FOREWARD
The reason for writing this monograph is that there have been some excellent questions in ALevel Physics, almost “classical” evise by the !"!#$!L %oar between&''( ) *++& the author consiere these worthwhile resources for tutors an stuents, especially the more challenging an mathematically-base questions arising from the P. /0ynoptic1 papers2 The boo3 is intene to be rea in con4unction with the !"!#$!L 5oular 5oular examinations in A0 an A* Avance Avance Level Physics /0ub4ect $oes 6(7&, '(7&12 !xplanations an answers to questions set in A0 papers P&, P* an P8 an A* papers P7 an P. are provie2 9t is the author:s opinion that ;ption Topics Topics /examine within P8an P71 are best ealt with by the stuents themselves2 These 5oel Answers are purely suggestions mae by the author an no liability liabilit y for them rests with the examining boar2
www2alevel-physics2co2u3 $opyright, "r " < >uttall, *+&+ 90%>? '@6-&-6'6.@6-&.-6 &-6'6.@6-&.-*
PH1 JANUARY 1995 Question 1: Acceleration has units LT-* Belocity has units LT-&, so v* has units L*T-* Caius, r has units L v*Dr has units L *T-*L-& LT-2 0o, the expression is imensionally homogeneous2 The velocity of a mass may while its spee may be constant as in the case of circular motion2 0ince velocity is a vector /constantly changing1 whereas spee /a scalar1 may be constant2 Question 2:
The principal characteristics of a >ewton:s thir law pair of forces inclue? /i1 /ii1 /ii1 /iii /iii11 /iv /iv1
They must be of the same type They Th ey alwa always ys occu occurr in pair pairss /ac /acti ting ng on iff iffere erent nt boi boies es11 They Th ey are are eq equal ual in in mag magnnitu ituee They Th ey act act iinn op opposi posite te ire irect ctio ionns
Question 3: Esing the Principle of $onservation of !nergy? F mv* mgh v* *gh * x '26& x *2++ 8'2*7, giving v G/8'2*71 .2*. 0pee of ball !2 "s-1 Tangent Tangent of h-t curve at +2@* s at h + is approximately 72@ ms -& Length of time in contact with groun +2@* ) +2.7 +2+6 s2
ewton:s secon law
giving t +2+6 s, m +2&*+ 3g, u .2*. ms -&, v 72@ ms -& < +2&*+ x /72@ ) .2*.1D+2+6 2!3# N Question #: The centre of gravity of a boy may be efine as the point where the resultant force /or weight1 of the boy acts or appears to act2
Ta3ing moments about A? 7++ x +2. < x &2*+, since
sin-& /+2.1, giving F $ 2%% N
Bertical Bertical force 7++ > oriHontal force *++ > 5agnitue of the resultant G/7++* = *++*1 ##&!2 N Question 5: '() Ior3 Ior3 is efine as a s the prouct of force an istance move in the irection of force2 I ewton2metre1 >m 3gms -* x m 3gm *s-* Power is efine as the rate of oing wor32 Enit of power Iatt or Joule per secon2 3gm *s-8 '*) 0ince power force x velocity, power evelope by motor (++ x && $ 5 5%% W Also, power $urrent x voltage 92B, so 9 PDB ( (++D&*+ #5!+ A
Question :
Question &: /a1 A typical typical e2m2f2 e2m2f2 of a single single ry cell cell is 1!5 A typical terminal p22 of a ry cell, supplying a normal loa 1!#
/b1 0hort circuit with cells li3e nic3el-camium nic3el-camium gives rise to high currents flowing in the external circuit since they have very low internal resistances2 Power, P 9 *C an if 9, C are both high, then a great eal of heat woul be prouce2
Question +: $harge store in capacitor, $2B, so &++ x &+ -. x (2+ 5%%./ !nergy store in capacitor F $B * F x &++ x &+ -. /(1* 1!25 "J To show experimentally that charge store in a &++ M< capacitor is proportional to p22 over the range r ange + ) &+ B, B, please see stanar textboo32
PH1 JUNE 1995 Question 1: coulomb
force length mole newton
temperature interval
& volt &Joule per $oulomb, B JD$ & J & >m 3gm *s-* an 9t As, giving volts imensions of 0"2s-3A-1 Vectors have magnitue an irection whereas scalars have magnitue only2 Potential ifference is a s((4 quantity2 Question 2: < 8+ x '26& 29# N
The 87 3g mass accelerates ownwars because there is a resultant force ownwars since the weight excees the contact force2 Question 3: Ior3 one Area uner < ) s curve *7+ x /&+ x +2+&1 2# J !quating N! with the wor3 one in stretching catapult? F mv* wor3 one in stretching catapult F x +2+6 x v * *7, giving v G.++ 2#!5 "s-1
Question #: Potential energy changes occurring area s uner? tA an t%? Loss of gravitational P! an gain in N! t% an t$? N! is transferre into elastic P! when the ball eforms on the groun2 t$ an t"? The elastic P! is re-converte into N!2
Question 5: A boy can be moving at constant spee yet accelerating if we consier motion in a circle2 The spee may be constant but the velocity vector /tangential to circle1 is continuously changing ) therefore accelerating2 The force acts? to(46s t7e E(4t7 The force acts? on t7e E(4t78 to(46s t7e oon2
Question : ! 9C *++ x &+ -. /&+ x &+8 = &( x &+ 81 5!%
Total series resistance /(2+1D/*(+ x &+ -.1 *+ 3K &DC B = &D/&( +++1 &D/&+ +++1, giving C B 3% 0, Question &: The capacitance of a capacitor is a measure of the charge /in $oulombs1, store in it per volt or unit p22 that is use to charge it2
$urrent, 9 BDC &2(D7@+ x &+ 8 3!2 .A
!nergy in fully-charge capacitor F $B* F /*++ x &+ -.1 x /&2(1* %!225 "J
Question +:
PH1 JANUARY 199 Question 1: Ce-arranging the requation? O 7*r 8D5T* since 7* is constant, the imensions of O are? "30-1s-2
Two labelle boies acte upon by one force only Two forces /of same magnitue1 oppposite in irection/preferably in thew same line12
The forces on iagrams are consistent with >ewton:s Thir law of 5otion since? /i1 /ii1
They are equal in magnitue an opposite in irection They must be of the same 3in2
Question 2: >ewton:s secon Law of 5otion states that, “The rate of change of momentum is irectly proportional to the applie force an ta3es place in the same irection”2 5omentum is conserve in any collision2 Ninetic energy is conserve in elastic collisions2 Question 3: !nergy store Area uner force-extension graph F x 6++ x +2(+ 2%% J !quating 3inetic energy an elastic potential energy? F mv* *++, so v G/*++ x *D+2+.+1 +1!& "s-1
/i1 /ii1
oriHontal velocity component will ecrease slightly owing to air resistance The vertical velocity component will ecrease to Hero an then increase on ownwars motion ue to the effects of gravity2
Question #: $ircuit iagram showing? • • •
Bariable power supply unit Ammeter in series with labelle wire Boltmeter in parallel with wire2
Cate of wor3ing or power 9B +2&* x 82( %!#2 W 0ince 9 nAqv, giving v 9DnAq 82(D/&2@ x &+ *7 x & x &+ -. x &2. x &+ -&'1 1!29 ; 1% -# "s-1 Power
The total capacitance? &D$total &D*++ = &D& +++, giving capacitance &.@ M< The charge which flows from the battery? $B &.@ x &+-. x ' 1 5%% ./ The final p22 across the capacitor? B& D$& &2( x &+ -8D&+-8 1!5 B* D$* &2( x &+ -8D* x &+-7 &!5
Question :
The resistance of the L2"2C2 ecreases with an increase in light intensity2 Thus, there is a consequent increase in the ammeter or voltmeter2 Question &:
Question +: Please see P& June &''( /uestion 61 for etails2 9n orer to minimiHe errors in the experiment?
Ese large free-fall istances in orer to minimiHe timing errors or ta3e several reaings at each istance to minimiHe ranom errors2
PH1 JUNE 199 Question 1: The magnitue of a physical quantity may be written as the prouct of a number an unit, e2g2 6 >ewtons2 9f the units on one sie of an equation are ifferent from those on the other, then they relate to ifferent physical quantities an cannot therefore be equal2 An equation which is homogeneous, but still incorrect may be written? mgh mv* or s ut = at * etc2 Question 2: Power of athlete increase in potential energyDtime ta3en mghDt /(( x '26& x 82.1D&26 1 %+% W Power to weight ratio >ms -&D> "s-1 Power to weight ratio of Athlete & +6+D/(( x '26&1 2!% "s-1 Question 3: The time, t lies in the range? *2+( s ˂ t ˂ *2&+ s The ownwars sloping lines of the v-t curves are straight since these represent the acceleration ue to gravity ) which is constant2 v* u* = *as (2+* +* = */'26&1s s $ 1!25 "
Free fall means that the only force acting on the boy is that of gravity2 The height remains constant since we are ealing with circular motion ) the centripetal force is provie by the gravitational attraction of the !arth for the satellite2 Question 5: Resisti
Question : %y Nirchoff:s
Question +: /i1 /ii1
•
Total Linear 5omentum before collision Total Linear 5omentum after collision2
PH1 JANUARY 199& Question 1: A represents weight of parachutist % represents reaction of groun on parachutist2 These forces are unpaire because the parachutist has a negative acceleration, requiring a nett upwar force2 Question 2: 0pee angular spee x raius /v rQ1 &. x +26 12!+ "s-1 $entripetal acceleration Q*r &6* x +26 2%#!+ "s-2 The resultant acceleration is provie by the centripetal acceleration 2%#!+ "s-2 since the stone is horiHontal an the weight of the stone has no component in this irection2 The string is most li3ely to brea3 when the stone is nearest to the groun since thr tension at this point is a maximum mQ *r = mg2 Question 3: Oain of N! loss of P! v G/*gh1 G/* x '26 x +2&+1 1!# "s-1 s ut = F at* 0ince u + an a g s F gt *, giving t* *sDg, so t G/*sDg1 %!1# s The spee of % 4ust after the collision initial spee of A before collision /equal masses1 1!# "s-1 "istance spee x time &27 x +2&7 %!2 " % rops the istance of &+ cm more quic3ly than A because % is in free fall whereas the ownwars acceleration of A is constrcite by the upwards tension in the string2 Question #: 5aximum acceleration maximum graient of v-t curve &+D*2( # '>?- %!5) "s -2 "istance travelle Area uner v-t curve 33 '>?- 3) "
Question 5: s /u=v1 tD* 0ince u +, final spee * x average spee /* x +2'+1D+2&8 1!59 "s-1 Average acceleration imcrease in speeDtime &2('D&2&8 1!#1 "s-2 9n orer to test the constancy of the acceleration, tic3er tape is attache to the glier2 The tape is then cut into &+-ot lengths2 9f lai sie-by-sie, they shoul form a straight line graph for constant acceleration2 Question : Boltage rop across 7 K resistor, B 9C 7 x +2@( 8 B Then, 9& /' - 81D*7 %!25 A 9* /+2@( - +2*(1 +2(+ A C BD9 .D+2(+ 12 , Question &:
$urrent 9 PowerDBoltage *7D&* * A Cesistance BoltageD$urrent &*D* , The . K an *7 K resistors form a parallel networ3, of resistance 726 K2 >ow, C BD9 6D*2( 3!2 ,
Question +:
Cesistance BD9 8D/7+ x &+ -.1 &5 0,
PH1 JUNE 199& Question 1:
Question 2:
The >ewton:s Thir Law pair of forces are? /a1 !qual in magnitue /b1 ;pposite in irection2 Question 3: Ieight of lorry 7( +++ x '26& ##1!#5 0N Ta3ing moments about A? 9ncrease in upwars force at % x .+ 77& 7(+ x 7+ 29# 3%% N
$orresponing increase in upwwar force at A 77& 7(+ ) *'7 8++ 1#& 15% N Question #: Cesistance, C &2(D/&++ x &+ -.1 15 %%% , Aitional resistance to obtain half <0" 15 %%% , Aitional resistance to obtain quarter <0" #5 %%% ,
;n connecting the ;hmmeter to an uncharge *++ M< capacitor, an immeiate inication of current flow occurs, followe by a slow ecay of current magnitue towars Hero2 Question 5: >ewton:s 0econ Law of 5otion states that the rate of change of momentum is irectly proportional to the applie force an ta3es place in the same irection2 ewton:s 0econ Law, please see a stanar textboo32 The magnitue of the applie force relies upon oo3e:s Law behaviour ) i2e2 force is irectly proportional to the extension of the rubber elastic ban2 $alibration may be mae by hanging 3nown weights on the ban an noting extensions2 Tic3er-timerDtape enables accelerations to be etermine since each ot is +2+* s apart an the sistance between them is the istance travelle2 The experiment is repeate for ifferent extensions /i2e2 ifferent forces12 Acceleration may be etermine by cutting out the tape strips containing &+ ots an laying them sie-by-sie2 Acceleration may be calculate by the slope of this v-t graph2 A plot is then mae of force vs2 acceleration2 The Law is proven if this plot is a straight line passing through the origin2 Question : 9 nAvq "rift spee, v 9DnAq /6 x &+ -81D/@ x &+*8 x 8 x &+ -. x &2. x &+ -&'1 2!3+ ; 1% -3 "s-1 Although the rift spee in the copper wire is much lower, 9, A an q are the same for both nspecimens2 $onsequently, the electron concentratiuon /n1 must be much larger in copper than in the semi-conuctor2
Ihen the temperature rises, stronger thermal vibrations promote more electrons to the conuction ban, thereby increasing the carrier ensity2 Question &: "ecrease in potential energy per secon weight x height lossDsecon '++ x &2* 1 %+% J This potential energy is mainly transferre to the surrounings in the form of heat2 0hortfall in power & +6+ ) 7++ .6+ I is greater than can be provie over a sufficiently long perio for sustaine flight2 Question +: The perio of !arth:s rotation about the sun 1 =e(4 Angular spee, Q *D/8.( x *7 x .+ x .+1 1!99 ; 1% -& 4(6!s-1 $entripetal force mrQ* (2'6 x &+ *7 x &2(+ x &+ && x /&2'' x &+ -@1* 3!55 ; 1% 22 N This centripetal force is provie by the gravitational force of attraction of the 0un2 Question 9: $harge store, $B &++ x &+ -. x &* 1 2%% ./
The charge is share between the two capacitors2 >ew equivalent capacitance, $ /& *++ x &+-.1D/7++ x &+-.1 3!%
PH1 JANUARY 199+ Question 1:
Question 3:
The reaction of the floor on the crowbar is not involve in the energy transfer process since it oes not move any istance2 Advantage of keeping x as small as possible? the force on the nail hea is larger /Principle of 5oments12 Disadvantage of keeping x as small as possible? the istance move by thye nail is very small2 Question #:
F /+2*1 .* 82. J
After collision, N! of N = L F /+2*1 7 * = F /&2+1 * * &2. = * 82. J The impulse of a force, 9
Question 5: @4(7 / shows how the 3inetic energy of the boy /y-axis1 varies with the istance fallen /x-axis12 This is because N! F mv *2 0ince u +an m is constant, we may regar N! as the v*-axis2 >ow v* u* = *ax v* vs2 x shoul be a linear plot since a g constant @4(7 D shows how the istance fallen /y-axis1 varies with the time /x-axis12 This is because x ut = F at * an since u + an a g constant Gx W t2 @4(7 A shows the relationship between acceleration /y-axis1 an istance /x-axis12 This is because acceleration g constant2 Question : %y the Principle of $onservation of !nergy? mgh F mv* v G/*gh1 G/* x '26& x +261 G&(2.'. 3!9 "s-1 >ow, weight of chil mg *& x '26& *+. > $entripetal force mv*Dr /*& x 82'. *1D8 &+'26 >
/i1
Iith the switch 0 close, the * M< capacitor woul be Xshort-circuite:2 Thus, we nee consier only the charging of the 8 M< capacitor2 !nergy, I F $B * F x 8 x &+ -. x/.1* 5# .J
/ii1
Iith switch 0 opene, we nee to calculate the combine capacitance of the 8 M< an *M< capacitors in series? &D$ &D8 = F (D., giving $ &2* M<2 $harge store $B &2* x &+ -. x . @2* x &+ -. $ !nergy store in 8 M< capacitor F *D$ F /@2* x &+ -.1*D/8 x &+-.1 +!# .J
PH1 JUNE 199+ Question 1:
Question 2:
Question 3: The principle of moments states that Xfor a boy in a state of equilibrium, the sum of the cloc3wise moments is equal to the sum of the cloc3wise moments, ta3en about any point2: Ta3ing moments about %?
Question #:
The normal contact > ba l ances mg cos Y2 An unbalance force /mg sin Y1, perpenicular to >, acts own the plane2 >ow, since Y 8+o an sin 8+o +2(, mg sin Y +2&++ x '26& x +2( %!#91 N Ior3 one ew N!
Ceuce force /cause by friction1 x *+ cm /+27'& ) +2&'1 x +2*+ % "J
The wor3 one vs2 friction is less for the smooth plane than for the rough one more energy is transferre into N!2
Question 5: The fraction of the battery voltage obtaine across the ens of the resistance wire may be varie from + to &* B by moving the slier P2 The 9-B curve eviates from a straight line at higher current values because the wire becomes hotter2 At low current values, resistance 827D+2@ #!9 , 9n orer to etermine the resistivity of the wire, the two aitional quantities require are? ent7 (n6 6i("ete4 /giving cross-sectional area12 The factor having the greater influence on the error in a calculate value for resistivity woul be the area /or iameter12 The reason for this is that the error in area * x error in raius2 The error is small /an may be uneven1 ) thus a micrometer screw gauge shoul be use an the iameter of the wire measure at several locations2 Question : FALBE since resistors in series carry the same current an 9 nAve, if A is ecrease, it follows that v woul increase2 FALBE since we have the same charging current the same time, it follows that the charges must be equal2 TRUE since P 9*C, then if the resistance ecreases, then the power is increase2 FALBE since equal increments in voltage require larger charge on a larger capacitor2 Question &: ote? springs shoul be place at en of air gliers, so they reboun on impact2 A light gateDprecision stopcloc3 woul be use to etermine spees2 Physical quantities to be measure inclue? • • • •
masses of both trolleys their spees before an after collision measuring a particular time an istance spee istanceDtime2
9n orer to show that N! is conserve in the collision? N! before impact N! after impact, i2e2 Z/F mv* values before collision1 Z/F mv* values after collision12
PH1 JANUARY 1999 Question 1:
Question 2: /i1 /ii1
$hange of isplacement t + to t # ( x +2( 2!% " $hange of isplacement t + to t [ 8 x +2( 1!5 " 0hape of obstacle?
Question 3: 0calar quantities have magnitue, but no irection vector quantities nee both magnitue an irection to be specifie2 Cesultant force exerte on lamp by wire 72( cos 7+o x * !9 N Ieight of lamp also !9 N since weight supporting force since it is in equilibrium2
Question #:
%y similar triangles let the isplacement of $ of O x, then? 8D*7 xD( x &(D.7 %!25 "" %y the Principle of 5oments? m x &6 &++2+ x &6 = &*6 x +2+.*( mass, m 1%%!# The scale is not calibrate since the calibration changes if the masses on the scale pans change2 Question 5: To show that the collision is elastic? N! before impact F /** +++1/81 * = F /.. +++1/&1 * 132 0J N! after impact F /.. +++1/*1 * 132 0J 0ince the N! before impact N! after impact, then the collision is e(sti N! at mi-point F /66 +++1/&2(1 * 99 0J !nergy has been store elastically in the spring buffers2 9t is possible for the two truc3s to be in contact, but to travel at ifferent spees since the spring is being compresse /or expane12 9mpulse change of momentum mv ) mu m/v-u1 .. +++ /*-&1 0Ns The impulse is the s("e, even if the collision occurs over half the original time because the momentum exchange remains the same2 Question : $apacitance $hargeDBoltage /i2e2 charge store per unit p221 $urrent flows in the bell uring the charging part of the cycle when the capacitor is fully charge2
The bell tin3les when the switch is close an then opene again since the capacitor ischarges, the current flows through the bell2 The operation of the anti-tin3ling switch is to Xshort out: 8-( such that no current flows in the bell2 Question &: C RLDA /&2@* x &+ -( x .2++1D/+2*( x &+ -.1 %!#1 , 9 nAve &2&+ x &+ *' x +2*( x &+ -. x &2.+ x &+ -&' x +2+'8 x &+ -8 %!#1 A !lectrons behave li3e an Xincompressible flui: such that there are a large number of free electrons in the metallic lattice, they will start to move /li3e cars in a traffic 4am12
PH1 JUNE 1999 Question 1: Explanation of magnitude of force A w.r.t. weight of block: The force on A is greater than the weight of the bloc3 since the bloc3 is thrown upwars2
"isplacement area between origin an an &2( s 23!+ " Acceleration graient of tangent at *2+ s /@+ - *+1D/*2. ) +1 19 "s-2 N! F mv * F x 7*+ x .8 * %!+# J
Question 3: A piece of tic3er-tape is attache to A an run through a tic3er-timer2 The length of the truc3 is measure an the tape mar3e when it passes A2 Then, average spee length of truc3Dtime interval2 v* u* = *as a /v * ) u*1D*s /&2.71 * ) /&2(*1*D* x &2*+ *2.' ) *28&D*27+ %!15+ "s-2 Question #: Ior3 force x isplacement in irection of force2 9n the case of a particle moving in a circular path, the wor3 one on the particle is Hero since the isplacement in the irection of the force is Hero consequently the irection of motion must be 3ept at right angles to the irection of the force2 Belocity change vA ) v% an its irection is at '+ o to A%, towars L02 Thus, acceleration is towars the centre of the circle2
Question 5: P B*DC where the symbols have their usual meaning2 C B*DP /*8+1*D&++ 529 , #eason and explanation for drift speed of electrons in filament being higher than in remainder of circuit: 0ince 9 nAve, assuming n to be constant, then for a series circuit, 9 everywhere is the same so that with a ecrease in A, then v must necessarily increase2 Question :
Question &: $alculation of energy: I F $B* F /8 x &+ -.1/.1* 5# .J $alculation of total energy: $B /8 x &+ -.1/.1 1+ ./ $ $& = $* 8 = ( + .F I *D*$ /&61*D* x 6 2%!25 .J The ecrease in store energy is accounte for by heating of the resistor /or wires12
Question +: Cesistivity /Cesistance x $ross-sectional Area1Dlength
#eason for %& ' resistor: This is to prevent a high current flowing in the wire which woul change its resistivity /resistivity of metals increases with temperature12 Cesistance BD9 /or graient of graph1 +2&*D/(+ x &+ -81 2!# , Area of wire *D7 x /+2(' x &+ -81*D7 *2@8 x &+ -@ m* R *27 x *2@8 x &+ -.D+2(& 1!2+ ; 1% - ,!"
PH1 JANUARY 2%%% Question 1: A escription of force $ which forms a >ewton:s Thir Law Pair with A is X5an pulling !arth upwars, with a gravitational force:2 (imilarities )any *+: • • • • •
5agnitues are equal Line of action parallel Types of force same /i2e2 gravitational1 Time interval or uration $onstant in value /not true generally, but true in this case12
Differences: • •
Act in opposite irections Act on ifferent boies2
The two forces which show whether or not man is in equilibrium are A (n6 C2 Question 2:
Question 3:
,easurements: Cecor voltmeter an corresponing ammeter reaings2 Then , repeat for a range of supply voltage settings2
Question #: -otal amount of energy released during flight: &2@& x &+( x 86 !5 J nput power to engines: /.2( x &+&*1D7@ x 8.++ 3+ W Average speed of aircraft: 7& +++D7@ +&% 0"7-1 o4 2#% "s -1 ,ultiplying maximum thrust by engine speed: x *7+ ms -&
;hm:s Law for a complete circuit is? !D9 /C = r1 where the symbols have their usual significance2 Thus, ! 72( B 9 +28 A2 0o, C 82(D+28 &&2..222 K 72(D+28 /&&2.. = r1, where r internal resistance /8 cells1 &( &&2..222 r, giving r 8288 K Thus, internal resistance of one cell 8288D8 1!1 ,
Question : hm and Farad expressed in terms of ( units: ;hm BoltDAmpere2 0ince & B & Joule per $oulomb2 ;hm has imensions JD$2A />2m1D/A2s2A1 0ince & > & 3gms -*, then K 3g2m2s -*2mDA*2s 0o, base units for ;hm 0!"2!s-3!A-2
Explanation of shape of graph /any ;>!1? • • •
Line is straight ue to acceleration /g1 constant Oraient is negative /eceleration initially, followe by change in irection1 Belocity changes sign /upwars initially ownwars later12
$alculation of distance travelled by bullet ? Area enclose by v-t graph * x area of triangles whose height 7(+ ms -& an base 7. s * x F x /7(+ x 7.1 7(+ x 7. 2% &%% "
PH1 JUNE 2%%% Question 1:
Question 2: To be correct /physically1, the units on the L0 of an equation shoul be the same as those on the C02 x ut = F at * ;n the L0 of the equation, units are metres /m12 ;n the C0? ut has imensions ms -& x s m F at* has imensions ms -* x s* m Thus, the e"uation is homogeneous w2r2t2 units2 An equation may be correct w2r2t2 units, but still incorrect if mathematical constants, e2g2 F, etc2 Are omitte2 !nergy is conserve from A to % by? Loss of gravitational potential energy gain in 3inetic energy mg\h F mv* v* *gh v G/*gh1 G/* x '26& x 81 G/(626.1 &!& "s-1
Assu"tions "(6e '(n= ONE): • •
>o air resistance Cope is inextensible2
The tension in the rope will be a maximum at the bottom of the swing since centripetal force is ae to the weight at this point2 Question #:
The screws are usually situate as high as possible in orer to obtain maximum forceDmoment an maximiHe stability2 9f the screws were lower own, ifficulty woul be experience in getting the the cabinet vertical against the wall2 Question 5: Ihen switch 0& is move from A to %? • •
The electromagnet loses its magnetism /ball rops1 The cloc3 is activate2 s ut = F at * /u + an a g1 &2++ F /'26&1t * '26& t* *2++, giving t $ %!#5 s
The time for the ball to reach the groun would also take &.12 s, since the only ownwar force on the ball is ue to the Earth3s gravitational field 2 oriHontal velocity istance travelleDtime ta3en *2++D+27( #!#3 "s-1 Question : /a1
B ! ) 9r &*2+ ) 82+/81 &*2+ ) '2+ 3!%
Question &: The resistance of the thermistor decreases non4linearly with temperature2 This is ue to the fact that with increasing temperature /energy1, electrons are promoted from the valence to conduction band. !6! /(u(tion: p22 across thermistor *2+ ) +26 &2* B $urrent through thermistor current through resistor BDC +26D88+ *27* mA Cesistanceof thermistor BD9 &2*D/*27* x &+ -81 #95 , Enli3e metallic /ohmic1 conuctors which have a linear 9-B relationship /constant resistance1, that for thermistors is non-linear2 Therefore, the voltage across the voltmeter woul be 7i7e4 since that across the thermistor woul be oe4 /as a result of ecreasing resistance with temperature12 Question +: The slope of the graph represents ((it(ne2 The area shae represents ene4= sto4e62 I F $B* F x &++ x &+ -. x /*(+1* 3!125 J Power from cell &2( x +2* +28 I Power !nergyDtime t !DP 82&*(D+28 1%!# s
PH1 JANUARY 2%%1 Question 1: 5ase units for the 6oule? & J & >m >ewton has units 3g2m2s -* /< ma1 base unit 0!"2!s-2 7omogeneity of formula? R 3g2m-8 rm f s-& Enits of C0 /3g2m -81/m1(/s-&1* 3g2m*2s-* which is the same as L0 The formula might still be incorrect, since although imensionally correct, constants /such as F in the formula coul be wrong12 Question 2: 5omentum mass x velocity
Question 3: Ior3 average force x time area uner <-t curve F x +2+7+ x ** %!## J gpe mg\h +2+*7 x '26& x +2.+ %!1# J Ihen compare, the energy in compressing the spring is greater than the gpe gaine by the frog2 Ceasons to explain this /all involve the law of conservation of energy1 which states that the total energy of a close system remains constant, but energy may be converte from one form into another2 !xplanations may inclue? • • •
Air resistance 0oun Potential energy /of spring1 being converte into internal energy /heat12
Question #: n number of electrons per unit volume /m 81 v average /rift1 velocity2
Question 5: Although spee is constant, in the case of circular motion, the velocity is continually changing /velocity vector is a tangent to the circle12 This gives rise to an acceleration, since velocity is changing2 Then, >ewton 9 applies, < ma2 %oy A? !arth %oy %? Ieighing scales2 Q Angular spee of stuent * D/*7 x .+ x .+1 &!3 ; 1%-5 4(6!s-1 Cesultant force mrQ* (( x .7++ x &+ 8 x /@28 x &+ -(1* 1!9 N 12 This follows from>ewton:s Thir Law/i2e2 this is the overall force exerte by the stuent on the scales12 Question : ;hm:s Law gives? B 9C 0o, voltage across ballast +2( x 8++ 15% “
“
“ filament +2( x (+ 25 Bstarter *8+ ) &(+ ) *( ) *( 3%
The funamental change neceassary for the tube to conuct is that 7(4e6 (4ties nee to be present2 B ballast *8+ ) &&+ &*+ B 9 BDC &*+D8++ +27+ A Power 9B +27+ x *8+ 92 W The faulty component woul be the st(4te4 'still conucting12
Question &: $harge average current x time &( x 8++ x &+ -. #!5 "/ Estimation of capacitance?
$ DB /72( x &+ -81D' 5%% .F
Question +: C RLDA /&2@ x &+ -6 x *+1D/72+ x &+ -.1 %!%+5 , Boltage rop given by B 9C 8@ x +2+6( 82& B Total p22 * x 82& !2 $able with .2+ mm* conuctors woul have a resistance of *D8 x Xol: cable +2+(@ K $onsequently, power issipate in cable woul be less an the shower woul be more efficient2
PH1 JUNE 2%%1 Question 1: a /v ) u1Dt /&. ) +1D72+ x .+ +2+... ms -* >ewton:s 0econ Law gives < ma 67 +++ +++ x +2+... 5 %% N Free 5ody 5ody Force Diagram)all Diagram)all from one one point+? point+ ? Arrow vertically upwars, magnitue 67+ +++ > Arrow vertically ownwars, magnitue 67+ +++ 5 Arrow horiHontal, pointing right, magnitue &&* +++ > Arrow horiHontal, pointing left, magnitue &.6 +++ > Power <2v ow, electrical power supplie , P 9B 9 /&2. x &+.1D/*( x &+81 # A Question 2:
Physical quantities in shae ellipses are *(se u(ntities2 u(ntities2 These are not erive from any /other1 quantities2
Question 3:
Ta3ing moments about P? /& '++ x *2(1 ) 826 = /*7 8++ x 72'1 + 7 @(+ ) 826 = &&' +@+ + 32 5+#!2 N %ut P = C = I P ) I ) C 8* (672* ) & '++ ) *7 8++ 3+#!2 N Question #: Proviing no external forces act, the total momentum of a system of colliing boies remains constant2 The two laws of motion necessary to prove the Principle of $onservation of 5omentum are >ewton:s 0econ an Thir Laws2 Laws2 9t is necessary to measure the velocities of the trolleys before an after collision2 This may be one by tic3er-tapeDtic3er-timers or light gates2
9n this case, since the trolleys are of ientical mass, m&v& /m& = m*1v* v* F x v& an this woul verify the Principle2 The reason for iscrepancy is either? • •
Air friction
E;(n(tion? E;(n(tion? 9nitial momentum of car recoil momentum of !arth /= car12 Question 5: B B& = B* B 9C %ut B& 9C & B* 9C * or, 9C 9C & = 9C * C C & = C * This is a goo approximation since the resistance of the connecting lea is very small2 p22 9 x C 0ince C is very small, p22 is negligible2 $ircumstances in which the approximation a pproximation brea3s own? • •
9f the current is very high Cesistance of the remainer of the circuit is very small
C RLDA /&2@ x &+ -6 x +28+1D/ x +2+@( x &+ -81* x &. 1!+ ; 1% -2 , %ut, B 9C *2+ x &26 x &+ -* %!%3
Question : $urrent is the rate of flow of charge2 0ince current is constant, the charge on the capacitor / 9t1 increases at a constant rate2 0ince B D$ 9tD$, it follows that a plot of B vs2 t shoul be a straight line since the capacitance /$1 is constant2 $B 9 Dt or,
9t $B 9 $BDt /7 @++ x &+ -. x '2++1D7+ 1!% "A
The resistance ha to be 6e4e(se6 because 6e4e(se6 because as the capacitor charges, the voltage across the variable resistor ecreases2 ence, C must ecrease2 0ince 9 B C DC2 DC2 0econ graph? • •
!xponential rise from /+,+1 9nitial slope, same as original2
Qustion &: A%? uniform acceleration %$? 0uen eceleration Explanation of course of motion? motion ? A%? Attraction of /negatively-charge1 electron to the positive terminal of power supply2 %$? $ollision of electron with particles in the lattice of metallic wore2 Drift velocity? velocity? mean velocity of electron along wire2 9ts value lies between &D8 an*D8 of maximum velocity2 The wire gets warm because collisions of electron energy is transferre to the /metallic1 lattice2
PH2 JUNE 1995 Question 1: >o2 of electrons in a neutral atom of &7$. >o2 of neutrons in a neutral atom of &7$. + / $ 1#N& >%e-1
1#
Esing a O252 tube an ratemeter, ra temeter, the bac3groun reaing is ta3en2 Then, a thin sheet of paper shoul be inserte between source an the effect on the count rate etermine2 9f there is no effect, this shows that W-raiation to be absent2 0ubsequently, if a magnetic fiel is applie at '+o to the beam an the count rate is affecte, then the raiation must be ]-rays, since ^-rays remain unaffecte2 As a final test if a 8 mm sheet of aluminium is inserte in the beam an the count rate reuce to nearly Hero, this confirms presence of ]-rays2
Question 2: (imilarity? (imilarity? >uclear fission an fusion both release energy2 Difference 0? 0?
Question 3: ,aterial 5: 5: 0traight line, from origin, at a smaller graient than linear portion for line A2 [oung:s [oung:s 5oulus 5oulus graient of linear portion of graph A, equivalent to stressDstrain2 Enits of [oung:s 5oulus are Pa, >m -* or 3gm-&s-*
Question #: 0imple harmonic motion /051 may be efine as the motion of a particle about a fixe point such that the acceleration is proportional to its isplacement /x1 from the fixe point an is always irecte towars the fixe point, mathematically? ( $ 62;?6t2 $ - 2; a acceleration, Q constant, x isplacement an t time
The pair of curves illustrating the efinition of 05 are A (n6 C2 This illustrates that the proportionality between the acceleration an istance is illustrate an that they are inversely relate2
Question 5: 9n a transverse wave, the isturbe particles vibrate at '+ o to the irection of travel of the wave2 9n a longituinal wave, the particles vibrate in the irection of travel of the wave2 PolariHation is the reuction of many perpenicular vibration planes to one plane only2
Question : s may lie in the range %!1 to 1!% "" " may lie in the range %!5 to 1% " The bright fringe at P is forme by iffraction occurring at the slits2 0ince the waves are coherent, the first bright fringe occurs when the path ifference _ /i2e2 constructive interferenceDsuperposition occurs at P12 /i1 /ii1
9f we increase the slit separation s, the fringe with x is 6e4e(se62 9f we illuminate the slits with blue light, x is also 6e4e(se62 These results arise as a result of? $ ;s?6
$oherent sources are those having a constant phase relationaship2
Question &: Cefractive inex spee of light in airDspee of light in glass &2(+ spee of light in prism /8 x &+ 61D&2(+ 2!% ; 1% + "s-1 The critical angle, Yc is given by sin Y sin Yc &D&2(+ +2...222 Yc sin-&/+2...2221 #1!+o n &2(+ / sin / sin Y Y&D sin &62* sin &62*o1 G1 $ 2+o 9f the value of Y& is reuce, internal reflection will occur on face PC since Y c critical angle2
Question +: 7 represents represents the energy of the photon2 0e"(; N2!2 of emitte electron ϕ energy to release an electron from the surface /wor3 function1
p mv +2+( x '2&& '2&& x &+ -8& x 8 x &+ 6 1!3& ; 1% -23 0"s-1 The e %roglie wavelength, wavelength, _ hDp /.2.8 x &+ -871D/&28@ x &+ -*81 #!+5 ; 1% -11 " !lectrons of this wavelength are useful for stuying the structure of molecules since the wavelength, _ is similar to the spacing between atomsDmolecules an iffraction occurs2
PH2 JANUARY 199
Question 1: N(11 $ 22I1% > %1>
22
Ihere ]= is a osit4on2 osit4on2 9n & mol of ** >a&&, there are .2+* x &+ *8 atoms /i2e2 ** g12 Thus in +2** g of the isotope, we have +2+& mol2 $onsequently, no2 no2 of atoms present +2+& x .2+* x &+ *8 .2+* x &+ *& atoms2 _ ln*DT&D* +2.'8D/*2. x 8.( x *7 x .+ x .+1 6 x &+ -' s-& >Dt - _> 6 x &+ -' x .2+* x &+ *& 5!% ; 1% 13 C Precautions to be ta3en in orer to obtain a reliable result for a half-life of this magnitue are? /a1 $orrect $orrect for bac3groun bac3groun raiation raiation /b1 Ta3e Ta3e reaings reaings for several several wee3s2 wee3s2
Question 2: 0ince < - 3x 3
Question 3:
Bt4ess-st4(in u u4
Lo(6-e; -e;tension u u4
The ifference in molecular structure of rubber an steel is that rubber comprises long molecules /polymer1 which is coileDtangle up in an amorphous structure, whereas steel has a metallic structure ) orere lattice of positive ions2
Question #: The stationary wave has been prouce by superposition /interference1 of a reflecte wave with a wave of the same frequencyDwavelength moving in the opposite irection2 "oubling the frequency of the signal generator woul move the maximaDminima closer together since the wavelength is halve2 9n orer to etermine the spee of soun in air, the istance between successive noes shoul be measure at several points along the wire an the average ta3en2 The frequency of the signal generator is note an then since _ * x inter-noal istance, we may fin v from the equation v f x _2 5inima etecte near the sheet are smaller than those near the louspea3er since neat the sheet, there is almost complete cancellation moreover, the amplitue of the incient wave woul be less than that near the louspea3er /inverse square law12
Question 5: Luminous power of .+ I lamp /6D&++1 x .+ 726 I Area of sphere, raius, r 7r * 9ntensity /91 PD7r * 726D7/*1* %!%9 W!" -2 0ince & eB &2. x &+ -&' J2 Then, no2 of photons emitte at * eB energy +2+'.D/82* x &+ -&'1 2!9+ ; 1% 1& "2s-1 Question :
"ispersion may be explaine by the fact that white light /consisting of all the “rainbow” colours1 travels at the same spee in vacuum /or air1, then this light enters an optically enser meium /such as glass1, the variouis colours travel at ifferent spees, epening upon their wavelength2
Question &: /a1 9n a flame test test or ischarge ischarge tube, we may emonstrate emonstrate that elements have their own characteristic optical spectra /pattern of lines1 if the light is first passe through a iffraction grating or glass prism/e2g2 in a “spectrometer” arrangement12 /b1 9n the transition ) &82. to ) 827 eB, eB, the energyabsorbe energyabsorbe &+2* eB2$onsequently eB2$onsequently , there is an excess energy of &*2+ ) &+2* &26 eBof eBof the free electron after collision2 /c1 !nergy of photon emitte when the atom returns to its groun state, \! \! &+2* eB2 eB2 -87 6 -&' \! hcD_ _ hcD\! /.2.8 x &+ x 8 x &+ 1D/&+2* x &2. x &+ 1 1!22 ; 1% -& "
Question +: 9raph? 9raph? 0traight line of positive graient, (4(e to (4(e to soli line, 4o" ' %) to '12 2!#)2 2!#) 2 >o photoelectrons are emitte below frequencies of 727 x &+&7 H because the incient photon energy is insufficient /less than the wor3function12 The wor3 function of soium may be calculate by use of the equation, hf o ϕ an since f o 727 x &+ &7 H, ϕ .2.8 x &+-87 x 727 x &+ &7 *2'* x &+ &7 J %ut since e &2. x &+ -&' $ ϕ 1!+3 e Ce-arranging the photoelectric equation, equation, hf T = ϕ T hf ) ϕ which is of of the form y mx mx = c, the negative intercept on the T-axis giving ϕ /the wor3 function1 an the straight line shows the linear relationship between T an f2 A value of Planc3:s constan constantt coul be erive from the 4(6ient of the T-f graph2
PH2 JUNE 199
Question 1: The Oeiger-5arsen experiment showe that? /a1 5ost W-particle W-particless pass straight straight through through the gol foil /b1 0ome are are eflecte eflecte slightly slightly /c1 A very small number number /& in *+ *+ +++1 +++1 are turne turne through through angles angles ˃ '+ o2 These observations le to the following f ollowing conclusion? /i1 /ii1 /iii1 /iii1
Cepuls Cepulsion ion of positi positive ve W-part W-particl icles es le le to the concep conceptof tof a posi positiv tively ely charg charge e nucleu nucleus s 0ince 0ince a larg largee fracti fraction on of of W-par W-partic ticles les went went straig straight ht thro through ugh,, appar apparent ently ly une unevia viate te le to the concept of an atom being mainly empty space "ince "ince a small small propo proportio rtionn were were strong strongly ly evi eviate ate it was conclu conclue e that that the the nucleu nucleuss was tiny2
Approximate values for? 'i) 'ii)
"iameter of gol atom 1%-9 to 1%-11 " "iameter of gol nucleus 1%-13 to 1%-15 "
Question 2: 0ources of bac3groun raiation inclue? &2 $osmi $osmicc raiat raiation ion from from outer outer space space *2 Caio-a Caio-acti ctive ve roc3 roc3s, s, esp2 esp2 Oran Oranite ite22 23+
U92 > 1n% $ 13&/s55 >95R*3& > # 1n%
The raio-active ecay constant, _ is given by? _ ln*DT&D* > >o e-_t ln />oD>1 _t ln/(26 x &+ &(D&2. x &+ .1 +2+*8 t ln /82.*( x &+ '1 +2+*8 t t **2+&D+2+*8 95& =e(4s
Problems arising from the very long storage times inclue?
'1) /o44osion of container materials '2) Long-time "onito4in '3)
Question 3: Bolume of bloo passing per secon volume of “cyliner”, length v r *v where v +28 m, r 7 mm 7 x &+ -8 m volume x /7 x &+ -81* x +28 &2( x &+ -( m8 %ut mass volume x ensity &2( x &+ -( x &+.+ 1! ; 1%-2 0!s-1 The volume woul be measure in a suitably small-siHe measuring cyliner, pipette or syringe, the temperature a4uste to 8@ o$ an then the mass etermine in the same container /preferably precision top-pan balance weighing to =D- +2++& g12 Then, mass of bloo /total mass ) mass of container1 an ensity massDvolume /units? 3g2m -812
Question #: The values of length /l1 are poorly chosen since they are all on the low sie /all less than &2+ m1 ) this woul give small values of perioic time /T1 moreover, their spacing is unsatisfactory since the values of l are square-roote2 0ince T *G/lDg1 graient of T vs2 G/l1 graph *DG/g1 $ #M2?'4(6ient)2
Question 5: Bt(te"ent Ihen the frequency of the vibrator is &.+ H there will be eight loops on the string The spee of the wave is 8+ ms -& Cesonance will also occur when the frequency is 7+ H 9f the loa is ouble an the frequency is 3ept constant, there will be twice as many loops on the string Question :
T4ue F(se G G G G
The wave is onitu6in( since the vibrationsDoscillations of the particles are in the same irection of the wave propagation2 0ince v f2_ an f &DT _ TB
Question &:
The critical angle, $ is given by? sin $ &Dn &D&2( +2...222 $ sin-& /+2...2221 #1!+o 0ince n sin i constant, we may write? &288 sin Y &2( sin 7&26o Y #+!&5o '#9o)
Question +:
9oniHation energy &+27 eB &2. x &+ -&' x &+27 &2..7 x &+ -&6 J ! hf hcD_ /.2. x &+ -87 x 82+ x &+ 61D/.++ x &+-'1 828 x &+ -&' J !nergy Level change - 2!%& e
PH2 JANUARY 199&
Question 1:
,easurements to be taken include? &2 *2 82 72
;riginal length of wire !xtension of wire "iameter of wire Loa ae2
9n orer to obtain a value for the [oung moulus /!1, a plot of stress /y-axis1 vs2 strain /xaxis1 is mae an the best straight line rawn through the points2 Then, ! graient of the linear portion /elastic region12 >ote that 0tress loaDarea an 0train $hange in lengthDoriginal length2 $opper is use in the form of a long, thin wire in orer that a reasonable extension is obtaine measurements of extension will be less prone to error2 0ince the length of wire [ is one-thir that of #, given the same loa, the extension woul also be &D82 owever, since the iameter of # is twice that of [, then the cross-sectional area of [ is one-quarter that of # so that its extension woul be quaruple2 0ince extension is inversely proportional to area, the correction factor 7D82 !xtension of wire /6 x 71D8 11 ""
Question 2:
A % $ " !
Amplitue De4e(ses B"( B"( L(4est t7en 6e4e(ses B"(
A massive penulum is use to act as a river of penula of smaller mass2 0ince penulum " is of the same length /an therefore the same natural frequency as A1, will therefore resonate an be of maximum amplitue compare with other penula2
Question 3: 5ass of L0 of equation * x 82877 x &+ -*@ .2.66 x &+ -*@ 3g 5ass of C0 of equation (2++6 x &+ -*@ = &2.@( x &+ -*@ .2.68 x &+ -*@ 3g $hange in mass $ ( x &+-8+ 3g ! \mc* ( x &+ -8+ x /8 x &+ 61* #!5 ; 1% -13 J
Fission is the brea3ing up of nuclei Fusion is the combination of nuclei
Question #: >o2 of moles of Pu-*86 present *+++D*86 The Avogaro >umber, > o .2+* x &+ *8 >umber of atoms initially present /*+++D*861 x .2+* x &+ *8 5!% ; 1% 2# The ecay constant, _ ln*DT &D* ln*D/6@ x 82* x &+ @1 2!#+9 ; 1% -1% s-1 The rate of ecay, >Dt -_> (2+. x &+ *7 x *276' x &+ -&+ 1!2 ; 1% 15 C > >oe-_t %ut >D>o +2& an _ *276' x &+ -&+ +2& e -*276' x &+-&+ t ln /+2&1 -*276' x &+ -&+ t *28+8 *276' x &+ -&+ t t $ 9!25 ;1% 9 s 2+9 = At istances far from the 0un /i2e2 at ;uter Planets1, the incient Bo(4 Ene4= ou6 *e too o to oe4 t7e s(e 4o*e ) inverse square law relationship2 Also, the solar panels might be 6("(e6 *= "eteo4ites etc2
Question 5:
0imilarly, for violet light, n &287*, i '+ - &+ 6+ o sin r sin iDn sin 6+oD&287* +2@886 r sin-&/+2@8861 #&!2o 9f the refractive inex, n is the same for both re an violet light, then *ot7 4(=s ou6 4e4(t (on t7e s("e (t7 (t (n (ne o #& o
Question 8 '()
The wavelength, _ 7 x +26 3!2 "
'*)
v f_ '( x &+ . x 82* 3!%# ; 1% + "s-1 0ince this is the spee of light, suggesting that raio-waves are eet4o"(neti2
')
Question &: Iave-particle uality implies the ability to exhibit both wave an particle behaviour, e2g2 light may behave as a wave when it is iffracte whereas, it ta3es on particle-li3e nature in the photoelectric effect2 The e %roglie wavelength _ is given by _ hDp hDmv /.2.8 x &+ -871D/+2+. x *1 5!525 ; 1% -33 " This is too s"( (
PH2 JUNE 199&
Question 1: 22%
Rn+ $ 21Po+# > #He2
ext, 3eeping the O5 tube near to the source, at the same istance, the count rate over a perio of &+ s is obtaine at times of +, 8+, .+, '+, &*+ an 8++ s2 The results are then plotte as count ratevs2 Time ) the ecay curve woul permit T&D* to be etermine2 The experiment shoul be repeate if possible2 9f a straight line is require, then plot ln /count rate1 vs2 time in which case, the graient - _ where _ is the raio-active ecay constant2 T &D* may be obtaine from the equation T&D* ln *D_ Ceasons for errors in etermining half-life of 0r-'+ in contaminate mil3 inclue? /a1 The onent4(tion ou6 *e
Question 2: 9n the bra3ing system of a car, the bra3e cyliner peal has a small area compare to the bra3e pa cyliner2 0ince the pressure of the flui /incompressible1 is the same throughout the system an
Question 3: oo3e:s Law lays own that? !xtension W ow, wor3 one
9n the case of a gas, the molecules are moving aroun in a ranom fashion, at very high spees2 owever, in a soli, the molecules are in fixe positions, vibrating about their mean positions2 Thus, soun waves travel more quic3ly in solis than in a gas because the longituinal wave has particles more closely pac3e through which to propagate2 9n the equation v G/!DR1 v velocity, imensions 5L -& ! [oung:s moulus, imensions of stress forceDarea /5LT -*DL*1 5L-&T-* R ensity 5L -8 !DR has imensions /5L-&T-*1D/ 5L-81 L*T-* Ta3ing the square-root, this has imensions LT-& which has imensions of velocity2 [oung:s moulus, ! /LoaDArea1D/$hange in LengthD;riginal Length1 prouces an extension of *27 x &+ -8 m in a wire of length *2( m ! /7+DA1D/*27 x &+ -8D*2(1 $onsier the wire to be a cyliner of length l, cross-sectional area A, ensity, R an mass m2 Then
volume r *l Al an mass of wire 7 g +2++7 3g R2A x *2( R +2++7D*2( A +2++&.DA v G/!DR1 GU/7+DA1D/*27 x &+ -8D*2(1VDU/+2++&.DA1V 0ince area cancels, we may write? v G/7+ x *2(1D/+2++&. x *27 x &+ -81 G/&++1D/8267 x &+ -.1 *.+7&...2.@ v G/*.+7&...2.@1 51%3 "s-1
Question 5: 0imple harmonic motion /051 may be efine as the motion of a particle about a fixe point such that the acceleration is proportional to its isplacement /x1 from the fixe point an is always irecte towars the fixe point2 The time perio of a penulum is given by? T *G/lDg1 T* 7*lDg or l gT *D7* l '26&/*1*D7* %!99 s
Question :
0ix fringes occur over 7+ cm, thus fringe spacing .D/7 x 81 +2( cm Iavelength, _ xsD" Ihere x fringe with, " istance to screen, slit separation s _ /+2( x &+ -* x +2( x &+ -81D&2( 1!& ; 1% - "
The core of the optical fibre, a 5 -5% ." ;verall iameter of optical fibre, b 125 ." '(4o;!) 0nell:s law gives? n sin iD sin r sin r sin iDn sin &7oD&276 +2*7&6D&276 +2&.8( Y sin-& /+2&.8(1 9!#%o %y trigonometry, i &6+ ) '+ ) '27+ 6+2. o 0ince n sin i constant n& sin i& n* sin i*, where & core * claing sin $ n*Dn& 1!#
Question +:
Explanations$alculations?
/a1 The groun state /lowest energy1 of the hyrogen atom woul be ) &82. eB, so this is a t4ue statement2 /b1 To excite an electron to the first energy level from the groun state nees &+2* eB, so this statement is (se2 /c1 Photons are emitte only when electrons fall from higher to lower energy levels2 Therefore, this statement is (se2 /1 ! hf hcD_ /.2.8 x &+-87 x 8 x &+ 61D/.(+ x &+-'1 82+. x &+ -&' J %ut e &2. x &+ -&' $ !nergy /expresse in eB1 /82+. x &+ -&'1D/&2. x &+-&'1 &2'& eB2 The transition from ) 827 to ) &2( eB &2' eB2 $onsequently, we may euce that the light has sufficient energy to carry out the transition ) t4ue statement2
PH2 JANUARY 199+ Question 1: 8
& is an isotope of 7=64oen2 H1 $ 3I2 > %e-1
3
alf-life is the time ta3en for the activity in a raio-active sample to fall to one-half of its original value2 Total mass of proucts 72++*. = &2++6@ (2+&&8 u Total mass of reactants *2+&8. = 82+&.+ (2+*'. u 5ass ifference +2+&68 u %ut & u &2.. x &+ -*' 3g \m 82+7 x &+ -*' 3g \! \mc * 82+7 x &+ -*' /8 x &+ 61* 2!&3 ; 1% -12 J
Question 2: 5aterial [oung moulusD&+&+ Pa Eltimate tensile stressD&+6 Pa >ature A 1!% 2! 6utie % +287 82* brittle 9raph? Line % ) straight line of positive graient from origin to /+2+', 82*12
Question 3: % "isplacement > Acceleration Belocity %
$ % % -
" > %
! % % >
< > %
"ecrease in g2p2e2 on the first fall mgh 6+ x '26& x(+ 39 2#% J This energy has been converte into elastic potential energy in the rubber ban /an some 32e21
Therefore, the force constant, 3 is given by? 0tore energy F 3x* or F
Question #: 9n a ripple tan3 experiment, the frequency of the waves coul be measure by counting the number of waves passing a fixe point in /say &+ s1 an iviing the number by &+2 This woul reuce the error2 Alternatively, a stroboscope coul be use to “freeHe” the image of the wave motion2 The frequency of the flashes /first, lowest setting1 woul then be equal to the frequency of the waves2 The wavelength coul be measure by simply measuring the pea3-to-pea3 /or trough -to- trough1 istance2 The wave spee coul be etermine by timing one particular wave travelling the full length of the ripple tan32 Then, v istanceDtime2 Alternatively, we coul calculate the velocity, v from v f_ where f frequency an _ wavelength2 v G/g_D*1 f_ %ut T &Df _Dv T* _*Dv* %ut v* g_D* T* *_Dg T G/*_Dg1 T G/* x 62+D'26&1 G/(2&*71 2!3 s
Question 5: A plane polari;ed wave is one in which the vibrations responsible for creating a transverse wave are limite to one irection only in the plane perpenicular to the irection of the wave2 An experiment to test whether or not the waves are plane polariHe is to interceptthe beam with a Polaroi2 9f light is un-polariHe, bright light is seen in all orientations2 9f, however, the light is polariHe, bright light is only seen in one orientation ) ar3ness at all other angles2
Question :
The critical angle /$1 is given by? sin $ n*Dn&, where n& is the core refractive inex an n * is the /slightly smaller1 claing refractive inex2 sin $ &27.D&276 +2'6.( $ sin-& /+2'6.(1 +%!o >ow, the spee of light in optical fibre spee of light in vacuumDrefractive inex 82++ x &+6D&27@ *2+7 x &+ 6 ms-& time istanceDvelocity /(2+ x &+ 81D/*2+7 x &+ 61 2!#5 ; 1% -5 s
Question &: !xperiment reveals that electrons are not emitte when incient light has a frequency lower than a threshols frequency, which varies from one metal to another2 The 3inetic energy of the electrons emitte varies from Hero to a maximum value2 The maximum value epens upon the frequency of the light, not upon its intensity2 The above observations cannot be explaine if we consier light to have wave-li3e properties2 9ncient photon energy .2* eB .2* x &2. x &+ -&' '2'* x &+ -&' J %ut \! hf hcD_ _ hcD\! /.2.8 x &+ -87 x 82+ x &+ 61D/'2'* x &+ -&'1 2!%%5 ; 1% -& " This belongs to the ut4(-
PH2 JUNE 1999 Question 1: \m for A &(2+++7 ) &.2&8*+ - +2&8*( u \m for % &@2++7' ) &@2&7+@ - +2&8(6 u %ining energy for A \! A \mc* &2.. x &+ -*@ x +2&8*. x /8 x &+ 61* 1!9+ ; 1% -11 J 0imilarly? %ining energy for % \!% \mc* &2.. x &+ -*@ x +2&8(6 x /8 x &+ 61* 2!%3 ; 1% -11 J %ining energy per nucleon for A /&2'6 x &+ -&&1D&. &2*7 x &+ -&* JDnucleon %ining energy per nucleon for % /*2+8 x &+ -&&1D&@ &2&' x &+ -&* JDnucleon Thus, the bining energy per nucleon is greater for A than %, means that A is more stable2
Question 2:
"ifferences between soun waves an raio waves /any <;EC1? • • • • •
Caio waves are transverse soun waves are longituinal Caio waves may travel through vacuum soun nees meium Caio waves travel at the spee of light soun much slower Caio waves can be polariHe soun cannot be polariHe Caio waves are electromagnetic soun waves pressure variation
Longer wavelength waves iffract aroun tall builings an hills thus the waves ten to go to receiver2
Question 3:
!xamination of the graph shows a non-onst(nt 7(-ie leaing to the conclusion that isotope 5 is impure2 0ince the plot has been compensate for “bac3groun” when the graph flattens out out, the level of activity of $ 15% " Ta3ing into account the activity of $ /&(+ cpm1 an averaging two sets of reaings /eg2 8 +++ to & (++ an * +++ to & +++ cpm1, we may estimate the half-life of 5 to be 1!2 "ins %eta-ecay may be written as? n% $ 1H1 > %e-1
1
To etermine the nature of raiation emitte by isotope $, we shoul wait until isotope 5 is has ecaye /ie until at least @26 mins12 Then a piece of paper is inserte into the beam an the new reaing note, using a O5 tubeDcounter2 9f very little ifference in level, then alpha is absent2 Then, placing a sheet of aluminium 8-( mm thic3 in the beam, the activity shoul be reuce to Hero /correcte for bac3groun12
Question #: 0train +2& area *( x &+ -. m* ! stressDstrain /
Assumptions mae for the calculation /any TI;1? /i1 /ii1 /iii1
Temperature remains constant $ross-sectional area remains constant oo3e:s Law is obeye2
At one particular frequency, a large amplitue is obtaine, stationary waves being prouce2 The secon harmonic * x frequency of funamental2 owever, the higher frequency harmonics have lower amplitue2
Question 5: 0imple harmonic motion /051 may be efine as the motion of a particle about a fixe point such that the acceleration is proportional to its isplcement /x1 from the fixe point an is always irecte towars the fixe point2 T *G/mD31 T * 7*mD3 3 7*mD T* 7* x &27++D/&2**1 * 3&!1 N"-1 0ince T W G/m1, we may write? T&*DT** m&Dm* m* m&T**DT&* &27++ x /&2761 *D/&2**1* 2!% 0 %ut, tray has a mass of +27++ 3g mass of animal *2+. ) +27++ 1! 0 9f a similar experiment were to be carrie out on !arth, then the s("e result woul have been obtaine2 This is because 3 is everywhere the same an mass is the same in outer space as on !arth2
Question : n spee of light in vacuumDspee of light in meium /82+ x &+ 61D/&266 x &+ 61 $ 1!% $ritical angle for yellow light in glass is given by? sin $ &Dn &D&2.+ +2.*( $ sin-& /+2.*(1 3+!&o
Angle between critical angle an prism face /'+ ) 862@1 (&28 o 9n the “top” triangle, angle between r an other prism face &6+ )/(&28 = ..1 .*2@ o r '+ ) .*2@ 2&!3o %ut, n sin YiD sin Yr sin Yi n sin Yr &2.+ x sin /*@281 +2@87 Yi sin-& /+2@871 #&!2o
Question &:
Photons from the incient monochromatic raiation emit electrons at the photocathoe subsequently, these electrons travel to the anoe, constituting a current2 9n this case, the photon energy excees the wor3 function of the photocathoe material2 owever, these electrons are emitte with a range of 3inetic energies2
$onsequently, the lower N! electrons are “stoppe” at lower p22:s since these p22:s oppose release of these electrons2
increasing only the intensity of the incient raiation woul have no eet increasing only the frequency of the incient raiation woul be to increase stoin otenti(2
PH2 JANUARY 1999 Question 1: $hange in mass *862+++8 ) /'* x &2++@81 ) /&7. x &2++6@1 &2'7&( u Total bining energy &2'7&( x &2.. x &+ -*@ x /82+ x &+ 61* *2'+ x &+ -&+ J & 6++ 5eB %ining energy per nucleon & 6++D*86 $ &!5 e Nue(4 ission implies the splitting up of a nucleus in two /or more1 fragments with the emission of energyDneutrons2 !lements with mass numbers aroun *86 ten to unergo nuclear fission since these elements of lower mass number2 The consequence is that they transmute into more stable nuclei2
Question 2: 0ince the atomic number ecreases by /&&+ ) &+71 . an that the W-particle may be represente by 7e*, it follows that A 25&2 _ ln*DT&D* +2.'8D/*++ x &+ -.1 3 #5 s >Dt - _> 8 7.( x &2* x &+ &( #!1 ; 1% 1+ C "ue to the
Question 3: %oth solis an liquis have atomsDmolecules fairly ensely pac3e /i2e2 similar istances apart12 owever, in the case of solis, there is a regular arrangement, thus permitting closer pac3ing2 /i1 /ii1
Large increase /gases are very compressible1 0mall or no change /liquis are well-nigh incompressible1
"ensity massDvolume B mDR +2&'@D&' +++ 1!%3& ; 1% -5 "3 Bolume of & atom /&2+8@ x &+ -(1D/.2+ x &+ *81 1!& ; 1%-29 "3 r 8G /&2@ x &+ -*'1 2!5 ; 1% -1% "2 This is the orer of &+ -&+ m2 r nucl S /&D&+(1 x r atom Bnucleus S /&D&+&(1 x Batom "ensity of nucleus S &+ &( x ensity of atom Assumptions mae in the above calculation for nuclear ensity, any ;>! of? • • •
5ass of electrons negligible All mass resies in the nucleus >uclei are spheres
Question #: Progressive waves t4(nse4 energy whereas stationary waves sto4e energy2 c f_ c&D_& c*D_* since f constant cshallow /+2.D&2+1 x +2*( %!15 "s-1 Angle of incience at C0 3%o
Y sin-& /+26882221 5!#o
Time perio, T &27 s
Question 5:
T *G/mD31 &2* *G/mD31 an T *G/*mD731 T*D/&2*1* /*mD731D/mD31 +2( T* /&2*1* x +2( &277 x +2( +2@* T G/+2@*1 %!+5 s
Question : Esing a microwave transmitter, metal plate with two slits as an obstacle an a receiver, the latter being connecte to a meter, louspea3er or $C; equipment, the receiver is move in an arc or straight line parallel to the slit plane, then maxima an minima are observe2 An appropriate slit separation for this experiment woul be between 1 (n6 + "2
9n orer to etermine the wavelength of the microwaves, using the formula? _ xsD", where _ wavelength of wave x istance between maxima /or minima1 " slit-receiver istance s istance between slits Then, measure " with a metre rule an s, x with vernier callipers2
Question &:
Question +: F mv* 62+ x &+ -*& J m &2++6@ x &2.. x &+ -*@ &2.@7 x &+ -*@ 3g v* /* x 62+ x &+ -*&1D/&2.@7 x &+-*@1 '2(. x &+ . v G/'2(. x &+ .1 82+'* x &+ 8 ms-& 5omentum, p mv &2.@7 x &+ -*@ x 82+'* x &+ 8 5!1+ ; 1% -2# Ns >eutrons, being un7(4e6, are better than protons for iffraction stuies of molecular structure2 [es, neutrons of this e %roglie wavelength woul be suitable for such stuies since their wavelength is similar to inter-atomic spacings2
PH2 JUNE 1999 Question 1:
Question 2: "euction of properties of alpha-particles /any <;EC1? • • • • •
They are all of the same energies They are of two istinct energies They have a short range They travel in straight linesDhave “large” mass They are chargeDhighly ioniHing
Ese of Oeiger counter to etermine contributions from W- an ]-particles from a source? • •
A reaing shoul be ta3en very close to the source /$ &1 A secon reaing is ta3en through a sheet of paper1 or (-&+ cm from source1, $ *2
Then, W-emission $ & ) $*2 Question 3: /i1
/ii1
9nitial activity of isotope is given by ln Ao .26 Ao e.26 9%% C
0ince A Aoe-_t ln A ln Ao - _t thus, graient of line - _ /.26 ) 82+1D*7+ +2+&. s -& alf-life, T&D* ln*D_ ln*D+2+&. #3!+ s
Question #: The shape of the graph is typical of 4u**e4
The crystalline structure has an orere arrangement of atomsDions in the case of polymers, these consist of long moleculesDchains of atoms in ranom orer2
Question 5: $alculation of time period of the oscillation? a - Q*x 0o, the graient - Q * (D* *2( %ut, T *DQ .2*6D&2(6 82'@S #!% s
Question : The wave travels from L0 to C0 from transmitter an is reflecte by the vertical metal sheet2 At various points, superposition provies minima at noes /estructive interference1 an maxima at anti-noes /constructive interference12 Thus, a stationary wave is establishe2
Question &: Two connecte ippers, 4ust above the water are vibrate electrically in a shallow tan32 The pattern is pro4ecte on to a screen via a bright lamp above /alternatively a stroboscope may be use to “freeHe” the pattern12
9f only the separation of the sources were increase, the angle between lines A an % woul 6e4e(se2 9f only the wavelength of the waves were increase, the angle between lines A an % woul in4e(se2 9f only the epth of the water in the ripple tan3 were increase, the angle between lines A an % woul in4e(se2
Question +: $ritical angle /$1 for glassDair interface is given by sin $ &Dn &D&2(+ +2..@ $ sin-& /+2..@1 #1!+o -o calculate the critical angle for glassli"uid interface? 0ince
n sin i constant &2( sin $ &27 sin '+o / $ 9o
Explanation? /i1 /ii1
Angle of incience ˃ critical angle, so light reaches etector ue to total internal reflection Angle of incience ˂ critical angle so light oes not reach etector /light refracte into liqui12
Question 9: 9oniHation energy of atom 2 +1% e * 6&+ eB &2. x &+ -&' 72( x &+ -&. J !o hf o hcD_o _o hcD!o /.2.8 x &+-87 x 82+ x &+ 61D/72( x &+-&.1 #!#2 ; 1% -1% " This photon woul belong in I-4(= o4 -4(= part of the electromagnetic spectrum2 e %roglie relationship gives? _ hDp /.2.8 x &+ -871D/*+@ x '2&& x &+ -8& x +2&& x 82+ x &+ 61 1!%& ; 1% -13 "
PH2 JANUARY 2%%%
Question 1: The type of raioactive ecay is by -e"ission2 >uclear equation for this ecay? I2 $ 1#3Y% > #He2
1#&
Question 2: • • •
• •
Esing a O5 tube an ratemeter, etermine the bac3groun raiation Place soil in container whose opening faces the etector Iith etector close to sample, insert sheet of thin paper ) if count rate is reuce, W present 9nsert thin /8-( mm1 aluminium sheet, if further reuction in count rate ] present 9nsert lea sheet, if count rate still above bac3groun, then ^ present2
Question 3:
5any crystal materials are o=4=st(ine, that is, they exist as a large collecting of tiny crystals all pointing in ifferent /ranom1 irections2 !ach tiny crystal is 3nown as a 4(in an is connecte together at the 4(in *oun6(4ies2 The existence of grains appears to be ue to the soliification process in manufacture which begins simultaneously at several places2 The surface is the first to soliify or freeHe2 ;n complete soliification, the structure consists of grains pointing in ifferent irections, as shown iagrammatically2 The grain bounaries assist the strength of a material2
Aitional information require for [oung:s 5oulus is length an cross-sectional area2 !stimate of energy store in wire area uner
@(
=
&(+
=
7+
*.( >2mm %!2 J
Question #: • •
•
•
• • •
Iith a small mass ae, there is a slight increase in the amplitue of %2 At mass 5, resonance occurs an A an % have the same natural frequency since the springs are of the same spring constant Ihen the mass on % is greater than 5, the oscillations will again be of small amplitue !ventually, both will stop oscillating as energy is issipate in the form of internal friction, heat to surrounings etc2
Question 5: -ime period of simple pendulum whose length is 81.< m? T *G/lDg1 *G/*72'D'26&1 *G/*2(861 * x &2('8 1%!%1 s 5aximum spee, v max *fA * x +2& x 82*( 2!%# "s-1 Acceleration, a - Q*x This is a maximum at x A /i2e2 at the amplitue or maximum isplacement1 amax - Q*A where Q *DT /*D&+1* x 82*( 1!2+ "s-2
Question : $alculation of maximum distance? 9 PD7r * Ihere the symbols have their ususal significance2 *2( x &+ -&* /.27 x &+ -81D7r * r * /.27 x &+ -81D/*2( x &+-&* x 71 4 $ 1!#3 ; 1% #
$omment ? The answer seems rather implausible since it is very unli3ely that we coul hear at this istance2 5oreover, the theoretical value is greater than the true value in practice ) e2g2 other noise, win, obstacles etc2 Explanation of why the speed of sound in a gas is less than the speed of sound in a solid )any F=#+? •
• • •
0oun is a longituinalDpressure wave requiring a meium /atomsDmolecules for its propagation Particles in gas much more wiely space than in a soli Bibrations are passe on by the interaction of particles Oas particles move about ranomly soli particles vibrate about a “mean” position2
Demonstration that the e"uation v / >)E?+ is homogeneous w.r.t. units ? v has units of ms -& ! has units of stress /Pa or >m -*1, i2e2 3g2m-&2s-* R has units of 3g2m -8 !quating? ms-& G/ 3g2m-&2s-*D 3g2m-81 /!"1 $alculation of [oung:s 5oulus for steel? !DR v* ! v *R /( *++1* x @ 6++ 2!11 ; 1%11 P(
Question &: $alculation of fringe spacing ? _ xsD" x _"Ds /.'+ x &+ -' x 82(1D/+2( x &+ -81 #!+3 ""
˂----˃ #!+ "" 4ine s(in Description of how appearance of fringe would change? • •
!hich fringes overlap? • •
$entral fringes At path ifference 8r2 0hort fringe with * n2 Long fringe since 8 x 7.+ * x .'+2
Question +: =se of graph to estimate work function of metal ? wo hf o .2.8 x &+ -87 x .2+ x &+ &7 3!9+ ; 1% -19 J
PH2 JUNE 2%%% Question 1: • • • • •
Alpha-particles 0cattere Positively charge &+-&( m 5ost of the mass2
Question 2: Dt - _> +2+&' x 82+ x &+ *+ 5!&9 ; 1% 1+ C Ce-arranging, _ />Dt1D> /(2@' x &+ &61D/82+ x &+*+1 1!93 ; 1% -2 s-1 5easurement of half-life woul be "o4e 4ei(*e since the mass of raio-nuclie may be very small an the half-life is 4e(son(*= on2
Question 3: A is st4one4 since the resultant stress is higher than %2 A is "o4e *4itte than % since there is no plastic eformation2 % requires more wor3 to exten it by && mm since the area uner the <-e graph is larger2
Question #: < - mQ*x Towars the fixe point /usually centre1 At a maximum /amplitue1 5aximum $alculation? T *G/mD31 T* 7*mD3 3 7 *mDT* /7* x +261D/&2(1 * 8&2(6D*2*( 1#!% N!" -1
Question 5: Two progressive waves prouce a stationary /staning1 wave by the superposition of two progressive waves, e2g2 reflection of a progressive wave with its reflecte wave2 Experiment ? Please see stanar textboo32 9n orer to show how a stationary wave ha been prouce, a sensor may be move between source an metal reflecting plate in which case maxima an minima are observe /antinoes an noes respectively1 ) at points of constructive an estructive interference2
Question :
_ 11!2 " A %!5 "
Question &: sin Y$ &Dn n &D sin 7*o &D+2..'* 1!5
$entre diagram? n sin iD sin r2 0ince gna &Dang &D&2(+ sin 7+oD sin r *D8 +2.78D sin r sin r /8 x +2.781D* +2'.7 r sin-& /+2'.71 &#!o #7( diagram? Laws of reflection are obeye /critical angle exceee1 i r %o Cegion A22222222222222n &27@ Cegion b22222222222222n &27( $ommercial optical cables are much thic3er than &*+ Mm in orer to provie e;t4( 4o*ustness (n6 st4ent72
Question +: Ihen ultra-violet light is irecte towars the Hinc plate, the leaf collapses graually as electrons are emitte from the Hinc plate2 9f re light is use, no such collapse is observe2
Question 9:
- &82. eB is the “groun state” which is the lowest energy level, where the hyrogen atom is most stable2 $alculation? ! hf hcD_ /.2.8 x &+ -87 x 82+ x &+ 61D/..+ x &+-'1 82+& x &+ -&' J & eB &2. x &+-&' J !nergy transition &&266 eB, corresponing to a rop from? K 1!51 to K 3!39 e2
PH2 JANUARY 2%%1
Question 1: U92 $ 23#T79% > #He2
23+
23#
T79% $ 23#I91 > %e-1
A strong magnetic fiel coul be use to istinguish alpha-particles from beta-particles since if the %-fiel is perpenicular to the irection of motion of particles? /a1 Particles eflecte in opposite irections /b1 %eta-particles curve more than alpha-particles
Question 2:
%ining energy is the energy neee to split a nucleus into protons an neutrons2 U4(niu" woul be the element most li3ely to unergo nuclear fission since the proucts are near the pea3 an so more stable2
Question 3: ! hf ) ϕ an ! hf hcD_ /.2.8 x &+ -87 x 82+ x &+ 61D/&*2* x &+-'1 &2.8 x &+-&@ J .2*+ eB .2*+ x &2. x &+ -&' +2&+& x &+ -&@ J N2!2 /&2.8 ) +2&1 x &+ -&' &2(8 x &+ -&@ J N2!2 F mv* &2(8 x &+ -&@ F /'2&& x &+ -8&1 v* v* /* x &2(8 x &+ -&@1D/'2&& x &+ -8&1 827 x &+ -&8 v 5!+ ; 1% "s-1 de 5roglie wavelength given? _ hDp /.2.8 x &+ -871D/'2&& x &+ -8& x (26 x &+ .1 1!25 ; 1% -1% " These photoelectrons woul be suitable for stuying molecular crystals since iffraction effects woul be maximum since inter-atomic spacing is the same orer of magnitue as wavelength2
Question #: This is an example of resonance since these are force vibrations /river an riven12 The vibrations have a maximum amplitue at the “natural frequency” of the steering wheelDcar system2 Ihen the forcing frequency natural frequency, then resonance occurs2 5aximum acceleration, a Q*2A where A amplitue an Q *f a /* x *271 * x .2+ x &+ -8 1!3 "s-2
Question 5: 9 PD7C * /+2&* x .+1D7 /82(1 * %!%#& W!" -2 9f the lamp is observe through a sheet of Polaroi, then intensity is reuce2 This is because the light from the lamp is uno(4ie62
0ince the light is unpolariHe, there will be no eet on the light intensity when the Polaroi is rotate2 Question :
Question &:
/i1 /ii1
0lit separation may range from +2& to &+ mm 0lit-screen istance, +2( to ( m2
/shoul measure, e2g2 8 an then ivie by number1 Light from the two slits has travelle the same istance at position D2 Light from the two slits is out of position at positions / (n6 F2 There is a path ifference of three wavelengths between light from the two slits at osition A on=2
9f one of the slits is now covere, one bright fringe only is seen2 Also, it is wier an more iffuse /less sharp12 Question +: Cay % is uneviate since this hits the interface at '+ o2 As ray A enters an optically enser material, the spee of light is ecrease an the ray is refracte towars the normal2 At the other surface, the ray bens away from the normal2
PH2 JUNE 2%%1
Question 1: Cefractive inex, n sin rD sin q2 As light enters the bloc3, its spee 6e4e(ses2 The frequency of the light insie the glass bloc3 is t7e s("e (s the frequency in air2 As angle p is ecrease, angle s will 6e4e(se2 Ihen angle q equals the critical angle, angle s will be %o
Question 2: 5ass eficit, \m /&782'**6( = '&2'*.*@1 ) /&2++6@+ =*8(2+78'71 u *8(267'&* ) *8.2+(*.7 - +2*+8(* u &2.. x &+-*@ x +2*+8(* 828@6 x &+ -*6 3g \! \mc* 828@6 x &+ -*6 x /8 x &+ 61* 3!%# ; 1% -11 J $alculation of power output ? !nergy per mole 82+7 x &+ -&& x .2+* x &+ *8 &268 x &+ &8 J Power !nergyDtime &268 x &+&8D(2+ 3! ; 1% 12 W
Question 3: P15 $ 32B1 > %e-1
32
Esing a O5 tube an ratemeter, the bac3groun count shoul be measure2 Then, the O5 tube is place close to the source an the count ta3en2 0ubsequently, paper or car is inserte into the beam an the count reta3en2 There shoul be little or no change in count rate2
%eta-ecay involves the change from a neutron to a proton The nucliemoves towars the otte line "ecay gives rise to greater stability ;n the iagram, this means , ` or at a iagonal /0!12
Question #: The range of extensions over which oo3e:s Law is obeye ranges from + to '-'2( mm2 Addition to diagram? Bertical metre rule with pointer on loaDhanger2 @ength to be measured ?
Question 5: !avelength of microwaves? Path ifference _ 77* ) 7*+ 22 "" Fre"uency of microwaves? c f_ f cD_ /8 x &+ 61D/** x &+-81 1!3 ; 1% 1% H
A maximum woul not be etecte at P since wavelength of the soun wave _ vDf 88+D&&++ +28 m2 $onsequently, the path ifference at P is not a whole wavelength2
Question : Beriod of oscillation of mass4spring system? T *G/mD31 *G/&.D8'++1 %!#% s ,aximum acceleration of mass? amax Q*xo where xo amplitue >ow, Q *DT *D+27+ &(2@ s -& 0ubstituting in the above equation gives? amax Q*xo /&.2@1* x 627 x &+ -8 2!%& "s-2 9raph of displacemen4time?
9raph of displacement4time within motor oil ?
Question &: The ioniHation energy of atomic hyrogen is &82. eB2 0ince energy is neee to raise the electrons to + eB, then the levels must start from a negative value2 \! 827+ ) &2(& &26' eB %ut, &26' eB &26' x&2. x &+ -&' 82+* x &+ -&' J >ow, \! hf hcD_ _ hcD\! /.2.8 x &+ -87 x 82+ x &+ 61D/82+* x &+-&'1 !59 ; 1% -& " The line spectrum of atomic hyrogen woul be prouce in a laboratory using a ischarge tube which consists of low pressure hyrogen gas with a high voltage across it2 Light emitte from this is then examine by passing it through a iffraction grating or prism in which case, a number of unequally-space vertical lines are seen on a blan3 bac3groun2 Atomic spectrum of hydrogen?
PH3 JANUARY 199
Question 1:
Let the un3nown temperature be Y o$ an assuming the !252<2 to be Hero at the ice-point, Y /#Y ) #o1D/#&++ ) #o1 x &++ /&27@ ) +1D/&2.( ) +1 +9o/
Question 2:
The constant spee implies Hero acceleration ) which in turn suggests Hero resultant force2 9f the contents of the meteorological balloon /hyrogen1 were replace by air, the weight of the balloon woul increase, so there woul be a net ownwar force2 9f the balloon an equipment rise a significant istance through the atmosphere, then the pressure of the hyrogen woul in4e(se since the pressure of the surrouning air 6e4e(ses! owever, the volume of the hyrogen in4e(ses ) this is a result of %oyle:s Law? pB constant an the pressure is ecreasing2
Question 3: Two esign features accounting for the high efficiency of the heat-pipe solar collector inclue? /a1 0pecial coate absorber plate absorbs all incient solar raiation /b1 The glass tube provies a “greenhouse” effect2 9f we assume that the temperature rise /\Y1 is ( to (( o$ /i2e2 (+o$1, then energy require 6+ x 7 +++ x (+ &. 5J !nergy collecte &.D+2@ *8 5J Assuming that the ay length &+ hours an that he average flux +27( 3I2m -* Area /*8 x &+ .1D/+27( x &+8 x &+ x 8 .++1 1! "2
Question #: The #+ J, wor3 one on the filament by the power supply2 \ - #+J, the energy radiated from filament by heating2 Typical filament lamps have an efficiency of only a few percent2 This means that only a small proportion is given out as light the rest of the energy is lost as heat to the surrounings2
Question 5: A “biofuel” is a fuel which is prouce by biological activity2 !xamples of biofuels inclue? woo /also peat, grass etc21 9t woul be inefficient to use biofuels to generate electricity for omestic use since the generation of electricity involves large inefficiencies by thermal losses to coolant2 owever, if the fuel is burnt in the house, all the energy is use for space heating2
PH3 JUNE 199
Question 1: A mercury-in-glass thermometer is in a state of thermal equilibrium when the length of the mercury threa is constant /i2e2 the thermometer reaing is constant12 The thermometer must be in thermal contact with the water /or, they must be at the same temperature12 >ow, Y /#Y ) #o1D/#&++ ) #o1 x &++ .82' /# Y ) .2*&1D/*@28( ) .2*&1 x &++ .82' /#Y ) .2*&D*&2&71 x &++ .82'D&++ /# Y ) .2*&1D*&2&7 /*&2&7 x .82'1D&++ # Y ) .2*&, giving the length 19!&2 " Two avantages of thermocouple thermometers over mercury-in-glass thermometers inclue? /i1 /ii1 /iii1
5uch wier range of tewmperatures /*( ) & 7++ N compare with *87 ) @*8 N1
Question 2: Ninetic energy transferre F mv * F /+2++@*1/8*1* 3!9 J $ooling of air in the cyliner uring expulsion of the isc may be explaine by the 3inetic theory of gases in that the energy comes from the wor3 one by the air on the isc which in turn is erive from the N2!2 of the air molecules2 5olecular 3inetic energy is irectly proportional to the absolute temperature consequently the air temperature falls2 Although wor3 is one by the air on the isc, no wor3 is one by the isc on the air because, as state previously, the isc gains energy from the air or, the isc moves in the irection of the force /air movement1 applie to it2
Question 3: eat capacity mass x specific heat capacity Total heat capacity of system /mass of water x 022 of water1 = /mass of aluminium x 022 of aluminium1 /+2(++ x 7 *++1 = /&2*+ x & +6+1 3 1+% J
Question #: 9n the relationship, pB constant, the following two variables must remain constant They are? /a1 5ass /or quantity1 of gas, /b1 Temperature2
Balues of pressures an volumes are recore at several ifferent pressures2 0ubsequently, a plot of p vs2 &DB shoul yiel a straight line2
Question 5: The purposes of a "o6e4(to4 in a thermal fission reactor is to slow own the spee of the neutrons2 The ont4o 4o6s, by absorbing neutrons, control the neutron reprouction rate2 !nergy is transferre from the fuel ros to the boiler via the following route? &2 *2 82 72
!nergy i ssupplir freomt the fuel aN2!2 in the fast-moving molecules The neutrons transfer heat to the moerator The moerator yiels up its heat to thge coolant
PH3 JANUARY 199& Question 1:
Assuming that the expansion of mercury is uniform, that mercury woul freeHe an that the thermometer is of uniform bore, the mar3 may be mae by simple calculation as shown on the iagram2
Question 2:
Question 3:
9n twenty years, the proportion of coal woul probably have ecrease ue to environmental consierations2 e2g2 “aci rain”2 9n two hunre years time, the use of biofuels may increase ue since the supplies of other power sources may have been eplete2
Question #: A heat engine is a evice which absorbs heat from a “hot source”, converts a fraction of this into useful an transfers the remainer to a “col sin3”2 0ince the efficiency of a heat engine is given by? /T& ) T*1DT& where T& temperature of hot source an T* temperature of col sin3, then it follows that a higher wor3ing temperature woul give rise to higher efficiencies2
Question 5: The value of , the energy flow out of the freeHer *2+ = 72( !5 J This follows from the
Question : Please see June &''., uestion 7 for an account of the experimental arrangements2 The 4iti( te"e4(tu4e, i2e2 the temperature above which a gas cannot be liquefie, whatever the pressure2
PH3 JUNE 199& Question 1:
5easurements to be ta3en inclue the mass of the aluminium bloc3 /m1 an the initial temperature /Y&12 The current is turne on an the stop-cloc3 starte2 9n aition, the voltmeter an ammeter reaings were ta3en /B an 9 respectively12 After a while /after an appreciable temperature rise1, the final temperature /Y*1 an time /t1 were note2 eat transferre to bloc3 92t2B 9ncrease in internal energy of bloc3 m2c /Y * ) Y&1 where c 022 capacity of aluminium c /9tB1Dm /Y* ) Y&1
Question 2: 5aximum N2!2 of bloc3 F mv* F /.( x &+ -81/+27.1* !9 ; 1% -3 J
Question 3: Let nA an n% be the number of molecules in containers A an % respectively2 Then,
nA /pABADCTA1 n% /p%B%DCT%1
%ut, since BA B%, pA p%, TA T% an C is constant n A n% an the number of molecules are equal2
0ince
p &D8 />DB1 m ˂c*˃
an the average molecular 3inetic energies are the same at the same temperature, then it follows that the pressures must be equal if the numbers of molecules are the same2
Question #: 5ass of submarine Bolume of submarine x "ensity of sea-water *++ x & +*( 2!%5 ; 1% 5 0 Ior3 one pressure x volume change, where \B &+ m 8 an total pressure /p1 atmospheric pressure = gRh Pressure ue to epth *( x & +*( x '26& *2(& x &+ ( Pa Atmospheric pressure &2++ x &+ ( Pa Total pressure /&2++ = *2(&1 x &+ ( 82(& x &+ ( Pa 0o, wor3 one p\B 82(& x &+ ( x &+ 3!51 J >ett upwar force weight of water pumpe out mg, where m BR an g '26& ms -* < &+ x & +*( x '26& 1!%1 ; 1% 5 N %y >ewton:s secon law, < ma a
Question :
PH3 JANUARY 199+
Question 1:
Question 2: Epthrust weight of flui isplace volume x ensity x “g” &2(+ x &28+ x '26& x &+ -8 %!%19 N
"ensity of air in balloon *2&(D&2(+ 1!#33 !it4e-1 The ensity of air in the balloon is greater than the surrouning air because there are more air molecules per unit volume insie the balloon compare with the outsie air2
Question 3: !nergy is transferre from the 0un to the !arth by a process of thermal raiation high temperatures in the 0un are create by nuclear fusion in which hyrogen nuclei combine to form helium2 The 0olar constant is the rate at which energy is receive at the !arth:s surface from the 0un /unit? I2m-*12 Assuming, on average, 6 h of aylight per ay /this ta3es into account summerDwinter = clouy ays etc212 Then, no2 of secons per year that energy is receive in EN 6 x 8.(2*( x .+ x .+ *2&+ x &+ @ !nergy receive per square metre *++ x &2+( x &+ @ *2&+ x &+ ' J2 >o2 of tonnes of 5iscanthus grownDm * &*D&+ +++ +2++&* %ut, & tonne of 5iscanthus yiels &2@ x &+ &+ J !nergy yiel +2++&* x &2@ x &+ &+ $ 2!%# ; 1% & J2 ;ne reason for the ifference between the total energy per square metre available from the 0un an the maximum energy yielDm * of 5iscanthus crop is that photosynthesis of the growing plant requires solar energy2
Question #:
A thermocouple operates as a simple heat engine since heat /energy1 wants to flow from the “hot source” to the “col sin3”2 9t oes this by transferring electrons /wor3 output shown as voltage on the meter12
;ne way of increasing the efficiency of a thermocouple is to increase the temperature of the hot source2 This is because efficiency is given by? /T& ) T*1DT& Ihere T& temperature of “hot source” T * temperature of “col sin3”2
Question 5:
PH3 JUNE 199+ Question 1: As the loae spring rises to its equilibrium position, the energy transfers ta3ing place inclues /any TI;1? /i1 /ii1 /iii1
An increase in 3inetic energy An increase in gravitational potential energy Loss of heat to the surrounings
The energy associate with the oscillations is lost as internal friction )damping+ within the springair resistance causing the spring to warm up slightly2 9t woul not be feasible to recover this lost energy since this is Clow grade heat i.e. dispersed too widely
Question 2:
Question 3: At steay state, the temperature across the interface, although ifferent, remains constant2 $onsequently, the flow of heatDsecon is constant2 Thermal equilibrium means that two boies are in thermal contact an at the same temperature2 E /Cate of heat flow1D/Area1 x /temperature ifference1 .&D/&28 x&81 3!1 W!" -2!S -1 9f the panes of glass were move further apart, there woul be more heal lost by on
Question #: Pressure ifference gRh '26& x 6.+ x +2&&* '772' Pa Pressure in container Atmospheric ) ifference above &+& *++ '772' 1%%!2 0P( The atmosphere wor3ing on the system increases the gravitational potential energy store in the oil on the L0 of the manometer2 9f the temperature rises, the 3inetic energy of the molecules increases ) the faster molecules collie with greater force an with greater frequency on the walls of the container, thus causing a rise in pressure2
Question 5:
Question : /a1 eat loss through chimneyDflue 9nefficient combustionDlosses from flames by raiation2 /b1 !scaping steam carries away energy Thermoynamic efficiency of heat engines limite by temperatures of hot sourceDcol sin32 /c1
PH3 JANUARY 1999 Question 1: ! mc&\Y& = mL = mc *\Y* where m *28 3g ! /*281/7 *++1/&(1 = /*281/88+ +++1 = /*281/* &++1/8+1 &772' 3J = @(' 3J
= &772' 3J
1!%#9 J
$ost of freeHing mil3 /62* x &2+7' x &+ .1D/& +++ x 8 .++1 2!#
Question 2:
5ass of petrol isplace submerge volume x ensity of petrol &( x &+-7 x 8 x &+ -* x @&+ +2+8* 3g Ieight of petrol isplace +2+8* x '26& %!31 N Ieight of float weight of flui isplace %!31 > !xcess pressure gR\h '26& x @&+ x 8 x &+ -* 2%9 P(
Question 3:
/a1/i1/ii1 \E is e4o \ is e4o because the system is isolate \I is e4o because the system is isolate The thermocouple is unable to power the small motor 5 because t7e4e is no te"e4(tu4e 6ie4ene2
The thermocouple now powers the small motor 5 because t7e untion te"e4(tu4es (4e 6ie4ent2
As time progresses, the !252<2 of the thermocouple 6e4e(ses because the te"e4(tu4e 6ie4ene 6e4e(ses2 The motor stops wor3ing when the te"e4(tu4e 6ie4ene (s to e4o2 9n terms of energy flow, this is because so"e ene4= (*so4*e6 (t t7e 7ot untion is t4(nso4"e6 into eet4i( ene4=2
Question #: First Assumption? ETHER:
A large volume change occurs on change of state implies large spacing of gas molecules
OR:
Capi iffusion rates in gases implies more room for motion of molecules2
(econd Assumption? %rownian motion in gases2 0mo3e particles in ranom motion bombar air molecules2
Question 5: First Argument ?
Example?
%urning of coal or oil releases carbon ioxie to the atmosphere, causing Olobal Iarming by the Oreenhouse !ffect2
(econd Argument ?
Example?
$oal, oil2
PH3 JUNE 1999
Question 1: 9eal gas equation gives that? pB nCT C pBDnT />m-*1/m81D/mol1/N1 0!"2!s-2!"o-1!S -1 The graph plotte shoul be p /y-axis1 vs2 T /y-axis12 9t shoul be a straight line through the origin /temperature, T in N12 The assumption to be mae to enable gas pressure measurements to be use to efine a practical temperature scale is? pressure W absolute temperature /proviing the gas is ieal, the mass of gas an volume are constant12
Question 2:
Question 3: !nergy given out mc\Y &2* x & +++ x 7 *++ x /'6 ) .(1 1!32 J Time !nergyDpower /&2.. x &+ 61D/. x &2( x &+ 81 1+ #+% s 9n the morning, the temperature ifference woul be greater than in the evening2 $onsequently, there is a greater power output in the morning than in the evening2
Question #: !1 #enewable? win, wave, tial, solar power /any ;>!1 ;ne metho of harnessing solar power is a solar panel which is a blac3-coate /goo absorber1 metal /goo conuctor1 pipe in an empty box with a sheet of glass on top /Oreenhouse effect12 $ol water fe in becomes hot as a result of solar gain2 Area /* +++ x &+ .1D/+2&( x **+1 $ !% ; 1% & "2 0olar power stations are unli3ely to be the ma4or solution to energy eman ue to the large lan area involve2
Question 5: !xternal area of refrigerator /7 x &2+ x +2(1 = /* x +2( x +2(1 * = +2( 2!5 "2 Dt - 3A/TDx1 +2+&6 x *2( x /*+ ) &(1D/(2* x &+ -*1 12!9+ W The refrigerator acts as a 7e(t u", which ta3es heat from the col sin3 /insie refrigerator1 to the hot source /outsie air1 ) these rates are equal2 \E Hero because the temperature of the contents is constant \ has two components? • •
eat flowing in from room eat flowing out from contents
\I Hero since no wor3 is one on /or by1 the contents2
PH3 JANUARY 2%%%
Question 1:
• • • • • •
Question 2: 9nitial rate of rise of temperature graient of graph at origin (D/*2( x.+1 +2+88 o$2s-& !stimate of initial rate of gain of heat from surrounings Dt mc/YDt1 +27 x 7 *++ x +288 % W Explanation of 8 min. delay: Time is neee for inflow of heat to melt the ice2 eat absorbe \ /Dt1 x t mL where m mass of ice L 02L22 of fusion of ice .+ x *@ x .+ m x *2*@ x 8 .++, or m /*@ x 8 .++1D/*2*@ x &+ .1 %!%#3 0
Question 3:
Explanation of how gravitational force drives convection current ? Air near the heater warms up, expans an becomes less ense 2 $onsequently, a pressure graient “rives” the convection current since there is a weight ifference /gravitational in origin1 acting2 Explanation of why the heater powers the convection current ? Ninetic energy is store in the corrosion current ) this energy can on= come from the heater2
Question 5: /Coot mean square spee1, ˂c˃ G/n&c&* = n*c** = 22221D> where > Total number of particles / n& = n* = 2221 c&, c*,222 are the iniviual spees of the particles n&, n* are the numbers of particles with spees c &, c* etc2 ˂ c˃
GU/& x 7++* = & x 8++ * = & x (++* = & x .++ * = & x *++*1D(V #2# "!s-1
Assumption in algebraic form? "˂ 2˃ $ '3?2) 0T Derivation of the deal 9as E"uation? pB F m˂ c*˃ x /*D81 > >3T n>A 3T nCT
Question 5: Explanation of why fuel rods rods heat up? up? • • •
A nuclear fission reaction occurs in the uranium ro This fission releases heat Therefore the ro heats up2
Explanation of how energy energy released released reaches the the coolant ? •
This occurs by a conuction process, relying on the temperature ifference between the fuel ro an the carbon ioxie gasDliqui soiumDpressuriHe water cooling meium2
Explanation of energy energy flow to coolant via moderator moderator ? • • •
#ole of moderator in sustaining sustaining chain reaction reaction?? • • •
PH3 JUNE 2%%% Question 1: 5ass of mercury Bolume x ensity +2(++ x &8 .++ x &+ -. %!%%+ 0 '!+ ) eat capacity 5ass x specific eat $apacity +2++.' x &7+ %!952 J!S -1 The heat capacity of the thermometer woul be greater than the calculate value since the mercury has to be containe in glass /itself having heat capacity12
The graph becomes less steep as time progresses since heat transfer from the hot liqui to the thermometer is by conuction2 As the temperature becomes closer, the thermal graient ecreases so therefore the rate of heat flow ecreases2 The temperature levels off below 6+o$ since the thermometer /mercury an glass1 absorbs some of the heat from the hot liqui2 Also, the insulation is not perfect, so some heat will be lost from the walls of the container2
Question 2: /a1 From the the power supply to the element ? this is by o40in since o40in since electrons o wor3 on the element 9B\t where the symbols have their usual significance2 /b1 From /b1 From the the element to surrounding surrounding air ? is 7e(tin an represents the heat loss to the surrounings2
Question 3: p represents the pressure of the gas /Pa1 B represents the volume of the gas /m 81 > represents the number of gas particles present /no unit1 5 represents the mass of one molecule of gas /3g1 ˂ c*˃ represents the root mean square of the molecules square /m *2s-*1
Nine Nineti ticc ene energ rgyy F m˂ c*˃2222222222222222 /&1 pB /&D81 >m˂ c*˃222222222222222222222222222/*1 0ince F m˂ c*˃ /8D*1 3T, substituting in /*1 gives? pB /*D81> /F m˂ c*˃1 /*D81>/8D*13T $ N0T which is the ieal gas equation2
Question #: The energy flows from the outsie air into the interior of the builing2 This is because the temperature outsie is greater than that insie an heat flows own the thermal graient2 9n terms of energy flows, heat must be ta3en from the insie an transferre to the outsie /in a similar way to a heat pump or refrigerator1 ) i2e2 an energy input is require2 \D\t EA\T Power
!nergy transfer mc\T && x &+ 8 x '*+ x /88 ) *(1 6+2'. 5J Average Average power flow !nergyDtime /6+2'. x &+ .1D/.+ x .+1 22!5 0W This is a rather large value an consieration shoul be given to extening the time perio require for “coolown”2
Question 5: Assuming 0&&G efficiency? efficiency ? !nergy output +2&* x (& .2&* 5J %ut this is supplie over & hr / 8 .++ s1 Power output /.2&* x &+ .1D8 .++ @ess efficiency would be expected since? since? •
•
There are “9*C” power losses /cause by heat in cables1 in the electricity transmission system2 There is a maximum thermoynamic efficiency relating to the power station, base on the temperatures of the “hot source an “col sin3”, since it acts as a “heat engine”2
Efficiency could be increased by by /any ;>!1? • •
9ncreasing the voltage of overhea cables to reuce losses EtiliHing a $P /combine heat an power system1 whereby excess heat from the power station is transferre to houses in its locality2
PH3 JANUARY 2%%1 Question 1:
The smo3e particles move ranomly ue to the air molecules colliing with them2 0mo3e particles act as “mar3ers” since air molecules too small to be seen2 0ince smo3e are much more massive than air molecules, it follows that air molecules must be moving at high spee /!quipartition of !nergy12
Question 2: !lectrical energy supplie 9tB *8 x 8+ x +27* 2+9!+ J VU $ > 29% J This is positive since the internal energy increases on a temperature rise2 VQ $ % The bloc3 is thermally insulate ) no lossDgain of energy2 VW $ > 29% J This is the electrical energy supplie /as wor3 one by supply12 Average force applied by hammer ? I <2 *'+ < x *27 x &+ -8 < 121 0N
Question 3: The pressure law gives pDT constant where p pressure an T temperature /N1 p&DT& p*DT* p* p&T* DT& /&2++ x &+ ( x 8@81D*@8 1!3& ; 1% 5 P(
Question #:
Question 5: /i1 /ii1
elium has a lower ensity than surrouning air because helium particles are ess "(ssi
Epthrust weight of air isplace >ow, mass of air isplace volume x ensity &2'+ x &+-8 x &28+ 2!#& Ta3ing “g” as '26&m2s -*, Epthrust /force1 *27@ x &+ -8 x '26& %!%2#2 N
PH3 JUNE 2%%1
Question 1:
Explanation of why line might break ? • • •
Ieight remains the same Epthrust ecreases Tension therefore increases2
Question 2: \ mL
/eat neee for vaporiHation1
\ Pt
/!lectrical energy supplie1
Pt mL t mLDP /+2(+ x *2* x &+ .1D* 7++ #5+ s "emonstation that volume is approximately +2' m 8 pB nCT B nCTDp /*@26 x 628& x 8@81D/&2+& x &+ (1 %!+ "3 I p\B &2+& x &+( x +26. +!+ ; 1% # J
\ +2( x *2* x &+. 1!1 ; 1% J \I - +!+ ; 1% # J \E \ = \I 1!%1 ; 1% J
Question 3:
Explanation of shape of graph? As the volume increases, then the pac3ing ensity of the molecules ecreases hence the collision rate with the walls of the container ecreases2 Finding pressure of the air in syringe? /IeightDArea of piston1 = atmospheric pressure2 Bossible sources of error /any ;>!1? • • • •
Temperature variations
Question #: Total area /* x +2. x +2.1 = /7 x +2. x +261 *2.7 m * Dt - 3A/TDx1 /+2+7 x *2.7 x *+1D/8+ x &+ -81 &%!# W -he answer will be approximate /any TI;1? • • • •
9ncomplete insulation aroun oor seal Bariable thic3ness of insulation /e2g2 corners1 5etal case ignore 9nterface temperatures will be ifferent from bul3 temperatures2
The interior temperature remains constant when energy is remove (t t7e s("e 4(te as it flows in2 !ays for efficient design of condenser /any TI;1? • • •
5etal conenser pipes ai on6ution Large area promotes on
Leaving the refrigerator open on a hot ay is not a sensible suggestion since conenser emits energy into 3itchen (t ( 4e(te4 4(te than energy remove from insie the frige2
Question 5: The role playe by neutrons in proucing a self-sustaining chain reaction is fission ) cause by neutron impact2 9f neutrons from the fission of one nucleus go on to split other nuclei, a chain reaction may result2 The function of a moerator is to slow own the spee of the neutrons2
Explanation of arrangement ?
To maximiHe the chance of fresh fission events in the uranium fuel ros2
PH# JANUARY 199 Question 1: /a1
/b1 The electric potential at a point may be efine as the wor3 one in bringing a unit point positive charge from infinity to that point2 !lectric potential is a s((4
The electric fiel, ! BD D/ oA1 /&2+ x &+ -.1D/626( x &+-&* x +27*1 &!% ; 1% 5 !"-1
Question 2: $B /Alternatively, we may write /oAD1 x B1 The electric fiel, ! BD D oA /& x &+ -.1D/626( x &+-&* x +27*1 &!% ; 1% 5 !"-1
Question 3: Esing calibrate all probe /in the correct orientation1, the magnetic flux ensity /%1 is measure as a function of? • • •
$urrent, 9 >umber of turns, > "istance from centre, r
two out of these three variables are constant, the thir is varie2 The experiment is repeate twice an the results average aroun the toroi2 5athematically, plots of % vs2 >, % vs2 9 an % vs2 &Dr shoul give straight line plots through the origin2 0ince the relative permeability Mr of the iron ring is about & +++ /compare to air1, virtually no flux travels “outsie” an iron ring2
Question #: !ssentially, the microphone is a transucer in which soun waves /the oscillations of air molecules1 are receive at the iaphragm which vibrates in sympathy with the air molecules, thereby moving the coil which in turn cuts the lines of magnetic force, thus inucing an !252<, thereby proucing A2$2 signals2 9f A2$2 were fe into the microphone, it woul act li3e a louspea3er, moving the iaphragm in an out because of the changing fiel in the coil interacts with the magnetic fiel of the permanent magnet thus proviing a force at right angles to the fiel /
Question 5:
PH# JUNE 199
Question 1: $oulomb:s Law states that the magnitue of the force between two electrically charge boies is inversely proportional to the istance between them an irectly proportional to the prouct of the charges2 0ince < /&D7o1/&*Dr *1 Ce-arranging? o /&*D72m* A*2s*D/3g2m2s-*2m*1 o has imensions A2!s2!0-1!s-2!"-3
Question 2: /a1 A fiel may be efine as a region of space in which forces exist between two boies, not in contact2 Any TI; of the following? &2 !lectric fiels act on all charges whereas magnetic fiels only act on moving charges *2 !lectric fiels can be cause by a single, point charge whereas magnetic fiels are always “ipole” in nature 82 ewton 99, < ma a
Question 3:
The maximum charge store, $B 7@+ x &+ -. x &* 5!# "/ Explanationscalculations? The maximum current, 9max BDC &*D*2* x &+8 %!5# "A The time constant $C secons 7@ x &+ -. x ** x &+ 8 1%!3# s The time to halve $C ln * &!1 s
Question #:
9n the case of 05, acceleration, a - Q*x
Thus, graient - Q * $onsequently, T *DQ 2M?'-4(6ient)
x xo sin Qt x &( *( sin Qt >ow T *DQ Q *DT *D&* 0o, +2. sin /D.1 t, giving t &2*8 hrs “Ceal time” :1# "
Question 5:
< %9*l or, < /M o9&9* l1D/*1
The ampere is the constant current which, when flowing in to ininite= on, straight parallel conuctors of negligible circular cross-section, place in ( <(uu" & m apart, giving between them, a force of * x &+-@ > per metre2 9n the above equation, 9 & 9* & A an & m, then F? $ '#M ; 1% -& ; 1 ; 1)?'2M ; 1)
PH# JANUARY 199&
Question 1: < Om&m*Dr *2222222222222222222222222222222>ewton:s Law of gravitation < &*D7or *222222222222222222222222222$oulomb:s Law Differences between gravitational and electric fields? /a1 !lectric fiels can be attractive or repulsive gravitational fiels are always attractive2 /b1 %oth have infinite range2
!lectric force ! &++ x &2. x &+ -&' 1! ; 1% -1& N Ieight mg '26& x &+ -&6 > >et force !2 ; 1% -1+ N 'u(46s)
Question 2: Time constant $C secons 8+ x &+ -. x *+ x &+ 8 %! s 0ince the time constant is the time ta3en for the charge to fall to &De / +28@1 of its original value, then it follows that the time ta3en for the charge to fall to '+ M$ S %! s
Question 3: The force < between two point charges & an * at a istance r apart is given by? < &*D7or * *D7or * /Assuming & * 1 As 9t , < 9 * x t* x &D/7 or *1 9 G/
0o 9 has imensions / o1&D* /5LT-*1&D* T-& L o&D* 5&D* L8D* T-* The force per unit length, <, on two infinitely long conuctors carrying currents 9 & an 9* is given by? < Mo9&9*D*r Mo9*D*r 9 G/< x * x rDM o1 0o, 9 has imensions M o-&D* /5LT-*1&D* L&D* Mo-&D* 5&D* L T-& The imensions of 9 must be the same irrespective of the system in which they are expresse2 0o, o&D* 5&D* L8D* T-* Mo-&D* 5&D* L T- & &DG/Moo1 &DG/@26( x &+ -&* x 7 x &+ -@1 3 ; 1%+ "!s-1 The velocity is equal to that of i7t2
Question #: P 9B 9 rms PDB 8 .++D*7+ &(A %ut 9max G* x 9 rms &( x G* *&2* A >ow, % Mo9D*r for a long, straight conuctor2 /7 x &+-@ x *&2*1D/* x +281 1!#1 ; 1% -5 T The magnetic fiel ue to the !arth:s fiel is constant whereas the magnetic fiel ue to the A2$2 in the wire is fluctuating2 This may inuce an !252<2
Question 5:
!lectric fiel strength, ! BD 7++D+2+*( 1 %%% !" -1
PH# JUNE 199&
Question 1: Free body body force diagram diagram for ball A? A?
Cesolving vertically? T cos (+ cos (+o mg T x +2.76 &2( x &+ -8 x '26& T /&2( x &+ -8 x '26&1D+2.76 2!29 ; 1% -2 N Cesolving horiHontally, horiHontally, the electrostatic force is given by? < T sin T sin (+ (+o *2*' x &+ -* x +2@..+ $ 1!&5 ; 1% -2 N $oulomb:s Law gives? < &*D7or * but & * * 7or * x < * 7 x 626( x &+ -&* x /&(28 x &+ -*1* x &26 x &+ -* 727. x &+ -&7 G/727. x &+ -&71 2!1& ; 1% -& / The gravitational force between the two balls woul be much smaller than the electrostatic force calculate above2
Question 2: The centripetal force, < is given by? F $ '"B 7) ewton:s Law of Oravitation? < m0g /Om05!1D/C ! = h1* The mass m0 cancels on either sie of the equation $ '@E)?'R E > 7)2 Enits of “g” woul be >23g -& or m2s-*2 >ow, the gravitational force of attraction provies the centripetal force2 Therefore, we may write? m0v0*D/C ! =h1 /O5!m01D/C ! = h1* v0* /O5!1D/C ! = h1 /m0 again cancelling on either sie of the equation12 Thus, as h increases, v woul increase since O, 5 ! remain constant2 9f a satellite slows own in its orbit, then the gravitational force of attraction woul excee the centripetal force, or mathematically? O5!m0D/C ! = h1* ˃ m0v0*D/C ! = h1
Question 3:
Question #:
The use of a “current balance” is shown in the iagram2 To investigate investigate how the force epens upon the current /measure by an ammeter1, it is convenient to fin the currents neee to balance one, two an three riers /<, /<, *< an an 8< respectively12 A plot of < vs2 9 shoul shoul yiel a straight line through the origin2 %y
Question 5:
T *G/mD31 T *G/&2.@ x &+-*@D&2&8x &+ 81 @2. x &+ -&( s < &DT &D@2. x &+ -&( 1!31 ; 1% 1# H Light of wavelength *2*' x &+ -. m woul be strongly absorbe by the hyrogen molecule since c f_ _ cDf /82++ x &+ 61D/*2*' x &+-.1 &28& x &+ &7 H This is the s("e 4euen= as 4euen= as the hyrogen atoms in the moel2 Thus resonanceDstrong absorption woul occur2
PH# JANUARY 199+
Question 1: A neutral point is a place where two fiels are equal an opposite an the resultant force is Hero2
The magnetic flux ue to a long solenoi is given by? % Mon9 where n no2 of turnsDunit length an 9 current flowing /A1 0o, %A Mo x *n x 79 6M on9 %% Mo x n x 9 M on9 The magnetic flux ensity of A is 6 times that of %2 0ince the istance A-% & m2 9t follows that the neutral point will be at a point +2&& m from A an +26' m from %2
Question 2: ;n switching on the large current, !y currents are inuce in the aluminium ring /nonmagnetic12 0ince, by LenH:s Law, this is in a irection in opposition to the pole forme at the top of the coil, then magnetic repulsion woul occur an the aluminium washer woul 4ump up2 owever the washer woul 4ump bac3 because the current is "2$2 an the !y current woul ecay tom Hero since there woul then be no change of flux lin3age /necessary for inuce !252<:s12
Question 3:
9f the isolate charge were negative, the graph woul be a mirror image, i2e2 negative potential below the x-axis1 an 4isin to Hero at infinite istance2 0ince potential, B wor3 one in bringing unit charge from infinity to that point, we may write? B /& x *1D7ox where & charge on W-particle = * e * charge on Au-nucleus = @' e 9f x is the closest approach, potential energy at x ue to Au /@'e x *e1D7ox 7 5eB 7 x &+ . x &2. x &+ -&' .27 x &+ -&8 J /@' x *e*1D 7ox .27 x &+ -&8
This gives x $ 5!9 ; 1% -1# " Question #: The gravitational potential, B at a point is efine as numerically equal to the wor3 one in ta3ing a unit mass from infinity to that point2 B at the surface of the !arth is negative, inicating that the potential at infinity /Hero1 is 7i7e4 than the potential close to the !arth2 >ewton:s Law of Oravitation gives that? < O5mDr *, but this force mg where m mass of “test” mass an 5 mass of !arth2 O5mDr * mg $ancelling m, we get? g O5Dr * >ow,
g '26& O5Dr * B - O5Dr '26& x .27 x &+ . .2*6 x &+ @
%ut,
N2!2 F mv* O5mDr F v* O5Dr .2*6 x &+ @
;r,
v G/*O5Dr1 G/.2*6 x &+@1 1!1 ; 1% # "!s-1
9n calculating the escape spee from a space probe travelling outwars from the 0olar 0ystem, 5 woul represent the "(ss o t7e Bun an r woul represent its 6ist(ne 4o" t7e Bun2
Question 5: 9rms /&DG*1 x 9o /&D&27&71 x 8*( 229!+ 0 Delay between p.d. in conductors 0 and 8? This is '&?2%) T ,aximum difference in voltage? ;n the positive half of the cycle, this is /@D61 B o2 0o this is effectively * x /@D61 x 8*( 5+!&5 Hon4;ero vector sum? "ue to the phase lag between the conuctors, the vector sum of three currents in the return conuctor might not be Hero2
PH# JUNE 199+
Question 1: 0ince the oil rop carries a positive charge, plate A must be ne(ti
! BD ( +++D/*2( x &+ -81 2 ; 1%5 !"-1 0ince mg q! q /'2@' x &+ -&( x '26&1D/* x &+ (1 #!+ ; 1% -19 / This is equivalent to 8e2 Therefore t74ee electrons woul have ha to be remove for it to acquire this charge2
Question 2:
% Mo9D*r2 Thus, total %-fiel MoD* /*D+2+8 = 7D+2&*1 2 ; 1%-5 T Question 3: >ewton:s Law of Oravitation lays own that? < O5mDr * where < represents the /attractive1 force between two point masses m & an m*, istance r apart an O universal constant of gravitation2 #easons why it is extremely difficult to obtain a reliable value for 9 in a labotatory /any TI;1? • • • • • •
The gravitational fiel becomes very wea3 at large values of r, consequently the wor3 one approaches Hero2 0ince gravitation is an attractive fiel only, wor3 is one in moving mass away from !arth /alternatively, B is Hero at infinity an increases as we move away from the !arth12
Question #: !lectromagnetic inuction is the generation of an !252<2 cause by a moving conuctor, cutting the lines of magnetic force2 Experiment to Demonstrate Faraday3s @aw of Electromagnetic nduction? To “explain” electromagnetic inuction,
the spee of motion of the magnet or coil, the number of turns on the coil, the strength of the magnet2
These facts le to his law? The siHe of the inuce !252<2 is irectly proportional to the rate at which the conuctor cuts magnetic fiel lines2
9nuce !252<, %lv /. x &+ -( x (7 x 6.+ x &+ 81D/.+ x .+1 %!&& 9n orer to etermine the polarity of the wing tips, the irection of the fiel must be 3nown2
Question 5: The frequency of the supply is 5% H
$alculation of resistance of kettle? Power issipate F 9 oBo P $alculation of resistance of kettle? Power issipate F 9 oBo P where 9o, Bo represent pea3 values2 * +++ F 9 o2 8*+, giving C 25! X
PH# JANUARY 1999
Question 1: /i1
/ii1
E 1?42 An example of a region in which we woul expect a uniform electric fiel woul be *eteen 7(4e6 (4(e (tes /central region12
Question 2:
f . +++D.+ 1%% H Amplitue F /istance LT1 F x 62. #!3 " a - Q*x - /*f1 * x amax 7* x &++* x 728 x &+ -* 1!& ; 1%# "!s-2 The acceleration will be Hero 7((= *eteen T (n6 L2 The motion is not perfect 02252 6ue to 4ition *eteen iston?=in6e42
Question 3:
(uitable instrument ? igh resistance voltmeter ;C $C; ;C ata-logger ;C igital voltmeter2 ,aximum charge stored in capacitor ? $B &++ x ( 5%% ./
Average charging current ? 9 D$ (++D' 5 .A nitial charging current ? Oraient at origin (D*2. &2'* B2s -& 9nitial charging current, 9o &++ x &2'* 192 .A
Question #:
< mv*Dr p < %qv >ow, %qv mv*Dr p qDm vD%r p Ce-arranging, r vmD%q ence, 4: 4 $ 2:1
Question 5: LenH:s Law of electromagnetic inuction states that “the direction of the induced E.,.F. is such as to oppose the change causing it ”.
9n T8, lines of magnetic flux cut the copper tube /an electrical conuctor1 such that inuction occurs an the current in the copper tube 4e(tes ( "(neti ie6 in su7 ( (= t7(t it is in oosition to t7(t o t7e *(4 "(net, thus slowing it own2 T& is plastic so no eet4o"(neti in6ution ou4s, i2e2 no current can flow in the tube /since plastic is an electrical insulator12 9n T*, the falling cyliner is un"(netie6 so no electromagnetic inuction occurs2 Thus, in both cases /T & an T*1, the cyliners only have the force of gravity acting on them2
PH# JUNE 1999 Question 1: < O5O5JDr * < 5OrQ* !quating the above two expressions? O5O5JDr * 5OrQ* $ancelling 5O from either sie of the equation, we get? O5J r 8Q* .2.@ x &+ -&&5J /&2+@ x &+ '18 x 7*D/@2&. x &+ x *7 x .+ x .+1 * 5J U&2**( x &+ *@D.2.@ x &+ -&&V x U8'276D/82'8x &+ &&V 1!+95 ; 1% 11 0
Question 2:
$alculation of maximum speed ? vmax *fxo * x *+ x &26 x &+ -* 2!2 "!s-1
Question 3:
!lectric fiel strength, ! - BDx &*D/+2*( x &+ -81 #+ %%% !" -1 $apacitance, $ oAD /626( x &+ -&*1 x +2+77D/+2*( x &+ -81 1!5 ; 1% -9 F $harge store on plates $B &2(. x &+ -' x &* $ 1!+& ; 1% -+ / The charge on the plates st(=s t7e s("e2 The capacitance of the arrangement in4e(ses2
Question #: -otal magnetic flux through loop *& cm from magnet3s end ?
Question 5: This is the “5otor Principle” ) i2e2 a current-carrying conuctor experiences a force when place in a magnetic fiel2 The current is at '+o$ to the magnetic fiel2 %y
Factors affecting the magnitude of force? /&1 9ncrease the siHe of the current /*1 9ncrease the strength of the %-fiel /81 !ither increase the no2of turns of coil or increase the length of P2 Explanation of observation that current reduces in coil the faster it spins? As flux is cut, an !252<2 is inuce2 %y LenH:s Law, this tens to oppose the applie p22 hence the current is less2
PH# JANUARY 2%%%
Question 1:
Esing a Cee switch circuit /iagram above1, the area /A1 of plate overlap is measure2 Then, if the switch operates at frequency f, then current 9 f an capacitance is calculate from $ DB2 0o, 3eeping , istance between plates constant, we change A an repeat the process2 9t follows that a plot of $ vs2 A shoul yiel a straight line through the origin2 Estimation of area of the plates? $ r oAD A $Dr o A /+2& x &+ -. x & x &+ -(1D/626( x &+ -&* x *261 #!% ; 1% -2 "2
Question 2: $alculation of magnetic flux density? % Mon9 7 x &+ -@ x /@*D+27(1 x *2( 5!%3 ; 1% -5 T bservations on the voltmeter ? /a1 A small pulse is registere, which then returns B to Hero2 /b1 A small pulse in the 4e
Question 3: Explanation /any TI;1? • • •
The coil carries a current at '+o to the magnetic fiel Accoring to
Explanation of unusually4shaped magnet ? The 4(6i( magnetic fiel ensures that the current ensures that the current in the coil is always at '+o to the %-fiel2
Question #:
Amplitue of tie 3!1 " Time of next mi-tie 12:%% 'noon) Time of next low-tie 3:%% " x xo sin Qt &2' 82& sin /*tD&*1 +2.&8 sin /tD.1 sin /+2.&81 tD. t &2*. h Time at C &*?++ h = &?*. h 1:1 "
Question 5: $alculation of escape speed ? >ewton:s Law of Oravitation gives that? < O5mDr *, but this force mg where m mass of “test” mass an 5 mass of !arth2 O5mDr * mg $ancelling m, we get? g O5Dr * %ut,
N2!2 F mv* O5mDr F v* O5Dr
;r,
v G/*O5Dr1
v!DvP G/*r !Dr !1 or vP v!DG* &&DG* &!&+ 0"!s-1 The space probe shoul be as small as possible to "ini"ie ue onsu"tion /N2!2 require F mv*12
PH# JUNE 2%%%
Question 1:
B D7or The plot confirms the relationship since the B2r prouct is constant, e2g2 . (++ x &2@( && 8@( ( (++ x *2& S && ((+ approximately Balue of ? 7orB 7 x 626( x &+ -&* x . (++ x &2@( x &+ -* 1!2& ; 1% -+ /
Question 2:
$ or AD where the symbols have their usual significance2 $ 626( x &+ -&* x *2@+ x +26@+ *D/+2+* x &+ -81 %!9%# .F $harge, $B +2'+7 x ' +!1# ./ 9nitial current, 9 !DC 'D/*2* x &+ .1 #!%9 .A Time constant $C secons +2'+7 x &+ -. x *2* x &+ . 1!99 s 2!% s
Question 3:
Question #: % Mon9 where n number of turns per metre2 9 %DMon +2++&6 x +2&7D/7 x &+ -@ x *(+1 %!+%2 A 5agnetic flux ensity, % ϕDA /(27 x &+-.1D/.2+ x &+-(1 9!% ; 1% -# T The magnetic flux ensity at the en of the solenoi is +2( x that at the centre since insie the coil, many coils contribute to the %-fiel2 At the en, the formula approximates to that of a narrow circular coil which is? % Mo9D*r
Question 5:
amax =D- Q*xo where xo amplitue of oscillation2 >ow, Q *DT *D82* 1!9 4(6!s -1 amax =D- &2'.* x .+ x &+ -8 %!%23 "!s-
-he mass may not oscillate with (.7.,. because /any ;>!1? • •
The elastic limit may be exceee The spring constant may not be uniform over the extensions use2
PH# JANUARY 2%%1
Question 1:
Question 2: ! D7or *, where '* e an r @27 x &+ -&( m ! U'* x &2. x &+ -&VDU7 x 626( x &+ -&* x /@27 x &+-&(1 *V 2!#2 ; 1% 22 !"-1 The irection of the electric fiel is ((= 4o" t7e nueus2 (imilarities and differences between electric and gravitational fields produced by the nucleus? 0imilarity? %oth obey the inverse square law "ifference? Oravitational fiel attractive only electric fiel may be attractive or repulsive2
Question 3: Hewton3s @aw of 9ravitation? F $ @"1"2?62 where < force of attraction between two point masses m &, m* , istance apart O Eniversal constant of gravitation2
5ase units of gravitational constant ? O 3g2ms -* x m*D3g* 0-1!"-1!s-2 Broblems to be overcome when determining 9 from a lab experiment /any ;>!1? • • • • • •
/a1 #eason why spheres are made from lead ? Lea is a very ense metal, thus allowing masses to be closer together2 /b1 #eason why suspended masses are small ? To 3eep the beam as light as possible so that the small masses will move further2
Question #: -he time constant $C secons2 9t ta3es this time for the initial voltage to fall to &De or 8@ of its value2 ow, the time constant, $C *. s gives $ *.D7@ 8++ 55% .F Addition to graph showing how p.d. across the capacitor varies with time over the same period ?
Question 5: Explanation of how expression leads to definition of the ampere? • • • •
The * wires are & m apart 9n a vacuum The * currents are both & A The force between them is * x &+ -@ > per metre
A “efine value” cannot be measure experimentally2
Question : $alculation of E.,.F. induced across falling rod ? %lv, where v u = at + = '26& x *2( *( m2s -& *2+ x &+-( x &2( x *( &!5 ; 1% -# Explanation of why vertical component of Earth3s field is not re"uired ? This component of !arth:s fiel is parallel to the irection of vertically falling boy an therefore no flux is cut2
Question &: 5aximum voltage G* x Brms &27&7 x *8+ >?- 325
$alculation of peak current in toaster ? 9rms @6+D*8+ 828' A 9 pea3 G* x 828' #!+ A
PH# JUNE 2%%1
Question 1: An evenly istribute spray is obtaine since t7e 7(4es 4ee2 Explanation? Positive paint rops are attracte to the metal ob4ect since eet4ons "o
Question 2: $alculation of potential difference? ! BD B ! @2( x &+ ( x &* x &+ -* 9% 0 $alculation of maximum kinetic energy of electrons? !3 eB &2. x &+ -&' x '+ +++ 1!## ; 1% -1# J $alculation of maximum electron speed ? !3 F mv*, where m mass of electron2 v G/*!3 Dm1 G/* x &277 x &+ -&7D'2& x &+ -8&1 1!&+ ; 1% + "!s-1
Electric field due to isolated electron? Expression for electric potential /B1? B D7or, where is the charge /e1 $ '1?#Mo)'1! ; 1%-19?4)
Question 3: >ewton:s law of gravitation gives that “the force of attraction between two point masses is irectly proportional to the prouct of the masses an inversely proportional to the square of the istance between them”2 $alculation of force exerted on 0.&& kg mass on surface of ,ars? < Om&m*Dr * .2.@ x &+ -&& x &2++ x .27* x &+ *8D/827+ x &+ .1* 3!&% N 5ars woul have a s"(e4 raius than !arth since “g” is less, but their ensities are similar2
Question #:
Explanation of compass )8+ direction? The compass neele is o(te6 in t7e E(4t7Zs ie6 an the current is at '+ o to page at /*12 5oreover, the compass at /*1 is a (4e 6ist(ne from the current-carrying wire2 At this istance, the ie6 ou6 *e e(0 2
Question 5:
/i1 /ii1
At low frequency, the wire vibrates up an own continuously As the frequency is increase, the wire vibrates faster2 As *+ H is reache, large amplitue vibrations occur ) which is repeate again at 7+ H ) with staning waves set up2
Question : Flux through window? ϕ %A *+ x &+ -. x &28 x &+ -@ 1!& ; 1% -5 W*
Average E.,.F. induced ? ϕDt /&2@ x &+-(1D+26 2!% ; 1%-5 %y converting winow to sliing mechanism, Hero !252<2 inuce since no flux is cut2
PH JANUARY 199
Question 1: /a1 Hucleus? is central part of an atom Hucleon? comprises protons anDor neutrons Huclear ,atter ? consists of matter foun in the nucleus ther states of matter /any TI;1? inclue soli, liqui, gas an plasma2 /b1 The most stable nucleus woul occur at the top of the curve /in this case ucleons can be emitte
W(te4 64os !xist as spheres ave ensity 5olecules can evaporate
/e1 < &*D7o* (( x &2. x &+ -&' x 8@ x &2. x &+ -&' x '2+ x &+ 'D/82+ x &+ -&71* 521 N The electric potential energy is very high2
/f1
The ifference between the paths of W-particles an electrons is that W-particles are repelle by nuclei whereas electrons are attracte to the nucleus2 5oreover, since the charge is less n the electron, they are only slightly eflecte2 /g1 The e %roglie relationship lays own that? hDp /.2. x &+ -871D/*2+ x &+-&61 3!3 ; 1% -1 "
Question 2: '() ,aximum length 8 x unstretche length 8 x '+ 2&% "" '*) 9radient /62+ ) +2+1D/*2*( ) &2+1 6D&2*( !# F?N + &2+ *2+ 82+ 72+ (2+ .2+ @2+ & &2&@ &286 &2.8 &2'* *2*( *2.& 82++ 2 K 1? + +277 +267 &2*( &2.( *2+( *27. *26' @ *2*@ *286 *27+ *27* *277 *277 *27*
Question 3: /a1/i1 Bertical component , [ .( x '26& 3&!& N oriHontal component , # (*+ > /tension in tow rope1 /ii1 $omponent [ an the weight /.8@2@ >1 form an anti-cloc3wise moment2 !quilibrium is achieve if sum of cloc3wise moments sum of anti-cloc3wise moments2 /b1 >ewton:s 0econ Law gives? < ma a
Question #: /a1/i1
Question 5: /a1/i1 Power, P mghDt /(2. x '26& x &271D/@ x *7 x .+ x .+1 1!2& ; 1% -# W /ii1 mc\Y \Y Dmc /(2. x '26& x &271D/(2. x 8.+1 %!%3+ S The assumption mae is that all the g2p2e2 is converte into heat /internal1 energy2 /b1 An !252<2 will be inuce between the top an bottom of the steel penulum since it swings an therefore cuts lines of magnetic flux, arising from the !arth:s magnetic fiel2
/c1 The suggestion that a “perpetual motion” machine be constructe ) i2e2 Law of $onservation of !nergy is being violate2 9n any case, any inuce !252<2 woul prouce a current which woul issipate current2
PH JUNE 199
Question 1: /a1 Light travels at 8 x &+6 m2s-& /practically instantaneously12 0ince soun travels at 87+ m2s-&, time ta3en for soun to travel &2( 3m & (++D87+ #!# s Thus, measuring time enables istance to be estimate2 /b1 0heet lightning comprises an electrical ischarge either within a clou or from clou to clou2 -hunder occurs by air being heate giving rise to a rapi expansion an a consequent shoc3 wave /soun12 /c1
/1 A lightning stro3e prouces visible light by an electrical ischarge which excites electrons to higher energy levels within the air molecules, which when falling bac3 to their groun state, emit light /photons12 Flicker is cause by a whole series of stro3es in rapi succession2 /e1 Power /P1 7 x &+ &+ I B PD9 7 x &+&+D*+ +++ * x &+ . B ! BD * +++ +++D7++ $ 5 0!" -1 /f1 Esing a van er Oraaf generator, connecte to a high voltage voltmeter an two metal spheres, the conitions for arcing may be estimate using the formula ! BD2 Atmospheric conitions woul iffer between his scenario an that obtaining in the thuner clou2
/g1 Let the temperature of the air *'6 N an temperature insie lightning flash 8+ *@8 N /8+ +++ o$12 0ince PDT constant? P* 8+*@8 x &++D*'6 1% %%% 0P(
Question 2: /a1/i1 The raius of the balloon when \p + woul be 3!# " /intercept on r-axis1 /ii1 Two places where the rate of change of \h with r is Hero are? 5!1 " (n6 +!# "2 /iii1 Caius of balloon at which excess pressure is &++ mm of water &&2' cm2 Bolume /7D81r 8 &%59 "3 /iv1 The rate of change of \h with r at r @2+ cm '8D&7 .2. mm2cm -& /imensionless1 /b1 4?" ' &+ && &* &8 7?"" 77 .+ 6+ &+7 &8* 3 3 4 ?" @*' & +++ & 88& & @*6 * &'@ The comment is vali /straight line through origin12
Question 3: Two methos are possible, Any ;>! from? Electrical ,ethod ? Esing an electrical heater, immerse in a 3nown mass of water in a polythene container, with a thermometer2 $urrent /91, voltage /B1 an time /t1 are measure an the temperature rise /\Y1 note2 Then, electrical energy supplie 9tB mc\Y ,ethod of ,ixtures? The 3nown temperature of a 3nown mass of a goo conucting material /e2g2 copper1 is roppe into a 3nown mass of water in a polythene container at 3nown temperature an the temperature rise /\Y1 note2 Then, heat lost by hot boy mc\Y where c 022$2 of water2 The 022$2 of copper nees to be 3nown /see of Physical $onstants, e2g2 Naye Laybe12 >ote? Precautions for both methos? 9nsulation of container, li for container an stirring the water2 Polythene is a low-heat capacity material2 /b1/i1 Latent heat, supplie by the 4ogger, provies the energy for the fasterDmore energetic molecules to escape /evaporate12 $onsequently, the remaining ones have less 3inetic energy when the bons are bro3en2 /ii1 7+ of 67+ 3J 88. 3J2 mL m DL 88.D* *.+ %!15 0 /c1/i1 The area boune by the <-t curve represents impulse or change in momentum /i2e2 the <2t prouct12 Area? approximate by triangle F x +2&( x 8++ 22!5 Ns /ii1 0ince the net impulse is Hero, the 4ogger is moving at constant velocity Question #:
/a1
A neutral point is locate at a point where two fiels cancel, proviing a Hero resultant fiel2 /b1 < %9l 9
Question 5: '() '*)
')
'6)
An activity of &(+ 3%q means &(+ +++ isintegrations per secon2 At P, current flow is ue to the flow of negatively charge electrons2 At , current is ue to ion flow2 /i1 9 BDC 827D&+' 3!# ; 1% -9 A /ii1 Assuming that the ions are singly charge, an since e &2. x &+ -&' $, > /827 x &+-'1D/&2. x &+-&'1 2!125 ; 1% 1% 0everal explanations may be put forwar? %ac3groun raiation causes ioniHation 9nsulation is not perfect Boltmeter may have a Hero error2 _ ln*DT&D* +2.'8D/& .++ x 8.( x *7 x .+ x .+1 1!3& ; 1% -11 s-1 A >Dt - _> > />Dt1D_ /&(+ +++1D/&28@ x &+ -&&1 1!%9 ; 1% 1 • • •
'e)
PH JANUARY 199&
Question 1:
'()
/i1 -o ground ? means to the !arth:s surface /ii1 @eakage current ? is the current prouce by the fair weather fiel an is in the reverse irection to a lightning stri3e2 /iii1 7ori;ontally polari;ed ? means waves oscillate in one plane ) either the %- or !-fiel is horiHontal2 '*) • • • •
There is no scope for tapping into thunerstorms as an enegy source because? 0torms are sprea out geographically 0tri3es last for a very short time Low average current /& A1 0torms occur at ranom intervals of time2
')
! D7or * /( x &+ (1D U7 x 62' x &+ -&* x /.27 x &+ .1*V 1%9 !" -1
A problem which might arise is that there woul be more thunerstormsDelectrical equipment coul be upset2 '6)
Question 2: /a1 @(s * 72. 72. ;* 728 (28 Ar 826 .2. $;* 82. @28 0;* 82+ &+2@ $l *2' &&2@ Nr *2@ &82'
<2 ?1%-11 "2s-2 *26& *2&* &26( &277 &28+ +2'+ +267 +2@8
1?" ?1%-25 0-1 82+8 *2&@ &26' &2(* &28@ +2'8 +26( +2@*
The graph is a straight line plot through the origin, therefore the relationship is vali2 Oraient '27 x &+ -8@ 3gms*m /or >m12 ence, v may be regare as iffusion velocity or 3inetic energy epens on ranom velocity2
Question 3: /a1/i1 Applying the Principle of $onservation of Linear 5omentum? 7 mv ( mv: + v: 7vD(, away from the goal /i2e2 in opposite irection1 /ii1 Esing masses of gliers in the ratio (?7, an air trac3 /see textboo31, they are mae to 4oin together with a pinDbluetac32 Their spees are measure using lightgates2 9n the experiment, the gliers are pushe together2 The problem associate with this experiment is is to level the air trac3 /coul be overcome by use of a spirit level12
/b1/i1 P EA\T, giving &* (++ (2( x 6(+ x E E *2.@ I2m -*2N -& E thermal conuctivityDthic3ness, so E varies with thic3ness2 /ii1 Pressure ow, the melting point of ice is reuce by high pressure wor3 one against friction melts the ice2
Question #: /a1/i1 9n the circuit shown, measure 9 & /current1 for capacitance $& hence calculate $&2 0imilarly, measure 9* for $*2 >ow, place $& in series with $ * an repeat the experiment, calculating the new “$”2 Neeping f an B constant throughout the experiments, if the currents agree with the relationship &D9 &D9 & = &D9*, it follows that &D$ &D$ & = &D$* /ii1 To show 9 f$B is homogeneous w2r2t2 units, 9 current /A1 $s-& f frequency /H or &Ds1 $ capacitance /$B-&1 Then, L0 of equation current /A1 an C0 /&Ds1 x $B-& x B $Ds A /b1/i1 $urrent will fall to &De of its original value in $C secons /time constant1 $C &8 ms +2+&8 s $ +2+&8D& (++ +!& .F /ii1 • •
Oraph will be the same slope Time )axis ientical
0lope of vs2 t is current, 9 Area uner 9-t graph is charge, 2
/iii1 9n another branch of Physics, raioactive ecay also follows exponential ecay2 9n this case, the y-axis woul be >o2 of atoms, the x-axis woul be time an the slope >Dt activity2
Question 5: /a1/i1 Iaves arriving at P are out of phase by raians /&6+o1 so that estructive interference occurs2 /ii1 "*P ) "&P path ifference 8_D* /*n2 minimum1 " *P 72( = 7.2( 51 " /iii1 A stationary wave oes not transfer energy, rather it stores energy by the superposition of the wave an its reflection2 >oe to noe _D* %ut we have . half-wavelengths between " &"* "&"* . x 82+D* 9!% " /b1/i1 The ipper moves with 02252 at (+ H /frequency of mains supply1 because the magnetic fiel of the solenoi alternates so that the magnet is alternately attracteDrepelle2 /ii1 vmax *fA QA where A amplitue * x (+ x +2@( x &+ -8 %!2# "!s-1
PH JUNE 199&
Question 1: /a1 #andom motion? illustrate by straight lines, various lengths 4oine together an in ifferent irections2 #.,.( displacement ? means to square isplacements, ta3e the average value an then ta3e the square root2 /b1 Average N2!2 /8D*1 3T 8D* x &286 x &+ -*8 x *'8 !%& ; 1% -21 J !quating the above answer to ! 3 F mv* an using m &2+ x &+ -&. 3g, gives? v G/* !3 Dm1 G/* x .2+@ x &+ -*&D&2+ x &+ -&.1 %!%11 "!s-1 The assumption mae in the above calculation is the 4inie o eui(4tition o ene4=2 /c1 !1? • • • •
pW &DB pW T pB W T p W ˂c*˃
/e1 5olecules o not settle to the bottom of the atmosphere because continual molecular bombarment opposes their tenency to settle uner the influence of gravity2 The expecte plot woul be R /ensity1 as y-axis an h /height1 on the x-axis2 An exponential “ecay” curve /e-x1 woul be expecte, starting on the R-axis as atmospheric pressure /h +12 The test for exponential fall off of gum resin with height woul be to calculate their number ensities at equal intervals of height an show that the ratio is constant2 /f 1 The median speed /rea at pea3 of curve1 3+% "!s-1 The mean speed woul be between 3+% (n6 5%% "s -1
Area uner graph is approximately *( large squares /representing (++ +++ particles12 %etween 6++ to & +++ ms -&, there is about one large square >o2 of particles &D*( x (++ +++ 2% %%%2 Question 2: '() The wavelengths of the ripples at the minimum spee is 1!5 "" The associate spee is 9 ""!s-1 8 of minimum spee is +2+8 x .' 2!%& ""!s-1 The spee is ess t7(n &1 ""!s -1 in the range of wavelengths from &2& to *2& mm2 Dispersion? The wave spee epens upon frequency /or wavelength12 '*) ?"" 1??""-1 ?""!s-1 2?""2!s-2
+2( &2+ &2( *2+ *2( 82+ 82( 72+ 72( *2+ &2+ +2.@ +2(+ +27 +288 +2*' +2*( +2** 66 @* .' @+2( @82( @@ 6&2( 6( 662( @@77 (&67 7@.& 7'@+ (7+* ('*' ..77 @**( @68*
&D_ is not proportional to c * since the graph is non-linear an oes t pass through /+,+12
(2+ +2*+ '* 67.7
Question 3: /a1 $apacitors may have a high capacitance, yet have a small siHe because the electroes may be “wrappe up li3e a 0wiss roll”2 >ow, $ or AD igh capacitance may be obtaine by having a small value of an high value of relative permittivity /r 12 Above 8+ B, the ielectric may brea3own2 /b1 /i1 9n the circuit, current flows from when the switch is close2 The voltmeter must have a large resistance2 >ow, charge 9t $B %ut, $B ** x &+ -. x @7 x &+ -8 &2.8 M$ An t D9 /&2.8 x &+ -.1D/+276 x &+ -81 3!# "s /ii1
Question #: /a1 /i1 The current in the coil prouces a varying magnetic fiel2 Lines of magnetic force are cut by the ring, thus inucing an !252<2 in the ring2 $onsequently, the ring experiences a %9l force which is repulsive /ue to LenH:s Law12 /ii1 P 9*C C PD9 *, giving C &2.D&7+ * +!2 ; 1% -5 X >ow, C RlDA, where l *r * x &* x &+ -8 an A * x &+ -8 x &( x &+ -8 R CADl /62* x &+ -( x 8+ x &+ -.1D /* x &* x &+ -81 3!2 ; 1% -+ X!" /b1 /i1 9n orer to etermine the initial temperature of the aluminium ring, the masses of the aluminium ring, the specific heat capacities of the aluminium an water, together with the initial an final temperatures of the water are require /i2e2 metho of mixtures12 /ii1 0ince there woul be heat loss from the sies of the container an evaporation of the water, it is li3ely that the calculate temperature woul be too low2
Question 5: '() !nergy equivalent, \! of mass change \m is given by \! \mc * where c velocity of light2 '*) 9n the case of a fission reaction, a large nucleus splits into two or more smaller fragments2 >eutrons cannot be etecte with a conventional O5 tube because they are uncharge an therefore cause no ioniHation2 1%
C5 > 1n% $ &Li3 > #He2
,omentum is also conserve uring this reaction2 ') !1? Air gliers 5agnets />D> or 0D01 0noo3erDglassDmetal balls • • •
nelastic collisions /any ;>!1? • •
BelcroD%lu Tac3DPin cor3 >0 magnets
Brecautions to ensure elastic collisions? Ese friction compensate slope or air trac32
PH JANUARY 199+
Question 1: /a1
/b1 $ritical (peed ? 3g2m2s -* >2s2m-* has imensions? 3g2m2s -*2s2m* 0!"-1s 'e) Ce-arranging the equation?
v C eMDR 0o, the lower the ensity, the higher the critical spee the higher the viscosity, the higher the higher the critical spee2 5ercury has a much higher ensity than tomato sauce an a viscosity that is much lower2 $onsequently? <"e4u4= ˂
') C e RvDM /68+ x +27* x +2&.1D/'2. x &+ -*1 5+1 Thus, it woul be expecte that the oil flows s"oot7=2
< Epwar rag mg weight
Question 2: /a1
/b1 ;ver the range 7++ ) & +++ B, the sensitivity of the electrometer is approximately constant2 0ensitivity of meter graient of Y-B graph /.' ) *81D/& +++ ) 7++1
7.D.++ %!%&& o? ot(e? G?o sin G 8++ &6 +28+' 7++ *8 +28'& (++ 8+ +2(++ .++ 8@ +2.+* @++ 7( +2@+@ /c1 A plot of B vs2 sin Y is shown below2 The graph supports a linear relationship between B an sin Y2
Question 3: /a1 /i1 Ihen % is move bac3wars an forwars, the reaing on C is high for some positions an low for others2 This is because staning waves are set up between T an 5 - the fixe metal sheet acts as a “mirror”, reflecting &++ of all incient microwaves upon it2 The harboar sheet /%1 reflects 8+ of waves incient upon it thus causing interference2 /ii1 The wavelength, _ * x &7+D&+ 2+ "" 'iii) As the harboar % is move towars or away from the receiver, the vertical trace on the $C; varies from a maximum to a minimum an the istance move by the reflector between two consecutive maxima or minima _D* where _ is the wavelength of the microwave2 The spee, v is obtaine by v f_2 9n practice, the reflector is move through several maxima or minima so that a greater istance is measure2 /b 1 /i1 9t is ifficult to explain the existence of stationary wavesDinterference on the photon moel because photons are “particles” the wave theory of electromagnetic waves is much better to explain these phenomena2 /ii1 !instein:s equation gives ! hf hcD_ /.2.8 x &+ -87 x 8 x &+ 61D/8+ x &+-81 .2.8 x &+ -*7 J /.2.8 x &+-*71D/&2. x &+-&'1 72&7 x &+ -( eB /iii1This is much lower energy than that of a typical photon of visible light raiation since the wavelength of microwaves are much longer than that of visible light2
Question #: /a1/i1
/ii1 The upthrust arises as the result of the ifference in ensities between hot air in the balloon an col air in the outsie air2 Archimees Principle lays own that the upthrust is equal to the weight of flui isplace by the ob4ect2 Factors affecting the magnitude of the upthrust forces during flight include? Ambient temperature of air outsie balloon ) if coler, more upthrust an viceversa Ambient pressure ) if less, balloon woul rise owing to volume of balloon increasing ) then Archimees Principle applies2 /b1 pB /mD51CT The ensity, R mDB p5DCT 0ince 5 /molar mass1 an C /gas constant1 are constant, we may write? W pDT an it follows that, if pressure is constant, then •
•
W &DT /i1 R&DR* T*DT& T* R&T&DR* /&2*' x *661D&2+( 353!+ S /ii1 Dt EA\T 82* x 7 x (2( * x /6&-&(1 +%!3 0W /c1 Air may be emonstrate to have mass by etermining the mass of an empty balloon, inflating it an re-weighing it2 The increase in mass gives mass of air2 Question 5: /a1 O represents the Eniversal gravitational constant /.2.@ x &+-&& >2m*23g-*12 9n principle, O coul be etermine by measuring the force between massive spheres, mae of ense metals such as lea or gol in close proximity, using sensitive torsion techniques, e2g2 mirrorDlamp2 9t is ifficult to measure O precisely because the magnitue of gravitational forces is very small moreover, in orer to get larger mass, the istance between their centres woul be increase2 /b1 /i1 go /7D81ORr m go has imensions of >23g -& O has imensions of >2m *23g-* R has imensions of 3g2m -8 r 5 has imensions of m 0ince /7D81 has no imensions, C2202 of equation >2m*23g-* 3g2m-82m >23g-& Bolume of 5oon /7D81r 58 "ensity of 5oon U@287 x &+ **VD U/7D81 x /& @7+ x &+ 81V8 go /7D81O5r 5 D/7D81r 58 O5Dr 5* /.2.@ x &+ -&& x @2*7 x &+ **1D/&2@7 x &+.1* 1!2 N!0 -1 /ii1 0uppose the bullet to be of mass m2 Then weight of bullet mg2 $entripetal force towars centre of 5oon mv *Dr 5 %ut, the gravitational pull of the 5oon on the bullet supplies the centripetal force? mgo mv*Dr 5 go v*Dr 5 v* gor 5 or v G/g or 51 1 &9 "!s-1
PH JUNE 199+ Question 1: /a1/i1 on pair ? positive an negative charge particles /ii1 (pace charge? region containing positively charge, slow-moving particles /iii1 Dead time? perio of time uring which a O5 tube is insensitive to the arrival of further particles Avalanche? !lectrons accelerate, thus causing ioniHation, e2g2 concept of a chain reaction2 /b1 \p /&+& ) &&1 x &+ 8 '+ x &+ 8 Pa < A\p /&* x &+ -81* x '+ x &+8 #%!& N The ifficulty in esigning O5 tubes to etect W-particles is that these particles are the least penetrating of any raiation2 Thus, a thin en-winow is neee, but forces are high ue to low pressure insie O5 tube2 /c1 /i1 Thic3ness of mica /* x &+-*1D/*6 +++1 @2&7 x &+ -. m >o2 of molecules /@2&7 x &+ -.1D/627 x &+-'1 +5% /ii 1 The W-particles cause enser ioniHation than ] since it has *x the charge an is slower moving than ]2 $onsequently, ] penetrates more reaily through thic3er winows than W2 /1
< q! &2'* x &+ -&7 > A
Question 2: /a1 G?4(6 &2+( &27+ &2@( &2'( *28+ *2.+ *26( 82&( n'P?N) *276 *2(' *2.6 *2@( *26( *2'* 82+* 82&+ /b1
/c1 P mgeMY ln P ln mg = MY M slope /82+( ) *27(1D/82++ ) &2++1 %!3% P mg when Y + mg antilog /*2*+1 '2+ 0ince g '26, m %!92 0
Question 3: /a1 !instein:s equation gives? ! hf hcD_ _ /.2. x &+ -87 x 82+ x &+ 61D&+-*8 2 ; 1% -2 " This correspons to microwaveDfar infra-re en of the spectrum2 Thus, we may euce that is infra-re an C is visible2 /b1
Question #: /a1
• •
/b1
/c1
ow, p has units of >2m -* an B of m8 p x B >2m -* x m8 N!" which has the same imensions as the Joule2 /ii1 p W T p#Dp[ T#DT[ T[ /p[Dp#1 x T# .7+ x /* 6++D'++1 1 99% S The assumption mae in the calculation is that the mass of the gas is constant2 05 theory gives that? a - Q*x /*f1*x amax - Q*xo /*f1*xo */6 +++D.+1 * x +2+7+ 2+ %%% "!s -2 Thus, high stresses are inuce in the ro2 $onsequently, the ro nees to have a high E2T202 an fatigue strength2
Question 5: /a1 0ince electrons are the current carriers, they will oscillate with 02252 as well as moving ranomly with thermal agitation an colliing with ion coresDnuclei of atoms2 9 nAve v 9DnAe, where 9 G* x (2+ 0o, v /G* x (2+1D/&2+ x &+ *' x +2*+ x &+ -. x &2. x &+ -&'1 2!2 ; 1%-3 "!s-1 9n the calculation, we have ignore the ranom thermal motion2 The amplitue of motion can be obtaine from? vmax *fA where A amplitue /b1 $urrent flowing in a cable prouces a magnetic fiel2 0ince this is A2$, !252<:s are inuce which will be large if the coil is tightly woun2 Esing a all probe /in the correct orientation1 the magnetic fiel may be investigate by connecting the leas to an oscilloscope2
PH JANUARY 1999 Question 1: /a1
yroelectricity erives its energy from t7e Bun2 /b1 The main energy transfer ta3ing place in the turbine is gravitational energy to 0ineti?eet4i( ene4= $ross-sectional area of turbine F /*(1 * 7'+ m* Bolume falling in & s ( +++ x 7'+ *27( x &+ . m8 5ass falling in & s .(+ x *27( x &+ . &2(' x &+ ' 3g gpe lost per sec2 mgh &2(' x &+ ' x '26& x *+ 313 ; 1% 9 W /c1 9n an ieal heat engine? T& ) temperature of hot source - sea /N1 + - 8+ o$ /*@8 ) 8+8 N1 T* ) temperature of col sin3 ) upper atmosphere /N1 9n 5ega Power? /T& ) T*1DT& +2* /8+8 ) T *1D8+8, giving .+2. 8+8 ) T * or, T* 2#2 S '(4o;) /1 The three forces acting on the structure are? Ieight of structure /gravitational pull of the !arth1 Epthrust from seawater Tension in cables /e1 /i1 Bolume of cable r *h 5ass of cable r *hR Ieight of cable r *hRg 0tress in cable r *hRgDr * hRg 0o, cable brea3s if 7 ˃ [?\ • • •
/e1/ii1 Enit for j >2m-* Enit for R 3g2m-8 Enit for g m2s-* Enit for jDRg 'N!"-2)?' 0!"-3! "!s-2) /f1 Environmental benefits? >o greenhouse gases /global warning1 or aci rain 5egapower uses a renewable source Broblems /any TI;1? AircraftDshipping haHar Lea3s of ammonia %rea3age of cables uring storms 0ea temperatures may be lower than thos anticipate2 • •
• • • •
Question 2: /a1 ?"A &2+ *2+ 82+ 72+ .2+ 62+ &+2+ n + +2.' &2&+ &28' &2@' *2+6 *28+ t?6(= *( && .2@ 726 *2' *2+ &2( n t 82** *27+ &2'+ &2(@ &2+. +2.' +27& /b1 Oraph ) see below The resultant plot of ln 9 vs2 ln t is a straight line2 This is of the form y mx = c where ln 9 n ln t = 3 an n slope of graph - *2.*(D82** $ - %!+2 This may be regare as about ) &2 The value of 3 is obtaine by the intercept on ln 9-axis, i2e2 ln 9 *2.*(, so that 9 13!+ "A
Question 3: /a1 0quaring both sies,
_ TG/g1
_* T*g C2202 has imensions m * L2202 has imensions s *2m2s -*2m m* Thus, the equation is homogeneous w2r2t2 units2 >ow, c f_ _DT c G/g1 G/'26& x * *++1 1#& "!s-1 /b1 Please see stanar textboo3 for etails2 /c1/i1 !nergy is issipate over a very large area an is lost by conuctionDconvectionDevaporation2 />ote? the fact that water has a high 022$2 may also be mentione12 /c1/ii1 The energy woul be converte into electrical energy /ifficult to store1 ;C energy is intermittent /varies with waves12 /c1/iii1 !lectrical power /&2.D&++1 x *2+ 8* 3I Thus, in *7 h, energy 8* x *7 &+ 0W7
Question #: /a1 /&28@ x &+ -&81D/62.* x &+71 1!59 ; 1% -1+ / The plates must be horiHontal in orer to ensure a unio4" ie6 st4ent7, so the two forces are parallel2 /b1 The ]-source emits electrons which ioniHe the air molecules by 3noc3ing out electrons, positive ions are create which are attracte to the sphere2
F $ U(46 64(8 " $ Wei7t /c1 Juanti;ed ? means that charge comes in iscrete amounts2 Another physical quantity which is quantiHe is electro-magnetic energy /e2g2 light12 0ituations in which this becomes evient are /any ;>!1? Photoelectric effect Line spectra of gases !nergy levels of atoms /1 This is C4oni(n "otion in which the spheres are being bombare by the air molecules which are in ranom motion2 9f we lower the air temperature, the spee /or 3inetic energy1 of the molecule is reuce2 • • •
Question 5: /a1/i1 !nergy /per s1 Ne /a1/ii1 ! Pt *27 x *+ #+ J mc\Y m \Dc\Y 76D/@8+ x 6(1 &!& ; 1%-# 0 Assumptions? • •
>o heat conucte away from the spot All energy transferre into heatDno energy transferre into light2
/b1 Please see stanar textboo32 "ifficulties leaing to errors? "ifficulty in preventing heat loss Olass is a poor conuctor of heat ) longer time lag an nee to allow for this2 /c1 ;ne cycle *(+ x &+-. s f &D/*(+ x &+ -.1 # %%% H Boltage rise +28+ B rate of rise +28+D/*(+ x &+ -.1 1 2%% !s -1 • •
PH JUNE 1999 Question 1: /a1/i1 (uperconducting ? Hero resistance an, by implication able to carry thousans of amps2 /ii1 Filament conductor ? a conuctor, consisting of many thin filaments2 /iii1 Juench? $ease to be a superconuctorDgain resistance2 /iv1 -emperature profile? Balues of temperature at several locations2 /b1/i1 #eason for containing #utherford cable in huge mass of aluminium ? Ihen fault conitions arise /i2e2 when cable loses superconucting properties1, the store current will transfer to the aluminium2 /b1/ii1 mc\Y \Y Dmc *++ x &+.D/&7+ x &+8 x (61 25!9o/ /c1/i1
/c1/ii1 (ketch? showing many filaments of >i-Ti alloy, encapsulate in copper2 C RlDA U72+ x &+ -6 x &( x &+ 8 x 72+VDU7+ x /*( x &+ -.1*V 3%! 0X /1 Bery slow cooling is use to ensure that no part is sub4ecte to unue stress as a result of thermal graients which are 3ept to a minimum2 /e1 /i1 9D*r, where r &2( m an 9 *+ +++ A an > lD*r % U7 x &+-@ x *+ +++D* x &2(V x U&( x &+ 8D* x &2(V 13!3 T
•
Question 2: '()
'*)
5inimum istortion, " m 3&!2o n sin 8+o sinU/.+ = 8@2*1D*V sin 762.o n $ 1!5% & of 8@o +28@o 0o, the values of " ˂ [email protected] lies in the range of Y ## K 53 o Question 3: /a1 Re(to4 He(t E;7(ne4 Tu4*ine @ene4(to4 !fficiency !lectrical Power ;utputD!lectrical Power input An increase in efficiency may be obtaine by raising the steam temperature or using a combine heat an power scheme /$22P21 /b1 d 3& >o2 of neutrons 2 $hange in mass mE ) /m$s = mCb1 *8(2+77 u ) /&8@2'*' u = '(2'*8 u1 &2&'* u &2'@' x &+ -*@ 3g %ut actual ifference 82+7 x &+-*6 3g mass of neutron &2'@' x &+ -*@ ) +28+7 x &+ -*@ 1!&5 ; 1% -2& 0 /c1 n order to show that like charges repel ? Two ros supporte on long threas are charge in the same way by friction2 0ubsequently, they move apart2
Question #: /a1
%y the Principle of 5oments? +2.
Question 5: /a1
9n the above graph, A amplitue an f frequency2 ere, f o occurs at a frequency of % H At the resonant frequency, the boy oscillates with a maximum amplitue2 This occurs when the riving frequency natural frequency2 Example /any ;>!1? Iine glass shattering with singingDmusical note $ar mirror vibrating at certain frequency 0uspension brige in win of critical velocity Ior3ing machinery, e2g2 washing machine at particular frequency2 • • • •
/b1 /i1 The plate is mae to oscillate with 0225, such that the istance A% /1 is mae to oscillate, so that the capacitance is force to oscillate in antiphase2 /b1/ii1 $ oAD oAD$ /62' x &+ -&* x 62+ x &+ -71D/7+ x &+-&*1 %!1&+ ""
/c1
Time constant, k $C secons 7+ x &+ -&* x &(+ x &+ . !% ; 1% -3 s ' "s) A frequency of ( +++ H gives a perioic time T &D( +++ *++ Ms Ten perios cover 6 ivs & ivision 25% .s
PH JANUARY 2%%% Question 1 /a1
/b1
"etermination of velocity near surface of Oanymee enables the value of “g” to be etermine since g a2 /c1/i1 Enstable nuclei which emit W-, ]- or ^- rays2 /c1/ii1 An inuce !252<2 which opposes the change causing it /accoring to LenH:s Law12 /c1/iii1 $onvection currents associate with flui motion cause by ensity change cause by temperature ifferences2 /c1/iv1 The phase bounary in this connotation refers to a soliDliqui bounary2
/1
9 +288 mr * m /7D81r 8R 9 +!1 ; 1% 3& 0!"2 /e1
$alculation? P /B = Bo1 3 Ce-arranging? B /3Dp1 - Bo where Bo intercept an 3 slope2 This gives Bo 1#!% "3 /c1 Average pressure /6+ = &*+1D* &++ 3Pa $hange in volume @' ) 76 8& cm 8 wor3 one &++ x &+ 8 x 8& x &+-. 3!1 J
Question 3: /a1 The acceleration of the trolley may be calculate from >ewton:s 0econ Law2 0ince the system pushes out gases, the carbon ioxie pushes on the system /by >ewton:s Thir Law12 /b1 /i1 %y the $onservation of Linear 5omentum? +2+&* v +2..6 x *2@ v 15%!3 "!s-1 Assumption made? >o rag or air friction, or all $;* expene or mass of $; * small cf2 system2 Ninetic energy of trolley F x +2.6 x /*2@1 * 2!#+ J /c1 /i1 !nergy is neee to overcome the attractive forces between the /liqui1 carbon ioxie to convert it into the gaseous form2 This energy is erive from the system, thus causing a fall in temperature2 /ii1 The best instrument to use woul be a thermocouple /or thermistor12 "ifficulties encountere? ensuring goo thermal contact or time-elay in registering values2 /iii1 9n orer to calculate loss in internal energy of cyliner, the mass an 022$2 of material of cyliner woul nee to be loo3e up2 Question #: /a1 0oun cannot be plane-polariHe because it is longituinal an the air is mae to vibrate in one irection only2 Pressure, p has imensions >2m -* "ensity, R has imensions 3g2m -8, 0pee, c has imensions m2s -&, ^ is imensionless c G/pDR1 0quaring both sies,
c* pDR
m*2s-* /3g2m2s -*2m-*1D/3g2m-81 which is consistent w2r2t2 units2 /b1 /i1 As the pressure increases, the contact between the carbon granules increases consequently the resistance ecreases2 0o, the current will rise , since the sum of the p2:s, /B m = BC 1 constant2 Therefore, the p22 across C will rise2 /ii1
Question 5:
/a1
The inverse square law is shown in the above graph, where y represents the intensity, 9 an x the istance2 /c1 /i1 Expalnation? Photon energy of 9C raiation insufficient to release electrons from the surface of magnesium2 /c1/ii1 $alculation? Qo hf o -87 Qo hcD_o /.2.8 x &+ x 82++ x &+ 61D/& ((+ x &+-'1 1!2+ ; 1% -19 J
PH JUNE 2%%%
Question 1: /a1 /i1
9nitial capacitance of capacitor ox*D >ew capacitance &+ o x +2+& x *D Catio 1 : 1% o2 of electrons requireDsecon soun frequency /&26 x &+-&&1D/&2. x &+-&'1 1!125 ; 1% + H The electron current measure by the stanar instruments shoul not epen upon the spee of soun since this shoul have no bearing upon the operation of the instrument2
A progressive wave transfers energy from one point to another2 At a trough, the isplacement is maximum an negative /i2e2 negative amplitue12 Au4(= refers to the closeness of the measurements to the “actual” or “real” value of the physical quantity, whereas the term 4eision is use to inicate the closeness with which the measurements agree with one another2 B D$ /&++ x - &2. x &+ -&'1D/* x &+-&*1 - +.
/ 1 /i1
/1 /ii1 ! >eD*oA 0ince > an * are pure numbers, they may be ignore for the purpose of imensional homogeneity2 ! has imensions B2m -& Therefore eDo2A shoul have the same imensions2 e has imensions of charge A2s A has imensions of area m * o has imensions <2m-&
Question 2: /a1 /i1 C C o = 3Y which is of the form y mx = c, where c C o an m 3 /graient12 >ow, 3 CDY &86 ) &++D&++ - + %!3+ X!o/-1 /a1 /ii1 Esing the relationship /y ) y&1D/x ) x&1 m +286 /C o ) +1D/+ ) Y1 Y - 23!2o/ The value of - *.82* o$ is within &+o$ of the absolute Hero of temperature /- *@82&(o$12
7++ (++ *(* *'+ *7@ *6& ( ' *2+* -
/c1 /iii1 9nterpolating, assuming reasonable linearity over small ranges, the value of Y where of \CDC m excees & woul be about 21%o/ Question 3: /a1 Assumptions behin the 3inetic theory of gases /any TC!!1? A gas consists of a very large number of molecules The gas molecules are in rapi, ranom motion There are no attractive forces between molecules $ollisions between gas molecules an walls of the container are perfectly elastic2 /b1 /i1 mgh has units of Joules since mg has units of > an h has units of m then, since & >m & J /ii1 p poe-mghD3T At half-pressure, p poD* UpoD*VDUpoV F e-mghD3T Ta3ing logarithms to base e on both sies of the equation? ln /F1 - mghD3T 0ince ln & + an ln /F1 ln & ) ln *, it follows that? -ln * -mghD3T, • • • •
or, 7 $ 0T n 2?" /iii1
/c1 /ii1 9n an inverse square law relationship, the graph is asymptopic to both the yan x-axes, in an exponential relationship the graph is asymptopic to the x-axis only an cuts the y-axis at unity or some other fixe value2 0econly, the “half-value” in
exponential relationships is constant in inverse square law relationships it is nonconstant2
/c1 /iii1 Exponential decreases /any ;>!1? Caio-active ecay $hange of voltage vs2 time in capacitor ischarge2 /c1 /iv1 nverse s"uare variation /any ;>!1? 9ntensity of sounDlight vs2 istance from point source 9ntensity of electric fiel vs2 istance from point charge2 • •
• •
Question #: /a1 /i1 9n ranom ecay, there is no way of preicting when a particular nucleus will ecay2 %ut, when there are large numbers involve, there are goo statistical patterns2 /ii1 >Dt - _>, where _ ln *DT &D* ln *D/&+ x .+1 ln *D.++ &2&. x &+ -8 s-& Activity of nitrogen-&8 &2&. x &+ -8 x *2( x &+ ( 2+9 C /iii1 &8 >@ &8#6 = +e-& /b1 /i1 The copper sulphate emerging from the burette may be regare as representing the particle emission2 Ihen the burette is full, the flow is fast /ue to the large pressure hea12 ;n nearing evacuation, the epth of copper sulphate solution /i2e2 pressure1 is very small so that the rate of fall falls to a low value2 /b1/ii1 C RlDA /+2&* x (2+ x &+ -*1D/72+ x &+-* x *2+ x &+ -*1 @2( ;hm:s Law gives? C BD9 9 BDC &2(D@2( %!2 A Assumption? copper sheets are clean an free from oxie film etc2 Question 5: '()
/i1 Desirable property /any ;>!1? igh tensile strength /strong1 igh [oung moulus /stiff1 /a1/ii1 The oil shoul be resistant to oxiation from the air an thermally stable2 /a1/iii1 Although force is magnifie, the istance move by the loa is much less than that move by the effort2 Area of cyliner r * /&( x &+ -81* @2& x &+ -8 m* P
'*)
')
'6)
Assuming we are ealing with pressure above atmospheric, the range of pressures woul be &++ ) 7++ 3Pa approximately, using oilD%ouron gauge2
PH JANUARY 2%%1 Question 1: '() /i1 Iith covere by trac3 /(6 ) *(1 88 mm >o2 of spirals /88 x &+-81D/&2. x &+-.1 2% %% /ii1 Length no2 of trac3s x average circumference Average circumference *r * /*( = (61D* x &+-8 %!2% " Length of trac3 +2*.+ x *+ .++ 5 3&% " v lengthDtime ( 8@+D//@( x .+1 1!19 "!s-1 '*) /i1 "estructive interference occurs when two beams are out of phase, e2g2 having a path ifference of _D* or a phase ifference of raians /&6+ o12 /ii1 "iffraction effects occur when light passes through a gap ) the light energyDwavefronts then sprea out2 /iii1 0everal orers of magnitue means powers of &+ ) either multiplying by or iviing by2 ') The scratchDhair is not large enough to cover the isc of light shining on the isc surface so some light gets to the trac3 for interference effects to ta3e place /A scratch of about +2( mm shoul be compare with the steps of +2( Mm use for interference effects12 '6) /i1 n sin iD sin r sin *@oD sin &@o +27(7+D+2*'*7 1!55 /ii1 0ince the semiconuctor laser gives light of @6+ nm, then _ @6+D&(( 5%2 n" /iii1 "estructive interference occurs when path ifference _D* >ow, since wavelength is about (++ nm /see ii1, _D* (++ *(+ nm2 %ut the light has to go up an own, hence step epth *(+D* 125 n" 'e) The wavelength of blue light is shorter than that of re light, so iffraction effects are reuce2 $onsequently, the spot on the music trac3 is smaller, allowing the trac3s to be closer together2 ') /i1 %inary coes involve the use of a string of &:s an +:s /i2e2 & on an + off12 Properties of recore soun are?
Question 2: /a1/i1 This coul be one in several ways? $alculate t2r an show constancy in all cases Plot t vs2 &Dr an show straight line through origin Plot lg vs2 lg r /shoul have a graient of ) &12 /ii1 Plot lg t vs2 lg r ) shoul be a straight line of slope - 32
/b 1 4?1%- " t?s 2 1?4 1%-12 "-2
&( &+8 +2777
&2. '* +28'&
&2@ 6& +287.
&26 @8 +28+'
&2' .( +2*@@
4?1%- " t?s 2 1?4 1%-12 "-2
*2& (7 +2**@
*2* *28 7' 7. +2*+@ +2&6'
*27 7* +2&@7
*2( 8' +2&.+
*2+ (' +2*(+
0ince the graph is a straight line /approximately through the origin1, then the relationship coul be sai to hol2
Question 3:
• • • •
• • •
/a1 /i1 Advantages that a thermocouple has over a mercury4in4glass thermometer /any TI;1? Capi response time Ability to eal with small, samples Cobustness "igital output /ii1 BD82. *6+D&++ B 1%!%+ " /iii) >ew voltage 8 x 82. 1%!+ " Assumption /any ;>!1? igh resistance voltmeter Boltmeter raws no current Cesistance of voltmeter ˃ resistance of thermocouple2 /b1 /i1 A heat engine is a evice in which heat flows from a hot source to a col sin3, wor3 being extracte en route2 /ii1
/c1 /i1 9t *+ x &+-8 x &+ x .+ 12 / /ii1 I B &* x 8 x &+-8 #2!2 " /iii1The efficiency of this type of heat engine may be increase by either increasing the temperature of the hot source or ecreasing the temperature of the col sin3 /or both12 Question #: /a1 Esing a bunch of threas, connecte to the top of the sphere, when charge, they “fan out” or repel each other2 Li3e charges repel2 /b1 9 has units A w has units m v has units m2s -& Ce-arranging, # 9Dwv ADm2m2s-& Asm-* $2m-* 0o that # represents 7(4e 6ensit= since $ As2
/c1/i1
/ii1 ! D7or * 7or * ! 7 x 626( x &+ -&* x /+2&(1* x 82. x &+ ( %!9% ./ B !2r 82. x &+( x +2&( 5# 0 /c1 /i1 The lea3age current comprises fast /ranom1 motion of a very slow rift velocity of electrons ownwars2 ;n the belt, however, there is a uniform velocity /up12 /c1 /ii1 y-axis ) voltage, + ) (7 3B x-axis ) time + ) &*+ s !xponential ecay curve from /+ s, &*+ s1 not reaching time axis2 • • •
Question 5: /a1
/b1
%y trigonometry, tan Y +2+@+D&2*+ Y tan-& /+2+(681 3!3#o Cesolving vertically? *T sin Y mg T mgD* sin Y /(+ x &+ -8 x '26&1D/* x +2+(61 #!2 N Esing an ammeter to fin the current through the wire an a voltmeter to fin the p22 across it, a series of values of 9 an B coul be plotte an the BD9 graient gives the resistance2 A rheostat woul be neee in series with the power pac3 to vary the current2
/c1
/1
/i1 A &8 A r2m2s2 current has the same heating effect as &8 A c2 /ii1 _ *27+D* &2*+ m f (+ H c f2_ (+ x &2*+ % "!s-1 /iii1 The wire oscillates ue to the !arth:s magnetic fiel proucing a /changing1 %9l force on the wire2 =nits for Kc 8? 0ince M has imensions 3g2m-& an c, m2s-& Mc* 3g2m-& x m2s-& 3g2ms-* which are the base units for >ewtons2
PH JUNE 2%%1 Question 1: /a1 /i1 (trength? The ultimate stress before fracture /ii1 @amination? plastic layer between sheets /iii1 Extended radially? sprea out from a point2
/b1/i1 Applie stress forceDarea /b1 /ii1 ! has units of >2m -* a has units of m j has units of >2m-* 6 has no units >2m-* G/>2m-*2EDm1 0quaring both sies an re-arranging? >*2m-7 m2>2m-*2E E >*2m-72mD>2m-* N!"-1 'o4 0!s-2) /c1 Tinte glass reuces solar gain2 Approximately half the 0un:s energy at wavelengths between +26 Mm an *2* Mm infra-re raiation, thus maintaining the insie of the car cooler2 /1 @ower ray? travels straight through at first surface =pper ray? refracte into glass /emerging below horiHontal1 Distortion? upper rays bent to ifferent extents2 /e1 /i1 Assuming mass of person @+ 3g @+ mph /@+ x 6 x & +++1D/( x .+ x .+1 8&2& m2s -& N2!2 F mv* F x @+ x /8&2&1 * 3# 0J '(4o;!) /ii1 The outer sutface is stretche /pushe out1 on imact ) leaing to tensile stresses2 /iii1 Area uner <-t graph represents momentum change /or impulse1 Area F x '+ x &+-8 x &++ x &+ -. #!5 N!s /f1 0ince resistors are connecte in parallel? &DC &DC & = &DC * = &DC 8 = &DC 7 = &DC ( (D8+ C . Put P B*DC &77D. 2# W
Assumptions? resistors connecte in parallel an that there are no other resistive losses in connections etc2 - up to battery for instance2 To eating elements? “wor3ing” /wor3 is one on electrons1
/b1 /i1 t?s
+
*2+
72+
.2+
62+
&+2+
&*2+
7o?" + &'2. @62( [email protected]. 8&7 7'+2( @+.28 /c1 /ii1 0ee graph
/1 /i1 Oraph becomes linear between &*2- an &.2+ s2 /ii1Belocity graient of lower portion /.'8 ) 7@+1D/&.2+ ) &*2+1 55!+ "!s-1 /iii1 %y rawing a tangent to the curve %, the graient has the same value as A at a time of !% s in the region of terminal velocity2 /iv1 "istance is approximately #&% " /see graph, *2+ s ifference12
Question 3: /a1 ;n stri3ingDrebouning from a vertical wall, the energy changes occurring in a tennis ball are? Sineti e(sti 'st4(in) ene4= /b1 /i1 %oyle:s Law gives pB constant, p&B& p*B* p* p&B&DB* &&. x BD+267B &8' 3Pa \p &86 ) &&. 22 0P( /b1/ii1 The increase in pressure is cause by the fact the spee /or 3e1 of the molecules are increase an therefore there are more collisions per sec2 Iith the walls an are also more violent /i2e2 greater momentum change per sec212 /c1 /i1 >ow, m (@2( x &+ -8 3g a 882( x &+ -8 m an assuming \p 8* 3Pa c GU* x /882( x &+ -818 x 8* x &+ 8D(@2( x &+ -8V 11!5 "!s-1 0ince the pulse travels half-way roun a %!1%5 " tc +2&+(D&&2( 9!2 "s /c1 /ii1 Barious methos may be use, e2g2 /any ;>!1? 7igh speed flash photography in which a large number of images are ta3en in short perios of time an then photographs counte2 @ight gate in which a narrow light beam is shone at the wall level an then a atalogger use2 C$onducting wall? An aluminium wrappe tennis ball completes a circuit on impact, then a ata-logger or computer or C$ circuit may be use2 •
•
•
Question #: /a1 /i1
/ii1 Electric field strength at L ? ! BDx .2+D/&( x &+ -*1 #% !"-1
/iii1 E"uipotential lines? /horiHontal1 shown in the above iagram2 /b1 /i1 ; $ 3!% because in the potential ivier, the two resistors are equal /7@+ 1 an the battery voltage is .2+ B2 The p22 across the milliammeter is e4o since # an [ are at the same potential2 /b1 /ii1 Esing a rheostat in place of one of the 7@+ resistors, this coul be varie an when the p22 reas Hero, the potential coul be foun by calculation2 /c1 /i1 C RlDA, where l x an area A xt C RDt /c 1 /ii1 Ce-arranging, R Ct & +++ x +2&7 x &+ -8 %!1# X
Question 5: /a1
/i1 9n simple harmonic motion, the acceleration is proportional to the isplacement an irecte to a fixe point /usually the centre12 /ii1
/b1
/i1 "ensity, R has units 3g2m -8 O has units >2m*23g-*
RO has units 3g2m -82>2m*23g-* %ut > has units 3g2m -* Cequire prouct 3g2m -823g2m2s-*2m* 3g-* s-2 /b1 /ii1 R5 55DB5, where B /7D81r 58 /7D81/&2.7 x &+ .18 &26+ x &+ &' m8
/c1
R5 /@2*7 x &+ **1D/&26+ x &+&'1 # %5% 0!" -3 tA% /8D7R5O1&D* 2 953 s /iii1 0ince the motion is 0225, then it follows that the time perio is inepenent of amplitue2 %y geometry, it follows longer tunnels must be nearer to the centre of the 5oon an the force therefore greater, hence the component of force along the tunnel greater2 Please see stanar textboo3 for apparatus2 0ince gravitational forces are very small, then raughts etc2 may isturb the beam arrangement2
