1993AP Physics B Examination

with Key

Copyright O 1993 by College Entrance Examinations Board and Educational Testing ServiceAll rights reserved

l . In which of the following situations would an objectbe 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 fieldwith negligible air resistance.

I onlyIII onlyI and II onlyII and III onlyI. II. and III

A ball falls straight down through the air under theinfluence of gravity. There is a retarding force .F ontheballwithmagnitudegivenby F = bu, where uis the speed ofthe ball and 6 is a positive constant.The magnitude of the acceleration a of the ball atany time is equal to which of the following?

(A)g-,

3.

(A)(B)

H

(c') c + b;

@\'-H4 fru;6il.*o

Y^

t

/\n c - bl. -- ilAq,-'0. l

A - tr l lk-bV1- '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 thisspring stretches the spring 0.075 meter. The value ofthe force constant for the spring is most nearly

0.33 N/m0.66 N/m6.6 N/m

33 N/m66 N/m

The figure above shows 4r@serr,ucircuter tractwhose ends are at a vertical height lr. A blockplaced at point P at one end of the track is releasedfrom rest and slides past the bottom ofthe track.Which of the following is true of the height to whichthe 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 tofriction.

l"-;)i, ll-a Afuo,r&An object is released from rest on a planet that hasno atmosphere. The object falls freely for 3.0 metersin the first second. What is the magnitude of theacceleration due to gravity on the planet?

1.5 mis23.0 m/s'6.0 m/s'

10.0 m/s212.0 m/sz 8.

lf Spacecraft X has twice the mass of SpacecraftI, then true statements about X and I includewhich 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 andare initially held at rest on a frictionless surface, asshown above. The pucks are then released simulta-neously. If puck I has three times the mass of puckII, which of the following quantities is the same forboth pucks as the spring pulls the two pucks towardeach other?

(A) Speed(B) Velocity(C) Acceleration(D) Kinetic enersv@ Magnitude oTmomentum

The two spheres pictured above have equal densitiesand are subject only to their mutual gravitationalattraction. Which of the following quantities musthave the saqe magnitude for both spheres?

(A) Acceleration(B) Velocity(C) Kinetic energy(D) Displacement from the oenter of massi€j c"iuitational force c,6rra.[ i. opg":,i<

When an object oscillating in simple harmonicmotion is at its maximum displacement from theequilibrium position, which of the following is trueof the values of its speed and the magnitude of therestoring force?

Speed

Zero

(B) Tnro

I2 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)

Itmarumum

Itmilomum

Gr*eqrvahA, ̂ok ilAn^\eqA/''4,-

t0. Which of the following is true when an object ofmass ,?r moving on a horizontal frictionless surfacehits and sticks to an object of mass M > m, whichis 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 togetherwill be less than the initial speed of the less-massive object.

(E) The direction of motion of the objects that arestuck together depends on whether the hit isa head-on collision.

Two objects having the same mass travel towardeach other on a flat surface, each with a speed of1.0 meter per second relative to the surface. Theobjects collide head-on and are repor"ted to reboundafter the collision, each with a speed of 2.0 metersper second relative to the surface. Which of thefollowing assessments of this report is most accu-rate?

(A) Momentum was not conserved, therefore thereport is false.

(D) If potential energy was released to the objectsduring the collision, the report could be true.

(C) If the objects had different masses, the reportcould be true.

(D) If the surface was inclined, the report could betrue.

(E) If there was no friction between the objects andthe surface, the report could be true.

An automobile moves at constant speed down onehill and up another hill along the smoothly curvedsurface shown above. Which of the followingdiagrams best represents the directions of thevelocity and the acceleration of the automobile atthe instant that it is at the lowest position, as shown?

(A) -+oIlai

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 superconductorsto suddenly decrease to essentially zero?

(A) Increasing the voltage applied to the materialbeyond a certain threshold voltage

(B) Increasing the pressure applied to the material

- beyond a certain threshold pressure($ Cootltrg the material below a certain thresholdv 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 anexpression of which of the following?

Conservation of chargeConservation of energyAmpdre's lawFaraday's lawOhm's law

Questions l5-16 rcfer to the circuit shown below.

3pF

The equivalent capacitance for this network is mostneady

l0/7 pF3l2trF713 trF7 trF

14 pF

16. The charge stored in the S-microfarad capacitor ismost neady

15.

360 pC500 pC710 pC

1,100 pC1,800 pC

(A)(B)

ffi(A)

I(D)(E)

(A)

I(D)(E)

t4.

Qzorl - s,'0[-)= 9upL

re,L-l

f f iu; ) %*'

lonT'eL

fr1,v

-\e ,-, *

i' {u r& - - - -,- - - - #- - - -,- - - - €

-fT-i--t-

n.M

17. Twolargeparallelcondrctingplates p and p areconnected 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 onthe 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" ftrargewhen it is at point I, but in the opposite -dirotion

(D) much greater in magnitude than the fiorce onthe charge when it is at point II, but in thesame direction

(E) much less in magnitude than the force on the9!arg" when it is at point II, but in the samedirection

19. T\vo long parallel r+,ires.are sgparated by a distane d,as shown above. One wire ca*es a sLaiy current finto the plane of thc page while thi other'wire carries3 sleady current I out of te page. At what pointsin t!.e ntang of the p-age aoa oirtslOe ttr'ru1.res,Dcsrdes potnts at infinity, is the magnetic fielddue tothe 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 .Rcaused 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 4.0ohms connected to a l6ohm and a 2Gohm rcsistor inscries. 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 does50 joules of work, what is the increase in the internalenerry ofthe gas?(A) l0o J(B) 200JG) 3so r(D) 400 J(E) 4s0 J

Questions 24-25

with e mass of 1.50 kilograms, specific

a mass of 3.00and initialrernoved after 520'C. Negloct anythc insulated jar.

0,-z(1 1t r ) - t D<)

-5?1NYKFs4f l

IntemalRcsistrc

I =0.3 A

NA

20. what,l*" "*tthe

battery? V **'ltq'*u

21. What is the potcntial differencc acrosE the terminalsX and I of the batterv? . - n\

(A) r.zv "'::':,

- (qi[''*)(D 6.ov [L\ ' l - \ " - ro( t@ ro.s v \tu'-(D) r2.ov o- '(E) 13.2 v

1.2 v6.0 v

10.8 v12.0 v13.2V

What power is dissipatcd by thc tl-ohm internalresistance of the batte4l?

/ \/ \i ratc at which hea\is transferred whilemetal is in the liqui\s

\Us\J/s \

(A)(B)

ffi

I(c)(D)(E)

24. ^t\e tempenrtureremoved is

0"c4"C8"C

l0 'c20" c

25. Theaverathe piee

4s

liquid after the metal is

(A)(B)(c)(D)(E)

(A)(B)(c)(D)(E)

0.36 W1.2 w3.2 W3.6 W4.8W

16(}

/e'/ /

(r flf.*.rut7'I 'C*{

edr

;f'|-: . \ ) .

lue,6n4t

r u 'm w v

Which three of the glass lenses above, whcn placedin air, will cause parallel rays of light to conv€rge?

I, II, and IIII, III, and VI, [V, and VII, III, and IVII, M and V

Qucstions 27-28

29.

(D)(E)

H(D)(E)

{' trt' Qdqs'D='ov'

r f ,od=Aq katr t't -- ca*\

zn--l

A standing wave of frequerrcy 5 hertz is set up on astring 2 meters long with nodes at both ends and in thccenter, as shown above.

27. The speed at which waves propaptc on the string is(A) 0.4 m/s(B) 2.5 m/sG) 5 m/s(9 l0 m/s(E) 20 m/s

The fundamental frcquency of vibration of the stringis

lHz2.5llz5Hz7.5H2

l0 Hz

Radio wavesInfrared radiationVisible lightUltraviol€t radiationGamma radiation

For the five types of electromagnetic radiation listedabove, which of the following correctly describes theway in which wavelength, frcquency, and photonenergy change as one gocs from the top of the list tothc bottom?

Wavelength Frcquency Photon Encrgy

Docreas€s Decreases lncreascsDecreases Increases IncreascsIncrcases Docreases DomeasesIncrcases Dccreascs IrrcreasesIncrcases Increases Increases

Sound in air can best be described as which of thefollowing types of waves?

@ Longitudinal(B) Tlansverse(9 Torsional(D) Elcctromagnetic(E) Polarizcd

H(D)(E)

.A

Objcct o

zVoBoc

zoDMinor

oE

free neutrons in

IraxI tf' f( --IIIIl

Igo!aril4'd

31. An object is placed near a plane mirror, as shownabove. Which of the labeled points is the position ofthe image?

Questions 32-33 deal with nuclear fission for which thefo-iiowi=gffion is a good example.uiu * fn-''tjn" + flrr * neutrons * released energy

ABcDE

the products of

L13cw

4

(A)(B)(c)

EL^tb\"t*

(A)(B)(c)

I

32. Thc total number ofthis rcaction is n(4) 2 wwEi BfL(D)5 '2(E) 5 lg

33. Which of the following statements is always true forneutron-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;crtroscIII. The total number of nucleons (protons plus

n€utrons) in the end products is less than thatin 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 thcphoton with the longcst wavelength?

n:2tor: ln:3toz: ln:3ton:2n=4toz=ln:4ton:3

A hypothetical atom has four energy states.s shownabove.

34. Which of the fiollowing photon energics could NOTbe found in the emission spectra of this atom after ithas 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 ofAfter many years will the

activity a new ofcobalt 60 be decreased toU8 its

2.5

a lifetime 2 x 10-6 second in its

5l0l5

on the original amount of cobalt 60. 41.

Of the following phenomena, which provides thebest 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€stevidene 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"tcttuO 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 constantmagnetic field, as shown above. The wire and thevelocity vector are perpendicular to each other andare both perpendicular to the field. Which of thefollowing graphs best represents the potential differ,ence I between the ends of the wire as a function ofthe speed u of the wire?

t =4I 'J

b'# rA'*^"-W

I"w"

I+Il - /l - /

I ,oe

III

oett /t /l , /l - /l -_

oetl \t \r \_

oI

l - -l , /l , /

o

37.

38.

in the upper atmo-sphere with a of 0.998c toward the Earth.The lifetime of tobserver on the

(B)

(c)

(D)

(E)

l0-a sl0-5 sl0-6 s

u'h*h4(}. The operator of a space station observes a space

vehicle approaching at a constant speed u. Theoperator sends a light signal at speed c toward thespace vehicle. The speed of thc light signal relative tothe space vehicle is

(A)c+u

(B) c-u,.>-(9) ctD 4JT-:717@) "Jr -717

l0- / sl0l3 s

:w 3 rwu . Mr 3w'ry^ry

4s \wn''lv5q/

a2 ( / ttTForces between trvo obirts which are inversclyproportional to thc squarc of thc distance berwecnthe ob!rcts include which of thc following?

I. Graviational forcc bctweqr rwo oelcstial bodicsII. Electrostatic forpc bctwccn two elcctrons

III. Nwlear force bctwocn two neutrons

bs42.

M5-1 -rta..Tz w5-ttt '

43. A particle oscillales up and down in simpleharmonic motion. Its height / as a function of time, is shown in the diagram above. At what time tdoes the particle achievc its maximum positive acoel-eration? r r

@ I t lfoo A l^ ftt^?a^ lu\rD -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 aheight i in time r. What is the average pow€routput of the weight lifter?

(A) ms(B) mh(Cl msh(p) msht(Q) nshlt

A block of mass 3m can move without friction on ahorizontal table. This block is atached to anotherblock of mass rz by a cord that passes over a fric-tionless pulley, as shown above. If the masses of thecord and the pulley arc negligible, what is themagnitude of the acocleration of the desoendingblock?(Al Tsro@ sl+(c) gi3(D) 2s13(E) s

A car initially travels north and then turns to the leftalong a circular curve. This causes a package on thescat of the car to slide toward the right side of thecar. Which of the following is rue of the nct forceon the package while it is sliding?

(A) The foroe is dirocted away from the center ofthe 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 fromsliding.

(A)trtI(E)

I onlyIII onlyI and II only 45.lI and III onlyI, 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 thencompresses a spring of force constant k and isbrought to rest. How much is the spring compressedfrom its natural length?

@*

e

r{*r

ilRr

e

r-l-ln, I

ffiTR2

hrallclCormection

R2 7d"?4L'ftt\

t t

' ty

-u ( t"4 ' l t \

: ugr:*?

SericsConncction

In the diagrams above, resistors.Rl and R2 arcshown in two different connections to the samesourc€ of emf € that has no internal resistance. Howdoes the power dissipated by the resistors in thesetwo 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 whichis greater.

It is different for each connection, but one mustknow 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-amperesl"

49. Rods P and Q are at rest an inertial rcferenceframe above. Both rods havelength ̂ L iq this frame. A person moves ata relativistic y direction. Which of thefollowing wcobserved 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," c6

VE *

The planet Mars has mass 6.4 x lOx kilograms andradius 3.4 x 106 meters. The acceleration 6f anobject in free-fall near the surface of Mars is mostnearly

(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.\zt t

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 HzIt' Hz108 Hz3 x l08Hzl0ro Hz

c.- b{a

Sturt = , 63 n't 4-

l . lOb"tLess

LessLessLtL/

( )(F)(c)(D)(E)

'[,,n\, YLyt

{1 t t ' f

(e{.efr'tq

53. In the photoeloctric effect, the nlgUimums€ofthe electrons emitted by a metal surface when it isilluminated by light dcpcnds on which of the \following? | \

I. Intensity orthe light - ̂ - try ".YY,'SII. 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 thesame 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 heatis abaorbed frorn the high-lemperature reservoir and60 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/".4In the Bohrthat thequantized can befollowing ways?

(A) An integral

The atom is

higher energy state.

tron wavelengthsrn's circular orbit.ist in each possible

u2.a small, positively

Two objrxts, of masscs 6 and 8 kilograms, are hungfrom the cnds of a stick that is 70 centimeters longand has marks wery l0 oentimeters, as shownabove. If the mass of the stick is ncgligible, at whichof the points indicated should a cord bc attached ifthe stick is to rcrnain horizontal whcn suspcndedfrom the cord?

/Y=o . \b ({) =x(")

?:l -'z(

In the Doppler effoct for sound waves, factors thataffect the frequeacy that the obeerver hears includewhich of the following?

",I. The speed ofthe source r/

IL The spced ofthe observer 7III. The loudnees of the.sound

(A) I only(!) III only@) I and II only(D) II and III only(E) I, II, and III

ABCDE

(A)(B)

8(E)

must fit into theOnly 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 areapproaching each other. Which of thc following bestshows thc shape of the resultant pulsc whcn thecentersofthepulses,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 plaoodat 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--lt__l

(B)

t\h2cL-E-B

(D)

(E)

The magnitude of the normal foroe exerted on theblock 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 awavelength much shorter than a centimctcr includewhich of thc following?

I. The colorpd pattern seen in a soap bubbleIL The color-ed pattern seen when light passes

through a diffraction gratingIII. The bending of light when it passes from one

medium to another medium fefic@drA

63. The work done on thc block by thc gravitationalforce during thc lmetcr slidc down the plane ismost ncarly

20J60JEOJ

r00 J130 J

(A)6l(c)(D)(E)

^^tr(A) I only(p) III onlY(p) I and II only(D) II and III only Xfie j r , I I ,andII I ' 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 onthe path. Points P and X arc the samc height abovc the ground.

66. Which of the fiollowing best indicates the diroctionof 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 pointsco-rnpare?

(A) Dr . re. uR

(B) un.re.rp(C) uo <oR<ap

ta\

(D) ,e I up: DR

(E) uf : aR <'ae

65. Which of the following diragrams best shows thedirectibn of thc acccleradon of thc ball at point P ?

(A) ,/t

(B) ,//

(c)

(D)

@

@l(B)

(c)

(D)

(E)

XBX X

l . . l ; II la

l " *1._LXXX

67. A square loop of wire of resistance R and side a isgrigltud with its plane perpendicular to a magneticfield B, as shown above. What must be the rate ofchange of the magnetic field in order to produoe acuffent / in the loop?

@ ryo' -?/- 6 ,7'A .-(B)Ia2lR b#t L/

, (C0.,

8,'ff, A?"h'Yy(E) IRa

X

X

xX

69. If the object distanoe for a converging thin lens ismore than twice the focal length of the lens, theimage 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 shownabove, each have charge - e. Which of thefollowing @curs when the two spheres areconnected with a conducting wire?(A) No charge flows.(B) Negative charge flows from the larger sphere to

the smaller sphere until thc electric field atthe surface of each sphere is the same.

(C) Negative charge flows from the larger sphere tothe smaller sphere until the electric potentialof each sphere is the same.

(D) Negative charge flows from the smaller spherrto 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, positivecharge Q. Point B istwice asfarawayfrom e aspoint ,,{ The ratio of the electric field strength atpoint ,{ to th€ electric field strength at point .B is

fon+ !(-

E(c)(D)(E)

8to4to2toI toI to2