroll in an AP course will go on to take the corresponding AP Exam. Because the College Board is committed to providing apcentral.collegeboard.com 1 homeschooled students and students whose schools do not offer AP
access to the AP Exams, it does not require students to take an AP course
prior to taking an AP Exam. AP Courses and Exams
Art
Art History
Studio Art (Drawing Portfolio)
Studio Art (2D Design Portfolio)
Studio Art (3D Design Portfolio) Government and Politics
Comparative Government and
Politics
United States Government and
Politics Biology History
European History
United States History
World History Calculus
Calculus AB
Calculus BC Human Geography
Chemistry
Computer Science
Computer Science A
Computer Science AB Latin
Latin Literature
Latin: Vergil
Music Theory Economics
Macroeconomics
Microeconomics
English
English Language and Composition
English Literature and
Composition
Environmental Science
French
French Language
French Literature Physics
Physics B
Physics C: Electricity and
Magnetism
Physics C: Mechanics
Psychology
Spanish
Spanish Language
Spanish Literature
Statistics German Language 2 apcentral.collegeboard.com Introduction to AP Physics
Shaded text indicates important new information about this subject. What We Are About
A Message from the Development Committee
The AP Physics Development Committee recognizes that curriculum,
course content, and assessment of scholastic achievement play complementary roles in shaping education at all levels. The committee believes
that assessment should support and encourage the following broad
instructional goals:
1. Physics knowledge — Basic knowledge of the discipline of physics,
including phenomenology, theories and techniques, concepts, and
generalizing principles.
2. Problem solving — Ability to ask physical questions and to obtain
solutions to physical questions by use of qualitative and quantitative
reasoning, and by experimental investigation.
3. Student attributes — Fostering of important student attributes,
including appreciation of the physical world and the discipline of
physics, curiosity, creativity, and reasoned skepticism.
4. Connections — Understanding connections of physics to other disciplines and to societal issues.
The ﬁrst three of these goals are appropriate for the AP and introductorylevel college physics courses which should, in addition, provide a background for the attainment of the fourth goal.
The AP Physics Examinations have always emphasized achievement of
the ﬁrst two goals. Over the years, the deﬁnitions of basic knowledge of the
discipline and problem solving have evolved. The AP Physics courses have
reﬂected changes in college courses, consistent with our primary charge. At
present we are increasing our emphasis on physical intuition, experimental
investigation, and creativity. We are including more openended questions
in order to assess students’ understanding of physical concepts. We are
structuring questions that stress the use of mathematics to illuminate the
physical situation rather than to show manipulative abilities.
The committee is dedicated to developing examinations that can be
graded fairly and consistently and that are free of ethnic, gender, economic, or other bias. We operate under practical constraints of testing
methods, allotted time, and large numbers of students at widely spread
apcentral.collegeboard.com 3 geographical locations. In spite of these constraints, the committee strives
to design examinations that promote excellent and appropriate instruction
in physics. The Courses
Two AP Examinations in Physics, identiﬁed as Physics B and Physics C, are
offered. These examinations are designed to test student achievement in the
Physics B and Physics C courses described in this booklet. These courses
are intended to be representative of courses commonly offered in colleges
and universities, but they do not necessarily correspond precisely to courses
at any particular institution. The aim of an AP secondary school course in
physics should be to develop the students’ abilities to do the following:
1. Read, understand, and interpret physical information — verbal,
mathematical, and graphical.
2. Describe and explain the sequence of steps in the analysis of a particular physical phenomenon or problem; that is,
a. describe the idealized model to be used in the analysis, including
simplifying assumptions where necessary,
b. state the concepts or deﬁnitions that are applicable,
c. specify relevant limitations on applications of these principles,
d. carry out and describe the steps of the analysis, verbally or
mathematically, and
e. interpret the results or conclusions, including discussion of
particular cases of special interest.
3. Use basic mathematical reasoning — arithmetic, algebraic, geometric, trigonometric, or calculus, where appropriate — in a physical
situation or problem.
4. Perform experiments and interpret the results of observations,
including making an assessment of experimental uncertainties.
In the achievement of these goals, concentration on basic principles of
physics and their applications through careful and selective treatment of
wellchosen areas is more important than superﬁcial and encyclopedic
coverage of many detailed topics. Within the general framework outlined on
pages 1619, teachers may exercise some freedom in the choice of topics.
In the AP Physics Examinations, an attempt is made through the use of
multiplechoice and freeresponse questions to determine how well these
goals have been achieved by the student either in a conventional course
or through independent study. The level of the student’s achievement is
assigned an AP grade of 1 to 5, and many colleges use this grade alone as
the basis for placement and credit decisions.
4 apcentral.collegeboard.com Introductory college physics courses typically fall into one of three categories, designated as A, B, and C in the following discussion.
Category A includes courses in which major concepts of physics are
covered without as much mathematical rigor as in more formal courses,
such as Physics B and Physics C, which are described below. The emphasis in Category A courses is on developing a qualitative conceptual understanding of general principles and models and on the nature of scientiﬁc
inquiry. Some courses may also view physics primarily from a cultural or
historical perspective. Category A courses are generally intended for students not majoring in a sciencerelated ﬁeld. The level of mathematical
sophistication usually includes some algebra and may extend to simple
trigonometry, but rarely beyond. These courses vary widely in content and
approach, and at present there is no AP course or exam in this category.
A high school version of a Category A course that concentrates on conceptual development and that provides an enriching laboratory experience
may be taken by students in the 9th or 10th grade and should provide the
ﬁrst course in physics that prepares them for a more mathematically rigorous AP Physics B or C course.
Category B courses build on the conceptual understanding attained in a
ﬁrst course in physics, such as the Category A course described above.
They provide a systematic development of the main principles of physics,
emphasizing problem solving as well as continuing to develop a deep
understanding of physics concepts. It is assumed that the student is familiar with algebra and trigonometry; calculus is seldom used, although some
theoretical developments may use basic concepts of calculus. In most colleges, this is a oneyear terminal course including a laboratory component
and is not the usual preparation for more advanced physics and engineering courses. However, Category B courses often provide a foundation in
physics for students in the life sciences, premedicine, and some applied
sciences, as well as other ﬁelds not directly related to science. The AP
Physics B course is intended to be equivalent to such courses.
Category C courses also build on the conceptual understanding attained
in a ﬁrst course in physics, such as the Category A course described above.
They normally form the college sequence that serves as the foundation in
physics for students majoring in the physical sciences or engineering. The
sequence is parallel to or preceded by mathematics courses that include
calculus. Methods of calculus are used wherever appropriate in formulating physical principles and in applying them to physical problems. The
sequence is more intensive and analytic than in Category B courses.
Strong emphasis is placed on solving a variety of challenging problems,
some requiring calculus, as well as continuing to develop a deep understanding of physics concepts. A Category C sequence may be a very apcentral.collegeboard.com 5 intensive oneyear course in college, but often will extend over one and
onehalf to two years, and a laboratory component is also included. The
AP Physics C course is intended to be equivalent to part of a Category C
sequence and covers two major areas; mechanics, and electricity and magnetism, with equal emphasis on these two areas.
In certain colleges and universities, other types of unusually highlevel
introductory courses are taken by a few selected students. Selection of
students for these courses is often based on results of AP Examinations,
other college admission information, or a collegeadministered examination. The AP Examinations are not designed to grant credit or exemption
for such highlevel courses but may facilitate admission to them. Course Selection
It is important for those teaching and advising AP students to consider the
relation of AP courses to a student’s college plans. In some circumstances
it is advantageous to take the AP Physics B course. The student may be
interested in studying physics as a basis for more advanced work in the life
sciences, medicine, geology, and related areas, or as a component in a nonscience college program that has science requirements. Credit or advanced
placement for the Physics B course provides the student with an opportunity either to have an accelerated college program or to meet a basic science requirement; in either case the student’s college program may be
enriched. Access to an intensive physics sequence for physics or science
majors is another opportunity that may be available.
For students planning to specialize in a physical science or in engineering, most colleges require an introductory physics sequence of which the
C course is the ﬁrst part. Since a previous or concurrent course in calculus is often required of students taking the C course, students who expect
advanced placement or credit for Physics C should attempt an AP course
in calculus as well; otherwise, placement in the nextinsequence physics
course may be delayed or even denied. Either of the AP Calculus courses,
Calculus AB or Calculus BC, should provide an acceptable basis for students preparing to major in the physical sciences or engineering, but
Calculus BC is recommended. Therefore, if such students must choose
between AP Physics or AP Calculus while in high school, they should
probably choose calculus.
There are two separate AP Physics Examinations, Physics B and
Physics C. Students take one examination or the other. Both examinations
contain multiplechoice and freeresponse questions. The Physics B examination is for students who have taken a Physics B course or who have
mastered the material of this course through independent study.
The Physics B examination covers topics in mechanics, electricity and
6 apcentral.collegeboard.com magnetism, ﬂuid mechanics and thermal physics, waves and optics, and
atomic and nuclear physics; a single examination grade is reported.
Similarly, the Physics C examination corresponds to the Physics C course.
One part of the Physics C examination covers mechanics; the other part
covers electricity and magnetism. Students are permitted to take either or
both parts of this examination, and separate grades are reported for the
two subject areas to provide greater ﬂexibility in planning AP courses and
making advanced placement decisions.
Further descriptions of the two kinds of AP Physics courses and their
corresponding examinations in terms of topics, level, mathematical rigor,
and typical textbooks are presented in the pages that follow. Information
about organizing and conducting AP Physics courses, of interest to both
beginning and experienced AP teachers, may be found in the Teacher’s
Guide — AP Physics. This publication includes practical advice from successful AP teachers and detailed sets of objectives for both examinations.
The 1998 AP Physics B & Physics C Released Exams booklet contains
the entire 1998 Physics B and Physics C examinations, the solutions and
grading standards for the freeresponse sections of these examinations,
sample student responses, as well as statistical data on student performance. For information about ordering these publications and others,
see the back of this booklet. Additional useful information may be found at
AP Central™ (apcentral.collegeboard.com). Instructional Approaches
It is strongly recommended that both Physics B and Physics C be
taught as secondyear physics courses. A ﬁrstyear physics course
aimed at developing a thorough understanding of important physical principles and that permits students to explore concepts in the laboratory provides a richer experience in the process of science and better prepares
them for the more analytical approaches taken in AP courses.
However, secondary school programs for the achievement of AP course
goals can take other forms as well, and the imaginative teacher can design
approaches that best ﬁt the needs of his or her students. In some schools,
AP Physics has been taught successfully as a very intensive ﬁrstyear
course; but in this case there may not be enough time to cover the material
in sufﬁcient depth to reinforce the students’ conceptual understanding or
to provide adequate laboratory experiences. This approach can work for
highly motivated, able students but is not generally recommended.
Independent study or other ﬁrstyear physics courses supplemented with
extra work for individual motivated students are also possibilities that
have been successfully implemented. apcentral.collegeboard.com 7 In a school that uses block scheduling, it is strongly recommended that
AP Physics be scheduled to extend over an entire year. A oneyear AP
course should not be taught in one semester, as this length of time is insufﬁcient for students to properly assimilate and understand the important
concepts of physics that are covered in the syllabus.
More detailed descriptions about alternate approaches can be found in
the Teacher’s Guide – Physics. Whichever approach is taken, the nature of
the AP course requires teachers to spend time on the extra preparation
needed for both class and laboratory. AP teachers should have a teaching
load that is adjusted accordingly. Laboratory Experience
Laboratory experience must be part of the education of AP Physics students and should be included in all AP Physics courses just as it is in introductory college physics courses. Students should be able to:
•
•
•
•
•
• design experiments,
observe and measure real phenomena,
organize, display, and critically analyze data,
determine uncertainties in measurement,
draw inferences from observations and data, and
communicate results, including suggested ways to improve experiments and proposed questions for further study. In textbooks and problems, most attention is paid to idealized situations: friction is assumed to be constant or absent; meters read true values; heat insulators are perfect; gases follow the ideal gas equation. In the
laboratory, the validity of these assumptions can be questioned because
there the student meets nature as it is rather than in idealized form.
Laboratory experience should also help students understand the topics
being considered. Students need to be proﬁcient in problem solving and in
the application of fundamental principles to a wide variety of situations.
Problemsolving ability can be fostered by investigations that are somewhat nonspeciﬁc. Such investigations are often more interesting and
valuable than “cookbook” experiments that merely investigate a wellestablished relationship, and which can take important time away from
the rest of the course. Thus it is often valuable to ask students to write
informally about what they have done, observed, and concluded, as well
as it is for them to keep wellorganized laboratory notebooks. 8 apcentral.collegeboard.com Some questions or parts of questions on the AP Physics Examinations
may distinguish between students who have had laboratory experience
and those who have not. In addition, understanding gained in the laboratory may improve the students’ test performance overall.
Laboratory programs in both college courses and AP courses differ
widely, and there is no clear evidence that any one approach is necessarily
best. This diversity of approaches should be encouraging to the high
school teacher of an AP course. The success of a given program depends
strongly on the interests and enthusiasm of the teacher and on the general
ability and motivation of the students involved.
Although programs differ, the AP Physics Development Committee has
made some recommendations in regard to school resources and scheduling.
Students in AP Physics should have adequate and timely access to computers
that are connected to the Internet and its many online resources. Students
should also have access to computers with appropriate sensing devices and
software for use in gathering, graphing, and analyzing laboratory data, and
writing reports. Although using computers in this way is a useful activity and
is encouraged, some initial experience with gathering, graphing, and manipulating data by hand is also important for students to be able to attain a better
feel for the physical realities involved in the experiments. And it should be
emphasized that simulating an experiment on a computer cannot adequately
replace the actual “handson” experience of doing an experiment.
Flexible or modular scheduling is best in order to meet the time requirements identiﬁed in the course outline. Some schools are able to assign daily
double periods so that laboratory and quantitative problemsolving skills may
be fully developed. At the very least, a weekly extended or double laboratory
period is needed. It is not advisible to attempt to complete highquality
AP laboratory work within standard 45 to 50minute periods.
If AP Physics is taught as a secondyear physics course, following a ﬁrstyear course with a strong laboratory component, then somewhat less time
might be devoted to labs in the AP course. However, the AP labs should
build on and extend the lab experiences of the ﬁrstyear course. Students
should be encouraged to save evidence of their ﬁrstyear lab work, such as
their lab reports or a lab notebook, as well as similar evidence of the lab
work in their AP course. The important criterion is that students completing an AP Physics course must have had laboratory experiences that are
roughly equivalent to those in a comparable introductory college course. apcentral.collegeboard.com 9 Therefore, school administrations should realize the implications, both
in cost and time, of incorporating serious laboratories into their program.
An AP course is a college course, and the equipment and time allotted to
laboratories should be similar to that in a college course.
To provide guidance for the development of the AP courses and exams,
the AP Program undertakes periodic surveys of introductory college courses.
A 1998 survey of both noncalculus and calculusbased introductory physics
courses obtained some information about the laboratory programs in these
courses. The survey revealed that nearly all the courses of either type
included a laboratory, and that on average from two to three hours per week
are devoted to laboratory activities. Secondary schools may have difﬁculty
scheduling this much weekly time for lab. However, the college academic
year typically contains fewer weeks than the secondary school year, so AP
teachers may be able to schedule a few more lab periods during the year
than can the colleges. Also, some college faculty have reported that some
lab time may be occasionally used for other purposes as well. Nevertheless,
in order for AP students to have sufﬁcient time for lab, at least one double
period per week is recommended for all AP Physics courses.
In response to a survey question about whether separate credit is given
for lab, the percent of the colleges indicating that credit is given separately was 39% for noncalculus courses and 34% for calculusbased
courses. For these separate lab courses the mean number of credit hours
awarded was just slightly higher than one, and the mean number of credit
hours awarded for the rest of the course was 3.4 for the noncalculus
courses and 3.7 for the calculusbased courses. For the courses for which
lab credit was not awarded separately, the lab component contributed on
average about 18% of ﬁnal course grade for both noncalculus and calculusbased courses. Thus it appears that when all the introductory courses are
considered together, about 20% of the total course credit awarded can be
attributed to lab performance.
One question in the survey asked the colleges for the percent of the
laboratory activities that can be classiﬁed depending on levels of student
involvement. The categories were: (1) prescribed or “cookbook,” (2)
limited investigations with some direction provided, and (3) open investigations with little or no direction provided. Most colleges (93% for noncalculus courses, 90% for calculusbased courses) reported that they do
labs in the ﬁrst category and of these colleges the mean percentage of
their labs in this category were 82% for noncalculus courses and 75% for
calculusbased courses. However, many colleges (55% for noncalculus
courses, 70% for calculusbased courses) also reported doing labs in the
second category, with the mean percentages being 40% for both types
of courses. Far fewer colleges (12% for noncalculus courses, 20% for
calculusbased courses) reported doing labs in the third category with
10 apcentral.collegeboard.com the mean percentages being about 2022% for both types of courses. While
many college professors believe that labs in the latter two categories do
have more value to students, they report often being limited in their ability
to institute them by large class sizes and other factors. In this respect, AP
teachers often have an advantage in being able to offer more openended
labs to their students.
Another question asked the colleges to indicate which of a number of
assessment techniques or instruments are used in assessing laboratory
performance or determining laboratory grades. They were told to check all
that apply. The percent of colleges indicating use of each type of assessment are shown below:
Noncalculus
courses (%)
Observation of lab performance
51
Lab practical exam
26
Written tests designed speciﬁcally for lab
29
Labrelated questions on regular written
17
lecture tests
Lab reports
93
Lab notebooks
25
Lab portfolios
1
Other
17
(most common comment was prelab
quizzes or assignments) Calculusbased
courses (%)
51
24
32
27
99
43
0
13 Finally, the survey asked the colleges to check which of a number of
skills were assessed if they attempted to assess laboratory skills with
written test questions. They were again told to check all that apply. The
percent of colleges indicating each type of skill are shown below: Design of experiments
Analysis of data
Analysis of errors
Evaluation of experiments and
suggestions for future investigations
Other apcentral.collegeboard.com Noncalculus
courses (%)
48
88
61
21 Calculusbased
courses (%)
29
73
62
18 18 27 11 A more detailed laboratory guide is scheduled for summer 2002, and
will be posted on AP Central. This guide contains descriptions of a number of experiments that typify the type and level of skills that should be
developed by AP students in conducting laboratory investigation. The
experiments are not mandatory; they can be modiﬁed or similar experiments substituted as long as they assist the student in developing these
skills. Each edition of the Teacher’s Guide also provides additional suggestions for the laboratory. It mentions speciﬁc experiments that other AP
teachers have tried and liked, and it lists publications and other sources of
information that may provide additional ideas for possible lowcost experiments. The guide may be helpful to experienced AP teachers as well as to
those just beginning to teach courses in AP Physics.
Documenting Laboratory Experience
The laboratory is important for both AP and college students. Students
who have had laboratory experience in high school will be in a better position to validate their AP courses as equivalent to the corresponding college
courses and to undertake the laboratory work in more advanced courses
with greater conﬁdence. Most college placement policies assume that students have had laboratory experience, and students should be prepared
to show evidence of their laboratory work in case the college asks for it.
Such experience can be documented by keeping a lab notebook or a portfolio of lab reports. Presenting evidence of adequate collegelevel laboratory experience to the colleges they attend can be very useful to students
as an adjunct to their AP grades if they desire credit for or exemption from
an introductory college course that includes a laboratory. Although colleges can expect that most entering AP students have been exposed to
many of the same laboratory experiments performed by their own introductory students, individual consultation with students is often used to
help determine the nature of their laboratory experience. 12 apcentral.collegeboard.com Physics B
The Physics B course includes topics in both classical and modern
physics. A knowledge of algebra and basic trigonometry is required for the
course; the basic ideas of calculus may be introduced in connection with
physical concepts, such as acceleration and work. Understanding of the
basic principles involved and the ability to apply these principles in the
solution of problems should be the major goals of the course.
The following textbooks are commonly used in colleges and typify the
level of the B course. However, the inclusion of a text in this list does not
constitute endorsement by the College Board, ETS, or the AP Physics
Development Committee.
Cutnell, John D. and Kenneth W. Johnson, Physics, 6th ed. New York, John
Wiley & Sons, 2003.
Giancoli, Douglas C., Physics: Principles with Applications, 5th ed. Upper
Saddle River, NJ, Prentice Hall, 1998.
Hecht, Eugene, Physics: Algebra/Trigonometry, 3rd ed. Paciﬁc Grove, CA,
Brooks/Cole Publishing, 2003.
Jones, Edwin R. and Richard L. Childers, Contemporary College Physics,
3rd ed. Columbus, OH, McGraw Hill, 2001 update.
Sears, Francis W., Mark W. Zemansky, and Hugh D. Young, College Physics,
7th ed. Boston, MA, Addison Wesley, 1991.
Serway, Raymond A. and Jerry S. Faughn, College Physics, 6th ed. Paciﬁc
Grove, CA, Brooks/Cole Publishing, 2003.
Wilson, Jerry D. and Anthony J. Buffa, College Physics, 5th ed. Upper
Saddle River, NJ, Prentice Hall, 2003.
Although these texts are commonly used, the list is not exhaustive. The
Teacher’s Guide includes some additional suggestions for other texts, supplementary books, and other materials.
The Physics B course seeks to be representative of topics covered in
similar college courses, as determined by periodic surveys. Accordingly,
goals have been set to the percentages on pages 16–19 for coverage of
ﬁve general areas: Newtonian mechanics, ﬂuid mechanics and thermal
physics, electricity and magnetism, waves and optics, and atomic and
nuclear physics. apcentral.collegeboard.com 13 Beginning in 2003, the subtopic “Speciﬁc and latent heat (including
calorimetry)” will be deleted from the topics covered by the B course.
Many colleges and universities include additional topics in their survey
courses. Some AP teachers may wish to add supplementary material to a
Physics B course. Many teachers have found that a good time to do this is
later in the year, after the AP Examinations have been given. Physics C
In the typical C course, roughly onehalf year is devoted to mechanics. Use
of calculus in problem solving and in derivations is expected to increase as
the course progresses.
In the second halfyear of the C course, the primary emphasis is on classical electricity and magnetism. Calculus is used freely in formulating principles and in solving problems.
The following textbooks are commonly used in colleges and typify the
level of the C course. However, the inclusion of a text in this list does not
constitute endorsement by the College Board, ETS, or the AP Physics
Development Committee.
Fishbane, Paul M., Stephen Gasiorowicz, and Stephen T. Thornton, Physics
for Scientists and Engineers, 2nd ed. Upper Saddle River, NJ, Prentice
Hall, 1996.
Giancoli, Douglas C., Physics for Scientists and Engineers, 3rd ed. Upper
Saddle River, NJ, Prentice Hall, 2000.
Halliday, David, Robert Resnick, and Jearl Walker, Fundamentals of
Physics, 6th ed. Enhanced Problems Version. New York, John Wiley,
2002.
Halliday, David, Robert Resnick, and Kenneth Krane, Physics, Parts I and
II, 5th ed. New York, John Wiley, 2001.
Serway, Raymond A. and Robert Beichner, Physics for Scientists and
Engineers, 5th ed. Paciﬁc Grove, CA, Brooks/Cole Publishing, 2000.
Serway, Raymond A. and John W. Jewett, Jr., Principles of Physics, 3rd ed.
Paciﬁc Grove, CA, Brooks/Cole Publishing, 2002.
Tipler, Paul A. and Gene P. Mosca, Physics for Scientists and Engineers,
5th ed. New York, W.H. Freeman, 2003.
Wolfson, Richard, and Jay M. Pasachoff, Physics for Scientists and
Engineers, 3rd ed. Boston, MA, Addison Wesley, 1999.
Young, Hugh D. and Roger A. Freedman, Sears and Zemansky’s
University Physics, 10th ed. Boston, MA, Addison Wesley, 2000. 14 apcentral.collegeboard.com Although these texts are commonly used, the list is not exhaustive. The
Teacher’s Guide includes some additional suggestions for other texts, supplementary books, and other materials.
Most colleges and universities include in a C course additional topics
such as wave motion, kinetic theory and thermodynamics, optics, alternating current circuits, or special relativity. Although wave motion, optics,
and kinetic theory and thermodynamics are usually the most commonly
included, there is little uniformity among such offerings, and these topics
are not included in the C examination. The Development Committee recommends that supplementary material be added to a Physics C course
when it is possible to do so. Many teachers have found that a good time
to do this is late in the year, after the AP Examinations have been given. Comparison of Topics in Physics B and Physics C
To serve as an aid for devising AP Physics courses and to more clearly
identify the speciﬁcs of the examinations, a detailed topical structure has
been developed that relies heavily on information obtained in college surveys. The general areas of physics are subdivided into major categories on
pages 1619, and for each category the percentage goals for each examination are given. These goals should serve only as a guide and should not be
construed as reﬂecting the proportion of course time that should be
devoted to each category.
Also for each major category, some important subtopics are listed. The
checkmarks indicate the subtopics that may be covered in each examination. Questions for the examination will come from these subtopics, but
not all of the subtopics will necessarily be included in every examination,
just as they are not necessarily included in every AP or college course.
It should be noted that although fewer topics are covered in Physics C
than in Physics B, they are covered in greater depth and with greater analytical and mathematical sophistication, including calculus applications. apcentral.collegeboard.com 15 Content Outline for Physics B
and Physics C
Content Area Percentage Goals
for Examinations
Physics B Physics C I. Newtonian Mechanics . . . . . . . . . . . . . . . . . . . . . . 35%
A. Kinematics (including vectors, vector
algebra, components of vectors, coordinate systems, displacement, velocity,
and acceleration)
1. Motion in one dimension
2. Motion in two dimensions,
including projectile motion
B. Newton’s laws of motion (including
friction and centripetal force)
1. Static equilibrium (ﬁrst law)
2. Dynamics of a single particle
(second law)
3. Systems of two or more bodies
(third law) 50% 7% 9% √
√ √
√ 9% 10%
√
√ √ √ C. Work, energy, power
1. Work and workenergy theorem
2. Conservative forces and potential
energy
3. Conservation of energy
4. Power 5%
√
√ 7%
√
√ √
√ √
√ D. Systems of particles, linear
momentum
1. Center of mass
2. Impulse and momentum
3. Conservation of linear momentum,
collisions 16 √
√ 4% 6% √
√ √
√
√ apcentral.collegeboard.com Content Area Percentage Goals
for Examinations
Physics B Physics C E. Circular motion and rotation
1. Uniform circular motion
2. Angular momentum and its
conservation
a. Point particles
b. Extended bodies, including
rotational inertia
3. Torque and rotational statics
4. Rotational kinematics and
dynamics 4%
√ 9%
√ √ √
√ F. Oscillations and gravitation
1. Simple harmonic motion (dynamics
and energy relationships)
2. Mass on a spring
3. Pendulum and other oscillations
4. Newton’s law of gravity
5. Orbits of planets and satellites
a. Circular
b. General 6%
√ 9%
√ √
√
√ √
√
√ √ √
√ √
√ II. Fluid Mechanics and Thermal Physics . . . . . . . . . 15%
A. Fluid Mechanics
1. Hydrostatic pressure
2. Buoyancy
3. Fluid ﬂow continuity
4. Bernoulli’s equation 6%
√
√
√
√ B. Temperature and heat
1. Mechanical equivalent of heat
2. Heat transfer and thermal expansion 2%
√
√ C. Kinetic theory and thermodynamics
1. Ideal gases
a. Kinetic model
b. Ideal gas law
2. Laws of thermodynamics
a. First law (including processes
on pV diagrams)
b. Second law (including heat
engines) 7% apcentral.collegeboard.com √
√
√
√ 17 Content Area Percentage Goals
for Examinations
Physics B Physics C III. Electricity and Magnetism . . . . . . . . . . . . . . . . . . . 25% 50% A. Electrostatics
1. Charge, ﬁeld, and potential
2. Coulomb’s law and ﬁeld and potential of point charges
3. Fields and potentials of other
charge distributions
a. Planar
b. Spherical symmetry
c. Cylindrical symmetry
4. Gauss’s law √ √
√
√
√ B. Conductors, capacitors, dielectrics
1. Electrostatics with conductors
2. Capacitors
a. Parallel plate
b. Spherical and cylindrical
3. Dielectrics 4%
√ 7%
√ √ √
√
√ C. Electric circuits
1. Current, resistance, power
2. Steadystate direct current
circuits with batteries and
resistors only
3. Capacitors in circuits
a. Steady state
b. Transients in RC circuits 7%
√
√ D. Magnetostatics
1. Forces on moving charges in
magnetic ﬁelds
2. Forces on currentcarrying wires
in magnetic ﬁelds
3. Fields of long currentcarrying wires
4. BiotSavart and Ampere’s law 4%
√ E. Electromagnetism
1. Electromagnetic induction (including
Faraday’s law and Lenz’s law)
2. Inductance (including LR and
LC circuits)
3. Maxwell’s equations
18 5%
√
√ √ 15%
√
√ 10%
√
√ √
√
10%
√ √ √ √ √
√ 5%
√ 8%
√
√
√ apcentral.collegeboard.com Content Area Percentage Goals
for Examinations
Physics B Physics C IV. Waves and Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 15%
A. Wave motion (including sound)
1. Properties of traveling waves
2. Properties of standing waves
3. Doppler effect
4. Superposition 5%
√
√
√
√ B. Physical optics
1. Interference and diffraction
2. Dispersion of light and the
electromagnetic spectrum 5%
√
√ C. Geometric optics
1. Reﬂection and refraction
2. Mirrors
3. Lenses 5%
√
√
√ V. Atomic and Nuclear Physics . . . . . . . . . . . . . . . . . 10%
A. Atomic physics and quantum effects
1. Photons and the photoelectric
effect
2. Atomic energy levels
3. Waveparticle duality 7%
√ B. Nuclear physics
1. Nuclear reactions (including
conservation of mass number
and charge)
2. Massenergy equivalence 3%
√ √
√ √ Laboratory and experimental situations: Each examination will include one
or more questions or parts of questions posed in a laboratory or experimental setting. These questions are classiﬁed according to the content area that
provides the setting for the situation, and each content area may include
such questions. These questions generally assess some understanding of
content as well as experimental skills, as described on the following pages.
Miscellaneous: Each examination may include occasional questions that
overlap several major topical areas, or questions on miscellaneous topics
such as identiﬁcation of vectors and scalars, vector mathematics, graphs
of functions, history of physics, or contemporary topics in physics.
apcentral.collegeboard.com 19 The Examinations
The AP Physics B Examination is three hours long, divided equally
between a 70question multiplechoice section and a freeresponse section.
The two sections are weighted equally, and a single grade is reported for
the B Examination.
The freeresponse section will normally contain from 6 to 8 questions.
Typical examples of its format are 6 questions, each taking about 15 minutes, or 4 questions of about 15 minutes each and 3 shorter questions of
about 10 minutes each. However, future examinations might include a
combination of questions of other lengths.
The AP Physics C Examination consists of two parts, each one and onehalf hours long. One part covers mechanics, the other part, electricity and
magnetism. A student may take either or both parts, and a separate grade
is reported for each. In addition, the time for each part is divided equally
between a 35question multiplechoice section and a freeresponse section;
the two sections are weighted equally in the determination of each grade.
The usual format for each freeresponse section has been three questions,
each taking about 15 minutes. However, future examinations might include
a larger number of shorter questions.
The percentages of each examination devoted to each major category
are speciﬁed in the preceding pages. Departures from these percentages
in the freeresponse section in any given year are compensated for in the
multiplechoice section so that the overall topic distribution for the entire
examination is achieved as closely as possible, although it may not be
reached exactly.
Some questions, particularly in the freeresponse sections, may involve
topics from two or more major categories. For example, a question may
utilize a setting involving principles from electricity and magnetism or
atomic and nuclear physics, but parts of the question may also involve the
application of principles of mechanics to this setting, either alone or in
combination with the principles from electricity and magnetism or atomic
and nuclear physics. Such a question would not be classiﬁed uniquely
according to any particular topic, but would receive partial classiﬁcations
by topics in proportion to the principles needed to arrive at the answers.
On both examinations the multiplechoice section emphasizes the
breadth of the students’ knowledge and understanding of the basic principles of physics; the freeresponse section emphasizes the application of
these principles in greater depth in solving more extended problems. In
general, questions may ask students to:
• determine directions of vectors or paths of particles;
• draw or interpret diagrams;
20 apcentral.collegeboard.com • interpret or express physical relationships in graphical form;
• account for observed phenomena;
• interpret experimental data, including their limitations and
uncertainties;
• construct and use conceptual models and explain their limitations;
• explain steps taken to arrive at a result or to predict future physical
behavior;
• manipulate equations that describe physical relationships;
• obtain reasonable estimates; or
• solve problems that require the determination of physical quantities in
either numerical or symbolic form and that may require the application of single or multiple physical concepts.
Laboratoryrelated questions may ask students to:
• design experiments, including identifying equipment needed and
describing how it is to be used, drawing diagrams or providing
descriptions of experimental setups, or describing procedures to be
used, including controls and measurements to be taken;
• analyze data, including displaying data in graphical or tabular form,
ﬁtting lines and curves to data points in graphs, performing calculations with data, or making extrapolations and interpolations from
data;
• analyze errors, including identifying sources of errors and how they
propagate, estimating magnitude and direction of errors, determining
signiﬁcant digits, or identifying ways to reduce errors;
• communicate results, including drawing inferences and conclusions
from experimental data, suggesting ways to improve experiments, or
proposing questions for further study.
The freeresponse section of each examination is printed in a separate
booklet in which each part of a question is followed by a blank space
for the student’s solution. The same questions without the blank answer
spaces are printed on green paper as an insert in the examination booklet.
This green insert also contains a Table of Information and tables of commonly used equations. The Table of Information, which is also printed near
the front of each multiplechoice section, includes numerical values of
some physical constants and conversion factors, and states some conventions used in the examinations. The equation tables are described in
greater detail in a later section. The green insert can be removed from the
freeresponse answer booklet and used for reference when answering the
freeresponse questions only.
apcentral.collegeboard.com 21 The International System (SI) of units is used predominantly in both
examinations. The use of rulers or straightedges is permitted on the freeresponse sections to facilitate the sketching of graphs or diagrams that
might be required in these sections.
Since the complete examinations are intended to provide the maximum information about differences in students’ achievement in physics,
students may find these examinations more difficult than many classroom examinations. The best way for teachers to familiarize their
students with the level of difficulty is to give them actual released
examinations (both multiplechoice and freeresponse sections) from
past administrations. Information about ordering publications is in the
back of this booklet. Recent freeresponse sections can also be downloaded from AP Central along with scoring guidelines and some sample
student responses. The FreeResponse Sections — Student Presentation
Students are expected to show their work in the spaces provided for
the solution for each part of a freeresponse question. If they need more
space, they should clearly indicate where the work is continued or they
may lose credit for it. If students make a mistake, they may cross it out or
erase it. Crossedout work and any work shown on the green insert will
not be graded, and credit may be lost for incorrect work that is not
crossed out.
In grading the freeresponse sections, credit for the answers depends on
the quality of the solutions and the explanations given, and partial solutions may receive partial credit, so students are advised to show all their
work. Correct answers without supporting work may lose credit. This is
especially true when students are asked speciﬁcally to justify their answer,
in which case the graders are looking for some verbal or mathematical
analysis that shows how the students arrived at their answer. Also, all ﬁnal
numerical answers should include appropriate units.
On the AP Physics Exams the words “justify,” “explain,” “calculate,”
“what is,” “determine,” and “derive” have precise meanings. Students
should pay careful attention to these words in order to obtain maximum
credit for their answers, and should avoid including irrelevant or extraneous material in their answers.
The ability to justify an answer in words shows understanding of the
principles underlying physical phenomena in addition to the ability to perform the mathematical manipulations necessary to generate a correct
answer. Students will be directed to justify or explain their answers on
many of the questions they encounter on the AP Physics Exams. The
words “justify” and “explain” indicate that the student should support the
22 apcentral.collegeboard.com answer with prose, equations, calculations, diagrams, or graphs. The prose
or equations may in some cases refer to fundamental ideas or relations in
physics, such as Newton’s laws, conservation of energy, Gauss’ law, or
Bernoulli’s equation. In other cases, the justiﬁcation or explanation may
take the form of analyzing the behavior of an equation for large or small
values of a variable in the equation.
The words “calculate,” “what is,” “determine,” and “derive” have distinct
meanings on the AP Physics Exams. “Calculate” means that a student is
expected to show work leading to a ﬁnal answer, which may be algebraic,
but which is more often numerical. “What is” and “determine” indicate
that work need not necessarily be explicitly shown to obtain full credit.
Showing work leading to answers is a good idea, as it may earn a student
partial credit in the case of an incorrect answer, but this step may be
skipped by the conﬁdent or harried student. “Derive” is more speciﬁc, and
indicates that the students need to begin their solution with one or more
fundamental equations, such as those given on the AP Physics Exam equation sheet. The ﬁnal answer, usually algebraic, is then obtained through the
appropriate use of mathematics.
Additional information about study skills and testtaking strategies can
be found at AP Central. Calculators and Equation Tables
Policies regarding the use of calculators on the examinations take into
account the expansion of the capabilities of scientiﬁc calculators, which
now include not only programming and graphing functions but also the
availability of stored equations and other data. For taking the sections of
the examinations in which calculators are permitted, students should be
allowed to use the calculators to which they are accustomed, except as
noted below.* On the other hand, they should not have access to information in their calculators that is not available to other students, if that information is needed to answer the questions.
Calculators are NOT permitted on the multiplechoice sections of
the Physics B and Physics C Exam. The purpose of the multiplechoice
sections is to assess the breadth of students’ knowledge and understanding of the basic concepts of physics. The multiplechoice questions
emphasize conceptual understanding and qualitative applications. * Exceptions to calculator use. Although most calculators are permitted on the freeresponse sections, they cannot be shared with other students, and calculators with
typewriterstyle (QWERTY) keyboards will not be permitted on any part of the exams.
apcentral.collegeboard.com 23 However, many physical deﬁnitions and principles are quantitative by
nature and can therefore be expressed as equations. The knowledge of
these basic deﬁnitions and principles, expressed as equations, is a part of
the content of physics that should be learned by physics students and will
continue to be assessed in the multiplechoice sections. However, any
numeric calculations using these equations required in the multiplechoice
sections will be kept simple. Also, in some questions, the answer choices
differ by several orders of magnitude so that the questions can be
answered by estimation. Students should be encouraged to develop their
skills not only in estimating answers but also in recognizing answers that
are physically unreasonable or unlikely.
Calculators are allowed on the freeresponse section of both
examinations. Any programmable or graphing calculator may be
used except as noted below*, and students will not be required to
erase their calculator memories before and after the examination.
The freeresponse sections emphasize solving indepth problems where
knowledge of which principles to apply and how to apply them is the most
important aspect of the solution to these problems.
Regardless of the type of calculator allowed, the examinations are
designed and graded to minimize the necessity of doing lengthy calculations. Except for some fundamental constants, most numerical values
are selected so that calculations with them are simple and can be done
quickly. When freeresponse problems involve calculations, most of the
points awarded in the grading of the solution are given for setting up the
solution correctly rather than for actually carrying out the computation.
Tables containing commonly used physics equations are printed
on the green insert provided with each examination for students
to use when taking the freeresponse section. The equation tables
may NOT be used when taking the multiplechoice section. The Table
of Information and the equation tables for the 2004 and 2005 examinations are included as an insert in this booklet so that they can easily be
removed and duplicated for use by students. In general, the tables for
each year’s exam will be printed and distributed with the Course Description at least a year in advance so that students can become accustomed to
using them throughout the year. However, since the equations will be provided with the exams, students are NOT allowed to bring their own copies
to the examination room. * Exceptions to calculator use. Although most calculators are permitted on the freeresponse sections, they cannot be shared with other students, and calculators with
typewriterstyle (QWERTY) keyboards will not be permitted on any part of the exams.
24 apcentral.collegeboard.com One of the purposes of providing the commonly used equations is to make
the freeresponse sections equitable for those students who do not have
access to equations stored in their calculators. The availability of these equations means that in the grading of the freeresponse sections little or no
credit will be awarded for simply writing down correct equations or for
ambiguous answers unsupported by explanations or logical development.
The equations in the tables express relationships that are encountered
most frequently in AP Physics courses and examinations. However, they
do not include all equations that might possibly be used. For example, they
do not include many equations that can be derived by combining others in
the tables. Nor do they include equations that are simply special cases of
any that are in the tables. Students are responsible for understanding the
physical principles that underlie each equation and for knowing the conditions for which each equation is applicable.
The equations are grouped in tables according to major content category. Within each table, the symbols used for the variables in that table are
deﬁned. However, in some cases the same symbol is used to represent
different quantities in different tables. It should be noted that there is no
uniform convention among textbooks for the symbols used in writing
equations. The equation tables follow many common conventions, but in
some cases consistency was sacriﬁced for the sake of clarity.
It should also be noted that, beginning with the 2002 examinations, a
change in the convention used for the sign of work in thermal physics
affected some of the equations in the Physics B list. The symbol W is now
deﬁned as the work done on a thermodynamic system, rather than the
work done by a system as before. This convention makes the treatment of
work consistent with the workenergy theorem in mechanics, which states
that the work done on a particle equals the change in the particle’s kinetic
energy. With this convention the ﬁrst law of thermodynamics is basically a
statement that adding heat to a system and doing work on it are alternate
ways of increasing its energy. Since thermal physics is not a Physics C
topic, this change in convention did not apply to the Physics C examination. Further information about this change can be found in the article “A
Consistent Sign Convention for Work,” published in The Physics Teacher,
Vol. 38, No. 3, page 160 (March 2000).
In summary, the purpose of minimizing numerical calculations in both
sections of the examinations and providing equations with the freeresponse sections is to place greater emphasis on the understanding and
application of fundamental physical principles and concepts. For solving
problems, a sophisticated programmable or graphing calculator, or the
availability of stored equations, is no substitute for a thorough grasp of the
physics involved. apcentral.collegeboard.com 25 Sample Questions for Physics B Physics B: Sample MultipleChoice Questions
Most of the following sample questions, illustrative of the Physics B examination, have appeared in past examinations. The answers are on page 35.
Note: Units associated with numerical quantities are abbreviated, using
the abbreviations listed in the table of information included with the
exams (see insert in this booklet.) To simplify calculations, you may use
g = 10 m/s2 in all problems.
Directions: Each of the questions or incomplete statements below is followed by ﬁve suggested answers or completions. Select the one that is
best in each case.
1. An object is thrown with a horizontal velocity of 20 m/s from a cliff
that is 125 m above level ground. If air resistance is negligible, the
time that it takes the object to fall to the ground from the cliff is most
nearly
(A) 3 s
(B) 5 s
(C) 6 s
(D) 12 s
(E) 25 s 2. The motion of a particle along a straight line is represented by the
position versus time graph above. At which of the labeled points on
the graph is the magnitude of the acceleration of the particle
greatest?
(A) A
(B) B
(C) C
(D) D
(E) E 26 apcentral.collegeboard.com Sample Questions for Physics B Questions 34 A 2 kg block, starting from rest, slides 20 m down a frictionless inclined
plane from X to Y, dropping a vertical distance of 10 m as shown above.
3. The magnitude of the net force on the block while it is sliding is most
nearly
(A) 10.1 N
(B) 10.4 N
(C) 12.5 N
(D) 15.0 N
(E) 10.0 N 4. The speed of the block at point Y is most nearly
(A) 107 m/s
(B) 110 m/s
(C) 114 m/s
(D) 120 m/s
(E) 100 m/s apcentral.collegeboard.com 27 Sample Questions for Physics B 5. A block of mass 2 kg slides along a horizontal tabletop. A horizontal
applied force of 12 N and a vertical applied force of 15 N act on the
block, as shown above. If the coefﬁcient of kinetic friction between
the block and the table is 0.2, the frictional force exerted on the
block is most nearly
(A) 1 N
(B) 3 N
(C) 4 N
(D) 5 N
(E) 7 N 6. A ball of mass M and speed v collides headon with a ball of mass 2M
v
and speed 2 , as shown above. If the two balls stick together, their
speed after the collision is
(A) 0
v
(B) 2
2v
2
3v
(D)
2
(E) 3v
2
(C) 28 apcentral.collegeboard.com Sample Questions for Physics B 7. A massless rigid rod of length 3d is pivoted at a ﬁxed point W, and
two forces each of magnitude F are applied vertically upward as
shown above. A third vertical force of magnitude F may be applied,
either upward or downward, at one of the labeled points. With the
proper choice of direction at each point, the rod can be in equilibrium if the third force of magnitude F is applied at point
(A) W only
(B) Y only
(C) V or X only
(D) V or Y only
(E) V, W, or X 8. An ideal monatomic gas is compressed while its temperature is held
constant. What happens to the internal energy of the gas during this
process, and why?
(A) It decreases because the gas does work on its surroundings.
(B) It decreases because the molecules of an ideal gas collide.
(C) It does not change because the internal energy of an ideal gas
depends only on its temperature.
(D) It increases because work is done on the gas.
(E) It increases because the molecules travel a shorter path between
collisions. apcentral.collegeboard.com 29 Sample Questions for Physics B 9. In the pV diagram above, the initial state of a gas is shown at point X.
Which of the curves represents a process in which no work is done
on or by the gas?
(A) XA
(B) XB
(C) XC
(D) XD
(E) XE P• •q T•
10. 30 An isolated positive charge q is in the plane of the page, as shown
above. The directions of the electric ﬁeld vectors at points P and T,
which are also in the plane of the page, are given by which of the
following?
Point P
Point T
(A) Left
Right
(B) Right
Left
(C) Left
Toward the top of the page
(D) Right
Toward the top of the page
(E) Left
Toward the bottom of the page apcentral.collegeboard.com Sample Questions for Physics B Questions 1112 relate to the following circuit in which the battery has
zero internal resistance. 11. What is the current in the 4 Ω resistor while the switch S is open?
(A) 0 A
(B) 0.6 A
(C) 1.2 A
(D) 2.0 A
(E) 3.0 A 12. When the switch S is closed and the 10 µF capacitor is fully charged,
what is the voltage across the capacitor?
(A) 110 V
(B) 116 V
(C) 112 V
(D) 160 V
(E) 120 V apcentral.collegeboard.com 31 Sample Questions for Physics B Flow 1• 13. A ﬂuid ﬂows steadily from left to right in the pipe shown above. The
diameter of the pipe is less at point 2 then at point 1, and the ﬂuid
density is constant throughout the pipe. How do the velocity of ﬂow
and the pressure at points 1 and 2 compare?
(A)
(B)
(C)
(D)
(E) 14. 32 •2 Velocity
v1 < v2
v1 < v2
v1 = v2
v1 > v2
v1 > v2 Pressure
p1 = p2
p1 > p2
p1 < p2
p1 = p2
p1 > p2 Two long parallel wires, separated by a distance d, carry equal currents I toward the top of the page, as shown above. The magnetic
ﬁeld due to the wires at a point halfway between them is
(A) zero in magnitude
(B) directed into the page
(C) directed out of the page
(D) directed to the right
(E) directed to the left apcentral.collegeboard.com Sample Questions for Physics B 15. A source S of sound and a listener L each can be at rest or can move
directly toward or away from each other with speed v0. In which of
the following situations will the observer hear the lowest frequency
of sound from the source?
(A)
S
L
•
•
v =0
v =0
(B) S
•
v =0 L
• S
• L
•
v =0 S
• L
• S
• L
• (C)
v=v0
(D)
v=v0
(E) 16. v=v0 v=v0 v=v0 v=v0 The wavelength of yellow sodium light in vacuum is 5.89 10–7 m.
The speed of this light in glass with an index of refraction of 1.5 is
most nearly
(A) 4 10–7 m/s
(B) 9 10–7 m/s
(C) 2 108 m/s
(D) 3 108 m/s
(E) 4 108 m/s apcentral.collegeboard.com 33 Sample Questions for Physics B 17. An object O is in front of a convex mirror. The focal point of the mirror is labeled F and the center of curvature is labeled C. The direction of the reﬂected ray is correctly illustrated in all of the following
EXCEPT which diagram? 18. A system initially consists of an electron and an incident photon. The
electron and the photon collide, and afterward the system consists
of the electron and a scattered photon. The electron gains kinetic
energy as a result of this collision. Compared with the incident
photon, the scattered photon has
(A) the same energy
(B) a smaller speed
(C) a larger speed
(D) a smaller frequency
(E) a larger frequency 34 apcentral.collegeboard.com Sample Questions for Physics B 19. In an experiment, light of a particular wavelength is incident on a
metal surface, and electrons are emitted from the surface as a result.
To produce more electrons per unit time but with less kinetic energy
per electron, the experimenter should do which of the following?
(A) Increase the intensity and decrease the wavelength of the light.
(B) Increase the intensity and the wavelength of the light.
(C) Decrease the intensity and the wavelength of the light.
(D) Decrease the intensity and increase the wavelength of the light.
(E) None of the above would produce the desired result. 20. When 27Al is bombarded by neutrons, a neutron can be absorbed and
an alpha particle (4He) emitted. The kinetic energy of the reaction
products is equal to the
(A) kinetic energy of the incident neutron
(B) total energy of the incident neutron
(C) energy equivalent of the mass decrease in the reaction
(D) energy equivalent of the mass decrease in the reaction, minus
the kinetic energy of the incident neutron
(E) energy equivalent of the mass decrease in the reaction, plus the
kinetic energy of the incident neutron Answers to Physics B MultipleChoice Questions
1–B
2–C
3–E
4–C 5–E
6–A
7–C
8–C apcentral.collegeboard.com 9–B
10 – E
11 – B
12 – B 13 – B
14 – A
15 – D
16 – C 17 – D
18 – D
19 – B
20 – E 35 Sample Questions for Physics B Physics B: Sample FreeResponse Questions
The following seven questions constituted the complete freeresponse
section of the 2002 AP Physics B Examination. Additional sample questions can be found at AP Central.
Directions: Answer all seven questions, which are weighted according to
the points indicated. The suggested time is about 15 minutes for answering
each of questions 14, and about 10 minutes for answering each of questions 57. The parts within a question may not have equal weight. Show all
your work in the pink booklet in the spaces provided after each part, NOT
in the green insert. 36 apcentral.collegeboard.com Sample Questions for Physics B 1. (15 points)
A model rocket of mass 0.250 kg is launched vertically with an engine
that is ignited at time t 0, as shown above. The engine provides an
impulse of 20.0 N• s by ﬁring for 2.0 s. Upon reaching its maximum
height, the rocket deploys a parachute, and then descends vertically
to the ground.
(a) On the ﬁgures below, draw and label a freebody diagram for the
rocket during each of the following intervals.
i. While the engine ii. After the engine iii. After the parais ﬁring
stops, but bechute is deployed
fore the parachute is
deployed (b) Determine the magnitude of the average acceleration of the
rocket during the 2 s ﬁring of the engine.
(c) What maximum height will the rocket reach?
(d) At what time after t 0 will the maximum height be reached? apcentral.collegeboard.com 37 Sample Questions for Physics B 2. (15 points)
A 3.0 kg object subject to a restoring force F is undergoing simple
harmonic motion with a small amplitude. The potential energy U of
the object as a function of distance x from its equilibrium position is
shown above. This particular object has a total energy E of 0.4 J.
(a) What is the object’s potential energy when its displacement is
4 cm from its equilibrium position?
(b) What is the farthest the object moves along the xaxis in the positive direction? Explain your reasoning.
(c) Determine the object’s kinetic energy when its displacement
is 7 cm.
(d) What is the object’s speed at x 0 ? (e) Suppose the object undergoes this motion because it is the bob
of a simple pendulum as shown above. If the object breaks loose
from the string at the instant the pendulum reaches its lowest
point and hits the ground at point P shown, what is the horizontal distance d that it travels?
38 apcentral.collegeboard.com Sample Questions for Physics B 3. (15 points)
Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at
120 V, are arranged in two different circuits.
(a) The two bulbs are ﬁrst connected in parallel to a 120 V source.
i. Determine the resistance of the bulb rated 30 W and the
current in it when it is connected in this circuit.
ii. Determine the resistance of the bulb rated 40 W and the
current in it when it is connected in this circuit.
(b) The bulbs are now connected in series with each other and a
120 V source.
i. Determine the resistance of the bulb rated 30 W and the
current in it when it is connected in this circuit.
ii. Determine the resistance of the bulb rated 40 W and the
current in it when it is connected in this circuit.
(c) In the spaces below, number the bulbs in each situation
described, in order of their brightness.
(1 brightest, 4 dimmest)
30 W bulb in the parallel circuit
40 W bulb in the parallel circuit
30 W bulb in the series circuit
40 W bulb in the series circuit
(d) Calculate the total power dissipated by the two bulbs in each of
the following cases.
i. The parallel circuit
ii. The series circuit apcentral.collegeboard.com 39 Sample Questions for Physics B 4. (15 points)
A thin converging lens of focal length 10 cm is used as a simple magniﬁer to examine an object A that is held 6 cm from the lens.
(a) On the ﬁgure below, draw a ray diagram showing the position
and size of the image formed. (b) State whether the image is real or virtual. Explain your
reasoning.
(c) Calculate the distance of the image from the center of the lens.
(d) Calculate the ratio of the image size to the object size. (e) 40 The object A is now moved to the right from x 6 cm to a position
of x = 20 cm, as shown above. Describe the image position, size, and
orientation when the object is at x 20 cm. apcentral.collegeboard.com Sample Questions for Physics B 5. (10 points)
A proton of mass mp and charge e is in a box that contains an electric
ﬁeld E, and the box is located in Earth’s magnetic ﬁeld BEarth. The proton moves with an initial velocity v vertically upward from the surface of Earth. Assume gravity is negligible.
(a) On the diagram above, indicate the direction of the electric ﬁeld
inside the box so that there is no change in the trajectory of the
proton while it moves upward in the box. Explain your reasoning.
(b) Determine the speed of the proton while in the box if it continues to move vertically upward. Express your answer in terms of
the ﬁelds and the given quantities.
The proton now exits the box through the opening at the top.
(c) On the ﬁgure on the previous page, sketch the path of the proton
after it leaves the box.
(d) Determine the magnitude of the acceleration a of the proton just
after it leaves the box, in terms of the given quantities and fundamental constants. apcentral.collegeboard.com 41 Sample Questions for Physics B 6. (10 points)
In the laboratory, you are given a cylindrical beaker containing a ﬂuid
and you are asked to determine the density r of the ﬂuid. You are to
use a spring of negligible mass and unknown spring constant k
attached to a stand. An irregularly shaped object of known mass m
and density D (D >> r) hangs from the spring. You may also choose
from among the following items to complete the task.
■
■
■ A metric ruler
A stopwatch
String (a) Explain how you could experimentally determine the spring
constant k. (b) The springobject system is now arranged so that the object (but
none of the spring) is immersed in the unknown ﬂuid, as shown
above. Describe any changes that are observed in the springobject system and explain why they occur.
(c) Explain how you could experimentally determine the density of
the ﬂuid.
(d) Show explicitly, using equations, how you will use your measurements to calculate the ﬂuid density r. Start by identifying any
symbols you use in your equations.
Symbol 42 Physical quantity apcentral.collegeboard.com Sample Questions for Physics B 7. (10 points)
A photon of wavelength 2.0 10 11 m strikes a free electron of mass
me that is initially at rest, as shown above left. After the collision, the
photon is shifted in wavelength by an amount l 2h/me c, and
reversed in direction, as shown above right.
(a) Determine the energy in joules of the incident photon.
(b) Determine the magnitude of the momentum of the incident
photon.
(c) Indicate below whether the photon wavelength is increased or
decreased by the interaction.
Increased Decreased Explain your reasoning.
(d) Determine the magnitude of the momentum acquired by the
electron. apcentral.collegeboard.com 43 Sample Questions for Physics C: Mech. Physics C Mechanics: Sample MultipleChoice Questions
Most of the following sample questions, illustrative of the Physics C
Mechanics examination, have appeared in past examinations. The answers
are on page 48.
Note: Units associated with numerical quantities are abbreviated, using
the abbreviations listed in the table of information included with the
exams (see insert in this booklet.) To simplify calculations, you may use
g = 10 m/s2 in all problems.
Directions: Each of the questions or incomplete statements below is
followed by ﬁve suggested answers or completions. Select the one that
is best in each case.
Questions 12
The speed v of an automobile moving on a straight road is given in
meters per second as a function of time t in seconds by the following
equation:
v = 4 + 2t3
1. What is the acceleration of the automobile at t = 2 s?
(A) 12 m/s2
(B) 16 m/s2
(C) 20 m/s2
(D) 24 m/s2
(E) 28 m/s2 2. How far has the automobile traveled in the interval between
t = 0 and t = 2 s?
(A) 16 m
(B) 20 m
(C) 24 m
(D) 32 m
(E) 72 m 44 apcentral.collegeboard.com Sample Questions for Physics C: Mech. 3. If a particle moves in a plane so that its position is described by the
functions x = A cos t and y = A sin t, the particle is
(A) moving with constant speed along a circle
(B) moving with varying speed along a circle
(C) moving with constant acceleration along a straight line
(D) moving along a parabola
(E) oscillating back and forth along a straight line 4. A system in equilibrium consists of an object of weight W that hangs
from three ropes, as shown above. The tensions in the ropes are T1,
T2, and T3. Which of the following are correct values of T2 and T3?
T2
(A) W tan 60˚
(B) W tan 60˚
(C) W tan 60˚
W
tan 60°
W
(E)
tan 60°
(D) apcentral.collegeboard.com T3
W
cos 60°
W
sin 60°
W sin 60˚
W
cos 60°
W
sin 60° 45 Sample Questions for Physics C: Mech. 5. The constant force F with components Fx = 3 N and Fy = 4 N,
shown above, acts on a body while that body moves from the point
P (x = 2 m, y = 6 m) to the point Q (x = 14 m, y = 1 m). How much
work does the force do on the body during this process?
(A) 16 J
(B) 30 J
(C) 46 J
(D) 56 J
(E) 65 J 6. The sum of all the external forces on a system of particles is zero.
Which of the following must be true of the system?
(A) The total mechanical energy is constant.
(B) The total potential energy is constant.
(C) The total kinetic energy is constant.
(D) The total linear momentum is constant.
(E) It is in static equilibrium. 46 apcentral.collegeboard.com Sample Questions for Physics C: Mech. 7. A toy cannon is ﬁxed to a small cart and both move to the right with
speed v along a straight track, as shown above. The cannon points in
the direction of motion. When the cannon ﬁres a projectile the cart
and cannon are brought to rest. If M is the mass of the cart and cannon combined without the projectile, and m is the mass of the projectile, what is the speed of the projectile relative to the ground immediately after it is ﬁred?
(A) Mv
m
(M + m)v
(B)
m
(M – m)v
(C)
m
mv
(D)
M
mv
(E)
(M – m) 8. A disk X rotates freely with angular velocity on frictionless bearings, as shown above. A second identical disk Y, initially not rotating,
is placed on X so that both disks rotate together without slipping.
When the disks are rotating together, which of the following is half
what it was before?
(A) Moment of inertia of X
(B) Moment of inertia of Y
(C) Angular velocity of X
(D) Angular velocity of Y
(E) Angular momentum of both disks apcentral.collegeboard.com 47 Sample Questions for Physics C: Mech. 9. The ring and the disk shown above have identical masses, radii, and
velocities, and are not attached to each other. If the ring and the disk
each roll without slipping up an inclined plane, how will the distances that they move up the plane before coming to rest compare?
(A) The ring will move farther than will the disk.
(B) The disk will move farther than will the ring.
(C) The ring and the disk will move equal distances.
(D) The relative distances depend on the angle of elevation of the
plane.
(E) The relative distances depend on the length of the plane. 10. Let g be the acceleration due to gravity at the surface of a planet of
radius R. Which of the following is a dimensionally correct formula
for the minimum kinetic energy K that a projectile of mass m must
have at the planet’s surface if the projectile is to escape from the
planet’s gravitational ﬁeld?
(A) K = gR (B) K = mgR
(C) K = mg
R
g
(D) K = m –
R
(E) K = gR Answers to Physics C Mechanics MultipleChoice Questions
1–D
2–A 48 3–A
4–E 5–A
6–D 7–B
8–C 9–A
10 – B apcentral.collegeboard.com Sample Questions for Physics C: Mech. Physics C Mechanics: Sample FreeResponse Questions
The following three questions constituted the complete freeresponse
section for the Mechanics part of the 2002 AP Physics C Examination.
Additional sample questions can be found at AP Central.
Directions: Answer all three questions. The suggested time is about 15
minutes for answering each of the questions, which are worth 15 points
each. The parts within a question may not have equal weight. Show all
your work in this booklet in the spaces provided after each part, NOT in
the green insert.
Mech 1.
A crash test car of mass 1,000 kg moving at constant speed of 12 m/s
collides completely inelastically with an object of mass M at time t 0.
The object was initially at rest. The speed y in m/s of the carobject system
after the collision is given as a function of time t in seconds by the
expression
8.
y
1 5t
(a) Calculate the mass M of the object.
(b) Assuming an initial position of x 0, determine an expression
for the position of the carobject system after the collision as a
function of time t.
(c) Determine an expression for the resisting force on the carobject
system after the collision as a function of time t.
(d) Determine the impulse delivered to the carobject system from
t 0 to t 2.0 s. apcentral.collegeboard.com 49 Sample Questions for Physics C: Mech. Mech 2.
The cart shown above is made of a block of mass m and four solid rubber
tires each of mass m/4 and radius r. Each tire may be considered to be a
1
disk. (A disk has rotational inertia
ML2, where M is the mass and L is
2
the radius of the disk.) The cart is released from rest and rolls without
slipping from the top of an inclined plane of height h. Express all algebraic
answers in terms of the given quantities and fundamental constants.
(a) Determine the total rotational inertia of all four tires.
(b) Determine the speed of the cart when it reaches the bottom of
the incline.
(c) After rolling down the incline and across the horizontal surface,
the cart collides with a bumper of negligible mass attached to an
ideal spring, which has a spring constant k. Determine the distance xm the spring is compressed before the cart and bumper
come to rest.
(d) Now assume that the bumper has a nonnegligible mass. After
the collision with the bumper, the spring is compressed to a
maximum distance of about 90% of the value of xm in part (c).
Give a reasonable explanation for this decrease. 50 apcentral.collegeboard.com Sample Questions for Physics C: Mech. Mech 3.
An object of mass 0.5 kg experiences a force that is associated with the
4.0
potential energy function U(x)
, where U is in joules and x is in
2.0
x
meters.
(a) On the axes below, sketch the graph of U(x) versus x. (b) Determine the force associated with the potential energy function given above.
(c) Suppose that the object is released from rest at the origin.
Determine the speed of the particle at x 2 m.
In the laboratory, you are given a glider of mass 0.5 kg on an air track.
The glider is acted on by the force determined in part (b). Your goal is
to determine experimentally the validity of your theoretical calculation in part (c).
(d) From the list below, select the additional equipment you will
need from the laboratory to do your experiment by checking the
line next to each item. If you need more than one of an item,
place the number you need on the line.
Meterstick Stopwatch Photogate timer String Spring Balance Wood block
Set of objects of different masses
(e) Brieﬂy outline the procedure you will use, being explicit about
what measurements you need to make in order to determine the
speed. You may include a labeled diagram of your setup if it will
clarify your procedure.
apcentral.collegeboard.com 51 Sample Questions for Physics C: E & M Physics C Electricity and Magnetism:
Sample MultipleChoice Questions
Most of the following sample questions, illustrative of the Physics C
Electricity and Magnetism examination, have appeared in past examinations. The answers are on page 59.
Note: Units associated with numerical quantities are abbreviated, using the
abbreviations listed in the table of information included with the exams
(see insert in this booklet.)
Directions: Each of the questions or incomplete statements below is
followed by ﬁve suggested answers or completions. Select the one that
is best in each case.
+q
•
–3a
1. 52 O +2q
•
3a x Two charges are located on the xaxis of a coordinate system as
shown above. The charge 2q is located at x = 3a and the charge
q is located at x = 3a. Where on the xaxis should an additional
charge 4q be located to produce an electric ﬁeld equal to zero at
the origin O?
(A) x
6a
(B) x
2a
(C) x
a
2a
(D) x
(E) x
6a apcentral.collegeboard.com Sample Questions for Physics C: E & M 2. A uniform electric ﬁeld E of magnitude 6,000 V/m exists in a region of
space as shown above. What is the electric potential difference,
VX – VY, between points X and Y?
(A) –12,000 V
(B)
0V
(C)
1,800 V
(D)
2,400 V
(E)
3,000 V apcentral.collegeboard.com 53 Sample Questions for Physics C: E & M 3. 54 Charge is distributed uniformly throughout a long nonconducting
cylinder of radius R. Which of the following graphs best represents
the magnitude of the resulting electric ﬁeld E as a function of r, the
distance from the axis of the cylinder? apcentral.collegeboard.com Sample Questions for Physics C: E & M 4. A proton p and an electron e are released simultaneously on opposite
sides of an evacuated area between large, charged parallel plates, as
shown above. Each particle is accelerated toward the oppositely
charged plate. The particles are far enough apart so that they do not
affect each other. Which particle has the greater kinetic energy upon
reaching the oppositely charged plate?
(A) The electron
(B) The proton
(C) Neither particle; both kinetic energies are the same.
(D) It cannot be determined without knowing the value of the potential difference between the plates.
(E) It cannot be determined without knowing the amount of charge
on the plates. 5. Two capacitors initially uncharged are connected in series to a battery, as shown above. What is the charge on the top plate of C1?
(A) –81 C
(B) –18 C
(C)
0C
(D) +18 C
(E) +81 C apcentral.collegeboard.com 55 Sample Questions for Physics C: E & M b X
6. 56 • b
b •Y Wire of resistivity r and crosssectional area A is formed into an equilateral triangle of side b, as shown above. The resistance between
two vertices of the triangle, X and Y, is
(A) 3 A
2 rb
(B) 3 A
rb
2 rb
(C)
3A
(D) 3 r b
2A
(E) 3 r b
A apcentral.collegeboard.com Sample Questions for Physics C: E & M Questions 78 A particle of electric charge +Q and mass m initially moves along a
straight line in the plane of the page with constant speed v, as shown
above. The particle enters a uniform magnetic ﬁeld of magnitude B
directed out of the page and moves in a semicircular arc of radius R.
7. Which of the following best indicates the magnitude and the direction
of the magnetic force F on the charge just after the charge enters the
magnetic ﬁeld?
Magnitude
kQ2
(A)
R2
kQ2
(B)
R2
(C)
QvB
(D)
QvB
(E)
QvB 8. Direction
Toward the top of the page
Toward the bottom of the page
Out of the plane of the page
Toward the top of the page
Toward the bottom of the page If the magnetic ﬁeld strength is increased, which of the following will
be true about the radius R?
I. R increases if the incident speed is held constant.
II. For R to remain constant, the incident speed must be
increased.
III. For R to remain constant, the incident speed must be
decreased.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only apcentral.collegeboard.com 57 Sample Questions for Physics C: E & M 9. 58 A bar magnet is lowered at constant speed through a loop of wire as
shown in the diagram above. The time at which the midpoint of the
bar magnet passes through the loop is t1. Which of the following
graphs best represents the time dependence of the induced current in
the loop? (A positive current represents a counterclockwise current
in the loop as viewed from above.) apcentral.collegeboard.com Sample Questions for Physics C: E & M 10. A loop of wire enclosing an area of 1.5 m 2 is placed perpendicular to
a magnetic ﬁeld. The ﬁeld is given in teslas as a function of time t in
seconds by
B(t) = 20t – 5
3
The induced emf in the loop at t = 3 s is most nearly
(A) 10 V
(B) 15 V
(C) 10 V
(D) 15 V
(E) 20 V Answers to Physics C Electricity and Magnetism
MultipleChoice Questions
1–A
3–A
5–D
7–E
9–B
2–D
4–C
6–C
8–B
10 – C apcentral.collegeboard.com 59 Sample Questions for Physics C: E & M Physics C Electricity and Magnetism:
Sample FreeResponse Questions
The following three questions constituted the complete freeresponse
section for the Electricity and Magnetism part of the 2002 AP Physics C
Examination. Additional sample questions can be found at AP Central.
Directions: Answer all three questions. The suggested time is about 15
minutes for answering each of the questions, which are worth 15 points
each. The parts within a question may not have equal weight. Show all
your work in this booklet in the spaces provided after each part, NOT in
the green insert. E&M 1.
A rod of uniform linear charge density l
1.5 10 5 C/m is bent into an
arc of radius R 0.10 m. The arc is placed with its center at the origin of
the axes shown above.
(a) Determine the total charge on the rod.
(b) Determine the magnitude and direction of the electric ﬁeld at the
center O of the arc.
(c) Determine the electric potential at point O.
A proton is now placed at point O and held in place. Ignore the effects of
gravity in the rest of this problem.
(d) Determine the magnitude and direction of the force that must be
applied in order to keep the proton at rest.
(e) The proton is now released. Describe in words its motion for a
long time after its release. 60 apcentral.collegeboard.com Sample Questions for Physics C: E & M E&M 2.
Your engineering ﬁrm has built the RC circuit shown above. The current is
measured for the time t after the switch is closed at t 0 and the bestﬁt
curve is represented by the equation I(t) 5.20 e t/10, where I is in
milliamperes and t is in seconds.
(a) Determine the value of the charging voltage V0 predicted by the
equation.
(b) Determine the value of the capacitance C predicted by the
equation.
(c) The charging voltage is measured in the laboratory and found to
be greater than predicted in part (a).
i. Give one possible explanation for this ﬁnding.
ii. Explain the implications that your answer to part i has for
the predicted value of the capacitance.
(d) Your laboratory supervisor tells you that the charging time must
be decreased. You may add resistors or capacitors to the original
components and reconnect the RC circuit. In parts i and ii below,
show how to reconnect the circuit, using either an additional
resistor or a capacitor to decrease the charging time.
i. Indicate how a resistor may be added to decrease the charging time. Add the necessary resistor and connections to the
following diagram. ii. Instead of a resistor, use a capacitor. Indicate how the capacitor may be added to decrease the charging time. Add the necessary capacitor and connections to the following diagram. apcentral.collegeboard.com 61 Sample Questions for Physics C: E & M E&M 3.
A circular wire loop with radius 0.10 m and resistance 50 is suspended
horizontally in a magnetic ﬁeld of magnitude B directed upward at an
angle of 60° with the vertical, as shown above. The magnitude of the
ﬁeld in teslas is given as a function of time t in seconds by the equation
B 4(1 0.2t).
(a) Determine the magnetic ﬂux fm through the loop as a function
of time.
(b) Graph the magnetic ﬂux fm as a function of time on the axes
below. 62 apcentral.collegeboard.com Sample Questions for Physics C: E & M (c) Determine the magnitude of the induced emf in the loop.
(d) ii. Determine the magnitude of the induced current in the loop.
ii. Show the direction of the induced current on the following
diagram. (e) Determine the energy dissipated in the loop from t
t 4 s. apcentral.collegeboard.com 0 to 63 AP® Program Essentials
The AP Reading
In June, the freeresponse sections of the exams, as well as the Studio Art
portfolios, are scored by college faculty and secondary school AP teachers
at the AP Reading. Thousands of readers participate, under the direction
of a Chief Reader in each ﬁeld. The experience offers both signiﬁcant
professional development and the opportunity to network with likeminded educators.
If you are an AP teacher or a college faculty member and would like to
serve as a reader, you can visit AP Central for more information on how to
apply. Alternatively, send an email message to [email protected], or call
Performance Scoring Services at 609 4065383. AP Grades
The readers’ scores on the essay and problemsolving questions are combined with the results of the computerscored multiplechoice questions,
and the total raw scores are converted to AP’s 5point scale:
AP GRADE
5
4
3
2
1 QUALIFICATION
Extremely well qualiﬁed
Well qualiﬁed
Qualiﬁed
Possibly qualiﬁed
No recommendation Grade Distributions
Many teachers want to compare their students’ grades with the national
percentiles. Grade distribution charts are available at AP Central, as is
information on how the cutoff points for each AP grade are calculated.
Grade distribution charts are also available on the AP student site at
www.collegeboard.com/apstudents. Earning College Credit and/or Placement
Credit, advanced placement, or both are awarded by the college or university, not the College Board or the AP Program. The best source of speciﬁc
and uptodate information about an individual institution’s policy is its
catalog or Web site.
64 apcentral.collegeboard.com Why Colleges Grant Credit and/or Placement for
AP Grades
Colleges know that the AP grades of their incoming students represent a
level of achievement equivalent to that of students who take the same
course in the colleges’ own classrooms. That equivalency is assured
through several Advanced Placement Program processes:
• College faculty serve on the committees that develop the course
descriptions and examinations in each AP subject.
• College faculty are responsible for standard setting and are involved
in the evaluation of student responses at the AP Reading.
• AP courses and exams are updated regularly, based on both the
results of curriculum surveys at up to 200 colleges and universities
and the interactions of committee members with professional organizations in their discipline.
• College comparability studies are undertaken in which the performance of college students on AP Exams is compared with that of
AP students to conﬁrm that the AP grade scale of 1–5 is properly
aligned with current college standards.
In addition, the College Board has commissioned studies that use a
“bottomline” approach to validating AP Exam grades by comparing the
achievement of AP versus nonAP students in higherlevel college courses.
For example, in the 1998 Morgan and Ramist “21College” study, AP students
who were exempted from introductory courses and who completed a
higherlevel course in college were compared favorably, on the basis of their
college grades, with students who completed the prerequisite ﬁrst course in
college, then took the second, higherlevel course in the subject area. Such
studies answer the question of greatest concern to colleges — are AP students who are exempted from introductory courses as well prepared to continue in a subject area as students who took their ﬁrst course in college? To
see the results of several college validity studies, go to AP Central. (The
Morgan and Ramist study can be downloaded from the site in its entirety.) Guidelines on Granting Credit and/or Placement for
AP Grades
If you are an admissions administrator and need guidance on setting an
AP policy for your college or university, you will ﬁnd the College and
University Guide to the Advanced Placement Program useful; see the
back of this booklet for ordering information. Alternatively, contact your
local College Board ofﬁce, as noted on the inside back cover of this
Course Description.
apcentral.collegeboard.com 65 Finding Colleges That Accept AP Grades
In addition to contacting colleges directly for their AP policies, students
and teachers can use College Search, an online resource maintained by the
College Board through its Annual Survey of Colleges. College Search can
be accessed via the College Board’s Web site (www.collegeboard.com). It
is worth remembering that policies are subject to change. Contact the college directly to get the most uptodate information. AP Awards
The AP Program offers a number of awards to recognize high school students who have demonstrated collegelevel achievement through AP
courses and exams. Although there is no monetary award, in addition to
an award certiﬁcate, student achievement is acknowledged on any grade
report sent to colleges following the announcement of the awards. For
detailed information on AP Awards, including qualiﬁcation criteria, visit AP
Central or contact the College Board’s National Ofﬁce. Students can ﬁnd
this information at www.collegeboard.com/apstudents. AP Calendar
The AP Program Guide and the Bulletin for AP Students and Parents provide education professionals and students, respectively, with information on
the various events associated with the AP year. Information on ordering and
downloading these publications can be found at the back of this booklet. Test Security
The entire AP Exam must be kept secure at all times. Fortyeight hours
after the exam has been administered, the green and blue inserts
containing the freeresponse questions (Section II) can be made
available for teacher and student review.* However, the multiplechoice section (Section I) MUST remain secure both before and
after the exam administration. No one other than students taking the
exam can ever have access to or see the questions contained in Section
1 — this includes AP Coordinators and all teachers. The multiplechoice section must never be shared, copied in any manner, or reconstructed by teachers and students after the exam.
*The alternate form of the freeresponse section (used for late testing administration) is NOT
released.
66 apcentral.collegeboard.com Selected multiplechoice questions are reused from year to year to
provide an essential method of establishing high exam reliability,
controlled levels of difﬁculty, and comparability with earlier exams.
These goals can be attained only when the multiplechoice questions
remain secure. This is why teachers cannot view the questions and
students cannot share information about these questions with anyone
following the exam administration.
To ensure that all students have an equal opportunity to demonstrate
their abilities on the exam, AP Exams must be administered in a uniform
manner. It is extremely important to follow the administration
schedule and all procedures outlined in detail in the most recent
AP Coordinator’s Manual. Please note that Studio Art portfolios and
their contents are not considered secure testing materials; see the AP
Coordinator’s Manual for further information. The manual also includes
directions on how to deal with misconduct and other security problems.
Any breach of security should be reported to Test Security immediately
(call 800 3538570, fax 609 4069709, or email [email protected]). Teacher Support
You can ﬁnd the following Web resources at AP Central:
• Teachers’ Resources (reviews of classroom resources).
• Institutes & Workshops (a searchable database of professional
development opportunities).
• The most uptodate and comprehensive information on AP courses,
exams, and other Program resources.
• The opportunity to exchange teaching methods and materials with
the international AP community using electronic discussion groups
(EDGs).
• An electronic library of AP publications, including released exam
questions, the AP Coordinator’s Manual, Course Descriptions, and
sample syllabi.
• Opportunities for professional involvement in the AP Program.
• Information about state and federal support for the AP Program.
• AP Program data, research, and statistics.
• FAQs about the AP Program.
• Current news and features about the AP Program, its courses and
teachers. apcentral.collegeboard.com 67 AP teachers can also use a number of AP publications, CDROMs, and
videos that supplement these Web resources. Please see the following
pages for an overview and ordering information. PreAP®
PreAP® is a suite of K–12 professional development resources and services
to equip middle and high school teachers with the strategies and tools they
need to engage their students in highlevel learning, thereby ensuring that
every middle and high school student has the depth and understanding of
the skills, habits of mind, and concepts they need to succeed in college.
PreAP rests upon a profound hope and heartfelt esteem for teachers and
students. Conceptually, PreAP is based on two important premises. The ﬁrst
is the expectation that all students can perform at rigorous academic levels.
This expectation should be reﬂected in curriculum and instruction throughout the school such that all students are consistently being challenged to
expand their knowledge and skills to the next level.
The second is the belief that we can prepare every student for higher
intellectual engagement by starting the development of skills and acquisition of knowledge as early as possible. Addressed effectively, the middle
and high school years can provide a powerful opportunity to help all students acquire the knowledge, concepts, and skills needed to engage in a
higher level of learning.
Since PreAP teacher professional development supports explicitly the
goal of college as an option for every student, it is important to have a
recognized standard for collegelevel academic work. The Advanced
Placement Program (AP) provides these standards for PreAP. PreAP
teacher professional development resources reflect topics, concepts, and
skills found in AP courses.
The College Board does not design, develop, or assess courses labeled
“PreAP.” Courses labeled “PreAP” that inappropriately restrict access to
AP and other collegelevel work are inconsistent with the fundamental
purpose of the PreAP initiatives of the College Board. We encourage
schools, districts, and policymakers to utilize PreAP professional development in a manner that ensures equitable access to rigorous academic
experiences for all students. 68 apcentral.collegeboard.com PreAP Professional Development
PreAP professional development is administered by PreAP Initiatives,
a unit in K–12 Professional Development, and is available through
workshops and conferences coordinated by the regional offices of
the College Board. PreAP professional development is divided into
two categories:
1. Articulation of content and pedagogy across the middle and
high school years — The emphasis of professional development in
this category is aligning curriculum and improving teacher communication. The intended outcome from articulation is a coordinated program of teaching skills and concepts over several years.
2. Classroom strategies for middle and high school teachers —
Various approaches, techniques, and ideas are emphasized in professional development in the category.
For a complete list of PreAP Professional Development offerings, please
contact your regional ofﬁce or visit AP Central at apcentral.collegeboard.com. AP Publications and Other Resources
A number of AP resources are available to help students, parents, AP
Coordinators, and high school and college faculty learn more about the AP
Program and its courses and exams. To identify resources that may be of
particular use to you, refer to the following key.
AP Coordinators and Administrators . . . . . . . . . . . . A
College Faculty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C
Students and Parents . . . . . . . . . . . . . . . . . . . . . . . . . SP
Teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T Ordering Information
You have several options for ordering publications:
• Online. Visit the College Board store at store.collegeboard.com.
• By mail. Send a completed order form with your payment or credit
card information to: Advanced Placement Program, Dept. E06, P. O.
Box 6670, Princeton, NJ 085416670. If you need a copy of the order
form, you can download one from AP Central.
apcentral.collegeboard.com 69 • By fax. Credit card orders can be faxed to AP Order Services at
609 7717385.
• By phone. Call AP Order Services at 609 7717243, Monday through
Friday, 8:00 a.m. to 9:00 p.m. ET. Have your American Express,
Discover, JCB, MasterCard, or VISA information ready. This phone
number is for credit card orders only.
Payment must accompany all orders not on an institutional purchase order
or credit card, and checks should be made payable to the College Board.
The College Board pays UPS ground rate postage (or its equivalent) on all
prepaid orders; delivery generally takes two to three weeks. Please do not
use P.O. Box numbers. Postage will be charged on all orders requiring
billing and/or requesting a faster method of delivery.
Publications may be returned for a full refund if they are returned
within 30 days of invoice. Software and videos may be exchanged within
30 days if they are opened, or returned for a full refund if they are
unopened. No collect or C.O.D. shipments are accepted. Unless otherwise
speciﬁed, orders will be ﬁlled with the currently available edition; prices
and discounts are subject to change without notice.
In compliance with Canadian law, all AP publications delivered to
Canada incur the 7 percent GST. The GST registration number is 13141
4468 RT. Some Canadian schools are exempt from paying the GST.
Appropriate proof of exemption must be provided when AP publications
are ordered so that tax is not applied to the billing statement. Print
Items marked with a computer mouse icon can be downloaded for free
from AP Central. m Bulletin for AP Students and Parents SP This bulletin provides a general description of the AP Program, including
how to register for AP courses, and information on the policies and procedures related to taking the exams. It describes each AP Exam, lists the
advantages of taking the exams, describes the grade reporting process,
and includes the upcoming exam schedule. The Bulletin is available in
both English and Spanish. m AP Program Guide A This guide takes the AP Coordinator stepbystep through the school
year — from organizing an AP program, through ordering and administering the AP Exams, payment, and grade reporting. It also includes infor70 apcentral.collegeboard.com mation on teacher professional development, AP resources, and exam
schedules. The AP Program Guide is sent automatically to all schools that
register to participate in AP.
College and University Guide to the AP Program C, A This guide is intended to help college and university faculty and administrators understand the benefits of having a coherent, equitable AP
policy. Topics included are validity of AP grades; developing and maintaining scoring standards; ensuring equivalent achievement; state
legislation supporting AP; and quantitative profiles of AP students by
each AP subject. m Course Descriptions SP, T, A, C Course Descriptions provide an outline of the AP course content, explain
the kinds of skills students are expected to demonstrate in the corresponding introductory collegelevel course, and describe the AP Exam. They also
provide sample multiplechoice questions with an answer key, as well as
sample freeresponse questions. Note: The Course Description for AP
Computer Science is available in electronic format only. m PreAP A, T This brochure describes the PreAP concept and the professional
development opportunities available to middle school and high
school teachers.
Released Exams T About every four to ﬁve years, on a rotating schedule, the AP Program
releases a complete copy of each exam. In addition to providing the
multiplechoice questions and answers, the publication describes the
process of scoring the freeresponse questions and includes examples
of students’ actual responses, the scoring guidelines, and commentary
that explains why the responses received the scores they did.
Teacher’s Guides T For those about to teach an AP course for the ﬁrst time, or for experienced AP teachers who would like to get some fresh ideas for the classroom, the Teacher’s Guide is an excellent resource. Each Teacher’s Guide
contains syllabi developed by high school teachers currently teaching the
apcentral.collegeboard.com 71 AP course and college faculty who teach the equivalent course at colleges
and universities. Along with detailed course outlines and innovative teaching tips, you’ll also ﬁnd extensive lists of suggested teaching resources.
AP Vertical Team Guides T, A An AP Vertical Team (APVT) is made up of teachers from different grade
levels who work together to develop and implement a sequential curriculum in a given discipline. The team’s goal is to help students acquire the
skills necessary for success in AP. To help teachers and administrators
who are interested in establishing an APVT at their school, the College
Board has published these guides: A Guide for Advanced Placement
English Vertical Teams; Advanced Placement Program Mathematics
Vertical Teams Toolkit; AP Vertical Teams in Science, Social Studies,
Foreign Language, Studio Art, and Music Theory: An Introduction;
AP Vertical Teams Guide for Social Studies; AP Vertical Teams Guide
for Fine Arts, Vol.1: Studio Art; AP Vertical Teams Guide for Fine Arts,
Vol. 2: Music Theory; and AP Vertical Teams Guide for Fine Arts, Vol.1
and 2 (set). Multimedia
APCD® (home version),
(multinetwork site license) SP, T These CDROMs are available for Calculus AB, English Language, English
Literature, European History, Spanish Language, and U.S. History. They
each include actual AP Exams, interactive tutorials, and other features,
including exam descriptions, answers to frequently asked questions, studyskill suggestions, and testtaking strategies. There is also a listing of
resources for further study and a planner to help students schedule and
organize their study time.
The teacher version of each CD, which can be licensed for up to 50
workstations, enables you to monitor student progress and provide individual feedback. Included is a Teacher’s Manual that gives full explanations along with suggestions for utilizing the APCD in the classroom. 72 apcentral.collegeboard.com College Board Ofﬁces
National Ofﬁce 45 Columbus Avenue, New York, NY 100236992
212 7138066
Email: [email protected]
Middle States Serving Delaware, District of Columbia, Maryland, New Jersey, New York, Pennsylvania,
and Puerto Rico
Two Bala Plaza, Suite 900, Bala Cynwyd, PA 190041501
610 6704400
Email: [email protected]
Midwestern Serving Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska,
North Dakota, Ohio, South Dakota, West Virginia, and Wisconsin
1560 Sherman Avenue, Suite 1001, Evanston, IL 602014805
847 8661700
Email: [email protected]
New England Serving Connecticut, Maine, Massachusetts, New Hampshire,
Rhode Island, and Vermont
470 Totten Pond Road, Waltham, MA 024511982
781 8909150
Email: [email protected]
Southern Serving Alabama, Florida, Georgia, Kentucky, Louisiana, Mississippi, North Carolina,
South Carolina, Tennessee, and Virginia
3700 Crestwood Parkway, Suite 700, Duluth, GA 300965599
678 3803300
Email: [email protected]
Southwestern Serving Arkansas, New Mexico, Oklahoma, and Texas
4330 South MoPac Expressway, Suite 200, Austin, TX 787356734
512 8918400
Email: [email protected]
Western Serving Alaska, Arizona, California, Colorado, Hawaii, Idaho, Montana, Nevada,
Oregon, Utah, Washington, and Wyoming
2099 Gateway Place, Suite 550, San Jose, CA 951101087
408 4521400
Email: [email protected]
Dallas Metroplex Ofﬁce Box 19666, 600 South West Street, Suite 108, Arlington, TX 76019
817 2727200
Email: [email protected]
Canada 1708 Dolphin Avenue, Suite 406, Kelowna, BC, Canada V1Y 9S4
250 8619050; 800 6674548 in Canada only
Email: [email protected]
AP International Serving all countries outside the United States and Canada
45 Columbus Avenue, New York, NY 100236992
212 7138091
Email: [email protected] 200203 Development Committee and
Chief Reader
Gay Stewart, University of Arkansas, Fayetteville, Chair
Laurence Cain, Davidson College, North Carolina
Stephen Eshleman, Upper Darby High School, Pennsylvania
Hasan Fakhruddin, The Indiana Academy for Science, Muncie, Indiana
Joseph Keane, St. Thomas Aquinas College, Sparkill, New York
Martha Lietz, Niles West High School, Skokie, Illinois
Chief Reader: Patrick Polley, Beloit College, Wisconsin
ETS Consultants: Will Pfeiffenberger, Ann Marie Zolandz apcentral.collegeboard.com
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This note was uploaded on 04/24/2010 for the course PHYSICS 12 taught by Professor Maiad during the Spring '10 term at Art Inst. San Diego.
 Spring '10
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 Physics

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