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1993 AP Physics B Examination with Key Copyright O 1993 by College Entrance Examinations Board and Educational Testing Service All rights reserved

l. In which of the following situations would an object be accelerated? I. It mover in a straight line at constant speed. I[. [t moves with uniform circular motion. III. It travels as a projectile in a gravitational field with negligible air resistance. I only III only I and II only II and III only I. II. and III A ball falls straight down through the air under the influence of gravity. There is a retarding force .F on theballwithmagnitudegivenby F = bu, where u is the speed ofthe ball and 6 is a positive constant. The magnitude of the acceleration a of the ball at any time is equal to which of the following? (A)g-, 3. (A) (B) H (c') c + b; @\'-H 4 fru; 6 il.*o Y^ t / c - bl. -- ilAq,- '0 .l A - trllk-bV 1-'vr (D) f @)* (A) (B) (c) (D) I ^X ,^F Q,u l)r,u _, 61. -bV (,vt v:t-oF An ideal spring obeys Hooke's law, F : - kx. A mass of 0.50 kilogram hung vertically from this spring stretches the spring 0.075 meter. The value of the force constant for the spring is most nearly 0.33 N/m 0.66 N/m 6.6 N/m 33 N/m 66 N/m The figure above shows 4r@serr,ucircuter tract whose ends are at a vertical height lr. A block placed at point P at one end of the track is released from rest and slides past the bottom ofthe track. Which of the following is true of the height to which the block rises on the other side of the track? (A) It is equal to hl2n. (B) It is equal to hl4. (C) Itisequal to hl2. (D) It is equal to &. f,E) It is between zero and h; the exact height depends on how much energy is lost to friction.

l"-;)i, ll-a Afuo,r& An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the first second. What is the magnitude of the acceleration due to gravity on the planet? 1.5 mis2 3.0 m/s' 6.0 m/s' 10.0 m/s2 12.0 m/sz 8. lf Spacecraft X has twice the mass of Spacecraft I, then true statements about X and I include which of the fiollowing? I. On Earth, X experienoes twice the gravita- tional force that Y experiences. II. On the Moon, X has twice the weight of I/. III. When both are in the samecircular orbit. X has twice the centripetal acceleration of Y. (A) I only (B) III only $ f and II only (D) II and III only (E) I, II, and III 7. Two pucks are attached by a stretched spring and are initially held at rest on a frictionless surface, as shown above. The pucks are then released simulta- neously. If puck I has three times the mass of puck II, which of the following quantities is the same for both pucks as the spring pulls the two pucks toward each other? (A) Speed (B) Velocity (C) Acceleration (D) Kinetic enersv @ Magnitude oTmomentum The two spheres pictured above have equal densities and are subject only to their mutual gravitational attraction. Which of the following quantities must have the saqe magnitude for both spheres? (A) Acceleration (B) Velocity (C) Kinetic energy (D) Displacement from the oenter of mass i€j c"iuitational force c,6rra.[ i. opg":,i< When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position, which of the following is true of the values of its speed and the magnitude of the restoring force? Speed Zero (B) Tnro I 2 maxJmum Maximum (E) Maximum Zmo I Vtv -a.l 5. (A) (B) @(D) (E) 6. 9. 4?='{woo . w,-f"o @t Restoring Force Maximum ltl'tf* ?{' 7*ro (c) (D) I tmarumum I tmilomum Gr*eqrvahA, ^ ok ilAn^\eqA/''4,-

t0. Which of the following is true when an object of mass ,?r moving on a horizontal frictionless surface hits and sticks to an object of mass M > m, which is initially at rest on the surface? (A) The collision is elastic. (B) All of the initial kinetic energy of the less- massive object is lost. (C) The momentum of the objects that are stuck together has a smaller magnitude than the ". initial momentum of the less-massive object. (E Th" speed ofthe objects that are stuck together will be less than the initial speed of the less- massive object. (E) The direction of motion of the objects that are stuck together depends on whether the hit is a head-on collision. Two objects having the same mass travel toward each other on a flat surface, each with a speed of 1.0 meter per second relative to the surface. The objects collide head-on and are repor"ted to rebound after the collision, each with a speed of 2.0 meters per second relative to the surface. Which of the following assessments of this report is most accu- rate? (A) Momentum was not conserved, therefore the report is false. (D) If potential energy was released to the objects during the collision, the report could be true. (C) If the objects had different masses, the report could be true. (D) If the surface was inclined, the report could be true. (E) If there was no friction between the objects and the surface, the report could be true. An automobile moves at constant speed down one hill and up another hill along the smoothly curved surface shown above. Which of the following diagrams best represents the directions of the velocity and the acceleration of the automobile at the instant that it is at the lowest position, as shown? (A) -+o I lai 12. l l. @ _+D tI lo (c) ---!+ +A (D) +o #a (E) 4"

r3. Which of the following will cause the eloctrical resis- tance of certain materials known as superconductors to suddenly decrease to essentially zero? (A) Increasing the voltage applied to the material beyond a certain threshold voltage (B) Increasing the pressure applied to the material - beyond a certain threshold pressure ($ Cootltrg the material below a certain threshold v temperature (D) Stretching the material to a wire of sufficiently small diameter (E) Placing the material in a sufliciently large magnetic field Kirchhoffs loop rule for circuit analysis is an expression of which of the following? Conservation of charge Conservation of energy Ampdre's law Faraday's law Ohm's law Questions l5-16 rcfer to the circuit shown below. 3pF The equivalent capacitance for this network is most neady l0/7 pF 3l2trF 713 trF 7 trF 14 pF 16. The charge stored in the S-microfarad capacitor is most neady 15. 360 pC 500 pC 710 pC 1,100 pC 1,800 pC (A) (B) ffi (A) I(D) (E) (A) I(D) (E) t4. Qzorl - s,'0[-) = 9upL re, L-l ffiu ;) %*' lonT'eL fr1,v

-\e ,- , * i' {u r & - - - -,- - - - #- - - -,- - - - € -fT-i--t- n.M 17. Twolargeparallelcondrctingplates p and p are connected to a battery ofemf g, as shown aFove, A test_charge is placed succcssively at points I, II, ald III. If edge effects are negligible, the force on the charge when it is at poiniili is ' (A) of equal magnitude and in the same direction as /R ^the force on.the charge when it is at point I (yl oI equal magnitude and in the same direction as the torce on the charge when it is at point II (C) equal in magnitude to t-he force on tt" ftrarge when it is at point I, but in the opposite - dirotion (D) much greater in magnitude than the fiorce on the charge when it is at point II, but in the same direction (E) much less in magnitude than the force on the 9!arg" when it is at point II, but in the same direction 19. T\vo long parallel r+,ires.are sgparated by a distane d, as shown above. One wire ca*es a sLaiy current f into the plane of thc page while thi other'wire carries 3 sleady current I out of te page. At what points in t!.e ntang of the p-age aoa oirtslOe ttr'ru1.res, Dcsrdes potnts at infinity, is the magnetic fielddue to the currents zero? (A) Only atryint p (B) At all points on the line ,S,S' (C) At a-ll points on the line connecting the two wircs (D) At all points on a circle of radius 2d centered on Point P @ nt nopoints fa I 18. The direction of the magnetic field at point .R caused by the currcnt .{ in the wire shbwn above is (A) to the left (B) to the right (C) toward the wire (D) into the page @ outofthlfage

Questions 2G22 relate to the following circuit diagram, which shows a battery with an intcrnal resistance of 4.0 ohms connected to a l6ohm and a 2Gohm rcsistor in scries. The current in the 20-ohm rcsistor is 0.3 amperes. 23. If thc gas in a containcr apsor[s 275 joules of heat, has 125 joules of work done on it, and then does 50 joules of work, what is the increase in the internal enerry ofthe gas? (A) l0o J (B) 200J G) 3so r (D) 400 J (E) 4s0 J Questions 24-25 with e mass of 1.50 kilograms, specific a mass of 3.00 and initial rernoved after 5 20'C. Negloct any thc insulated jar. 0,-z(1 1 tr)- t D

/e' // (r flf.*.rut7' I 'C*{ edr ;f'|- :.). lue,6n4t r u'm w v Which three of the glass lenses above, whcn placed in air, will cause parallel rays of light to conv€rge? I, II, and III I, III, and V I, [V, and V II, III, and IV II, M and V Qucstions 27-28 29. (D) (E) H(D) (E) {' trt' Qdqs'D='ov' rf,od=Aq k atr t't -- ca*\ zn--l A standing wave of frequerrcy 5 hertz is set up on a string 2 meters long with nodes at both ends and in thc center, as shown above. 27. The speed at which waves propaptc on the string is (A) 0.4 m/s (B) 2.5 m/s G) 5 m/s (9 l0 m/s (E) 20 m/s The fundamental frcquency of vibration of the string is lHz 2.5llz 5Hz 7.5H2 l0 Hz Radio waves Infrared radiation Visible light Ultraviol€t radiation Gamma radiation For the five types of electromagnetic radiation listed above, which of the following correctly describes the way in which wavelength, frcquency, and photon energy change as one gocs from the top of the list to thc bottom? Wavelength Frcquency Photon Encrgy Docreas€s Decreases lncreascs Decreases Increases Increascs Incrcases Docreases Domeases Incrcases Dccreascs Irrcreases Incrcases Increases Increases Sound in air can best be described as which of the following types of waves? @ Longitudinal (B) Tlansverse (9 Torsional (D) Elcctromagnetic (E) Polarizcd H(D) (E)

.A Objcct o z VoBoc zoD Minor oE free neutrons in Irax I tf' f( -- IIII l I go!aril 4'd 31. An object is placed near a plane mirror, as shown above. Which of the labeled points is the position of the image? Questions 32-33 deal with nuclear fission for which the fo-iiowi=gffion is a good example. uiu * fn-''tjn" + flrr * neutrons * released energy A B c D E the products of L13cw 4 (A) (B) (c) E L^t b\"t* (A) (B) (c) I 32. Thc total number of this rcaction is n (4) 2 ww Ei BfL (D)5 '2 (E) 5 lg 33. Which of the following statements is always true for neutron-induoed fission reacrions invotving f,jU ? I. The end products always include Ba and Kr, II. The rest mass of the end products is less than thatof 'zfju + in. D(rvb{uq fl&oh;crtrosc III. The total number of nucleons (protons plus n€utrons) in the end products is less than that in f;ltr + jn. ($ II only (B) III only (C) I and II only (D) I and III only (E) I, U, and III Qlestions 34-35 n-2 r= I 35. Which of the fiollowing transitions will produce thc photon with the longcst wavelength? n:2tor:l n:3toz:l n:3ton:2 n=4toz=l n:4ton:3 A hypothetical atom has four energy states.s shown above. 34. Which of the fiollowing photon energics could NOT be found in the emission spectra of this atom after it has been excited to thc z - 4 state? (A) I ev (B) 2 eV (O 3eV @ +ev (E) 5 eV ffq"\6

about 39. A muon, frame of (A)3x (B)3x (C)3x (D)3x (E)3x uon. as melpured by an tri',1W*env (A) (B) (c) (D) (E) 60 is a radioactive with a half-life of After many years will the activity a new ofcobalt 60 be decreased to U8 its 2.5 a lifetime 2 x 10-6 second in its 5 l0 l5 on the original amount of cobalt 60. 41. Of the following phenomena, which provides the best evidene that light can have particle properties? (A) Interference of light in thin films tpsvr (B) Electromagnetic radiation,lctu( @ nhotocteciric effect ?^pfldl (D) Electron diffraction urrrft' (E) X-ray diffraction rp*lv Of the following phenomena, which provides the b€st evidene that particles can have wave properties? (A) The absomtion of photons bv electrons in an atom Qttrnue,ta*ac ' - r | . C{ (D l'-he a-decay of radioactive nuclei ?arrQ"tcttu O The il$Sfnc" g3!te,rn produced by neutrons incidenFon a crystal (D) The production of *-tays by electrons striking a metal target (E) The scattering ofphotons by eloctrons at rest A wire of constant length is moving in a constant magnetic field, as shown above. The wire and the velocity vector are perpendicular to each other and are both perpendicular to the field. Which of the following graphs best represents the potential differ, ence I between the ends of the wire as a function of the speed u of the wire? t =4I'J b'# rA'*^"-W I"w" I+ I l-/l-/ I, o e II I o e tt/ t/l,/ l-/l-_ o e t l\t\r\_ o I l--l,/ l,/ o 37. 38. in the upper atmo- sphere with a of 0.998c toward the Earth. The lifetime of t observer on the (B) (c) (D) (E) l0-a s l0-5 s l0-6 s u'h*h 4(}. The operator of a space station observes a space vehicle approaching at a constant speed u. The operator sends a light signal at speed c toward the space vehicle. The speed of thc light signal relative to the space vehicle is (A)c+u (B) c-u ,.>-(9) c tD 4JT-:717 @) "Jr -717 l0-/ s l0l3 s

:w 3 rwu . Mr 3w'ry^ry 4s \wn''lv5 q/ a2 (/ t tT Forces between trvo obirts which are inverscly proportional to thc squarc of thc distance berwecn the ob!rcts include which of thc following? I. Graviational forcc bctweqr rwo oelcstial bodics II. Electrostatic forpc bctwccn two elcctrons III. Nwlear force bctwocn two neutrons bs 42. M5-1 -rta.. Tz w5-ttt ' 43. A particle oscillales up and down in simple harmonic motion. Its height / as a function of time , is shown in the diagram above. At what time t does the particle achievc its maximum positive acoel- eration? r r @ I t lfoo A l^ ftt^?a^ lu D -r- (B) 2s (C) 3s (D) 4s (E) Nonc of the above, bccausc the acccleration is constant 4,4. A wcight lifrcr lifts a mass m at @nstant sp€cd to a height i in time r. What is the average pow€r output of the weight lifter? (A) ms (B) mh (Cl msh (p) msht (Q) nshlt A block of mass 3m can move without friction on a horizontal table. This block is atached to another block of mass rz by a cord that passes over a fric- tionless pulley, as shown above. If the masses of the cord and the pulley arc negligible, what is the magnitude of the acocleration of the desoending block? (Al Tsro @ sl+ (c) gi3 (D) 2s13 (E) s A car initially travels north and then turns to the left along a circular curve. This causes a package on the scat of the car to slide toward the right side of the car. Which of the following is rue of the nct force on the package while it is sliding? (A) The foroe is dirocted away from the center of the circle. (B) The foroe is dirocted north. (C) There is not enough forcc dirccted north to keep the packagc from sliding. @) There is not enough force tangential to the car's path to keep the packagc from sliding. (!f There is not enough force directed toward the center of the circle to keep the package from sliding. (A) trt I(E) I only III only I and II only 45. lI and III only I, I[, and III 4'^ ?= *6 ''1 ,q

47. A block of mass rz slides on a horizontal fric- tionless table with an initial s@ u6. It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed from its natural length? @* e r{*r il Rr e r-l- ln, I ffiT R2 hrallcl Cormection R2 7d" ?4L'ftt\ tt 'ty -u (t"4'lt\ : ugr:*? Serics Conncction In the diagrams above, resistors.Rl and R2 arc shown in two different connections to the same sourc€ of emf € that has no internal resistance. How does the power dissipated by the resistors in these two cases comparc? lt is greater for the series connection. It is greater for the parallel connection. It is the same for both connections. It is different for each connection, but one must know the values of R1 and R2 to know which is greater. It is different for each connection, but one must know the value of € 0o know which is grcater. The product 2ampercs x 2volts x 2soconds is eqrral 1s (A) 8 coulombs (9I 8 newtons @) 8 joules (D) 8 calories (E) 8 newton-amperes l" 49. Rods P and Q are at rest an inertial rcference frame above. Both rods have length ^L iq this frame. A person moves at a relativistic y direction. Which of the following wc observed for by the person? as compared to Z, than I Greater than l, Less than tr @T,o {c)ffw Yv''* fli tlf {-ry {z- q," c 6 VE * The planet Mars has mass 6.4 x lOx kilograms and radius 3.4 x 106 meters. The acceleration 6f an object in free-fall near the surface of Mars is most nearly (A) @(c) (D) (E) ( rure'7 C" Q,c= (E) (A) zero (B) 1.0 m/s2 (C) 1.9 m/s2 @y l.z m7s2 (D 9.9 m/s2 51. \ztt Lb,L Y(A f i2i> w-v 'b ? ,C > W orl1 "r (f A radar operates at a wavelength of 3 centimeters. The frequency of these waves is (A) (B) (c) (D) l0-ro Hz It' Hz 108 Hz 3 x l08Hz l0ro Hz c.- b{ a Sturt = , 63 n't 4- l.lOb" t Less Less Less Lt L/ () (F) (c) (D) (E) '[,,n\, YLyt {1 tt 'f (e{.efr'tq

53. In the photoeloctric effect, the nlgUimums€of the electrons emitted by a metal surface when it is illuminated by light dcpcnds on which of the \ following? | \ I. Intensity orthe light - ^- try ".YY,'S II. Frequencyof the-light -f (wuc( riln"'t7 IIL Nature of the photoelectrii surface -)r. L ,/.r ) (A) I only v (B) III only (Q I and II only (E II and III only (E) I, I[, and III 54. Atoms of isotopes of the same element contain the same number of @ ptotont but a different number of neutrons (B) electrons but a different number of protons (C) neutrons but a different number of protons (D) neutrons as electrons (E) protons as neutrons 55. In each cycle of a C-arnot engine, 100 joules of heat is abaorbed frorn the high-lemperature reservoir and 60 joules is exhausted to the low-temperature reser- voir. What is the effrciency of the engine? 57. 6fr) 4oo/o (D ffi% (c) 67% (D) 150% (E) 167% (B) (c) (D) (E) w--Y/".4 In the Bohr that the quantized can be following ways? (A) An integral The atom is higher energy state. tron wavelengths rn's circular orbit. ist in each possible u2.a small, positively Two objrxts, of masscs 6 and 8 kilograms, are hung from the cnds of a stick that is 70 centimeters long and has marks wery l0 oentimeters, as shown above. If the mass of the stick is ncgligible, at which of the points indicated should a cord bc attached if the stick is to rcrnain horizontal whcn suspcnded from the cord? /Y=o . \ b ({) =x(") ?:l -'z( In the Doppler effoct for sound waves, factors that affect the frequeacy that the obeerver hears include which of the following? ", I. The speed ofthe source r/ IL The spced ofthe observer 7 III. The loudnees of the.sound (A) I only (!) III only @) I and II only (D) II and III only (E) I, II, and III A B C D E (A) (B) 8(E) must fit into the Only one elecfion electron state. An electron has a charged nucleus r6rbite$by el.ect r-ons

59. The figure above shows two wave pulscs that are approaching each other. Which of thc following best shows thc shape of the resultant pulsc whcn the centersofthepulses,points P and 9, coincide? Qucstions 6l{3 A plane 5 mctsrs in lcnglh is inclincd at an anglc of 37', as shown above. A block of wcigflt 20 nefions is plaood at the top of the plane and alloured to slide down. 61. Thc mass of the block is most nearly (A) 1.0 kg (B) 1.2 kg (Q l.6kg (D 2.0 kg (E) 2.s ke t^)r-il K (s t--l t__l (B) t\h2 cL- E-B (D) (E) The magnitude of the normal foroe exerted on the block by thc plane is most ncarly (A) roN /1* B I?N NI; h9, (D) 20 N ,,v (E)33N / 1o{3 Observations that indicatc that visible light has a wavelength much shorter than a centimctcr include which of thc following? I. The colorpd pattern seen in a soap bubble IL The color-ed pattern seen when light passes through a diffraction grating III. The bending of light when it passes from one medium to another medium fefic@drA 63. The work done on thc block by thc gravitational force during thc lmetcr slidc down the plane is most ncarly 20J 60J EOJ r00 J 130 J (A) 6l(c) (D) (E) ^^tr (A) I only (p) III onlY (p) I and II only (D) II and III only Xf iej r,II,andIII' r t ** Kv*- cl.

0,MrJ 'A 0o$!4( - \Nu d- +b ,-r-f'--. /'\t\,\ Pr' ta.R , aa A ball is thrown and follows the parabolic path shown Bbov€. Air friction is negligiblc. Point Q is the highest point on the path. Points P and X arc the samc height abovc the ground. 66. Which of the fiollowing best indicates the diroction of the nct fore, if any, on the ball at point p ? \ Thcre is no rH force on thc ball at poinr 0. Questisns 64-66 64. How do the spoeds of the ball at the three points co-rnpare? (A) Dr . re. uR (B) un.re.rp (C) uo

XBX X l..l;IIla l" *1._L XXX 67. A square loop of wire of resistance R and side a is grigltud with its plane perpendicular to a magnetic field B, as shown above. What must be the rate of change of the magnetic field in order to produoe a cuffent / in the loop? @ ryo' -?/- 6 ,7'A .- (B)Ia2lR b#t L/ , (C0., 8,'ff, A?"h'Yy (E) IRa X X x X 69. If the object distanoe for a converging thin lens is more than twice the focal length of the lens, the image is (A) virtual and erecr (B) larger than the object (9 locarcd inside the focal point (D) located at a distance between f and 2f \-/ from the lens (E) located at a distance more than 2f from the lens 70. Tro conducting spheres of different radii, as shown above, each have charge - e. Which of the following @curs when the two spheres are connected with a conducting wire? (A) No charge flows. (B) Negative charge flows from the larger sphere to the smaller sphere until thc electric field at the surface of each sphere is the same. (C) Negative charge flows from the larger sphere to the smaller sphere until the electric potential of each sphere is the same. (D) Negative charge flows from the smaller spherr to the larger sphere until the electric field at a;| the surface of each sphere is the same. (E)Negative charge flows from the smaller sphere \-/ to the larger sphere until the electric potential of each sphere is the same. >-----4-----3--+Q 68. The diagram above shows an isolated, positive charge Q. Point B istwice asfarawayfrom e as point ,,{ The ratio of the electric field strength at point ,{ to th€ electric field strength at point .B is fon+ ! (- E(c) (D) (E) 8to 4to 2to Ito I to2