AP Physics 2: Algebra-Based

Transcription

1 08 P Physcs : lgebra-based Free-Response Questons 08 The College Board. College Board, dvanced Placement Program, P, P Central, and the acorn logo are regstered trademarks of the College Board. Vst the College Board on the Web: P Central s the offcal onlne home for the P Program: apcentral.collegeboard.org.

2 Proton mass, Neutron mass, Electron mass, vogadro s number, m p m n m e P PHYSICS TBLE OF INFORMTION CONSTNTS ND CONVERSION FCTORS kg kg kg 3 N mol Unversal gas constant, R 8.3 J (mol K) 3 Boltzmann s constant,.38 0 J K k B Electron charge magntude, 9 e.60 0 C 9 electron volt, ev.60 0 J 8 Speed of lght, c m s Unversal gravtatonal G m kgs constant, cceleraton due to gravty g 9.8 m s at Earth s surface, 7 unfed atomc mass unt, u.66 0 kg 93 MeV c Planck s constant, 34 5 h Js evs Vacuum permttvty, 5 3 hc.99 0 J m.4 0 evnm e C Nm 9 Coulomb s law constant, k 4pe Nm C Vacuum permeablty, Magnetc constant, 0 7 m0 4p 0 (Tm) k m 7 4 p 0 (Tm) 5 5 atmosphere pressure, atm.0 0 N m.0 0 Pa 3 UNIT SYMBOLS meter, klogram, second, ampere, kelvn, m kg s K mole, hertz, newton, pascal, joule, mol Hz N Pa J watt, coulomb, volt, ohm, henry, W C V W H farad, tesla, degree Celsus, electron volt, F T C ev PREFIXES Factor Prefx Symbol 0 tera T 9 0 gga G 6 0 mega M 3 0 klo k 0 cent c 3 0 mll m 6 0 mcro m 9 0 nano n 0 pco p VLUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON NGLES q snq cosq tanq The followng conventons are used n ths exam. I. The frame of reference of any problem s assumed to be nertal unless otherwse stated. II. In all stuatons, postve work s defned as work done on a system. III. The drecton of current s conventonal current: the drecton n whch postve charge would drft. IV. ssume all batteres and meters are deal unless otherwse stated. V. ssume edge effects for the electrc feld of a parallel plate capactor unless otherwse stated. VI. For any solated electrcally charged object, the electrc potental s defned as zero at nfnte dstance from the charged object --

3 à à x x0 at x x x0 Ãx0t a x Ãx 0 x x t à a x x F F a net m m F m F f n à a c r p mv Dp F Dt K mv MECHNICS 0 DE W Fd Fdcosq P DE Dt q q0 w0t at w w0 at w p t x cos t cos f x cm a mx m t I t I net t rf rfsnq L Iw DL t Dt K Iw F k x s P PHYSICS EQUTIONS a = acceleraton = ampltude d = dstance E = energy F = force f = frequency I = rotatonal nerta K = knetc energy k = sprng constant L = angular momentum = length m = mass P = power p = momentum r = radus or separaton T = perod t = tme U = potental energy v = speed W = work done on a system x = poston y = heght a = angular acceleraton m = coeffcent of frcton q = angle t = torque w = angular speed kx DU mgdy Us T T s g p w f p T p p m k g mm Fg G r g U G F g m Gm m r ELECTRICITY ND MGNETISM qq = area FE 4pe B = magnetc feld 0 r C = capactance F E E d = dstance q E = electrc feld e = emf q E F = force 4pe 0 r I = current DU = length E qdv P = power q V Q = charge 4pe0 r q = pont charge R = resstance DV E r = separaton Dr t = tme Q U = potental (stored) DV C energy V = electrc potental C ke v = speed 0 d k = delectrc Q constant E e r = resstvty 0 q = angle UC QDV CDV F = flux I DQ Dt R r P I DV I R DV R s R C p p R R C C C s B m0 I p r FM qv B F qv snq B M FM I B F I snq B M FB B FB Bcosq e DF Dt e Bv B -3-

4 r P P PHYSICS EQUTIONS FLUID MECHNICS ND THERML PHYSICS m V F P P rgh Fb v 0 rvg v P rgy rv P rgy rv Q Dt k DT L PV nrt Nk T K W 3 k T B PDV DU Q W E hf K hf f max l E h p mc B MODERN PHYSICS = area F = force h = depth k = thermal conductvty K = knetc energy L = thckness m = mass n = number of moles N = number of molecules P = pressure Q = energy transferred to a system by heatng T = temperature t = tme U = nternal energy V = volume v = speed W = work done on a system y = heght r = densty E = energy f = frequency K = knetc energy m = mass p = momentum l = wavelength f = work functon WVES ND OPTICS v d = separaton l f f = frequency or focal length c n h = heght à L = dstance n M = magnfcaton sn q n sn q m = an nteger n = ndex of s so f refracton s = dstance h s M v = speed ho so l = wavelength DL ml q = angle dsn q ml GEOMETRY ND TRIGONOMETRY Rectangle bh Trangle bh Crcle pr C pr Rectangular sold V wh Cylnder V pr S pr pr Sphere 4 V pr 3 S 4pr 3 = area C = crcumference V = volume S = surface area b = base h = heght = length w = wdth r = radus Rght trangle c a b a snq c b cosq c a tanq b q c b 90 a -4-

5 08 P PHYSICS FREE-RESPONSE QUESTIONS PHYSICS Secton II Tme hour and 30 mnutes 4 Questons Drectons: Questons and 4 are short free-response questons that requre about 0 mnutes each to answer and are worth 0 ponts each. Questons and 3 are long free-response questons that requre about 5 mnutes each to answer and are worth ponts each. Show your work for each part n the space provded after that part.. (0 ponts, suggested tme 0 mnutes) The fgures above show a rectangular conductng loop at three nstants n tme. The loop moves at a constant speed v nto and through a regon of constant, unform magnetc feld B drected nto the page. The magnetc feld s zero outsde the regon. (a) In a coherent paragraph-length response, compare the magntude and drecton of the current at tmes t, t, and t 3. Include an explanaton of why there s or s not a current and the drecton of the current f one s present. Use fundamental physcs concepts and prncples n your explanaton. 08 The College Board. Vst the College Board on the Web: GO ON TO THE NEXT PGE.

6 08 P PHYSICS FREE-RESPONSE QUESTIONS (b) The loop s removed. proton travelng to the rght n the plane of the page, as shown below, then enters the 5 regon of magnetc feld wth a speed v = m s. The magntude of the feld s T. The effects of gravty are neglgble.. Calculate the magntude of the force on the proton as t enters the feld.. On the fgure below, sketch a possble path of the proton as t travels through the magnetc feld. Clearly label the path P.. second proton now enters the magnetc feld at the same pont and from the same drecton but at a greater speed than the frst proton. On the fgure above, draw the path of the second proton as t travels through the feld. Clearly label the path P. v. Next an electrc feld s appled n the same regon as the magnetc feld, such that there s no net force on the frst proton as t enters the regon. Calculate the magntude and ndcate the drecton of the electrc feld relatve to the coordnate system shown n part (b). 08 The College Board. Vst the College Board on the Web: GO ON TO THE NEXT PGE.

7 08 P PHYSICS FREE-RESPONSE QUESTIONS. ( ponts, suggested tme 5 mnutes) Students are gven resstor wth resstance R connected n seres wth the parallel combnaton of a swtch S and resstor wth resstance R, as shown above. The crcut elements cannot be dsconnected from each other, and other crcut components can only be connected at ponts and B. The students also are gven an ammeter and one 9 V battery. The teacher nstructs the students to take measurements that can be used to determne R and R. (a) Complete the dagram below to show how the ammeter and the battery should be connected to expermentally determne the resstance of each resstor. Descrbe the experment by lstng the measurements to be taken and explanng how the measurements would be used to calculate resstances R and R. Complete the Dagram Descrbe the Experment second group of students s gven a combnaton of crcut elements that s smlar to the prevous one but has an ntally uncharged capactor n seres wth the open swtch, as shown above. The combnaton s placed n a crcut wth a power supply so that the potental dfference between and B s mantaned at 9 V. The students close the swtch and mmedately begn to record the current through pont B. The ntal current s 0.9, and after a long tme the current s 0.3. (b). Compare the currents through resstor, resstor, and the swtch mmedately after the swtch s closed to the currents a long tme after the swtch s closed. Specfcally state f any current s zero.. Calculate the values of R and R.. Determne the potental dfference across the capactor a long tme after the swtch s closed. thrd group of students now uses the combnaton of crcut elements wth the capactor. They connect t to a 9 V battery that they treat as deal but whch s actually not deal and has nternal resstance. (c) How does the thrd group s value of R calculated from the data they collected compare to the second group s value? Explan your reasonng wth reference to physcs prncples and/or mathematcal models. 08 The College Board. Vst the College Board on the Web: GO ON TO THE NEXT PGE.

8 08 P PHYSICS FREE-RESPONSE QUESTIONS 3. ( ponts, suggested tme 5 mnutes) Monochromatc lght of frequency f shnes on a metal, as shown above. The frequency of the lght s vared, and for some frequences electrons are emtted from the metal. The maxmum knetc energy K e of the emtted electrons s measured as a functon of the frequency of the lght. (a). Based on conservaton of energy, the relatonshp between K e and f s predcted to be f = B + K e when f > f 0 and K e = 0 when f f 0, where and B are postve constants. graph of ths relatonshp s shown below. Indcate whch aspects of the graph correspond to and B. lso, explan the physcal meanng of, B, and f 0.. Explan the physcal meanng of the horzontal secton of the graph between the orgn and f 0.. second metal wth dfferent propertes than the frst metal s now used. On the fgure below, the dashed lnes are the same lnes shown n the prevous graph. Sketch lnes on the fgure below that could represent the data for the second metal. Explan one dfference between the two graphs. 08 The College Board. Vst the College Board on the Web: GO ON TO THE NEXT PGE.

9 08 P PHYSICS FREE-RESPONSE QUESTIONS (b) The fgure below shows an electroscope. sphere s connected by a vertcal bar to the leaves, whch are thn, lght strps of materal. The sphere, leaves, and bar are all made of metal. The electroscope ntally has a negatve charge, so the leaves are separated.. Ultravolet (UV) lght shnes on the sphere, causng the leaves of the electroscope to move closer together. Explan why ths happens.. Green lght then shnes on an dentcal negatvely charged electroscope. No movement of the leaves s observed. Explan why the green lght does not make the leaves move, whle the UV lght does. (c) The brghtness of the green lght s ncreased untl the ntensty (power per unt area) s the same as that of the UV lght. What aspect of the green lght changes when ts brghtness s ncreased? Would shnng the brghter green lght on the electroscope result n movement of the leaves? Explan why or why not. 08 The College Board. Vst the College Board on the Web: GO ON TO THE NEXT PGE.

10 08 P PHYSICS FREE-RESPONSE QUESTIONS 4. (0 ponts, suggested tme 0 mnutes) large boat lke the one shown above has a mass M b and can dsplace a maxmum volume V b. The boat s floatng n a rver wth water of densty r water and s beng loaded wth steel beams each of densty r steel and volume V steel. The boat owners want to be able to carry as many beams as possble. (a) Derve an expresson for the maxmum number N of steel beams that can be loaded on the boat wthout exceedng the maxmum dsplaced volume, n terms of the gven quanttes and physcal constants, as approprate. (b) The captan realzes that ol s leakng from the boat, creatng a thn flm of ol on the water surface. In one area of the ol flm the surface looks mostly green. Explan n detal how constructve nterference contrbutes to the green appearance. ssume the ndex of refracton of the ol s greater than the ndex of refracton of the water. (c) Later the boat s floatng down the rver wth the water current, headng for a town. The rver has a wdth of 60 m and a constant depth and flows at a speed of 5 km hr. Partway to the town, the rver narrows to a wdth of 30 m whle ts depth remans the same. Calculate the speed of the water n the narrow secton. STOP END OF EXM 08 The College Board. Vst the College Board on the Web: -0-