Student Answer Sheet for

the Multiple-Choice Section

Use this section to capture student responses. (Note that the following
answer sheet is a sample, and may differ from one used in an actual exam.)
 AP Exam Label PAGE 1
AP Number Label
(from Student Pack) (from Section I Booklet)
Answer Sheet
2016 B123456789T
COMPLETE THIS AREA AT EVERY EXAM. USE NO. 2 PENCIL ONLY D. EXAM DATE E. EXAM G. ONLINE
F. MULTIPLE-CHOICE BOOKLET
To maintain the security of the exam and the validity of my AP score, I will allow no one else to see the multiple-choice questions. I will C. YOUR AP NUMBER START PROVIDER
seal the multiple-choice booklet when asked to do so, and I will not discuss these questions with anyone at any time after completing the Month Day TIME SERIAL NUMBER CODE
section. I am aware of and agree to the AP Program’s policies and procedures as outlined in the 2015-16 Bulletin for AP Students and
Parents, including using testing accommodations (e.g., extended time, computer, etc.) only if I have been preapproved by College Board AM PM S
Services for Students with Disabilities.
Sign your legal name as it will appear on your college applications. Date
0 0 0 0 0 0 0 0 0 0 0 0 6 12 0 0 0 0 0 0 0 0 0 0 0 0 0
A. SIGNATURE
1 1 1 1 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 2 2 2 2 2 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2
B. LEGAL NAME Omit apostrophes, Jr., II. 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3
Legal Last Name — First 15 Letters Legal First Name — First 12 Letters MI 4 4 4 4 4 4 4 4 4 4 10 4 4 4 4 4 4 4 4 4 4 4 4 4 4

5 5 5 5 5 5 5 5 5 5 11 5 5 5 5 5 5 5 5 5 5 5 5 5 5
A A A A A A A A A A A A A A A A A A A A A A A A A A A A 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
B B B B B B B B B B B B B B B B B B B B B B B B B B B B 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
C C C C C C C C C C C C C C C C C C C C C C C C C C C C 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
D D D D D D D D D D D D D D D D D D D D D D D D D D D D 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
E E E E E E E E E E E E E E E E E E E E E E E E E E E E
COMPLETE THIS AREA ONLY ONCE. K. DATE OF BIRTH
F F F F F F F F F F F F F F F F F F F F F F F F F F F F I. AREA CODE AND
G G G G G G G G G G G G G G G G G G G G G G G G G G G G PHONE NUMBER J. SCHOOL YOU ATTEND Month Day Year
SCHOOL CODE School Name
H H H H H H H H H H H H H H H H H H H H H H H H H H H H Jan
I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0 0 0 0 0 0 0 0 0 0 Feb 0 0 0 0
J J J J J J J J J J J J J J J J J J J J J J J J J J J J 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 Mar 1 1 1 1
K K K K K K K K K K K K K K K K K K K K K K K K K K K K 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 Apr 2 2 2 2
L L L L L L L L L L L L L L L L L L L L L L L L L L L L 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 May 3 3 3 3
M M M M M M M M M M M M M M M M M M M M M M M M M M M M 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 City Jun 4 4 4
N N N N N N N N N N N N N N N N N N N N N N N N N N N N 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 Jul 5 5 5
O O O O O O O O O O O O O O O O O O O O O O O O O O O O 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 State Aug 6 6 6
P P P P P P P P P P P P P P P P P P P P P P P P P P P P 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 Sep 7 7 7
Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 7 Oct 8 8 8
Country
R R R R R R R R R R R R R R R R R R R R R R R R R R R R 9 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 Nov 9 9 9
S S S S S S S S S S S S S S S S S S S S S S S S S S S S INTERNATIONAL PHONE 9 9 9 9 9 9 Dec
T T T T T T T T T T T T T T T T T T T T T T T T T T T T
M. COLLEGE TO RECEIVE YOUR
U U U U U U U U U U U U U U U U U U U U U U U U U U U U N. CURRENT
L. SOCIAL SECURITY AP SCORE REPORT
GRADE LEVEL
V V V V V V V V V V V V V V V V V V V V V V V V V V V V NUMBER (Optional) COLLEGE CODE Using the college code listed
in the AP Student Pack,
indicate the ONE college Not yet in
W W W W W W W W W W W W W W W W W W W W W W W W W W W W 11th
that you want to receive 9th grade
X X X X X X X X X X X X X X X X X X X X X X X X X X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 your AP score report. 9th 12th
Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y 1 1 1 1 1 1 1 1 1 1 1 1 1 College Name 10th No longer in
high school
Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z 2 2 2 2 2 2 2 2 2 2 2 2 2

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TAKING USING THIS
ANSWER SHEET 6 6 6 6 6 6 6 6 6 6 6 6 6 Would you like us to supply your information?
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1 2 3 4 5 6 7 8 9 1 Option 1 2 Option 2 9 9 9 9 9 9 9 9 9 9 9 9 9 providing your information.
PAGE 2
COMPLETE THIS AREA AT EACH EXAM (IF APPLICABLE).

P. SURVEY QUESTIONS — Answer the survey questions in the AP Student Pack. Do not put responses to exam questions in this section.

1 A B C D E F G H I 4 A B C D E F G H I 7 A B C D E F G H I

2 A B C D E F G H I 5 A B C D E F G H I 8 A B C D E F G H I

3 A B C D E F G H I 6 A B C D E F G H I 9 A B C D E F G H I

Q. LANGUAGE — Do not complete this section unless instructed to do so.

If this answer sheet is for the French Language and Culture, German Language and Culture, Italian Language and Culture, Spanish Language
and Culture, or Spanish Literature and Culture Exam, please answer the following questions. Your responses will not affect your score.
1. Have you lived or studied for one month or more in a country where the language of the 2. Do you regularly speak or hear the language at home?
exam you are now taking is spoken?

Yes No Yes No

QUESTIONS 1–75

Indicate your answers to the exam questions in this section (pages 2 and 3). Mark only one response per question
for Questions 1 through 120. If a question has only four answer options, do not mark option E. Answers written in
the multiple-choice booklet will not be scored.

A B C D You must use a No. 2 pencil and marks must be complete. Do not use a mechanical pencil. It
EXAMPLES OF
COMPLETE MARK is very important that you fill in the entire circle darkly and completely. If you change your response,
INCOMPLETE MARKS A B C D erase as completely as possible. Incomplete marks or erasures may affect your score.

1 A B C D E 26 A B C D E 51 A B C D E
2 A B C D E 27 A B C D E 52 A B C D E
3 A B C D E 28 A B C D E 53 A B C D E
4 A B C D E 29 A B C D E 54 A B C D E
5 A B C D E 30 A B C D E 55 A B C D E
6 A B C D E 31 A B C D E 56 A B C D E
7 A B C D E 32 A B C D E 57 A B C D E
8 A B C D E 33 A B C D E 58 A B C D E
9 A B C D E 34 A B C D E 59 A B C D E
10 A B C D E 35 A B C D E 60 A B C D E
11 A B C D E 36 A B C D E 61 A B C D E
12 A B C D E 37 A B C D E 62 A B C D E
13 A B C D E 38 A B C D E 63 A B C D E
14 A B C D E 39 A B C D E 64 A B C D E
15 A B C D E 40 A B C D E 65 A B C D E
16 A B C D E 41 A B C D E 66 A B C D E
17 A B C D E 42 A B C D E 67 A B C D E
18 A B C D E 43 A B C D E 68 A B C D E
19 A B C D E 44 A B C D E 69 A B C D E
20 A B C D E 45 A B C D E 70 A B C D E
21 A B C D E 46 A B C D E 71 A B C D E
22 A B C D E 47 A B C D E 72 A B C D E
23 A B C D E 48 A B C D E 73 A B C D E
24 A B C D E 49 A B C D E 74 A B C D E
25 A B C D E 50 A B C D E 75 A B C D E

ETS USE ONLY

R W O R W O
0 1 2 3 4 5 6 7 8 9 SELECTED MEDIA EXAMS OTHER EXAMS
Exam
0 1 2 3 4 5 6 7 8 9
PT02 TOTAL
0 1 2 3 4 5 6 7 8 9
Exam PT03 Subscore (if applicable)
0 1 2 3 4 5 6 7 8 9
PT04 Subscore (if applicable)

DO NOT WRITE IN THIS AREA

 PAGE 3
QUESTIONS 76–120

Be sure each mark is dark and completely fills the circle. If a question has only four answer options, do not mark option E.

76 A B C D E 91 A B C D E 106 A B C D E
77 A B C D E 92 A B C D E 107 A B C D E
78 A B C D E 93 A B C D E 108 A B C D E
79 A B C D E 94 A B C D E 109 A B C D E
80 A B C D E 95 A B C D E 110 A B C D E
81 A B C D E 96 A B C D E 111 A B C D E
82 A B C D E 97 A B C D E 112 A B C D E
83 A B C D E 98 A B C D E 113 A B C D E
84 A B C D E 99 A B C D E 114 A B C D E
85 A B C D E 100 A B C D E 115 A B C D E
86 A B C D E 101 A B C D E 116 A B C D E
87 A B C D E 102 A B C D E 117 A B C D E
88 A B C D E 103 A B C D E 118 A B C D E
89 A B C D E 104 A B C D E 119 A B C D E
90 A B C D E 105 A B C D E 120 A B C D E

QUESTIONS 121–126

For Students Taking AP Biology

Write your answer in the boxes at the top of the griddable area and fill in the corresponding circles.
Mark only one circle in any column. You will receive credit only if the circles are filled in correctly.

121 122 123 124 125 126

/ / / / / / / / / / / / / / / / / /

– . . . . . – . . . . . – . . . . . – . . . . . – . . . . . – . . . . .

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

QUESTIONS 131–142

For Students Taking AP Physics 1 or AP Physics 2

Mark two responses per question. You will receive credit only if both correct responses are selected.

131 A B C D 135 A B C D 139 A B C D

132 A B C D 136 A B C D 140 A B C D
133 A B C D 137 A B C D 141 A B C D
134 A B C D 138 A B C D 142 A B C D

© 2015 The College Board. College Board, AP, Student Search Service and the acorn logo are registered trademarks of the College Board.

DO NOT WRITE IN THIS AREA

 COMPLETE THIS AREA ONLY ONCE. PAGE 4
R. YOUR MAILING ADDRESS Use the address abbreviations from your AP Student Pack. Fill in only one circle per column. Indicate a space in your address by leaving a blank box; do not grid that column. V. SEX
COUNTRY
STREET ADDRESS (include street number, street name, apartment number, etc.) CITY ZIP OR POSTAL CODE CODE Female Male

W. WHICH LANGUAGE DO YOU

A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 0 0 0 KNOW BEST?
B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B 1 1 1 English
C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C 2 2 2 English and another language
about the same
D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D 3 3 3 Another language

E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E 4 4 4

F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 5 5 5 X. RACIAL/ETHNIC GROUP

G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G 6 6 6 Please answer both questions about

Hispanic origin and about race. For the
H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H 7 7 7
following questions about your identity,
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 8 8 8 Hispanic origins are not races.

J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J 9 9 9
(You may mark all that apply.)
K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K
a. Are you of b. What is your race?
L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L Hispanic,
Latino, or
American Indian or
M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M Spanish origin? Alaska Native
N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N No, not of Asian (including Indian
Hispanic, Latino, subcontinent and
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O or Spanish origin Philippines origin)

P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P Yes, Cuban Black or African American

(including Africa and
Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Yes, Mexican Afro-Caribbean origin)

R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R Yes, Puerto Rican Native Hawaiian or other

Pacific Islander
S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S Yes, another White (including Middle
Hispanic, Latino, Eastern origin)
T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T or Spanish origin

U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V Y. PARENTAL EDUCATION LEVEL
In the first column, indicate the highest level of education of
W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W
one parent/guardian, and indicate whether this is your mother/
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X female guardian or father/male guardian. Then, if applicable,
indicate the highest level of education of your other parent/
Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y guardian in the second column, and indicate whether this is
Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z your mother/female guardian or father/male guardian.

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 STATE MI NY VT 0 0 0 0 0 0 0 0 0 Mother or female guardian

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AK HI MN OH WA 1 1 1 1 1 1 1 1 1 Father or male guardian

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 AL IA MO OK WI 2 2 2 2 2 2 2 2 2 Grade school

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 AR ID MS OR WV 3 3 3 3 3 3 3 3 3 Some high school

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 AZ IL MT PA WY 4 4 4 4 4 4 4 4 4 High school diploma or equivalent

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 CA IN NC RI Puerto 5 5 5 5 5 5 5 5 5 Vocational or trade school

Rico
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 CO KS ND SC 6 6 6 6 6 6 6 6 6 Some college

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 CT KY NE SD AA 7 7 7 7 7 7 7 7 7 Associate or two-year degree

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 DC LA NH TN AE 8 8 8 8 8 8 8 8 8 Bachelor’s or four-year degree

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 DE MA NJ TX AP 9 9 9 9 9 9 9 9 9 Some graduate or professional school

/ / / / / / / / / / / / / / / / / / / / / / / / FL MD NM UT Other / / / / / / / Graduate or professional degree

GA ME NV VA T. STUDENT IDENTIFIER (Student ID Number)
S. FOR STUDENTS OUTSIDE If your address does not fit in the spaces provided in Item R, fill in as
THE UNITED STATES ONLY many circles as you can, then fill in the circle in Item S and print the remainder of your address in the spaces provided.
Address City State or Province Country ZIP or Postal Code

By providing your email address, you are granting the College Board
U. EMAIL ADDRESS permission to use your email in accordance with the policies in the
2015-16 Bulletin for AP Students and Parents.
Section I: Multiple-Choice Questions

This is the multiple-choice section of the 2016 AP exam.

It includes cover material and other administrative instructions
to help familiarize students with the mechanics of the exam.
(Note that future exams may differ in look from the following content.)
 ®
AP Physics C: Mechanics Exam
SECTION I: Multiple Choice 2016
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.
Instructions
At a Glance
Section I of this exam contains 35 multiple-choice questions. For these questions, fill in
Total Time only the circles for numbers 1 through 35 on your answer sheet. A table of information
45 minutes and lists of equations that may be helpful are in the booklet. Calculators, rulers and
Number of Questions straightedges may be used in this section.
35
Percent of Total Score Indicate all of your answers to the multiple-choice questions on the answer sheet. No
50% credit will be given for anything written in this exam booklet, but you may use the booklet
Writing Instrument for notes or scratch work. After you have decided which of the suggested answers is best,
Pencil required completely fill in the corresponding circle on the answer sheet. Give only one answer to
Electronic Device each question. If you change an answer, be sure that the previous mark is erased
Calculator allowed completely. Here is a sample question and answer.

Use your time effectively, working as quickly as you can without losing accuracy. Do not
spend too much time on any one question. Go on to other questions and come back to
the ones you have not answered if you have time. It is not expected that everyone will
know the answers to all of the multiple-choice questions.
Your total score on the multiple-choice section is based only on the number of questions
answered correctly. Points are not deducted for incorrect answers or unanswered
questions.

Form I
Form Code 4MBP4-S

80
 ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION
CONSTANTS AND CONVERSION FACTORS
Proton mass, m p = 1.67 ¥ 10 -27 kg Electron charge magnitude, e = 1.60 ¥ 10 -19 C
Neutron mass, mn = 1.67 ¥ 10 -27 kg 1 electron volt, 1 eV = 1.60 ¥ 10 -19 J
Electron mass, me = 9.11 ¥ 10 -31 kg Speed of light, c = 3.00 ¥ 108 m s
Avogadro’s number, N 0 = 6.02 ¥ 10 23 mol -1
Universal gravitational
constant,
G = 6.67 ¥ 10 -11 Nm 2 ( ) kg 2

R = 8.31 J (mol K) Acceleration due to gravity

Universal gas constant,
at Earth’s surface, g = 9.8 m s2
Boltzmann’s constant, k B = 1.38 ¥ 10 -23 J K
1 unified atomic mass unit, 1 u = 1.66 ¥ 10 -27 kg = 931 MeV c 2
Planck’s constant, h = 6.63 ¥ 10 -34 J s = 4.14 ¥ 10 -15 eV s
hc = 1.99 ¥ 10 -25 J m = 1.24 ¥ 103 eV  nm
Vacuum permittivity, e0 = 8.85 ¥ 10 -12 C2 N  m 2 ( )
Coulomb’s law constant, k = 1 ( 4 pe0 ) = 9.0 ¥ 10 N m
9 2
( ) C2
Vacuum permeability, m0 = 4 p ¥ 10 -7 (T m) A
Magnetic constant, k ¢ = m0 ( 4 p ) = 1 ¥ 10 -7 (T m) A
1 atmosphere pressure, 1 atm = 1.0 ¥ 105 N m 2 = 1.0 ¥ 105 Pa

meter, m mole, mol watt, W farad, F

kilogram, kg hertz, Hz coulomb, C tesla, T
UNIT second, s newton, N volt, V degree Celsius, ∞C
SYMBOLS
ampere, A pascal, Pa ohm, W electron volt, eV
kelvin, K joule, J henry, H

PREFIXES VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES


Factor Prefix Symbol q 0 30 37 45 53 60 90
109 giga G sin q 0 12 35 2 2 45 3 2 1
106 mega M cos q 1 3 2 45 2 2 35 12 0
103 kilo k tan q 0 3 3 34 1 43 3 •
10 -2 centi c
10 -3 milli m The following assumptions are used in this exam.
-6 micro m I. The frame of reference of any problem is inertial unless otherwise
10
stated.
10 -9 nano n II. The direction of current is the direction in which positive charges
10 -12 pico p would drift.
III. The electric potential is zero at an infinite distance from an isolated
point charge.
IV. All batteries and meters are ideal unless otherwise stated.
V. Edge effects for the electric field of a parallel plate capacitor are
negligible unless otherwise stated.

-3-
 ADVANCED PLACEMENT PHYSICS C EQUATIONS
MECHANICS ELECTRICITY AND MAGNETISM
Ãx = Ãx 0 + a x t a = acceleration 1 q1q2 A = area
E= energy FE = B = magnetic field
1 2 4pe0 r 2
x = x0 + Ãx 0 t + at F = force C = capacitance
2 x
f = frequency FE d = distance
Ãx2 = Ãx 0 2 + 2 a x ( x - x0 ) E =
h = height q E = electric field
I = rotational inertia e = emf
a=
 F = Fnet   Q
Ú
J = impulse E  dA= F = force
m m e0
K = kinetic energy I = current
dp k = spring constant J = current density
F = dV
dt = length Ex = - L = inductance
L = angular momentum dx  = length
 
J = Ú F dt = 'p m=
P =
mass
power
'V = - Ú E dr
n = number of loops of wire
per unit length
p = mv p = momentum N = number of charge carriers
q
r = radius or distance V =
1
4pe0 Â rii P =
per unit volume
power
i
F f £ m FN T = period
t = time Q = charge
1 q1q2
 UE = qV = q = point charge
Ú F dr
U= potential energy
'E = W = 4pe0 r R = resistance
v = velocity or speed
1 2 W= work done on a system r = radius or distance
K = mà Q
2 x = position 'V = t = time
C
m = coefficient of friction U = potential or stored energy
dE k e0 A V= electric potential
P= q = angle C =
dt d
t = torque v = velocity or speed
  w = angular speed r = resistivity
P = F v Cp = Â Ci
a = angular acceleration i ) = flux
'Ug = mg 'h f = phase angle k = dielectric constant
1 1
=Â FM = qv ¥ B
Fs = - k ' x Cs C
i i
Ã2
ac = = w2r
r
Us =
1
2
k ( 'x )
2
I =
dQ Ú Bid = m0 I
dt
t = r¥F
x = xmax cos( wt + f) m0 I d ¥ r
1 1 dB =
Ât t UC = Q'V = C ( 'V )2 4p r 2
a = = net 2p 1 2 2
I I T = = r
w f R=
A
F = ÚI d ¥B
I = Ú r dm = Â mr
2 2
m Bs = m0 nI
Ts = 2 p E = rJ
k
 mi xi
xcm =
 mi Tp = 2p
I = Nevd A )B = Ú B dA
g
à = rw 'V d )B
Gm1m2
I =
R
e = Ú E id =-
dt
FG =
L = r ¥ p = Iw r2
Rs = Â Ri e = -L
dI
Gm1m2 i dt
K =
1 2
Iw UG = -
2 r 1 1 1 2
Rp
= ÂR UL =
2
LI
i i
w = w0 + at

1 2 P = I 'V
q = q0 + w0 t + at
2

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 ADVANCED PLACEMENT PHYSICS C EQUATIONS

GEOMETRY AND TRIGONOMETRY CALCULUS

Rectangle A = area df d f du
=
A = bh C = circumference dx du dx
V = volume
Triangle
S = surface area
d n
dx
( x ) = nxn -1
1
A= bh b = base

Circle
2 h = height
dx
(e ) = aeax
d ax
 = length
d
A = pr2 w = width
(ln ax ) = 1
r = radius dx x
C = 2p r
s = arc length d
s = rq q = angle dx
[sin (ax )] = a cos (ax)
Rectangular Solid
d
V = wh dx
[cos (ax )] = - a sin (ax)
Cylinder s
1 n +1
Úx
n
r dx = x , n π -1
V = pr 2 n +1
q
1 ax
Úe
ax
S = 2p r + 2p r 2
dx = e
a
Sphere
dx
4
V = pr3
Úx+a = ln x + a
3
1
S = 4p r 2 Ú cos (ax) dx = a sin (ax)
1
Right Triangle Ú sin (ax) dx = - a cos (ax)
a 2 + b2 = c2
VECTOR PRODUCTS
a  
sin q =
c A B = AB cosq
c
cos q =
b a A ¥ B = AB sin q
c q 90°
b
a
tan q =
b

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 PHYSICS C: MECHANICS
SECTION I
Time—45 minutes
35 Questions

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 and then fill in the corresponding circle on the answer sheet.

Note: To simplify calculations, you may use g = 10 m/ s2 in all problems.

1. A projectile is launched with a speed of 40 m s 2. A small sphere hangs from a string attached to the
at an angle of 30∞ above the horizontal, as shown ceiling of a uniformly accelerating train car. It is
in the figure above. The projectile lands on a
plateau 3 s later. The height Dy of the plateau is observed that the string makes an angle of 37
most nearly with respect to the vertical. The magnitude of the
(A) 15 m acceleration a of the train car is most nearly
(B) 30 m (A) 6.0 m s2
(C) 45 m
(D) 60 m (B) 7.5 m s2
(E) 75 m
(C) 8.0 m s2
(D) 10 m s2
(E) 13 m s2

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3. Which of the following statements must be true
for a falling object that has been dropped from
rest near the surface of Earth?
(A) The derivative of the distance the object falls
with respect to time equals 9.8 m s2 .
(B) The object falls a vertical distance of 9.8 m
during the first second only.
(C) The object falls a vertical distance of 9.8 m
during each second.
(D) The speed of the object as it falls is a constant
9.8 m s . 4. The position x as a function of time t for an object
moving in a straight line is shown in the graph
(E) The speed of the object increases by 9.8 m s above. Which of the following best describes the
during each second. object’s speed and direction of motion during the
time interval shown?
Speed Direction of Motion
(A) Decreasing Positive
(B) Increasing Positive
(C) Constant Positive
(D) Decreasing Negative
(E) Increasing Negative

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5. The force F exerted on a ball during a collision
with a wall is given as a function of time t by the
equation F (t )   t   t 2 , where   400 N s
and   4000 N s 2 . The ball first contacts the
wall at t = 0, and the collision lasts for 0.10 s.
What is the magnitude of the change in 6. Two spheres of uniform density are located a
momentum of the ball? distance L apart, as shown in the figure above.
The left sphere has a mass M1 , and the right
(A) 0
(B) 0.67 kg  m s sphere has a mass M2 . The center of mass of the
two spheres is labeled point P. Which of the
(C) 3.33 kg  m s
following is a correct expression for the distance
(D) 3.60 kg  m s from point P to the center of the left sphere?
(E) The change in momentum of the ball cannot
be determined without knowing the mass of M1
(A) L
the ball. M2

( M1 + M2 )
(B) L
M1

( M1 + M2 )
(C) L
M2

M2
(D) L
( M1 + M2 )
M1
(E) L
( 1 + M2 )
M

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Questions 7-8

A 2 kg block is initially at rest on a horizontal

frictionless table. A force of 15 N is then exerted
on the block at an angle of 37 to the horizontal,
as shown above.

7. The change in the kinetic energy of the block after 9. A wheel of radius R is fixed to an axle of
moving a distance of 3 m is most nearly radius R 3 and rotates at constant angular
(A) 60 J speed  , as shown in the figure above. A force
(B) 45 J of magnitude F1 is applied tangent to the outer
(C) 36 J
(D) 27 J edge of the wheel. A second force of magnitude
(E) 24 J F2 is applied tangent to the edge of the axle to
keep the wheel rotating at constant angular speed
8. The magnitude of the force exerted on the block  . The magnitude F2 is equal to
by the table is most nearly
(A) 35 N (A) F1 9
(B) 32 N (B) F1 3
(C) 29 N
(D) 20 N (C) F1
(E) 11 N (D) 3F1
(E) 9F1

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Questions 10-11

On a level horizontal table, a toy race car of 12. A horizontal uniform plank is supported by ropes
mass M moves with constant speed v around I and II at points P and Q, respectively, as shown
a flat circular racetrack of radius R. above. The two ropes have negligible mass. The
tension in rope I is 150 N. The point at which rope
10. Which of the following best represents the II is attached to the plank is now moved to point
minimum coefficient of static friction required for R halfway between point Q and point C, the
the race car to continue to follow the circular path center of the plank. The plank remains horizontal.
shown? Which of the following are most nearly the new
Rg tensions in the two ropes?
(A)
v2 Tension in I Tension in II
Mv2 (A) 75 N 225 N
(B)
R (B) 100 N 200 N
(C) 112.5 N 112.5 N
v2 (D) 112.5 N 187.5 N
(C)
g (E) 150 N 300 N
v2
(D) 13. The potential energy U as a function of
Rg
the position x of an object is given by
v2 U ( x ) = - 400 x , where U is in joules and x is
(E)
2Rg in meters. The object is released from rest at
position x = 30 m and is free to move along the
x-axis. When the object has moved a distance of
10 m from its initial position, the magnitude of the
force associated with this potential energy
function is
(A) 20 N
11. The car is now going around a banked curve, as (B) 10 N
shown in the figure above. The banked curve is (C) 4.0 N
higher toward the outside of the circular turn. The (D) 1.0 N
car can now travel at a higher speed without (E) 0.25 N
sliding because the banked curve
(A) increases the coefficient of friction between
the car and the track.
(B) increases the momentum of the car.
(C) allows a component of the normal force to
point toward the center of the track.
(D) allows a component of the weight of the
car to point toward the center of the track.
(E) allows gravity to do work on the car.

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14. A student pushes a box across a rough horizontal
floor. If the amount of work done by the student
on the box is 100 J and the amount of energy
dissipated by friction is 40 J, what is the change
in kinetic energy of the box?
15. Three blocks of masses m, 3m, and 2m resting on
(A) 0J a frictionless horizontal surface are connected to
(B) 40 J identical ideal springs, as shown above. A force of
(C) 60 J magnitude F directed to the left is then applied to
(D) 100 J the left end of spring A. Which spring is stretched
(E) 140 J the most when the blocks are all moving with the
same acceleration?
(A) A
(B) B
(C) C
(D) None, because the springs do not stretch.
(E) None, because the springs all stretch the
same amount.

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16. At time t = 0 , a ball is thrown with initial speed 18. Two balls, A and B, have the same mass and
v0 at an angle  above the horizontal. Air diameter but are made from different types of
resistance is negligible. Which of the following rubber. The balls are dropped from the same
best represents the speed of the ball as a function height above the floor. After colliding with the
of time t while the ball is in flight? floor, ball A bounces higher than ball B bounces.
Which of the following quantities must
(A) v0 sin q - gt necessarily be larger for ball A than for ball B ?
(B) v0 cos q - gt (A) The average force exerted by the floor
(B) The amount of time in contact with the floor
v02 cos2 q + (v0 sin q - gt )
2 (C) The impulse exerted by the floor
(C)
(D) The momentum just before colliding with
(D) (v0 cos q - gt )2 + v02 sin2 q the floor
(E) The kinetic energy just before colliding with
the floor
(E) (v0 cos q - gt )2 + (v0 sin q - gt )2
19. Object A of mass M is moving east at speed v.
17. The position x of an object is given as a function It collides with object B of mass 2M that was
initially at rest. The motion of the objects before
of time t by the equation x = 8 + 4t - 6t 3 ,
and after the collision is along the same line. After
where x is in meters and t is in seconds. What is the collision, object A is moving west at a speed
the maximum positive velocity attained by this
of v 3 . What is the speed of object B immediately
object?
after the collision?
(A) 4 m s
(A) v 3
(B) 8 m s
(B) v 2
(C) 18 m s
(C) 2v 3
(D) 36 m s
(D) v
(E) There is no maximum positive velocity (E) 2v
because the object never moves in the
positive direction.

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-12-
Questions 20-21 22. An airplane

travels horizontally at a constant
velocity v . An object is dropped from the plane,
A wheel of mass m, which has a rotational inertia I and one second later another object is dropped
and a radius r, rotates with an angular speed w about from the plane. If air resistance is negligible,
an axis through its center. A retarding force F is what happens to the vertical distance between
applied tangentially to the rim of the wheel. the two objects while they are both falling?
(A) It increases.
20. Which of the following is equal to the magnitude (B) It decreases.
of the angular acceleration of the wheel? (C) It remains the same.
Fw (D) It depends on the mass of the objects.
(A) (E) It depends on the horizontal speed of
m
the plane.
Fr
(B)
I 23. A boat moves across a river. The river’s velocity

relative to the land is vRL , and the boat’s velocity
w2 
(C)
r relative to the river is vBR . Which of the
(D) I w following best represents the velocity of the boat
relative to the land?
(E) wr  
(A) vBR + vRL
 
21. The retarding force F finally stops the rotation of (B) vBR - vRL
the wheel. Which of the following best represents  
the total reduction in mechanical energy in the (C) - vBR + vRL
process of stopping the wheel?  
(D) vBR + vRL
(A) Fr  
(E) vBR - vRL
(B) Iw2

(C) w2r

(D) Fr 2
1 2
(E) Iw
2

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-13-
Questions 24-25 26. The acceleration due to gravity on the surface
 of the Moon is about 1 6 of that on the surface
The following graph shows the force F exerted on of Earth. An astronaut weighs 600 N on Earth.
a 2 kg object as a function of the distance d that the The astronaut’s mass on the Moon is most nearly
object travels. The object is at rest at d = 0 and travels
(A) 600 kg
on a horizontal, frictionless surface along the line of
(B) 360 kg
action of the force.
(C) 100 kg
(D) 60 kg
(E) 10 kg


24. The work done on the object by the force F
during the first 10 m of travel is most nearly
(A) 7.5 J
(B) 10 J
(C) 50 J 27. Planet X has a mass M, radius R, and no
(D) 75 J atmosphere. An object of mass m is located a
(E) 100 J distance 2R above the surface of planet X, as
shown in the figure above. The object is released
25. The kinetic energy of the 2 kg object when from rest and falls to the surface of the planet.
d equals 20 m is the same as when d is What is the speed of the object just before it
most nearly reaches the surface of planet X ?

(A) 0 m 2GM
(A)
(B) 5 m 3R
(C) 10 m
(D) 12.5 m 4GM
(E) 15 m (B)
3R

8GM
(C)
3R

3GM
(D)
R

6GM
(E)
R

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-14-
28. A ball is kicked from the ground with an initial
speed v0 at an angle  above the horizontal.
Which of the following best describes the
magnitudes of the velocity and acceleration of
the ball when it reaches the highest point of its
trajectory?
Velocity Acceleration
29. A block of mass m is attached to a spring and
(A) 0 0 placed on an inclined plane. The spring has a
(B) v0 cos 0 spring constant k, and there is negligible friction
(C) v0 sin  0 between the block and inclined plane. The block
is released from rest at the position shown in the
(D) v0 cos 9.8 m s2 figure above with the spring initially unstretched.
(E) v0 sin  9.8 m s2 What distance d does the block slide down the
plane before coming momentarily to rest?
2mg
(A)
k
mg
(B)
k
mg sin q
(C)
k
2 mg sin q
(D)
k
mg sin q
(E)
k

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-15-
30. A 5.0 kg object suspended on a spring oscillates 31. Consider Earth to be stationary, and the Moon
such that its position x as a function of time t is as orbiting Earth in a circle of radius R. If the
masses of Earth and the Moon are M E and M M ,
given by the equation x (t ) = A cos ( wt ) , where
respectively, which of the following best
A = 0.80 m and w = 2.0 s -1 . What is the represents the total mechanical energy of the
magnitude of the maximum net force on the Earth-Moon system?
object during the motion? GM E M M
(A)
(A) 3.2 N 2R
(B) 4.0 N GM E M M
(C) 8.0 N (B)
R
(D) 12.8 N
GM E M M
(E) 16.0 N (C) -
2R
GM E M M
(D) -
R
2GM E M M
(E) -
R

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32. A small rock is launched straight upward from the
surface of a planet with no atmosphere. The initial
speed of the rock is twice the escape speed ve of
the rock from the planet. If gravitational effects
from other objects are negligible, the speed of the
rock at a very great distance from the planet will
approach a value of
(A) zero
(B) ve 2
(C) ve
(D) 2ve
(E) 3ve

33. Identical blocks 1 and 2 start from rest at height h

and travel down two differently shaped tracks
onto identical rough horizontal surfaces, as shown
in the figures above. Both tracks are frictionless,
and both blocks make a smooth transition onto the
rough horizontal surfaces. Block 1 comes to rest
at a horizontal distance d1 from the bottom of the
track. Which of the following best describes and
explains the horizontal distance d2 that block 2
travels before coming to rest?
(A) d 2  d1 , because block 2 reaches its
maximum speed later than block 1
(B) d 2  d1 , because block 2 has a lower
maximum speed than block 1
(C) d 2  d1 , because the blocks have the
same mass
(D) d 2  d1 , because the blocks start at the same
height
(E) 2  d1 , because the track for block 2 is
d
shorter

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 ( )
35. An equation for the motion of an object is given
Mass (kg) Area cm2 s
as 2 vt - 4 x = Bt 2 , where B is a constant.
Block 1 0.75 75 0.20 The variable v indicates velocity, in meters
per second; t indicates time, in seconds; and
Block 2 3.0 100 0.40 x indicates displacement, in meters. What is
the unit of measure for B ?
34. In an experiment, two blocks of different (A) s
roughness are placed on the same rough wooden (B) m s
board. The table above shows three values for (C) m s2
each block: the mass, the area of the block in
contact with the board, and the coefficient of (D) m 2 s
static friction  s between the block and the (E) m 2 s2
board. The experiment begins with the board
horizontal. One end of the board is then slowly
raised. Which of the following correctly identifies
the block that will start sliding down the board
first and why?
(A) Block 1, because it has less mass
per unit area
(B) Block 1, because the coefficient of friction is
smaller
(C) Block 2, because it has greater mass
(D) Block 2, because it has a smaller
surface area
(E) Block 2, because the coefficient of friction is
larger

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-18-
 STOP
END OF MECHANICS SECTION I
IF YOU FINISH BEFORE TIME IS CALLED,
YOU MAY CHECK YOUR WORK ON MECHANICS SECTION I ONLY.

DO NOT TURN TO ANY OTHER TEST MATERIALS.

MAKE SURE YOU HAVE DONE THE FOLLOWING.

 PLACED YOUR AP NUMBER LABEL ON YOUR ANSWER SHEET

 WRITTEN AND GRIDDED YOUR AP NUMBER CORRECTLY ON YOUR

ANSWER SHEET

 TAKEN THE AP EXAM LABEL FROM THE FRONT OF THIS BOOKLET

AND PLACED IT ON YOUR ANSWER SHEET

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