AP Physics B 2009 Free-Response Questions

Transcription

1 AP Physcs B 009 Free-Response Questons The College Board The College Board s a not-for-proft membershp assocaton whose msson s to connect students to college success and opportunty. Founded n 1900, the assocaton s composed of more than 5,600 schools, colleges, unverstes and other educatonal organzatons. Each year, the College Board serves seven mllon students and ther parents,,000 hgh schools and,800 colleges through major programs and servces n college readness, college admssons, gudance, assessment, fnancal ad, enrollment, and teachng and learnng. Among ts best-known programs are the SAT, the PSAT/NMSQT and the Advanced Placement Program (AP ). The College Board s commtted to the prncples of excellence and equty, and that commtment s emboded n all of ts programs, servces, actvtes and concerns. 009 The College Board. All rghts reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are regstered trademarks of the College Board. PSAT/NMSQT s a regstered trademark of the College Board and Natonal Mert Scholarshp Corporaton. Permsson to use copyrghted College Board materals may be requested onlne at: AP Central s the offcal onlne home for the AP Program: apcentral.collegeboard.com.

2 Proton mass, Neutron mass, m p m n TABLE OF INFORMATION FOR 008 and 009 CONSTANTS AND CONVERSION FACTORS kg Electron charge magntude, e C kg electron volt, 1 ev J -1 8 Electron mass, m e kg Speed of lght, c m s -1 Unversal gravtatonal -11 Avogadro s number, N mol constant, G m kg s Unversal gas constant, R 8.1 J (mol K) Acceleraton due to gravty at Earth s surface, g 9.8 m s - Boltzmann s constant, J K k B -7 1 unfed atomc mass unt, 1 u kg 91 MeV c Planck s constant, h Js ev s Vacuum permttvty, Coulomb s law constant, Vacuum permeablty, Magnetc constant, -5 hc J m ev nm C Nm 0 9 k 14p Nm C -7 m0 4p 10 (T m) A 7 0 k m 4 p - 10 (T m) A atmosphere pressure, 1 atm N m Pa UNIT SYMBOLS meter, m mole, mol watt, W farad, F klogram, kg hertz, Hz coulomb, C tesla, T second, s newton, N volt, V degree Celsus, C ampere, A pascal, Pa ohm, W electron-volt, ev kelvn, K joule, J henry, H PREFIXES VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES Factor Prefx Symbol q gga G snq mega M cosq klo k tanq cent c 10 - mll m mcro m nano n pco p The followng conventons are used n ths exam. I. Unless otherwse stated, the frame of reference of any problem s assumed to be nertal. II. The drecton of any electrc current s the drecton of flow of postve charge (conventonal current). III. For any solated electrc charge, the electrc potental s defned as zero at an nfnte dstance from the charge. IV. For mechancs and thermodynamcs equatons, W represents the work done on a system. --

3 ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 008 and 009 u u 0 + at 1 x x0 + u0t + at u NEWTONIAN MECHANICS ( x ) u0 + a x - 0  F F ma Ffrc a c net mn u r t rf sn q p mv J FDt Dp K 1 mu g D U mgh W FDr cos q P avg W Dt P Fucosq F s Us T s -k x 1 kx p T p p T F U G G 1 f m k g Gm m - r 1 Gm m - r 1 a acceleraton F force f frequency h heght J mpulse K knetc energy k sprng constant length m mass N normal force P power p momentum r radus or dstance T perod t tme U potental energy u velocty or speed W work done on a system x poston m coeffcent of frcton q angle t torque ELECTRICITY AND MAGNETISM 1 qq 1 A area F 4p 0 r B magnetc feld E F C capactance d dstance q E electrc feld 1 qq e emf 1 UE qv 4p 0 r F force I current V Eavg - length d P power 1 q Q charge V 4p  0 r q pont charge R resstance Q C r dstance V t tme 0 C A U potental (stored) energy d V electrc potental or potental dfference 1 1 Uc QV CV u velocty or speed r resstvty DQ Iavg q angle Dt r R f m magnetc flux A V P Cp IR IV  C 1 1  Cs C Rs  R 1 1  R R p FB qubsnq F BI snq B B m0 I p r fm BA cos q Df eavg - Dt e B u m --

4 ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 008 and 009 FLUID MECHANICS AND THERMAL PHYSICS P P + rgh Fbuoy Au 0 rvg A u P + rgy + ru D a H P 0 DT ka DT L F A PV nrt NkBT K u W avg rms kbt const. k T m RT B M - PDV D U Q + W e e c W Q T H H - T H T C ATOMIC AND NUCLEAR PHYSICS E hf pc Kmax hf - f l h p DE ( Dmc ) A area e effcency F force h depth H rate of heat transfer k thermal conductvty K avg average molecular knetc energy length L thckness M molar mass n number of moles N number of molecules P pressure Q heat transferred to a system T temperature U nternal energy V volume u velocty or speed u rms root-mean-square velocty W work done on a system y heght a coeffcent of lnear expanson m mass of molecule r densty E energy f frequency K knetc energy m mass p momentum l wavelength f work functon WAVES AND OPTICS u f l n n c u sn q n sn q 1 1 n snq c n s s0 f h s M - h s f dsn R x m 0 0 q ml mll d d separaton f frequency or focal length h heght L dstance M magnfcaton m an nteger n ndex of refracton R radus of curvature s dstance u speed x poston l wavelength q angle GEOMETRY AND TRIGONOMETRY Rectangle A bh Trangle 1 A bh Crcle A pr C pr Parallelepped V wh Cylnder V pr S pr + pr Sphere 4 V pr S 4pr Rght Trangle a + b c a snq c b cosq c a tanq b A area C crcumference V volume S surface area b base h heght length w wdth r radus q c b 90 a -4-

5 009 AP PHYSICS B FREE-RESPONSE QUESTIONS PHYSICS B SECTION II Tme 90 mnutes 7 Questons Drectons: Answer all seven questons, whch are weghted accordng to the ponts ndcated. The suggested tmes are about 17 mnutes for answerng each of Questons 1 and and about 11 mnutes for answerng each of Questons and 4-7. The parts wthn a queston may not have equal weght. Show all your work n ths booklet n the spaces provded after each part, NOT n the green nsert. 1. (15 ponts) In an experment, students are to calculate the sprng constant k of a vertcal sprng n a small jumpng toy that ntally rests on a table. When the sprng n the toy s compressed a dstance x from ts uncompressed length L 0 and the toy s released, the top of the toy rses to a maxmum heght h above the pont of maxmum compresson. The students repeat the experment several tmes, measurng h wth objects of varous masses taped to the top of the toy so that the combned mass of the toy and added objects s m. The bottom of the toy and the sprng each have neglgble mass compared to the top of the toy and the objects taped to t. (a) Derve an expresson for the heght h n terms of m, x, k, and fundamental constants. Wth the sprng compressed a dstance x 0.00 m n each tral, the students obtaned the followng data for dfferent values of m. (b) m (kg) h (m) What quanttes should be graphed so that the slope of a best-ft straght lne through the data ponts can be used to calculate the sprng constant k?. Fll n one or both of the blank columns n the table wth calculated values of your quanttes, ncludng unts. 009 The College Board. All rghts reserved. -5-

6 009 AP PHYSICS B FREE-RESPONSE QUESTIONS (c) On the axes below, plot your data and draw a best-ft straght lne. Label the axes and ndcate the scale. (d) Usng your best-ft lne, calculate the numercal value of the sprng constant. (e) Descrbe a procedure for measurng the heght h n the experment, gven that the toy s only momentarly at that maxmum heght. 009 The College Board. All rghts reserved. -6-

7 009 AP PHYSICS B FREE-RESPONSE QUESTIONS. (10 ponts) Two small objects, labeled 1 and n the dagram above, are suspended n equlbrum from strngs of length L. Each object has mass m and charge +Q. Assume that the strngs have neglgble mass and are nsulatng and electrcally neutral. Express all algebrac answers n terms of m, L, Q, q, and fundamental constants. (a) On the followng dagram, sketch lnes to llustrate a -dmensonal vew of the net electrc feld due to the two objects n the regon enclosed by the dashed lnes. (b) Derve an expresson for the electrc potental at pont A, shown n the dagram at the top of the page, whch s mdway between the charged objects. (c) On the followng dagram of object 1, draw and label vectors to represent the forces on the object. (d) Usng the condtons of equlbrum, wrte but do not solve two equatons that could, together, be solved for q and the tenson T n the left-hand strng. 009 The College Board. All rghts reserved. -7-

8 009 AP PHYSICS B FREE-RESPONSE QUESTIONS. (15 ponts) A metal rod of mass 0. kg les across two parallel conductng rals that are a dstance of 0.5 m apart on a tabletop, as shown n the top vew above. A.0 W resstor s connected across the left ends of the rals. The rod and rals have neglgble resstance but sgnfcant frcton wth a coeffcent of knetc frcton of 0.0. There s a magnetc feld of 0.80 T perpendcular to the plane of the tabletop. A strng pulls the metal rod to the rght wth a constant speed of 1.8 m/s. (a) Calculate the magntude of the current nduced n the loop formed by the rod, the rals, and the resstor. (b) Calculate the magntude of the force requred to pull the rod to the rght wth constant speed. (c) Calculate the energy dsspated n the resstor n.0 s. (d) Calculate the work done by the strng pullng the rod n.0 s. (e) Compare your answers to parts (c) and (d). Provde a physcal explanaton for why they are equal or unequal. 009 The College Board. All rghts reserved. -8-

9 009 AP PHYSICS B FREE-RESPONSE QUESTIONS 4. (10 ponts) The cylnder represented above contans. kg of water vapor ntally at a volume of.0 m and an absolute 5 pressure of.0 10 Pa. Ths state s represented by pont A n the PV dagram below. The molar mass of water s 18 g, and the water vapor can be treated as an deal gas. (a) Calculate the temperature of the water vapor at pont A. The absolute pressure of the water vapor s ncreased at constant volume to volume of the water vapor s ncreased at constant pressure to (b) Calculate the temperature of the water vapor at pont C Pa at pont B, and then the.5 m at pont C, as shown n the PV dagram. (c) Does the nternal energy of the water vapor for the process A B C ncrease, decrease, or reman the same? Increase Decrease Reman the same Justfy your answer. (d) Calculate the work done on the water vapor for the process A B C. 009 The College Board. All rghts reserved. -9-

10 009 AP PHYSICS B FREE-RESPONSE QUESTIONS 5. (10 ponts) Three objects of dentcal mass attached to strngs are suspended n a large tank of lqud, as shown above. (a) Must all three strngs have the same tenson? Yes No Justfy your answer. -5 Object A has a volume of m and a densty of object A s attached s N. (b) Calculate the buoyant force on object A. (c) Calculate the densty of the lqud. 100 kg m. The tenson n the strng to whch (d) Some of the lqud s now draned from the tank untl only half of the volume of object A s submerged. Would the tenson n the strng to whch object A s attached ncrease, decrease, or reman the same? Increase Decrease Reman the same Justfy your answer. 009 The College Board. All rghts reserved. -10-

11 009 AP PHYSICS B FREE-RESPONSE QUESTIONS 6. (10 ponts) In a classroom demonstraton, a beam of coherent lght of wavelength 550 nm s ncdent perpendcularly onto a par of slts. Each slt has a wdth w of m, and the dstance d between the centers of the slts s m. The class observes lght and dark frnges on a screen that s a dstance L of. m from the slts. Your notebook shows the followng setup for the demonstraton. (a) Calculate the frequency of the lght. (b) Calculate the dstance between two adjacent dark frnges on the screen. The entre apparatus s now mmersed n a transparent flud havng ndex of refracton 1.4. (c) What s the frequency of the lght n the transparent flud? (d) Does the dstance between the dark frnges ncrease, decrease, or reman the same? Increase Decrease Reman the same Explan your reasonng. 009 The College Board. All rghts reserved. -11-

12 009 AP PHYSICS B FREE-RESPONSE QUESTIONS 7. (10 ponts) A photon of wavelength 50 nm ejects an electron from a metal. The ejected electron has a de Brogle wavelength of 0.85 nm. (a) Calculate the knetc energy of the electron. (b) Assumng that the knetc energy found n (a) s the maxmum knetc energy that t could have, calculate the work functon of the metal. (c) The ncdent photon was created when an atom underwent an electronc transton. On the energy level dagram of the atom below, the transton labeled X corresponds to a photon wavelength of 400 nm. Indcate whch transton could be the source of the orgnal 50 nm photon by crclng the correct letter. Justfy your answer. END OF EXAM 009 The College Board. All rghts reserved. -1-