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! ! ! ! ! Physics B Practice Exam ! From the 201 3 Administration Rev ised April 201 4 ! ! ! This Practice 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 s etting only. To maintain the security of this exam, teachers should collect all materials after their administration and keep them in a secure location . Exams may not be posted on school or personal websites, nor electronically redistributed for any reason. 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 ma y 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 .

Contents Exam Instructions Student Answer Sheet for the Multiple -Choi ce Section Secti on I: Multiple -Choice Questions Section II: Free- Response Questions Multiple -Choice Answer Key Free -Response Scoring Guidelines Scoring Worksheet Note: This publication shows the page numbers that appeared in the 2012!13 AP Ex a m I n st r u c ti o n s book and in the actual exam. This publication was not repaginated to begin with page 1. © 2013 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: www.collegeboard.com/inquiry/cbpermit.html.

! ! ! ! ! B ! Exam Instructions The followin g c ontains instructions taken from the 2012!13 AP Ex a m I n stru c tio n s book.

202 AP® Physics B Exam Regularly Scheduled Exam Date: Monday a!ernoon, May 13, 2013 Late-Testing Exam Date: Friday morning, May 24, 2013 Section I: At a Glance Total Time: 1 hour, 30 minutes Number of Questions: 70 Percent of Total Score: 50% Writing Instrument: Pencil required Electronic Device: None allowed Section I: Multiple Choice Booklet Instructions Section I of this exam contains 70 multiple-choice questions. Fill in only the circles for numbers 1 through 70 on your answer sheet. A table of information that may be helpful is in the booklet. 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. A!er you have decided which of the suggested answers is best, completely "ll 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. Use your time e#ectively, 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. Section II: At a Glance Total Time: 1 hour, 30 minutes Number of Questions: 7* Percent of Total Score: 50% Writing Instrument: Either pencil or pen with black or dark blue ink Electronic Device: Calculator allowed Percent of Section II Score: See breakdown on test book cover *!e number of questions may vary slightly depending on the form of the exam. Section II: F ree Response Booklet Instructions $e question s 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 "nal 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. $erefore, you should show your work for each part in the space provided a!er 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 speci"c 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 "nish before the end of the exam is announced.

What Proctors Need to Bring to This Exam • • • • • • • • Exam packets Answer sheets AP Student Packs 2012-13 AP Coordinator’s Manual $is book — AP Exam Instructions School Code and Home-School/Self- Study Codes Extra calculators Extra rulers or straightedges • • • • • • • Pencil sharpener Extra No. 2 pencils with erasers Extra pens with black or dark blue ink Extra paper Stapler Wa t c h Signs for the door to the testing room “Exam in Progress” “Cell phones are prohibited in the testing room” – – Students are p ermitted to use four-function, scienti"c, or graphing calculators to answer the questions in Section II of the AP Physics B Exam. Students are not allowed to use calculators in Section I. 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 42 of the 2012-13 AP Coordinator’s Manual . See pages 39–42 of the 2012-13 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 40 of the 2012-13 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 a!er the exam. Students with Hewlett-Packard 48–50 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. Rulers and straightedges may be used for the entire exam. SECTION I: Multiple Choice ! Do not begin the exam instructions below until you have completed the appropriate General In structions for your group. $is exam includes survey questions. $e time allowed for the survey questions is in addition to the actual test-taking time. Make sure you begin the exam at the designated time. 203 AP Exam Instructions PHYSICS B

If you are giving the regularly scheduled exam, say: It is Monday afternoon, May 13, and you will be taking the AP Physics B Exam. If you are giving the alternate exam for late testing, say: It is Friday morning, May 24, and you will be taking the AP Physics B 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 2012-13 Bulletin for AP Students and Parents . 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. . . . 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 dark blue box near the top right-hand 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. $ey should not try to remove the label; their exam will 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 and read it completely. Look up when you have finished. . . . Are there any questions? . . . Section I is the multiple-choice portion of the exam. You may never discuss these specific multiple-choice questions at any time in any form with anyone, including your teacher and other students. If you disclose these questions through any means, your AP Exam score will be canceled. Are there any questions? . . . You must complete the answer sheet using a No. 2 pencil only. Mark all of your responses beginning on page 2 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 and straightedges may be used for the entire exam, but calculators are not allowed for Section I of the exam. Please put all of your calculators under your chair. Are there any questions? . . . You have 1 hour and 30 minutes for this section. Open your Section I booklet and begin. 204 Physics B

   Note Start Time here . Note Stop Time here . Check that students are mar king their answers in pencil on their answer sheets, and that they are not looking at their shrinkwrapped Section II booklets. A!er 1 hour and 30 minutes, say: Stop working and turn to the last page of your booklet. . . . You have 2 minutes to answer Questions 101–106. 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. To help you and your proctors make sure students are not working on the exam questions, the two pages with the survey questions are identi"ed with a large S on the upper corner of each page. Give students 2 minutes to answer the survey questions. $en 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. I will now collect your answer sheet. Collect an answer sheet from each student. Check that each answer sheet has an AP number label and an AP Exam label. $en say: Now you must seal your exam booklet. 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. . . . Collect a Section I booklet from each student. Check that each student has signed the front cover of the sealed Section I booklet. $ere is a 10-minute break between Sections I and II. When all Section I materials have been collected and accounted for and you are ready for the break, say: Please listen carefully to these instructions before we take a 10-minute break. Everything you placed under your chair at the beginning of the exam must stay there. Leave your shrinkwrapped Section II packet on your desk during the break. You are not allowed to consult teachers, other students, or textbooks about the exam during the break. You may not make phone calls, send text messages, check email, use a social networking site, or access any electronic or communication device. Remember, you are not allowed to discuss the multiple-choice section of this exam. If you do not follow these rules, your score could be canceled. Are there any questions? . . . You may begin your break. Testing will resume at .    SECTION II: Free Response A!er the break, 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. . . . 205 AP Exam Instructions PHYSICS B

Read the bulleted statements on the front cover of the exam booklet. Look up when you have finished. . . . Now place an AP number label 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 your pen, 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 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 2, 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 4. . . . Are there any questions? . . . I need to collect the Student Pack from anyone who will be taking another AP Exam. You may keep it only if you are not taking any other AP Exams this year. If you have no other AP Exams to take, place your Student Pack under your chair now. . . . While Student Packs are being collected, 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. $en say: Are there any questions? . . . Calculators may be used for Section II. You may get your calculators from under your chair and place them on your desk. . . . You have 1 hour and 30 minutes to complete Section II. You are responsible for pacing yourself, and you may proceed freely from one question to the next. You must write your answers in the exam booklet using a pen or a No. 2 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 piece of paper you use, be sure to write only your AP number and the number of the question you are working on. Do not write your name. Are there any questions? . . . You may begin. 206 Physics B

   Note Start Time here . Note Stop Time here . Check that students are writing their answers in their exam booklets. You should also make sure that Hewlett- Packard calculators’ infrared ports are not facing each other and that students are not sharing calculators. A!er 1 hour and 20 minutes, say: There are 10 minutes remaining. A!er 10 minutes, say: Stop working and close your exam booklet. Place it on your desk, face up. . . . If any students used extra paper for the free-response section, have those students staple the extra sheet/s to the "rst page corresponding to that question in their exam booklets. $en 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: $e student placed an AP number label on the shaded box, and printed his or her initials and today’s date. Exam booklet back cover: $e student completed the “Important Identi"cation Information” area. When all exam materials have been collected and accounted for, return to students 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 these specific free-response questions with anyone unless they are released on the College Board website in about two days. Your AP score results will be delivered online in July. If you are giving the alternate exam for late testing, say: None of the questions in this exam may ever be discussed or shared in any way at any time. Your AP score results will be delivered online in July. If any students completed the AP number card at the beginning of this exam, 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. $en say: You are now dismissed. All exam materials should be put in secure storage until they are returned to the AP Program a!er your school’s last administration. 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 2012-13 AP Coordinator’s Manual . Check your list of students who are eligible for fee reductions and "ll in the appropriate circle on their registration answer sheets. • • 207 AP Exam Instructions PHYSICS B

! ! ! ! ! B ! Student Answer Sheet for the Multiple -Choice Section Use this se ction to capture student responses. (Note that the following answer sheet is a sample, and may differ from one used in an actual exam.)









! ! ! ! ! B ! Section I: Multiple -Choice Questions This is the multiple -choice section of the 201 3 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 B Exam 2013 SECTION I: Multiple Choice DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time1 hour, 30 minutes Number of Questions70 Percent of Total Score50% Writing InstrumentPencil required Electronic DeviceNone allowed Instructions Section I of this exam contains 70 multiple -choice questions .Fill in only the circles for numbers 1 through 70 on your answer sheet .Atableofinformationthatmaybehelpfulis in the booklet .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 4JBP4-S 78

-2- TABLE OF INFORMATION DEVELOPED FOR 2012 CONST ANT S AND C ON VERSION FA CTORS Proton mass , Neutron mass , Electron ma ss, Avogadro’s nu mber , Universal gas constant , Boltzmann’s constant , Electron charge magnitude , 1 electron vo lt, Speed of light , Universal gravitational constant , Acce lera tion du e to gravity at Earth’s surface, 1 unified atom ic mass unit , Planck’s constant , Vacuum pe rm ittivity , Coulomb’s law constant , Vacuum pe rm eability , Magnetic constant , 1 atmosphere pressure , UNIT SYMBOLS meter, m kilogram, kg second, s ampere, A kelvin, K mole, mol hertz, Hz newton, N pascal, Pa joule, J watt, W coulomb, C volt, V ohm, henry, H farad, F tesla, T degree Celsi us, electron-volt, eV PREFIXES Factor Prefix Symbol giga G mega M kilo k centi c milli m micro nano n pico p VALUES O F TRIGO NO METRIC F UNCTIONS FO R COMM ON ANGLE S The followi ng conventi ons are used in this exam. I. Unless otherwise stated, the frame of reference of any pr ob lem is assumed to be inertial. II. The direction of any electric current is the direction of flow of posit ive charge (conventional current). III. For any isola ted electric charge, the elec tric potential is defined as zero at an infinite di stance from the charge. IV. For mechanics and thermodynamics equations, W represents the w ork done on a system.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -3- PHYSICS B SECTI ON I Time — 90 minutes 70 Questions Directions: E ach of the questions or in complete statements below is followed by five suggested an sw ers or com pletions. Select the one that is best in each cas e and then fill in the corresponding circle on the an sw er she et. Note: To simplify calculations, you may use in all problems. 1. Thr ee distinct fo rces are applied to an object, but the object remains stationary. Which of the following must be cor rect? (A) The fo rce s have the same magnitude. (B) The for ces have the same di rection. (C) The for ces are perpendicular to eac h other. (D) The vector sum of the for ces is z ero. (E) The sum of the magnitudes of the for ces is zero. 2. Which of the following is a true statement about the conservation of lin ear momentum? (A) It i s con served only when no net external force acts on the system under consideration. (B) It i s conserved only when the center of mass of a system is at rest. (C) It i s con served only in collisions bet we en ma croscopic objects. (D) It i s con served only in two-body collisions. (E) It i s conserved only in one-dimensional and two-dimensional motion. 3. A person of m ass 60 kg sliding along le ve l ice at a speed of 3.0 m/s collides with a second person who is initially at rest. Assume that friction is negli- gible. If the two people hold onto eac h other and their common final speed after co llid ing is 2.0 m/s, the m ass of the second person is (A) 10 kg (B) 30 kg (C) 40 kg (D) 80 kg (E) 90 kg 4. An automobile traveling on a straight, lev el road has an initial speed when the brakes are applied. In coming to rest with a constant acceleration, it travels a distance x. How far would the automobile travel in co mi ng to rest if it had the same acceleration but an initial speed ? (A) (B) (C) x (D) 2 x (E) 4 x

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -4- Questions 5-6 An isolated, hollow aluminum sphere is positively charged. A cross section through the center of the sphere is shown above. 5. The magnitude of the electric field is greatest at point (A) A (B) B (C) C (D) D (E) E 6. The direction of the electric field is correctly indicated in which of the following? I. To the left at point A II. To the righ t at point D III. To the righ t at point E (A) I on ly (B) II only (C) III only (D) I and III (E) II and III 7. The four ch arged part icles shown abo ve are he ld fixed at the co rners of a square. The el ectric field at point P, the center of the square, is directed (A) toward the left (B) toward the right (C) out of the plane of the pa ge (D) toward the bottom of the p age (E) toward the top of the pag e 8. How mu ch curr en t flows th rou gh a 5 resist or that is dissipating heat at a rate of 500 J /s? (A) 0 .01 A (B) 0.1 A (C) 1 A (D) 10 A (E) 100 A 9. A n obj ect begins at po sition x = 0 and moves one-dimensionally along the x-axis with a velocity u expressed as a function of time t ac cording to the graph above. At what time does the object pass through x = 0 again? (A) Between 10 s and 20 s (B) Between 20 s and 30 s (C) At 30 s exactly (D) Between 30 s and 40 s (E) After 40 s

10. A car with speed Unauthorized copying or reuse of any part of this page is illegal. and an identical car with speed both travel the sa me circular section of an unbanke d road. If the f rictional force required to keep the faster car on the road without skidding is F, then th e frictional fo rce required to keep the slower car o n the road wit hout ski dding is (A) 4 F (B) 2 F (C) F (D) (E) 11 . A planet with half Earth’s mass and half Earth’s radius is discovered. W hat would an astronaut who weighs 800 N on Ear th weigh on th e planet? (A) 1 00 N (B) 2 00 N (C) 4 00 N (D) 8 00 N (E) 16 00 N 12 . Two tuni ng fo rks with wh ich of the fol lowing pairs of frequencies will produce the greatest frequency of beats when sounded toge ther? (A) 250 an d 256 Hz (B) 300 an d 303 Hz (C) 634 an d 639 Hz (D) 763 an d 764 Hz (E) 142 0 and 1422 Hz 13 . The principle of superposi tion states that (A) every po int on a wave fron t may be co nsidered to behave li ke a point sou rce of waves (B) the width of a single-source diffraction pattern depends on the rat io of the wavelength to the size of the source (C) transverse wa ves can be polarized, but longit udinal waves cannot (D) as a w ave mo ve s from o ne medium to another, the wave speed changes (E) the displace ment of the medium at a point where waves meet is the sum of the disp lace ment s of the in div idua l waves 14 . A small metal sphere X is cha rged by los ing 500 electrons. An identical metal sphere Y is charged by ga ining 1000 el ectrons. The two spheres are first put in c ont act with each other and then separated. If is the charge on an electron, what is the charge on each sphere after separation? Sphere X Sphere Y (A) (B) (C) (D) (E) 15 . Two long , parallel, straight wires in the plane of the page each carry a cu rrent I to the right, as shown above . Points and are in t he plane of the page, w ith be ing mi dw ay be tw een the wires. Which of the follow ing is true of the net magnetic fie ld at the two points that result from the two currents? (A) Directed out of page Directed into page (B) Directed out of page Directed out of page (C) Has magnitude zero Directed into page (D) Has magnitu de zer o Directed out of page (E) Direc ted into page Direc ted into page

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -6- Questions 16-18 A particle with a charge is located a distance D from a particle with a charge , as sho wn in th e figure above . 16 . Which of the following best describes the location of a point , other than at in finity, at whi ch the net electr ic field crea ted by the two charge s is equal to zero? (A) In region I (B) In region II, closer to (C) In region II, midway bet ween the charges (D) In region II, closer to (E) In region III 17 . In which of the regions is there a locati on, other than at infinity, at which the electr ic potential is zero? (A) Region I on ly (B) Region II on ly (C) Region III only (D) Region I and region II (E) Region II and region III 18 . How much work must be done by an ex ternal force to move the particle with charge from rest at the position shown to rest at a distance of 2D from the oth er particl e? (A) (B) (C) (D) (E) 19 . If the charge of each of two particles is doubled and the separa tion between them is also doubled, the force betw een the two particl es is (A) quadrupled (B) doubled (C) th e sa me as before (D) halved (E) quartered 20 . A student ho lds a large concave mirror of focal length 1.0 m that faces a t eacher. Which of the followi ng describes the t eacher’s image as the student approaches the teacher from a distance of 2.0 m to a di stance of 0.5 m? (A) It c ontinuo usl y incr eases in size . (B) It continuously dec reas es in size. (C) It is first upr ight, the n it is upside down . (D) It is first upside down, th en it is upr igh t. (E) It i s a lwa ys sm aller than the teac her. 21 . A ray of ligh t has a wavelength of 800 nm in air. The light ray enters a material in which its wavelength is 600 nm. Assuming the index of refraction for air is 1.00, the index of re fraction of the material is most nea rly (A) 0.75 (B) 1.00 (C) 1.25 (D) 1.33 (E) 1.50 22 . A student th rows a rock h orizontally fr om the edge of a cliff that is 20 m high. Th e rock has an initial speed of . If air resistance is negligible, the distance fr om the base o f the cliff to where the rock hits the l evel ground b elow the cliff is most nearly (A) 5 m (B) 10 m (C) 20 m (D) 40 m (E) 200 m

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -7- 23. A block moving to t he right on a level surface with friction is pulled b y an increasing horizontal force also directed to the right. As the applied force increases, which of the following i s true of the normal force and the frictional force on the block? Normal Forc e Frictional Fo rce (A) Increases Increases (B) Increases Remains constant (C) Remains constant Increases (D) Remains constant Decreases (E) Remains constant Remains constant 24. The figures below indicat e forces actin g on a rod in different situations. The lengths of th e force vectors are proporti onal to the magnitu de s of the forces. In which situation is the rod in both translational and rotationa l equilibrium? (A) (B) (B) (C) (C) (D) (D) (E) (E) 25 . An object is in simple harmonic motion. Of the following qu antities relate d to the object, which set of three can have maximum magnitudes at the same instant of time? I. Disp lacement II. Velocity III. Acceleration IV. Kinetic ener gy V. Potential energy (A) I, II, and III (B) I, II, and IV (C) I, III, and V (D) II, III, and IV (E) II, III, and V 26 . A solid object of mass m is suspended vertically from a spring balance. The spring balance reads W when the object is in air. When the object is submerged in water while still attached to the balance, the reading on the balance is (A) always exact ly W (B) always grea ter than W (C) greater than W on ly if the density of the object is greater than the density of water (D) always less than W (E) less than W only if the density of the ob ject is greater than the density of water 27 . A f luid flows throu gh a pi pe of r adiu s r at a speed for a time t. The volume of fluid that flows past a point in the pipe duri ng this time is equal to (A) (B) (C) (D) (E)

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -8- 28 . A particular atomic s ystem has e nergy stat es as indicated in the energy-level diagram a bove. Such a system could, under the pr oper con ditions, abs orb an y of the follow ing amou nts of ene rgy wi thout being i onized EXCEPT (A) 2 eV (B) 4 eV (C) 6 eV (D) 8 eV (E) 10 eV 29 . A nuclear reactor uses uranium 235 t o produce energy. What is the order of magnitude of the energy equivalent of of uranium 235 ? (A) (B) (C) (D) (E) Questions 30-31 The pendulum illustrated above has a length of 2 m and a bob of mass 0.04 kg. It is held at an angle , as shown, where . 30 . If the pendu lum is released from rest, the maxim um speed the bob a ttains is most nearly (A) (B) (C) (D) (E) 31. The frequency of os cillation is most nearly (A) (B) (C) (D) (E)

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -9- 32. An obj ect of m ass m att ached to a spring with co nsta nt k o sci llates with amplitude A. Ass uming air r esi stance and the m ass of the spring to be negligibl e, which of the foll ow ing chang es alone wo uld cause the pe riod of this o scillation to increase? I. I nc reasin g m II. I ncreasi ng A III. Us ing a sp ring with g reate r k (A ) I only (B) II only (C) I or III only (D) II or III only (E) I , II, or III 33. Whi ch of th e following is a corr ect unit of measu reme nt for torque? (A) Joule/seco nd (B) Me ter/sec ond (C) New ton/meter (D) (E) 34. E ach of the following nuclei has b een s tripp ed of all el ectrons and pl ace d the same dist an ce from an alph a par ticle. Wh ich nuc leu s e xerts the strong est electrostatic fo rce on the alp ha particle? (A) (B) (C) (D) (E) 35. T he su ccess of the Einstei n photoel ect ric eff ect equation, , giv es strong support to wh ich of the foll ow ing models? (A) Rut he rford mo de l of th e atom (B) Pa rticle mo de l of light (C) Wa ve mode l of light (D) Pa rticle mo de l of the elec tron (E) Wa ve mo de l of t he el ectron 36. A b eam of whi ch of th e following wi ll p roduc e the wi des t diffr action pattern (i.e., adj ace nt mini ma will be the farth est apar t) if al l the particles have the same sp eed and p ass thro ugh the same slit? (A) El ectrons (B) Protons (C) Hydrogen atoms (D) He lium nu cle i (E) None of t he above; pa rticl es do not exhibit diffr action. 37. A gas undergoes an expans ion in w hich 400 J of en ergy is added to the gas by h eat ing. Th e int ernal energy of the g as c hang es from 700 J to 800 J. The work done by the gas is (A) 1,900 J (B) 1,100 J (C) 500 J (D) 300 J (E) 100 J 38. A metal cup that is left outdoors undergo es a temperatu re differen ce bet ween nightti me a nd daytime of . As the cup’s temperature increas es, which of th e following sta tem ents about the inner and outer circumferen ces of the cup is true? (A) The out er circumference will rem ain the same , but the inner ci rcumferen ce wi ll decrease. (B) The out er circumference will incr ease , but the inner ci rcumferen ce will remain t he same . (C) The out er circumference will incr ease, but the inner circumference will decrease. (D) Both the outer and the inner ci rcumf erence s will incr ease . (E) Nothing can be determined ab out the inn er or outer ci rcumferen ces w ith out kn ow ing their original v alues. 39. In a radio active deca y, a particle is emit ted from the nucleus of an atom and the atom’s atomic num be r incr eases by o ne . T he em itted part icl e coul d be which of the follow ing ? (A) A neutron (B) A proton (C) A gamma ray (D) An alpha particle (h elium nucleus) (E) A negative b eta particle ( elect ron )

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -10- 40. In t he c ircuit represe nted ab ove, the current in the 1 res istor is 4 A. Wh at is termin al voltage V of the battery? (A) 6 V (B) 12 V (C) 18 V (D) 19 V (E ) 30 V 41. A 100-turn wi re coil has a resista nce o f and a cro ss-sectional area of . The coil is placed in a magnetic field dir ecte d p arallel to the ax is of the coil. If the field ch an ges at a rate of , what is the curr en t induced in the coil? (A) (B) (C) (D) (E) 42. An o rga n pipe of length L is open at one end and closed at the ot he r. Th e s tan ding wave of next-to- lowes t frequenc y wh ich can exist in this pipe has a wa velength n earest to (A) (B) (C) L (D) (E) 43. When a light wa ve p asses from air into gl ass , the quantiti es tha t ch ange in clud e wh ich of the following? I. Fr eq uency II. Wa vel en gth III. Wave speed (A) I only (B) II only (C) I a nd III only (D) II and III only (E) I, II, and III 44. A parallel b eam of light of wa vel en gth is incid en t on a pair of sl its tha t are apart. The interferen ce pattern is fo cuse d on a screen 2.0 m from t he slit s. Th e separation bet wee n two adj ace nt brigh t fring es is most n early (A) (B) (C) (D) (E) 45. An air-filled paral lel -pl ate capacitor of capacitance C is conn ected to a battery and charged to a vol tag e V. The capacitor is then disconn ected fro m the ba ttery. If t he dis tanc e bet ween the capac itor p lates is hal ved while the charge on t he capac itor remains the same, wh ich of the following is true? (A) Neither C no r V will change. (B) Both C and V will be hal ve d. (C) C will be doubled an d V will be h alved. (D) C will be hal ve d and V will be dou bled. (E) Both C and V will be doubled.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -11- 46. Three identical conducting spheres, I, II, and III, are mounted on insulating stands and placed as shown above. Spheres I and II are each uncharged, and III carries a positive charge. Spheres I and II are connected to each other by a conducting wire. After the wire is removed, sphere III is moved far away. Which of the follow ing statements about the subsequent charges on spheres I and II is correct? (A) They are each still uncharged. (B) They are charged with equal positive charges. (C) They are charged with equal negative charges. (D) Sphere I is positively charged and sphere II is negatively charged. (E) Sphere I is negativel y charged and sphere II is positively charged. 47 . A bar magnet is pushed fr om left to righ t completely through a loop of metal wire, as shown in the figures above. The two po ssible directions for current in th e loop are also shown. Which of the following indi cates the directions of the induced cu rrent in the loop, i f any, as the magnet is m oving through the positions shown? Figure 1 Figure 2 (A) Direction 1 Direction 1 (B) Direction 1 Direction 2 (C) Direction 2 Direction 1 (D) Direction 2 Direction 2 (E) None (no cu rrent) None (no cu rrent) 48 . A circular c onductin g lo op is in a regio n of magnetic field B directed out of the pa ge , as shown above . The magnitude of the magnetic field is decreasing. The di rection of the induced current in the loop is (A) clockwise (B) counterclockwise (C) undefined b ecause the current is zero (D) impossible to determine without knowi ng the rate of change of the field (E) impossible to determine without knowi ng the radius of the loop

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -12- 49. Two fluids o f densities and are layered i n a c ylindri cal co ntai ner of diame ter d, as shown above. The height of each fluid is h, and the pressure at the top of the co lumn is . What is the abs olu te press ure a t the inside surfac e of the bottom of th e container ? (A) (B) (C) (D) (E) 50 . An undergr ou nd tu nnel has two openi ng s, with one openi ng a few meters higher than the other. If air moves past the higher openin g at a greater speed than it moves past the lower opening, what happens insi de the tunnel? (A) The air does not move. (B) Air moves from the lower opening toward the higher open ing. (C) Air moves from the highe r openin g to wa rd the lower opening. (D) Air enters both openi ng s. (E) Air leaves both open ings. 51 . A phot on of which of the fo llowing typ es of electromagnetic radiation carries the least amount of energy? (A) X-rays (B) Infrared ligh t (C) Ultraviolet light (D) Green light (E) Ga mm a rays 52 . An electron moves with speed . If the de Broglie wavelength of the electron doubles, then the new speed of the electron is (A) (B) (C) (D) (E) 53 . An engine h as an efficiency of 25 % and produces 200 0 J of mechanical work dur ing on e cycle. How much energy is transferred out of the en gine by heating the environment du ring one cycle? (A) 0 J (B) 500 J (C) 200 0 J (D) 600 0 J (E) 800 0 J 54 . A dog of mass 10 k g sits on a skateboard of mass 2 kg that is initially traveling sou th at 2 m/s. The dog jumps off with a velocity of 1 m/s north rela - tive to the g round. Wh ich of the followi ng is the best esti mate of the velocity of the skateboard immediately after the dog has jumped? (A) 1 m/s north (B) 1 m/s south (C) 3 m/s south (D) 7 m/s south (E) 17 m/s south

to a Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -13- 55 . A person ap plies an impulse of to a box in order to set it in mo tion. If the person is in contact with the b ox for 0.25 s, what is the average force exerted by t he person on the box? (A) 1.25 N (B) 2.00 N (C) 12 .5 N (D) 20 .0 N (E) 20 0 N 56 . A box of mass m han gs from ma ssless s trings, as shown in the figure above. The angle between strings 1 and 2 is and the angles that the strings make with the ceiling are and , respectively. If is the tension in string 1, which of the following are the magnitudes of the horizonta l and vertical components of the tensio n in strin g 2 ? Horizontal Componen t Verti cal Componen t (A) (B) (C) (D) (E) 57 . Planet 1 orbi ts Star 1 and Pl anet 2 orbits Star 2 in circular orbits of the same radius. However, the orbital perio d of Planet 1 i s longer than the orbital period of Pl an et 2. What could ex plain this? (A) Star 1 has le ss ma ss than Star 2. (B) Star 1 has more mass than Star 2. (C) Planet 1 has less ma ss tha n Planet 2. (D) Planet 1 has more ma ss t han Planet 2. (E) The masses of the planets are much less than the masses of the stars. 58 . A stationary source emits soun d waves of frequency f and wave leng th that travel through the a ir with speed . If the frequency of the source is changed to 2f, what will be the wavelength and speed of the new wave? Wavelengt h Speed (A) (B) (C) (D) (E)

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -14- 59. At separate tim es, red lig ht a nd blue ligh t pass thr ough the s am e two narrow slits, a nd each forms an interference pat tern on the screen represented above. How do the sp acings of the bright frin ges in the two patter ns comp are ? (A) The red fri nges are sp aced farther apart than the blue fri ng es are. (B) The blue fri ng es are sp aced farther apart than the red fri nges are. (C) The fri ng es ha ve the sa me spacing in both patterns. (D) The patterns cannot be compared without knowing the slit separation. (E) The patterns cannot be compared without knowing the distance from the slits to the scr een. 60 . A train moves at constant speed away from a stationary listener standing next to the track. The train’s whistle, which has a constant frequency, is sounded. Th e wavelength of the sou nd from the whistle as heard by the lis tener is (A) steadily increasing (B) steadily decr easing (C) constant but shorter than t he wavelength of the sound heard when the t rain is stationary (D) constant but longer than the wavelength of the sound heard when the t rain is stationary (E) alternately s horter and longer than the wavelength of the sound heard when the train is stationary Questions 61-62 An empty container is filled with helium to a press ure P at a temperature T. Neon, which has atom s that are 5 tim es more ma ssive than th ose of helium, is then added to the container until the new pressure in the contai ne r is 2 P at the same temperature T. 61. Th e ratio of the ave rag e s peed of t he he lium atom s to the a verag e s peed of the neon atoms is (A) 25 to 1 (B) 5 to 1 (C) to 1 (D) to 1 (E) 1 to 1 62 . The ratio of the number of helium atoms in the container to the number of neon atoms in the container is (A) 25 to 1 (B) 5 to 1 (C) to 1 (D) to 1 (E) 1 to 1

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -15- 63 . A board is hu ng from two sp rings, as shown in the figure above, with t he board in equil ibrium. Each spring ha s a spring constant of 1 0,0 00 N/m. How far will each spring stretch when a person of mass 50 kg s its on the bo ard and the bo ard again comes to equilibrium? (A) (B) (C) (D) (E) 64 . A student wants to determine the coefficient of static friction between a block of w oo d and an adjustable inclined pla ne. Of the following, the minimum a dditional equ ipm ent the student needs to determine a value for is a (A) pr otrac tor only (B) timer only (C) protractor and timer (D) meterstick and timer (E) meterstick a nd string 65 . A block is p rojected up a frictionless plane with an initial speed . The plane is inclined above the ho rizontal. What is the appro ximate acceleration of the block at the instant that it reach es its highest point on the inclined plane? (A) Zero (B) down the incline (C) down the incline (D) up the incline (E) It cannot be calculated without knowi ng the value of . 66 . Two blocks of masses m an d M are su spended as sho wn abov e by s trin gs of neglig ible mass. If a person hol ding the u pper string lowers t he blocks so that they have a consta nt downward acce lera - tion a, the tension in the string at po int P is (A) (B) (C) (D) (E)

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -16- 67 . A square loop is located i n a region con taining a magnetic field of magnit ude B. The foll ow ing figures show five possible directions of the magnetic field relative to the loop. For which of the directions is the magnetic flux thr oug h the loop greatest? (A) (B) (C) (D) (E) 68 . The figure above shows a metal bar that is supported by two sections of a fixed, c onductin g U-shaped horizontal rail. The rod and rail are located in a region of magnetic field B directed into the page . The bar is movin g to the right at a constant speed. Which o f th e following is true of the horizontal forces actin g on the bar? (A) There are no forces. (B) There is only a magnetic f orce. (C) There is only an external applied force. (D) There is both a magnetic f orce and an external applied force. (E) Nothing can be said about the forces without knowin g the magnitude of the magnetic field.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -17- Questions 69-70 A particle of charge and mass m moves toward a long wire t hat carries a c urrent I. At the instant shown above , the particle is a distance r from the wire and is movin g perpe ndicularly toward the wire with speed . There is a ma gnetic force on the particle as a result of the current. 69 . What is the d irection of the magnetic force on the pa rticle a t the inst ant s ho wn? (A) Toward the wire (B) Toward the left (C) Toward the right (D) Out of the pl an e of the pa ge (E) Into the plan e of the page 70. Of the following five quan tities, which could have a different value without ch anging the magnitude of the magnetic force on t he particle, assuming the other fou r quantities remain constant? (A) q (B) m (C) (D) I (E) r

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! ! ! ! ! B ! Section II: Free -Response Questions This is the free -response section of the 201 3 AP exam. It includes cover material and other admini strative 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 B Exam 2013 SECTION II: Free Response DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time1 hour, 30 minutes Number of Questions7 Percent of Total Score50% Writing InstrumentEither pencil or pen withblack or dark blue ink Electronic DeviceCalculator allowed Percent of Section II ScoreQuestions 1 and 2:37.5% Questions 3, 4, 5, 6and 7: 62.5% 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 .Atableofinformationandlistsofequationsthatmaybehelpfulareinthe 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 Z-4GBP2-S 78

-- TABLE OF INFORMATION DEVELOPED FOR 2012 CONST ANT S AND C ON VERSION FA CTORS Proton mass , Neutron mass , Electron ma ss, Avogadro’s nu mber , Universal gas constant , Boltzmann’s constant , Electron charge magnitude , 1 electron vo lt, Speed of light , Universal gravitational constant , Acce lera tion du e to gravity at Earth’s surface, 1 unified atom ic mass unit , Planck’s constant , Vacuum pe rm ittivity , Coulomb’s law constant , Vacuum pe rm eability , Magnetic constant , 1 atmosphere pressure , UNIT SYMBOLS meter, m kilogram, kg second, s ampere, A kelvin, K mole, mol hertz, Hz newton, N pascal, Pa joule, J watt, W coulomb, C volt, V ohm, henry, H farad, F tesla, T degree Celsi us, electron-volt, eV PREFIXES Factor Prefix Symbol giga G mega M kilo k centi c milli m micro nano n pico p VALUES O F TRIGO NO METRIC F UNCTIONS FO R COMM ON ANGLE S The followi ng conventi ons are used in this exam. I. Unless otherwise stated, the frame of reference of any pr ob lem is assumed to be inertial. II. The direction of any electric current is the direction of flow of posit ive charge (conventional current). III. For any isola ted electric charge, the elec tric potential is defined as zero at an infinite di stance from the charge. IV. For mechanics and thermodynamics equations, W represents the w ork done on a system.

-4- ADVAN CED PLACEMENT PHYSICS B EQ UAT IONS DEV ELOPED FOR 2012 NEWTONIAN( ME CHANICS a = acc eler ation = force = frequency h = hei ght J = impulse = kinetic energy = spring constant = length m = mass N = normal force = po wer = mome ntum r = radius or distance = period = time U = potential energy = veloc ity or speed W = work done on a system x = po sition = coefficient of f ric tion = angle ! = torque ! ELECTRICITY AND MAGNETISM A = area B = magnetic field C = capacitance d = distance E = electric field = emf F = force I = current = length P = po wer = cha rge = point ch arge = resistance = distance t = time U = potential (stored) !! ! energy = electric potential or potential difference = velocity or speed = resistivity = angle = magnetic flux

-5- ADVAN CED PLACEMENT PHYSICS B EQ UAT IONS DEV ELOPED FOR 2012 FLUI D MECHANICS A ND T HERMAL PHYSICS A= area e = eff iciency F = force = depth = rate of heat t ransfer k = thermal con du ctivity = aver ag e molecular kinetic energy = length = thi ckness = mass = molar mass = number of moles = number of mol ecules P = pr essure Q = heat transferred to a system T = tempe rature U = inter nal e nergy = volume = veloci ty o r speed = root- me an- squ are velocity W = work done on a system y = height ! = coefficient of linear expansion = mass of molecule = density ATOMIC AND NUCLEAR PHYSICS E = energy f = frequency K = kinetic energy = mass = momentum = wavelength = wo rk f un ction W AV ES AND OPTICS d = separation f = freq uen cy or focal length h = height L = distance = magnification = an integer n = index of refraction R = rad ius of curvature s = distance = speed x = position = wavel ength = angle ! GEOMETRY AND TRIGONOMETRY A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = rad ius Rectan gle Tria ngle Circle Rectangu lar Solid Cylinder Sph ere Right Triangle

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -6- PHYSICS B SECTI ON II Time — 90 minutes 7 Questions Directions: Answer all seven question s, which are weighted according to the points indicated. The suggested times are ab out 17 mi nu tes for answer ing each of Questions 1-2 and about 11 minutes for answering each of Questions 3-7. The part s within a que stion may not have equal weight. Show all your wo rk in this bookle t in the spaces provided aft er each part. 1. (15 po ints) You are assi gn ed to do some ca lculati ons for a mov ie stunt that involves a car on a straight road. The road, pictured above, has a hill that rises 8.0 m above the flat region. The top of th e hill is a circular arc of radius 20 m. You n eed to determine whether a car traveling under certain conditions wi ll lose contact with the road at the top of the hill. There is a stop sign 50 m from the beginn ing of th e hill. You are to assume that a car of mass 1600 kg accelerates uniformly from rest at the stop sign, has a speed of when it reach es the beginning of the hill, and then coasts with the eng ine off. A ssume energy losses due to friction and air re sistance are negligible. (a) Calculate the magnitude of the acce lerat ion of the car during the first 50 m. (b) Calculate the time it takes th e car to reach the beginn ing of the hill.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -7- (c) Ca lculate the magnit ude of the ne t forc e requi red t o accel erate the car dur ing th e firs t 50 m. (d) On the dot below t hat rep rese nts t he car, draw an d label t he f orce s (no t comp onents) t ha t act on the car at the top of the hill if it travels ove r the hill wit hou t lo sin g c on tact. (e) Ca lculate the min imum s peed the ca r mu st hav e at th e top of the hill to mome ntarily l ose co ntac t with the roa d. If you n eed to draw an yth ing other t han wha t you have shown in pa rt (d) to assist in your soluti on, use the sp ace below. D o NO T ad d an ything to t he figu re in pa rt (d ). (f) Ca lcu late the speed t he car mus t hav e at the be ginn ing of the h ill in orde r to ha ve t he spee d at the top of the hill y ou calcula ted in p art (e).

Unauthorized copying or reuse of any part of this page is illegal. 2. (15 po ints) A student is asked to determine w hether a particular carbon resistor obeys Ohm’s law by usin g all the equi pm ent listed below. Carbon resistor Ammeter Switch Voltmeter Variable voltage suppl y Wires (a) Draw a circuit diagram, using appr op riate circuit s ymbols, showin g how the stu dent should co nnect all the equipment listed above in a circuit. The student ob tains the data for current versus voltage shown in the table below. Cu rrent (mA ) 0 1.0 1.7 2.8 3.5 4.8 Voltage (V) 0 5 10 15 20 25 (b) Plot the data points on the grid below and draw a str aight line o r smooth curve th at best represents the data. (c) Base d on yo ur line o r curve , does the car bon resistor obey Ohm’s law? Justify your answer. GO ON TO THE NEXT PAGE. --

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -9- (d) Ca lculat e the r esistanc e of the car bon r esis tor from your l ine or curve. The stu den t now repl aces the car bon resist or wit h a lightbulb an d obtai ns the nonli ne ar graph of cur ren t v ersu s vol tage below. (e) In dicat e wh ether the resistan ce of the b ulb i ncreases, decreases, or remai ns the same as the cu rrent through it increases. Increases Dec reases Rema ins t he sa me Justi fy yo ur ch oice , b ased on the graph. (f) F rom th e g rap h, estima te the r esistanc e of the bulb at roo m tempe rature. Ex plai n yo ur meth od.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -10- 3. (10 po ints) The figure above shows a pr oton acc eleratin g horizontally from rest through a potential differ en ce of to veloci ty v. After tr av eling a sho rt di stanc e, t he proton enters the shaded regi on that contains a uniform m agne tic field B. Th e proton follo ws a ci rcular pa th of rad ius , leav es the magnet ic f ield through the opening at C, and m ov es vert ically downwar d. Assume g ravit y an d ai r resist ance can be negl ected. (a) Ind ica te the direction of th e magn etic field B. Into the pa ge To wa rd the to p of the page To the left Out of the page Toward the bottom of the pa ge To the righ t (b) Calculate the spe ed of the proton on ce it pass es through the hole in plate A. (c) Calculate the magni tude of the magnetic field B.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -11- (d) Af ter passi ng throu gh th e openi ng at C, the proto n travels in a vacuum down a ve rtical 20 m tube. If gravi ty is now no t neglected, calc ulate the incr ease in the proton’s kinetic energy due t o its descent as a fraction of its kinetic energy at C .

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -12- 4. (10 po ints) At a cer tain location, a river is 60 m wide and can be approximated as having a unifor m dep th of 3. 0 m. At that location the water is moving at . Assume the density of water is . (a) Calculate the number of kilograms of w ater that pass by that location each seco nd. At a point downstream, just before a wa terfall, the wi dth of the r ive r is 50 m, and it has a n ap proximately uniform dep th of 1 .6 m. (b) Calculate the speed of the water just be fore it reaches the waterfall . (c) Calculate the kinetic energy of the water that passes by the locatio n just before th e waterfall each second. (d) The water is moving ho rizontally as it go es over the wa ter fal l an d then d rops a dista nce o f 40 m. The dep th of the water at the top is sufficientl y small compared with the height of the waterfall that it can be ignored. Calculate the horizontal di stance the wa ter travels be twee n leaving the top of the waterfall and landing at th e bottom.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -13- 5. (10 po ints) A gasoline engine is used to run a water pump. The e ngine uses of gasoline eac h second. When the gasoline is burn ed, it releases thermal ener gy at the rate of . (a) Calc ulate t he the rmal ener gy available from the gasoline in 30 s. The efficiency of the gaso line engine part of the system is 0.32. (b) Calculate the work done by the engine in 30 s. (c) Calculate the thermal ener gy exhausted by the engine in 30 s. The pump raises 4.30 kg of water each second from a depth of 100 m to the surface of Earth. (d) Calculate the rate of increase in the potential energy of the water. (e) As well as the thermal en ergy exhauste d by the eng ine, additional energy goes unused in raising the water. Calculate the additional e nergy that go es unused in 30 s. (f) Where might the additiona l energy calculated in part (e) go?

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -14- 6. (10 po ints) A puddle of water has a thin film of oil on top of it. Fo r yellow light of wavelength 580 nm in air, the ind ex of refraction of the oil is 1. 47 and the inde x of refraction of the water is 1.33. A beam of this yellow light strikes the oil at an angle of incid ence of , as shown above. (a) On the figure above, draw rays to show the path of the beam of ligh t as it passes throu gh the o il and int o the wa ter. (b) Calculate the angle of refraction in the oi l. (c) Calculate the wavelength of the yellow l ight in the oil. (d) The yel low light is no w inc iden t norm ally on the oil. Calculate the minimum thickness of oil th at gives a maxim um brightness for the reflected light.

Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. -15- 7. 10 (points) A laser beam with a frequency of shines on a sheet of metal th at has a w ork f unct ion of 5.1 eV . (a) Calculate the energy per p hoton of the light, in eV. (b) Calculate the maxim um kinetic energy of an electron emitted from the metal, in eV. (c) Calculate the minimum frequency of in cident light needed to allow an elec tron to escape the metal. (d) Using values given and ca lculat ed above, construct a graph that s ho ws the relationship between maximum kinetic energy of an emitted elect ron and frequency of incident ligh t. Indicate the sca le on bo th axes. (e) What physical quantity do es the slope of your graph represent?

-16- THIS PAGE MAY BE U SED FOR S CRATCH WO RK. STOP END OF EXAM THE F OLLOWING INS TRUCT IO NS APP LY TO THE COV ERS O F T HE SECTION II BOOKLET. x MA KE S UR E YOU HA VE COMPL ETED THE ID ENTIFICAT IO N INFORMATION AS REQUESTED ON THE FRONT AN D BACK COVERS OF THE SECTION II BOOKLET. CHE CK TO SEE T HAT YO UR AP N UM BER L ABE L A PPE ARS IN THE BOX(ES) ON THE COVER(S). MA KE S UR E YOU HA VE US ED T HE S AME S ET OF AP NUMBER LABELS ON AL L AP E XAMS YOU HAVE TAK EN THIS YEAR. x x

! ! ! ! ! B ! Multiple -Choice Answer Key The following contains the answers to the multiple -choice questions in this exam.

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