Physics C: Mechanics. Practice Exam. From the 2017 Administration

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1 From the 017 Administration Physics C: Mechanics Practice Exam This exam may not be posted on school or personal websites, nor electronically redistributed for any reason. This Released Exam is provided by the College Board for AP Exam preparation. Teachers are permitted to download the materials and make copies to use with their students in a classroom setting only. To maintain the security of this exam, teachers should collect all materials after their administration and keep them in a secure location. Further distribution of these materials outside of the secure College Board site disadvantages teachers who rely on uncirculated questions for classroom testing. Any additional distribution is in violation of the College Board s copyright policies and may result in the termination of Practice Exam access for your school as well as the removal of access to other online services such as the AP Teacher Community and Online Score Reports. 017 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. Visit the College Board on the Web: AP Central is the offcial online home for the AP Program: apcentral.collegeboard.org

2 Contents Exam Instructions Student Answer Sheet for the Multiple-Choice Section Section I: Multiple-Choice Questions Section II: Free-Response Questions Multiple-Choice Answer Key Free-Response Scoring Guidelines Scoring Worksheet Question Descriptors and Performance Data Note: This publication shows the page numbers that appeared in the AP Exam Instructions book and in the actual exam. This publication was not repaginated to begin with page The College Board. College Board, Advanced Placement Program, AP, SAT and the acorn logo are registered trademarks of the College Board. All other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at:

3 Exam Instructions The following contains instructions taken from the AP Exam Instructions book.

4 AP Physics C: Mechanics Exam Regularly Scheduled Exam Date: Monday afternoon, May 8, 017 Late-Testing Exam Date: Friday afternoon, May 19, 017 Section I Total Time: 45 minutes Calculator Allowed Number of Questions: 35* Percent of Total Score: 50% Writing Instrument: Pencil required *The number of questions may vary slightly depending on the form of the exam. Section II Total Time: 45 minutes Calculator Allowed Number of Questions: 3 Percent of Total Score: 50% Writing Instrument: Pen with black or dark blue ink, or pencil Exam packets Answer sheets AP Student Packs AP Coordinator s Manual This book AP Exam Instructions AP Exam Seating Chart template School Code and Home-School/Self- Study Codes Extra calculators Extra rulers or straightedges Pencil sharpener What Proctors Need to Bring to This Exam Container for students electronic devices (if needed) Extra No. pencils with erasers Extra pens with black or dark blue ink Extra paper Stapler Watch Signs for the door to the testing room Exam in Progress Cell phones are prohibited in the testing room Before Distributing Exams: Check that the title on all exam covers is Physics C: Mechanics. If there are any exam booklets with a different title, contact the AP coordinator immediately. Students are permitted to use rulers, straightedges, and four-function, scientific, or graphing calculators for this entire exam (Sections I and II). Before starting the exam administration, make sure each student has an appropriate calculator, and any student with a graphing calculator has a model from the approved list on page 49 of the AP Coordinator s Manual. See pages of the AP Coordinator s Manual for more information. If a student does not have an appropriate calculator or has a graphing calculator not on the approved list, you may provide one from your supply. If the student does not want to use the calculator you provide or does not want to use a calculator at all, he or she must hand copy, date, and sign the release statement on page 47 of the AP Coordinator s Manual. During the administration of Section II, students may have no more than two calculators on their desks. Calculators may not be shared. Calculator memories do not need to be cleared before or after the exam. Students with Hewlett-Packard Series and Casio FX-9860 graphing calculators may use cards designed for use with these calculators. Proctors should make sure infrared ports (Hewlett-Packard) are not facing each other. Since graphing calculators can be used to store data, including text, proctors should monitor that students are using their calculators appropriately. Attempts by students to use the calculator to remove exam questions and/or answers from the room may result in the cancellation of AP Exam scores. 38

5 AP Exam Instructions Tables containing equations commonly used in physics are included in each AP Exam booklet, for use during the entire exam. Students are NOT allowed to bring their own copies of the equation tables to the exam room. Students may take both Physics C exams, Mechanics only, or Electricity and Magnetism only. The Mechanics exam is administered first, after which students taking both exams are given a break. Then the Electricity and Magnetism exam is administered. Prior to testing day, determine which exams students are taking. Those taking both Physics C exams and those taking Physics C: Mechanics only should report for the 1 noon start time (11 a.m. in Alaska). Those taking Electricity and Magnetism only should report to the testing room after the break (approximately p.m., 1 p.m. in Alaska). If all students are taking Electricity and Magnetism only, you must not begin the exam before p.m. The two exams are in separate exam packets, and require separate answer sheets. At the beginning of the session, you will distribute only the packets and answer sheets for Mechanics. The materials for Electricity and Magnetism will be distributed after the break.! SECTION I: Multiple Choice Do not begin the exam instructions below until you have completed the appropriate General Instructions for your group. This exam includes survey questions. The time allowed for the survey questions is in addition to the actual test-taking time. Make sure that you begin the exam at the designated time. Remember, you must complete a seating chart for this exam. See pages for a seating chart template and instructions. See the AP Coordinator s Manual for exam seating requirements (pages 51 54). If you are giving the regularly scheduled exam, say: It is Monday afternoon, May 8, and you will be taking the AP Physics C: Mechanics Exam. If you are giving the alternate exam for late testing, say: It is Friday afternoon, May 19, and you will be taking the AP Physics C: Mechanics Exam. In a moment, you will open the packet that contains your exam materials. By opening this packet, you agree to all of the AP Program s policies and procedures outlined in the Bulletin for AP Students and Parents. Look at your exam packet and confirm that the exam title is AP Physics C: Mechanics. Raise your hand if your exam packet contains any title other than AP Physics C: Mechanics and I will help you. Once you confirm that all students have the correct exams, say: You may now remove the shrinkwrap from your exam packet and take out the Section I booklet, but do not open the booklet or the shrinkwrapped Section II materials. Put the white seals aside PHYSICS C: MECHANICS

6 Physics C: Mechanics Carefully remove the AP Exam label found near the top left of your exam booklet cover. Now place it on page 1 of your answer sheet on the light blue box near the top right corner that reads AP Exam Label. If students accidentally place the exam label in the space for the number label or vice versa, advise them to leave the labels in place. They should not try to remove the label; their exam can still be processed correctly Read the statements on the front cover of Section I and look up when you have finished.... Sign your name and write today s date. Look up when you have finished.... Now print your full legal name where indicated. Are there any questions?... Turn to the back cover of your exam booklet and read it completely. Look up when you have finished.... Are there any questions?... You will now take the multiple-choice portion of the exam. You should have in front of you the multiple-choice booklet and your answer sheet. You may never discuss the multiple-choice exam content at any time in any form with anyone, including your teacher and other students. If you disclose the multiple-choice exam content through any means, your AP Exam score will be canceled. Open your answer sheet to page. You must complete the answer sheet using a No. pencil only. Mark all of your responses beginning on page of your answer sheet, one response per question. Completely fill in the circles. If you need to erase, do so carefully and completely. No credit will be given for anything written in the exam booklet. Scratch paper is not allowed, but you may use the margins or any blank space in the exam booklet for scratch work. Rulers, straightedges, and calculators may be used for the entire exam. You may place these items on your desk. Are there any questions?... You have 45 minutes for this section. Open your Section I booklet and begin. 9 Note Start Time here. Note Stop Time here. Check that students are marking their answers in pencil on their answer sheets and that they are not looking at their shrinkwrapped Section II booklets. After 35 minutes, say: There are 10 minutes remaining. After 10 minutes, say: Stop working and turn to the last page in your booklet.... You have minutes to answer Questions These are survey questions and will not affect your score. You may not go back to work on any of the exam questions. You may now begin. 40

7 AP Exam Instructions To help you and your proctors make sure students are not working on the exam questions, the two pages with the survey questions are identified with a large S on the upper corner of each page. Give students minutes to answer the survey questions. Then say: Close your booklet and put your answer sheet on your desk, face up. Make sure you have your AP number label and an AP Exam label on page 1 of your answer sheet. Sit quietly while I collect your answer sheets. Collect an answer sheet from each student. Check that each answer sheet has an AP number label and an AP Exam label. After all answer sheets have been collected, say: Now you must seal your exam booklet using the white seals you set aside earlier. Remove the white seals from the backing and press one on each area of your exam booklet cover marked PLACE SEAL HERE. Fold each seal over the back cover. When you have finished, place the booklet on your desk, face up. I will now collect your Section I booklet.... SECTION II: Free Response Check that each student has signed the front cover of the sealed Section I booklet. When all Section I materials have been collected and accounted for, say: May I have everyone s attention? Place your Student Pack on your desk.... You may now remove the shrinkwrap from the Section II packet, but do not open the exam booklet until you are told to do so.... Read the bulleted statements on the front cover of the exam booklet. Look up when you have finished.... Now take an AP number label from your Student Pack and place it on the shaded box. If you don t have any AP number labels, write your AP number in the box. Look up when you have finished.... Read the last statement.... Using a pen with black or dark blue ink, print the first, middle, and last initials of your legal name in the boxes and print today s date where indicated. This constitutes your signature and your agreement to the statements on the front cover.... Turn to the back cover and, using your pen, complete Item 1 under Important Identification Information. Print the first two letters of your last name and the first letter of your first name in the boxes. Look up when you have finished.... In Item, print your date of birth in the boxes.... In Item 3, write the school code you printed on the front of your Student Pack in the boxes.... Read Item Are there any questions? PHYSICS C: MECHANICS

8 Physics C: Mechanics I need to collect the Student Pack from anyone who will be taking another AP Exam. Keep it, however, if you will be taking the Physics C: Electricity and Magnetism exam this afternoon. If you have no other AP Exams to take, place your Student Pack under your chair now.... Read the information on the back cover of the exam booklet. Do not open the booklet until you are told to do so. Look up when you have finished.... Collect the Student Packs. Then say: Are there any questions?... Rulers, straightedges, and calculators may be used for Section II. Be sure these items are on your desk.... You have 45 minutes to complete Section II. You are responsible for pacing yourself and may proceed freely from one question to the next. You must write your answers in the exam booklet using a pen with black or dark blue ink or a No. pencil. If you use a pencil, be sure that your writing is dark enough to be easily read. If you need more paper during the exam, raise your hand. At the top of each extra sheet of paper you use, be sure to write only your AP number and the question number you are working on. Do not write your name. Are there any questions?... You may begin. 9 Note Start Time here. Note Stop Time here. You should also make sure that Hewlett-Packard calculators infrared ports are not facing each other and that students are not sharing calculators. After 35 minutes, say: There are 10 minutes remaining. After 10 minutes, say: Stop working and close your exam booklet. Place it on your desk, face up.... If any students used extra paper for a question in the free-response section, have those students staple the extra sheet(s) to the first page corresponding to that question in their exam booklets. Complete an Incident Report. A single Incident Report may be completed for multiple students per exam subject per administration (regular or late testing) as long as all of the required information is provided. Include all exam booklets with extra sheets of paper in an Incident Report return envelope (see page 6 of the AP Coordinator s Manual for complete details). Then say: Remain in your seat, without talking, while the exam materials are collected.... Collect a Section II booklet from each student. Check for the following: Exam booklet front cover: The student placed an AP number label on the shaded box and printed his or her initials and today s date. Exam booklet back cover: The student completed the Important Identification Information area. 4

9 AP Exam Instructions When all exam materials have been collected and accounted for, return to students who are taking Mechanics only any electronic devices you may have collected before the start of the exam. If you are giving the regularly scheduled exam, say: You may not discuss or share the free-response exam content with anyone unless it is released on the College Board website in about two days. Your AP Exam score results will be available online in July. If you are giving the alternate exam for late testing, say: None of the content in this exam may ever be discussed or shared in any way at any time. Your AP Exam score results will be available online in July. If any students completed the AP number card at the beginning of this exam and are about to be dismissed say: Please remember to take your AP number card with you. You will need the information on this card to view your scores and order AP score reporting services online. If no students are taking Physics C: Electricity and Magnetism, say: You are now dismissed. If some students are taking Physics C: Electricity and Magnetism, say: Those of you taking Mechanics only are now dismissed. The students taking the Electricity and Magnetism exam now get a 10-minute break. Remember that the Electricity and Magnetism exam cannot begin before p.m., but should start before 3 p.m. After the students taking Mechanics only have left, say: If you will also be taking the Physics C: Electricity and Magnetism exam, please listen carefully to these instructions before we take a 10-minute break. Please put all of your calculators under your chair. Your calculators and all items you placed under your chair at the beginning of this exam must stay there, and you are not permitted to open or access them in any way. You are not allowed to consult teachers, other students, notes, or textbooks during the break. You may not make phone calls, send text messages, check , use a social networking site, or access any electronic or communication device. If you do not follow these rules, your score will be canceled. Are there any questions? You may begin your break. Testing will resume at. If you will be administering Physics C: Electricity and Magnetism at p.m., be sure all exam materials are kept secure during the break. When the students return from break, turn to page 45 and begin the exam administration for Physics C: Electricity and Magnetism. If you have no students taking Physics C: Electricity and Magnetism, all exam materials must be placed in secure storage until they are returned to the AP Program after your school s last administration. 43 PHYSICS C: MECHANICS

10 Physics C: Mechanics Post-Exam Tasks Be sure to give the completed seating chart to the AP coordinator. Schools must retain seating charts for at least six months (unless the state or district requires that they be retained for a longer period of time). Schools should not return any seating charts in their exam shipments unless they are required as part of an Incident Report. The exam proctor should complete the following tasks if asked to do so by the AP coordinator. Otherwise, the AP coordinator must complete these tasks. Before storing materials, check the School Use Only section on page 1 of the answer sheet and: Fill in the appropriate section number circle in order to access a separate AP Instructional Planning Report (for regularly scheduled exams only) or subject score roster at the class section or teacher level. See Post-Exam Activities in the AP Coordinator s Manual. Check your list of students who are eligible for fee reductions and fill in the appropriate circle on their registration answer sheets. 44

11 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.)

12 UNLWEB1116 Q498/1-4 Answer Sheet 017 AP Number Label (from Student Pack) COMPLETE THIS AREA AT EVERY EXAM. 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 exam content. I will seal the multiple-choice booklet when asked to do so, and I will not discuss the exam content with anyone at any time after completing the section. I am aware of and agree to the AP Program s policies and procedures as outlined in the 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 Services for Students with Disabilities. Sign your legal name as it will appear on your college applications. Date A. SIGNATURE B. LEGAL NAME Omit apostrophes, Jr., II. Legal Last Name First 15 Letters A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C D D D D D D D D D D D D D D D E E E E E E E E E E E E E E E F F F F F F F F F F F F F F F G G G G G G G G G G G G G G G H H H H H H H H H H H H H H H I I I I I I I I I I I I I I I J J J J J J J J J J J J J J J K K K K K K K K K K K K K K K L L L L L L L L L L L L L L L M M M M M M M M M M M M M M M N N N N N N N N N N N N N N N O O O O O O O O O O O O O O O P P P P P P P P P P P P P P P Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q R R R R R R R R R R R R R R R S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T 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 W W W W W W W W W W W W W W W X X X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z H. AP EXAM I AM TAKING USING THIS ANSWER SHEET Exam Name: SCHOOL USE ONLY Section Number USE NO. PENCIL ONLY C.YOUR AP NUMBER Legal First Name First 1 Letters A A A A A A A A A A A A A B B B B B B B B B B B B B C C C C C C C C C C C C C D D D D D D D D D D D D D E E E E E E E E E E E E E F F F F F F F F F F F F F G G G G G G G G G G G G G H H H H H H H H H H H H H I I I I I I I I I I I I I J J J J J J J J J J J J J K K K K K K K K K K K K K L L L L L L L L L L L L L M M M M M M M M M M M M M N N N N N N N N N N N N N O O O O O O O O O O O O O P P P P P P P P P P P P P Q Q Q Q Q Q Q Q Q Q Q Q Q R R R R R R R R R R R R R S S S S S S S S S S S S S T T T T T T T T T T T T T 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 W W W W W W W W W W W W W X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z Form: Form Code: Fee Reduction Granted 1 Option 1 Option MI I. AREA CODE AND PHONE NUMBER INTERNATIONAL PHONE L. SOCIAL SECURITY NUMBER (Optional) D. EXAM DATE Month Day AP Exam Label (from Section I Booklet) E. EXAM START TIME AM PM F. MULTIPLE-CHOICE BOOKLET SERIAL NUMBER S COMPLETE THIS AREA ONLY ONCE. J. SCHOOL YOU ATTEND SCHOOL CODE School Name City State Country M. COLLEGE TO RECEIVE YOUR AP SCORE REPORT COLLEGE CODE Using the college code listed in the AP Student Pack, indicate the ONE college that you want to receive your AP score report College Name City State Country PAGE 1 G. ONLINE PROVIDER CODE O. STUDENT SEARCH SERVICE Colleges and scholarship programs may request your information to inform you of educational opportunities and financial aid. Would you like us to supply your information? Yes K. DATE OF BIRTH Month Day Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec N. CURRENT GRADE LEVEL Not yet in 9th grade 9th 10th th 1th No longer in high school No If you don t answer and previously chose to participate in this service, we will continue providing your information.

13 PAGE 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 F G H I 4 F G H I 7 F G H I F G H I 5 F G H I 8 F G H I 3 F G H I 6 F G H I 9 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 exam you are now taking is spoken?. Do you regularly speak or hear the language at home? Yes No Yes No QUESTIONS 1 75 Indicate your answers to the exam questions in this section (pages and 3). Mark only one response per question for Questions 1 through 10. If a question has only four answer options, do not mark option E. Answers written in the multiple-choice booklet will not be scored. COMPLETE MARK EXAMPLES OF INCOMPLETE MARKS A B C D A B C D You must use a No. pencil and marks must be complete. Do not use a mechanical pencil. It is very important that you fill in the entire circle darkly and completely. If you change your response, erase as completely as possible. Incomplete marks or erasures may affect your score ETS USE ONLY Exam Exam SELECTED MEDIA EXAMS PT0 PT03 PT04 R W O OTHER EXAMS TOTAL Subscore (if applicable) Subscore (if applicable) R W O DO NOT WRITE IN THIS AREA

14 QUESTIONS PAGE 3 Be sure each mark is dark and completely fills the circle. If a question has only four answer options, do not mark option E QUESTIONS 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 / / / / / / / / / / / / / / / / / / QUESTIONS For Students Taking AP Computer Science Principles, AP Physics 1, or AP Physics 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 13 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 14 A B C D 016 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

15 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. STREET ADDRESS (include street number, street name, apartment number, etc.) CITY ZIP OR POSTAL CODE COUNTRY CODE V. SEX Female Male 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 W. WHICH LANGUAGE DO YOU 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 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 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 C C C C C C C C C C C C C D D D D D D D D D D D D D C C C C C C C C C D D D D D D D D D English and another language about the same 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 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 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 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 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 G G G G G G G G G G G G G H H H H H H H H H H H H H I I I I I I I I I I I I I G G G G G G G G G H H H H H H H H H I I I I I I I I I Please answer both questions about Hispanic origin and about race. For the following questions about your identity, 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 (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 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 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 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 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 K K K K K K K K K K K K K L L L L L L L L L L L L L M M M M M M M M M M M M M N N N N N N N N N N N N N O O O O O O O O O O O O O K K K K K K K K K L L L L L L L L L M M M M M M M M M N N N N N N N N N O O O O O O O O O a. Are you of Hispanic, Latino, or Spanish origin? No, not of Hispanic, Latino, or Spanish origin b. What is your race? American Indian or Alaska Native Asian (including Indian subcontinent and 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 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 P P P P P P P P P P P P P Q Q Q Q Q Q Q Q Q Q Q Q Q P P P P P P P P P Q Q Q Q Q Q Q Q Q Yes, Cuban Yes, Mexican Black or African American (including Africa and 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 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 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 R R R R R R R R R R R R R S S S S S S S S S S S S S T T T T T T T T T T T T T R R R R R R R R R S S S S S S S S S T T T T T T T T T Yes, Puerto Rican Yes, another Hispanic, Latino, or Spanish origin Native Hawaiian or other Pacific Islander White (including Middle Eastern 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 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 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 U U U U U U U U U V V V V V V V V V Y. PARENTAL EDUCATION LEVEL 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 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 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 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 W W W W W W W W W W W W W X X X X X X X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z Z Z Z Z W W W W W W W W W X X X X X X X X X Y Y Y Y Y Y Y Y Y Z Z Z Z Z Z Z Z Z In the first column, indicate the highest level of education of one parent/guardian, and indicate whether this is your mother/ female guardian or father/male guardian. Then, if applicable, indicate the highest level of education of your other parent/ guardian in the second column, and indicate whether this is your mother/female guardian or father/male guardian STATE MI NY VT Mother or female guardian AK HI MN OH WA Father or male guardian AL IA MO OK WI Grade school AR ID MS OR WV Some high school AZ IL MT PA WY High school diploma or equivalent CA CO IN KS NC ND RI SC Puerto Rico Vocational or trade school Some college CT KY NE SD AA Associate or two-year degree DC LA NH TN AE Bachelor s or four-year degree DE MA NJ TX AP Some graduate or professional school / / / / / / / / / / / / / / / / / / / / / / / / FL MD NM UT Other / / / / / / / Graduate or professional degree S. FOR STUDENTS OUTSIDE THE UNITED STATES ONLY GA ME NV VA If your address does not fit in the spaces provided in Item R, fill in as many circles as you can, then fill in the circle in Item S and print the remainder of your address in the spaces provided. T. STUDENT IDENTIFIER (Student ID Number) Address City State or Province Country ZIP or Postal Code U. ADDRESS By providing your address, you are granting the College Board permission to use your address in accordance with the policies in the Bulletin for AP Students and Parents.

16 Section I: Multiple-Choice Questions This is the multiple-choice section of the 017 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.)

17 AP Physics C: Mechanics Exam SECTION I: Multiple Choice 017 DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time 45 minutes Number of Questions 35 Percent of Total Score 50% Writing Instrument Pencil required Electronic Device Calculator allowed Instructions Section I of this exam contains 35 multiple-choice questions. For these questions, fill in only the circles for numbers 1 through 35 on your answer sheet. A table of information and lists of equations that may be helpful are in the booklet. Calculators, rulers and straightedges may be used in this section. Indicate all of your answers to the multiple-choice questions on the answer sheet. No credit will be given for anything written in this exam booklet, but you may use the booklet for notes or scratch work. After you have decided which of the suggested answers is best, completely fill in the corresponding circle on the answer sheet. Give only one answer to each question. If you change an answer, be sure that the previous mark is erased 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 4NBP4-S 80

18 Proton mass, Neutron mass, Electron mass, Avogadro s number, ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION m p m n m e CONSTANTS AND CONVERSION FACTORS kg kg kg 3 1 N mol Universal gas constant, R 8.31 J (mol K) 3 Boltzmann s constant, J K k B Electron charge magnitude, 19 e C 19 1 electron volt, 1 ev J 8 Speed of light, c m s Universal gravitational G Nm kg Acceleration due to gravity at Earth s surface, 11 constant, g 9.8 m s 7 1 unified atomic mass unit, 1 u kg 931 MeV c Planck s constant, h J s evs 5 3 hc J m evnm 1 Vacuum permittivity, e C Nm Coulomb s law constant, k 1 4pe Nm C Vacuum permeability, 7 m0 4p 10 (Tm) A 7 Magnetic constant, k m0 4p 110 (Tm) A atmosphere pressure, 1 atm N m Pa UNIT SYMBOLS meter, kilogram, second, ampere, kelvin, m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J watt, coulomb, volt, ohm, henry, W farad, F C tesla, T V degree Celsius, C W electron volt, ev H PREFIXES Factor Prefix Symbol 9 10 giga G 6 10 mega M 3 10 kilo k 10 centi c 3 10 milli m 6 10 micro m 9 10 nano n 1 10 pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q sinq cosq tanq The following assumptions are used in this exam. I. The frame of reference of any problem is inertial unless otherwise stated. II. The direction of current is the direction in which positive charges 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-

19 ADVANCED PLACEMENT PHYSICS C EQUATIONS à x Ãx0 at x 1 x x0 Ãx0t axt Ãx Ãx0 axx x0 F F a net m m dp F dt J Fdt Dp p mv F f m F N D E W Fdr K 1 mã P de dt P Fv DUg à a c r mgdh w r t r F t t a I I net I r dm mr x cm mx i m à rw L r p Iw K 1 Iw w w a i 0 t 1 q q0 w0t at i MECHANICS a = acceleration E = energy F = force f = frequency h = height I = rotational inertia J = impulse K = kinetic energy k = spring constant = length L = angular momentum m = mass P = power p = momentum r = radius or distance T = period t = time U = potential energy v = velocity or speed W = work done on a system x = position m = coefficient of friction q = angle t = torque w = angular speed a = angular acceleration f = phase angle F kdx s U 1 s k x D x x max cos( wt f T T p 1 w f s T p F U G G p p m k g Gm m r 1 Gm m r 1 ELECTRICITY AND MAGNETISM 1 qq 1 A = area FE 4pe 0 r B = magnetic field C = capacitance F E E d = distance q E = electric field e = emf Q E da F = force e 0 I = current J = current density dv Ex L = inductance dx D = length V Edr n = number of loops of wire per unit length N = number of charge carriers 1 q V 4pe i per unit volume 0 r i i P = power Q = charge 1 qq 1 UE qv q = point charge 4pe0 r R = resistance DV Q r = radius or distance t = time C U = potential or stored energy ke 0 A V = electric potential C d v = velocity or speed r = resistivity Cp Ci i F = flux k = dielectric constant 1 1 Cs i C F i M qv B dq I B d m I 0 dt U 1 1 m 0 Id r C QDV C DV db 4p r r R F A Id B B E rj s m0ni I Nevd A FB B da D I V df e R B E d dt R s Ri i 1 1 R R p i P IDV i di e L dt UL 1 LI -4-

20 ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle A bh Triangle A Circle 1 bh A pr C pr s rq Rectangular Solid V wh Cylinder V pr S pr pr Sphere 4 V pr 3 S 4pr 3 Right Triangle A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius s = arc length q = angle s r q d f d f du dx du dx d n 1 x nx n dx d e ax ax ae dx d 1 ln ax dx x d sinax acosax dx d cosax asinax dx n 1 n1 x dx x, n 1 n 1 1 e ax dx e ax a dx ln x a x a 1 cosaxdx sinax a 1 sin ax dx cos ax a a b c a sinq c b cosq c a tanq b q c b 90 a VECTOR PRODUCTS AB ABcosq A B ABsinq -5-

21 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 = 10m/ s in all problems. 1. A plane starts at rest on a straight runway. For the first 30 s, the plane s acceleration a is given as a function of time t by the equation a = bt, where b = 190 m s 4 and t is in seconds. What is the plane s speed at t = 30 s? (A) 10 m s (B) 30 m s (C) 100 m s (D) 150 m s (E) 300 m s Unauthorized copying or reuse of any part of this page is illegal. -6- GO ON TO THE NEXT PAGE.

22 . Student 1 is standing on a cart holding a small stone, while student is standing at rest on the ground, as shown in the figure above. The cart is moving at a constant speed v in the +x-direction, as indicated by the coordinate system shown. Student 1 drops the stone precisely when passing student. Which of the following best represents the path of the falling stone relative to student 1 and the path of the falling stone relative to student? (A) (B) (C) (D) (E) Student 1 Student 3. A particle of mass.0 kg is moving in the xy-plane at a constant speed of 0.80 m s in the +x-direction along the line y = 4 m. As the particle travels from x = -3 m to x = +3 m, the magnitude of its angular momentum with respect to the origin is (A) not constant (B) 0 (C) 4.8 kg m s (D) 6.4 kg m s (E) 8.0 kg m s 4. Suppose that a spherical star spinning at an initial angular velocity w suddenly collapses to half of its original radius without any loss of mass. Assume the star has uniform density before and after the collapse. What will the angular velocity of the star be after the collapse? (A) w 4 (B) w (C) w (D) w (E) 4w 5. Two identical, unlabeled boxes are transported to an orbiting space station. The astronauts know that one box is filled with a light sample of ants for an experiment, and the other is filled with heavy tools for repairs. How can the astronauts tell, without opening the boxes, which box has the tools? (A) Weigh each box on a spring scale. The box with the tools will have a higher reading. (B) Shake each box. The box with the tools will be harder to move back and forth. (C) Push each box. The box with the tools will travel farther before it stops. (D) Place each box on opposite sides of a balance. The box on the side that goes down lower will be the box with the tools. (E) Toss each box straight up. The box with the tools will go higher before coming back down. Unauthorized copying or reuse of any part of this page is illegal. -7- GO ON TO THE NEXT PAGE.

23 6. A block of mass M 1 is connected by a string to a sphere of mass M. The block is on a frictionless plane inclined at an angle of 30, as shown in the figure above. The string passes over a pulley of negligible mass and friction, and the sphere hangs freely. Which of the following is always true if the block is accelerating down the incline? (A) (B) (C) M 1 < M M 1 = M M 1 < M (sin 30 ) (D) ( ) (E) M 1 sin 30 < M M 1 (sin 30 ) > M 7. Two carts of equal mass are on a horizontal surface with negligible friction. Cart A is approaching cart B, which is at rest, as shown in Figure 1 above. Attached to cart B is a spring that is initially compressed. At the moment cart A collides with cart B, the spring is released and pushes on cart A, as shown in Figure above. Which of the following correctly states what happens to the kinetic energy and the momentum of the two-cart system as a result of the collision compared to those quantities before the collision? Magnitude of Kinetic energy Momentum (A) Increases (B) Increases (C) Increases (D) Stays the same (E) Stays the same Decreases Stays the same Increases Increases Stays the same 8. A ball of mass m is dropped from rest from a height h and collides elastically with the floor, rebounding to its original height. What is the magnitude of the average force applied by the floor on the ball during the time the ball is in contact with the floor? (A) Zero (B) mg (C) mg (D) 4mg (E) It cannot be determined without knowing the length of time that the ball is in contact with the floor. Unauthorized copying or reuse of any part of this page is illegal. -8- GO ON TO THE NEXT PAGE.

24 Questions 9-10 Particle A and particle B, each of mass M, move along the x-axis exerting a force on each other. The potential energy of the system of two particles associated with the force is given by the equation U = b r, where r is the distance between the two particles and b is a positive constant. At time t = 0, particle A is located at x = D with an initial speed of v 0 to the left, and particle B is at rest at the origin, as shown in the figure above. 9. At time t = T 1, particle A is observed to be traveling with speed v 0 3 to the left. The speed and direction of motion of particle B is (A) v 0 3 to the left (B) v 0 3 to the left (C) v 0 3 to the right (D) v 0 3 to the right (E) 5v 0 3 to the right 10. Which of the following equations could be used to find r MIN, the minimum distance between the masses as particle A approaches particle B? (A) b b Ê v 0 ˆ + Mv = + M Á Ë 4D 0 rmin b 1 b Ê v 0 ˆ (B) + Mv 0 = + M Á 4D r Ë MIN b 1 b 1 (C) + Mv 0 = + Mv 0 4D r MIN b 1 b (D) + Mv 0 = 4D r MIN b b (E) + Mv 0 = 4D r MIN 11. A kg object is released from rest from a height of 3 m above Earth s surface. How much kinetic energy does the object have when it reaches a height of 1 m? (A).5 J (B) 10 J (C) 0 J (D) 30 J (E) 40 J 1. A sphere of mass m hangs from two strings that each make an angle of 30 with the horizontal, as shown in the figure above. What is the tension T in one of the strings? (A) (B) (C) (D) (E) mg 6 mg 4 mg mg 3mg 13. A skier is traveling down a slope that is inclined 30 above the horizontal. The coefficient of kinetic friction between the skier and the slope is Which of the following best describes the acceleration of the skier? (A) It is zero. (B) It is about 4.0 m s. (C) It is about 9.0 m s. (D) It is about 10 m s. (E) It cannot be determined without knowing the mass of the skier. Unauthorized copying or reuse of any part of this page is illegal. -9- GO ON TO THE NEXT PAGE.

25 Questions A ball of mass.0 kg is thrown vertically upward from the top of a building. The ball s velocity v is given as a function of time t by the equation vt ( ) = R - St, where R = 5 m s and S = 10 m s. The positive direction is upward. 14. What is the ball s acceleration at time t = 1 s? (A) -10 m s (B) -5 m s (C) 0 (D) 5 m s (E) 10 m s 15. At what time does the ball reach its maximum height above the building? (A) 0. s (B) 0.4 s (C) 0.5 s (D) 1.0 s (E).0 s 16. If the ball reaches the ground at t =.0 s, what is the height of the building? (A) 5 m (B) 10 m (C) 15 m (D) 0 m (E) 30 m Unauthorized copying or reuse of any part of this page is illegal GO ON TO THE NEXT PAGE.

26 Questions A solid disk of mass M and radius R is freely rotating horizontally in a counterclockwise direction with angular speed ω about a vertical axis through its center with negligible friction. The rotational inertia of the disk is MR. A second identical disk is at rest and suspended above the first disk with the centers of the two disks aligned, as shown in the figure above. There is no contact between the disks. The second disk is dropped onto the first disk, and after a short time they rotate counterclockwise with the same angular speed ω f. 17. Which of the following properties of the two-disk system must be conserved between the time the second disk is dropped on the first disk and the time that the two disks begin rotating with the same speed? (A) Kinetic energy only (B) Angular momentum only (C) Both kinetic energy and angular momentum (D) Neither kinetic energy nor angular momentum (E) It cannot be determined without knowing the nature of the forces between the two disks. 18. The interval of time Dt is the elapsed time from the moment of first contact between the two disks until they are both spinning at the same angular velocity. Which of the following expressions gives the magnitude of the average torque that the first disk exerts on the second disk? (A) MR w f MR w f (B) D t MR w f (C) D t MR w f (D) D t (E) It cannot be determined without knowing the nature of the forces between the two disks. 19. The two disks are now shifted so that the axis of rotation goes through a point on the edge of the disks. The rotational inertia of the two-disk system is now (A) MR (B) 3MR (C) 4MR (D) 5MR (E) 10MR Unauthorized copying or reuse of any part of this page is illegal GO ON TO THE NEXT PAGE.

27 0. A student throws a metal sphere, which follows the path shown above. If air resistance is negligible, which of the following is a correct relationship between the magnitudes of the accelerations a K, a L, and a M at the three points shown? (A) (B) (C) (D) (E) a a = a = a K L M = a > a K L M a K = a M > al a > a = a K L M a > a > a K M L 1. A cannonball is shot from the top of a 30 m high hill at a velocity of 5 m s and at an angle of 40 above the horizontal and lands on the ground below. The speed of the cannonball at the top of its path is most nearly (A) 0 (B) 16 m s (C) 19 m s (D) 5 m s (E) 9 m s. A 1500 kg car is pushing a 4000 kg truck. The car and truck are accelerating at.0 m s. Assuming that the frictional force on the truck is negligible, what force is the truck exerting on the car? (A) 0 N (B) 3000 N (C) 5000 N (D) 8000 N (E) 11,000 N 3. The figure above shows the directions and relative magnitudes of all three forces that are acting on an object. Which of the following best shows the direction of the object s acceleration? (A) (B) (C) (D) (E) Unauthorized copying or reuse of any part of this page is illegal. -1- GO ON TO THE NEXT PAGE.

28 Questions The ratio of the speeds v v 1 is (A) (B) (C) (D) (E) 1 R R 1 R 1 R m m 1 m m 1 Two satellites of masses m 1 and m orbit a planet of mass M in circular orbits. The satellites travel in opposite directions with speeds v and v 1, as shown in the figure above. Their orbital radii are R and R 1, respectively. Assume that M >> m > m The magnitude of the angular momentum of the two-satellite system is best represented by (A) (B) (C) (D) (E) mv + m v 11 mv - m v 11 mvr + m v R 11 1 mvr - m v R 11 1 mv R + m v R If U 1 is the potential energy of the planet-satellite system containing the satellite of mass m 1 and U is the potential energy of the planet-satellite system containing the satellite of mass m, which of the following expressions best represents the ratio U 1 U? (A) (B) (C) (D) (E) mr 1 1 mr mr mr 1 1 mr 1 mr 1 mr 1 mr 1 mr 1 mr 1 Unauthorized copying or reuse of any part of this page is illegal GO ON TO THE NEXT PAGE.

29 7. The graph above shows a variable force F that acts on an object as it moves along a straight line as a function of time t. What is the change in momentum of the object from t = s to t = 4 s? (A) 1 kg m s (B) kgm s (C) 4 kg m s (D) 6 kg m s (E) 8 kgm s 8. Blocks A, B, and C are aligned along a straight line on a horizontal frictionless surface. The masses of the blocks are M, M, and 3M, respectively. Block A is initially moving to the right along the same line at a speed v, as shown in the figure above. Blocks B and C are initially at rest. Block A collides with and sticks to block B. The two blocks then collide with and stick to block C. What is the speed of block C after the collisions? (A) 0 (B) v 6 (C) v 3 (D) v (E) 6v Unauthorized copying or reuse of any part of this page is illegal GO ON TO THE NEXT PAGE.

30 Questions The graph above shows a conservative force F x as a function of position x acting on an object in a closed system. If this is the only force acting on the object, what happens to the potential energy of the system as the object moves from 0 m to 0.10 m? (A) It increases only. (B) It decreases only. (C) It increases and then decreases. (D) It decreases and then increases. (E) It does not change. 30. How does the work required to accelerate a particle from 10 m s to 0 m s compare to that required to accelerate it from 0 m s to 30 m s? (A) It is less. (B) It is the same. (C) It is greater. (D) It cannot be determined without knowing the magnitude of the force exerted on the particle. (E) It cannot be determined without knowing the mass of the particle. A particle of mass m moves counterclockwise around a horizontal circle of radius r, as shown above. The angular speed of the particle is given as a function of time t by w( t ) = bt, where b is a positive constant and t Which of the following best describes the acceleration vector for the particle at the moment shown in the diagram? (A) It is directed toward the left. (B) It is directed toward the bottom of the page. (C) It is directed toward the top of the page. (D) It has components directed toward the right and toward the bottom of the page. (E) It has components directed toward the left and toward the bottom of the page. 3. What is the magnitude of the angular momentum of the particle about the center of the circle as a function of time? (A) (B) (C) (D) (E) mbt r mbrt mbr t mb rt mb r t Unauthorized copying or reuse of any part of this page is illegal GO ON TO THE NEXT PAGE.

31 Questions An object is initially hanging in equilibrium from a vertical spring. The object is pulled down 15 cm from its equilibrium position, as illustrated above, and released at time t = 0. The object then oscillates with a period of.0 s. Let x = 0 be the equilibrium position and let the positive direction be upward. 33. What is the position of the object at t = 3.0 s? (A) 15 cm (B) 7.5 cm (C) 0 cm (D) -7.5 cm (E) -15 cm 34. What is the total distance traveled by the object during the first.0 s of its motion? (A) 90 cm (B) 75 cm (C) 60 cm (D) 45 cm (E) 30 cm 35. Which of the following statements is true of the magnitude of the acceleration of the object at time t = 1.0 s? (A) It is equal to zero. (B) It is equal to g. (C) It has its minimum value that is not zero. (D) It has its maximum value. (E) It has a value between zero and its maximum value. Unauthorized copying or reuse of any part of this page is illegal GO ON TO THE NEXT PAGE.

32 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 -17-

33 Section II: Free-Response Questions This is the free-response section of the 017 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.)

34 AP Physics C: Mechanics Exam SECTION II: Free Response 017 DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time 45 minutes Number of Questions 3 Percent of Total Score 50% Writing Instrument Either pencil or pen with black or dark blue ink Electronic Device Calculator allowed Weight The questions are weighted equally. Instructions The questions for Section II are printed in this booklet. You may use any blank space in the booklet for scratch work, but you must write your answers in the spaces provided for each answer. A table of information and lists of equations that may be helpful are in the booklet. Calculators, rulers, and straightedges may be used in this section. All final numerical answers should include appropriate units. Credit for your work depends on demonstrating that you know which physical principles would be appropriate to apply in a particular situation. Therefore, you should show your work for each part in the space provided after that part. If you need more space, be sure to clearly indicate where you continue your work. Credit will be awarded only for work that is clearly designated as the solution to a specific part of a question. Credit also depends on the quality of your solutions and explanations, so you should show your work. Write clearly and legibly. Cross out any errors you make; erased or crossed-out work will not be scored. You may lose credit for incorrect work that is not crossed out. Manage your time carefully. You may proceed freely from one question to the next. You may review your responses if you finish before the end of the exam is announced. Form I Form Code 4NBP4-S 80

35 Proton mass, Neutron mass, Electron mass, Avogadro s number, ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION m p m n m e CONSTANTS AND CONVERSION FACTORS kg kg kg 3 1 N mol Universal gas constant, R 8.31 J (mol K) 3 Boltzmann s constant, J K k B Electron charge magnitude, 19 e C 19 1 electron volt, 1 ev J 8 Speed of light, c m s Universal gravitational G Nm kg Acceleration due to gravity at Earth s surface, 11 constant, g 9.8 m s 7 1 unified atomic mass unit, 1 u kg 931 MeV c Planck s constant, h J s evs 5 3 hc J m evnm 1 Vacuum permittivity, e C Nm Coulomb s law constant, k 1 4pe Nm C Vacuum permeability, 7 m0 4p 10 (Tm) A 7 Magnetic constant, k m0 4p 110 (Tm) A atmosphere pressure, 1 atm N m Pa UNIT SYMBOLS meter, kilogram, second, ampere, kelvin, m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J watt, coulomb, volt, ohm, henry, W farad, F C tesla, T V degree Celsius, C W electron volt, ev H PREFIXES Factor Prefix Symbol 9 10 giga G 6 10 mega M 3 10 kilo k 10 centi c 3 10 milli m 6 10 micro m 9 10 nano n 1 10 pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q sinq cosq tanq The following assumptions are used in this exam. I. The frame of reference of any problem is inertial unless otherwise stated. II. The direction of current is the direction in which positive charges 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-

36 ADVANCED PLACEMENT PHYSICS C EQUATIONS à x Ãx0 at x 1 x x0 Ãx0t axt Ãx Ãx0 axx x0 F F a net m m dp F dt J Fdt Dp p mv F f m F N D E W Fdr K 1 mã P de dt P Fv DUg à a c r mgdh w r t r F t t a I I net I r dm mr x cm mx i m à rw L r p Iw K 1 Iw w w a i 0 t 1 q q0 w0t at i MECHANICS a = acceleration E = energy F = force f = frequency h = height I = rotational inertia J = impulse K = kinetic energy k = spring constant = length L = angular momentum m = mass P = power p = momentum r = radius or distance T = period t = time U = potential energy v = velocity or speed W = work done on a system x = position m = coefficient of friction q = angle t = torque w = angular speed a = angular acceleration f = phase angle F kdx s U 1 s k x D x x max cos( wt f T T p 1 w f s T p F U G G p p m k g Gm m r 1 Gm m r 1 ELECTRICITY AND MAGNETISM 1 qq 1 A = area FE 4pe 0 r B = magnetic field C = capacitance F E E d = distance q E = electric field e = emf Q E da F = force e 0 I = current J = current density dv Ex L = inductance dx D = length V Edr n = number of loops of wire per unit length N = number of charge carriers 1 q V 4pe i per unit volume 0 r i i P = power Q = charge 1 qq 1 UE qv q = point charge 4pe0 r R = resistance DV Q r = radius or distance t = time C U = potential or stored energy ke 0 A V = electric potential C d v = velocity or speed r = resistivity Cp Ci i F = flux k = dielectric constant 1 1 Cs i C F i M qv B dq I B d m I 0 dt U 1 1 m 0 Id r C QDV C DV db 4p r r R F A Id B B E rj s m0ni I Nevd A FB B da D I V df e R B E d dt R s Ri i 1 1 R R p i P IDV i di e L dt UL 1 LI -4-

37 ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle A bh Triangle A Circle 1 bh A pr C pr s rq Rectangular Solid V wh Cylinder V pr S pr pr Sphere 4 V pr 3 S 4pr 3 Right Triangle A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius s = arc length q = angle s r q d f d f du dx du dx d n 1 x nx n dx d e ax ax ae dx d 1 ln ax dx x d sinax acosax dx d cosax asinax dx n 1 n1 x dx x, n 1 n 1 1 e ax dx e ax a dx ln x a x a 1 cosaxdx sinax a 1 sin ax dx cos ax a a b c a sinq c b cosq c a tanq b q c b 90 a VECTOR PRODUCTS AB ABcosq A B ABsinq -5-

38 THIS PAGE MAY BE USED FOR SCRATCH WORK. -6- GO ON TO THE NEXT PAGE.

39 PHYSICS C: MECHANICS SECTION II Time 45 minutes 3 Questions 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. 1. A spring of negligible mass and with a spring constant of 50 N m is hung vertically, as shown above in the figure on the left. A block of mass 1.0 kg is attached to the spring and slowly lowered a distance x 0 until it hangs at rest at the equilibrium position, as shown above in the figure on the right. (a) On the dot below that represents the block, draw and label the forces (not components) that act on the block when it is at the equilibrium position shown. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. (b) Calculate the distance x 0 that the spring is stretched from its original length to the equilibrium position. Question 1 continues on the next pages. Unauthorized copying or reuse of any part of this page is illegal. -7- GO ON TO THE NEXT PAGE.

40 While the 1.0 kg block is in equilibrium, a 0.0 kg ball of clay is launched with speed v 0 vertically from the ground 1.0 meter below the hanging block. The clay has speed v 1 = 5.0 m s when it collides with the block. (c) Calculate the speed v 0. Upon impact, the clay sticks to the 1.0 kg block. (d) i. Calculate the speed of the block immediately after the collision. ii. Calculate the kinetic energy lost in the collision. Unauthorized copying or reuse of any part of this page is illegal. -8- GO ON TO THE NEXT PAGE.

41 iii. Determine the period of oscillation for the block-clay-spring system. (e) When the oscillating block-clay-spring system reaches its maximum speed after the collision, will the spring be stretched from its original length by a distance greater than, less than, or equal to x 0? Greater than Less than Equal to Justify your answer. (f) The collision is repeated using a rubber ball with the same mass as the ball of clay. The rubber ball is launched vertically with the same speed v 0. The collision between the rubber ball and the block is elastic. Will the speed of the block immediately after colliding with the rubber ball be greater than, less than, or equal to the speed of the block you calculated in part (d)i? Greater than Less than Equal to Justify your answer. Unauthorized copying or reuse of any part of this page is illegal. -9- GO ON TO THE NEXT PAGE.

42 THIS PAGE MAY BE USED FOR SCRATCH WORK GO ON TO THE NEXT PAGE.

43 . A cart of mass M is on a level, horizontal track. The cart is attached to one end of an ideal spring, and the other end of the spring is attached to a vertical support. The spring has a spring constant k. The cart is pulled to the right, stretching the spring a distance d, as shown above, and released from rest at time t = 0. The cart-spring system begins to oscillate, and the position x of the cart as a function of time t is given by the equation xt () = d cos ( ωt ), where x is in meters, ω is in rad s, and t is in seconds. Assume the mass of the cart s wheels to be negligible. (a) Derive an equation for the velocity of the cart v as a function of time t. (b) On the axes below, sketch a graph of the velocity v of the cart as a function of time t for two complete oscillations. On the graph, T represents the time for one complete oscillation. Explicitly label asymptotes, maxima, or minima with algebraic expressions, as appropriate. (c) Express all answers in part (c) in terms of w, t, M, d, k, and physical constants, as appropriate. i. Determine an expression for the kinetic energy K of the system as a function of time t. ii. Determine an expression for the potential energy U of the system as a function of time t. iii. Using the equations from parts (c)i and (c)ii, show that the rate of change of the total energy of the system de dt is zero. Question continues on the next pages. Unauthorized copying or reuse of any part of this page is illegal GO ON TO THE NEXT PAGE.

44 Two springs identical to the spring above are attached to each side of the cart of unknown mass M, as shown in Figure 1 above. The cart is on a level, horizontal track of negligible friction. A piece of clay is added to the top of the cart so that it will stick to the cart. The cart is displaced to the left a distance d and released from rest, as shown in Figure above. The period of oscillation is recorded. This procedure is repeated for several different pieces of clay of different masses. In each trial, the cart is displaced the same distance d. The data are shown below on the linear graph of T as a function of m C, where T is the period of oscillation and m C represents the mass of the clay. (d) From the graph, determine the following. i. k, the spring constant of each spring Unauthorized copying or reuse of any part of this page is illegal. -1- GO ON TO THE NEXT PAGE.