ZXTape! 0Created with Ramsoft MakeTZXph1 mghm6:6:0: physics help tape 1  G C E Tutoring  June 1984 !w(25,8):2000 r(10 ) t(5):9069m# Lscrhdr=9300T$:qsthdr=9350$:endsec=9400$:getans=9450$ fig2=8950":fig=9030F#:axes2=9000(#:eg=9040P#:axes=9100#:triangle=9150#:diagram=218:praise=9720% 5br=8100:squrec=8850":squpar=8900" 6:" PHYSICS help ph1":" Waves and sound" #:"  G C E Tutoring June 1984" 2t:"Hello, what's your name ?":n$:n$:"OK, ";n$;",":"I'll begin by telling you how touse this physics program." 4Y:"This tape covers 6 subjects which all come under the headingof waves and sound." :>:"Press the key marked C so I can type the next screenfull" <a$=:a$="c"62> = 60< >:z=1100d:z AF:"Thanks. From now on when I want you to press the C key, I'll say" D:" Hit C to continue" F4:"Here's the list of subjects on this program": H"reflection wavelength and frequency transverse and longitudinal light and refraction diffraction velocity of waves" K2:"Which subject do you want to try ?":s$: Lc$=s$ N'(s$)>3s$=s$(13) Os$="vel"100d Ps$="ref"200 Qs$="lig" 300, Rs$="wav"400 Ss$="tra"500 Ts$="dif"600X ^Cs$"vel"s$"ref"s$"wav"s$"tra"s$"lig"s$"dif"9200# _ 70F c d f i velocity l n"Velocity of waves": p"Sound and light travel at very different velocities. The speed of sound in air is 330ms, whereas light travels at 300 000 000ms - nearly 1 000 000 times faster." tscrhdr vqsthdr }"Light travels": "1. 1 000 000 times faster than sound 2. 1 000 times faster than sound3. 100 000 times faster than sound ?": 4exp=1:egc=3:return=132:getans 2n$=c$:start=100d:return=198:endsec     reflection  "Reflection": "Both sound and electromagnetic radiation can be reflected. A sound reflection is commonly called an echo, and because sound travels slowly in comparison with light, the delaybetween the original sound occuring and the echo being heard can be measured.": scrhdr m"The sound path in an echo is twice the distance to the reflective surface, as shown below :": r10 ,2;"sound --------------------> echo <--------------------" scrhdr ܐ"So if the speed of sound is 330ms, an echo which takes 1s after the original sound has come from a reflecting surface 155m away.": "Radio waves, microwaves and infra-red, can all be reflected.Generally, the longer the wavelength, the more efficientlythe radiation will be reflected,even if the surface is far from being like a mirror. Radio-wavesfor example, can be reflected off a hill-side.": scrhdr qsthdr 0"The path a reflected wave follows is": "1. 2 x the distance to the reflective surface 2. 1/2 the distance to the reflective surface 3. distance to the reflective surface ?": 4exp=1:egc=3:return=238:getans %"Which of these can be reflected": T"1. electromagnetic radiation 2. sound 3. both ?": 4exp=3:egc=3:return=245:getans ;"Sound is heard after a distant event is seen because": "1. light travels faster than sound 2. light travels slower than sound 3. light is a transverse wave": 4exp=1:egc=3:return=252:getans )2n$=c$:start=200:return=298*:endsec * + , . 1 refraction 4 6"Refraction": 8"The velocity of light changes according to the medium it travels through. It is highest through a vacuum, and only very slightly slower through air, butthrough plastic or glass it travels at as little as 2/3rds its velocity through a vacuum.": 9scrhdr ;4"When light travels from one medium to another, the ratio of the speed of light through one to the speed of light through the other is very important. It is called the refractive index. The higher the refractive index,the more the light's path is deviated. This is shown in the diagram below.": <_70F,20:33!,173/3:33!,-173/3:-66B,0 =L43+,30:502,30:20,0:502,-30 >45-,34":502,30:0,-2:17,0:502,-24:15,3;"white":16,21;"red":18,21;"violet" ? :scrhdr @"The deviation is called refraction. Notice that violet is refracted more than red. Thisis because there is a slightly different refractive index for each wavelength.": Bscrhdr E5"The refractive index of a mediumis defined as :": H "ref. index = sin i / sin r": JK"where"::"i is the angle of incidence and r is the angle of refraction" L&:"These angles are shown below :": M" : : : : : : : : " N.14,7;"i":20,9 ;"r" Ou17,40(:100d,0:-502,0:-30,30:30,-30:17,-30 P19,0;" " Rscrhdr Tqsthdr U 542 V"Wavelength equals": YQ"1. v/f 2. f/v 3. v x f ?": \4exp=1:egc=3:return=350^:getans ^%"The velocity of sound in air is": `W"1. 330ms 2. 300 000 000ms 3. 3 300ms ?": c4exp=1:egc=3:return=358f:getans f#"The velocity of a wave equals": h_"1. wavelength/frequency 2. frequency/wavelength 3. frequency x wavelength": j4exp=3:egc=3:return=365m:getans 2n$=c$:start=400:return=398:endsec     wavelength and frequency  "Wavelength and frequency": w"The wavelength is the distance between two sucessive points on a wave which are in phase. This is shown below :-":  15,502:old=0 mz=16*0.09}8Q:new=(z)-old:1,2*new:old=new:z:12 ,14;"<--x-->" ::::scrhdr U"Wavelength, the velocity and itsfrequency are linked in the following way :": "Lambda = v/f": r"So the wavelength of a note witha frequency of 660Hz (assuming the speed of sound in air is 330ms) is :": ""Lambda = v/f = 330/60 = 0.5m": scrhdr E"By rewriting the equation, v or f can be calculated if unknown:": T"Lambda = v/f f = v/Lambda v = Lambda x f": q"eg. the frequency of light with Lambda = 600nm is 5x10^14Hz. What is the velocity of light ?": scrhdr P"v = Lambda x f = 600x10^-9x5x10^14 =3x10^8ms" scrhdr qsthdr  342V -"A longitudinal wave can travel through": M"1. a vacuum 2. air 3. both": 4exp=2:egc=3:return=450:getans /"A transverse wave can travel through :": M"1. a vacuum 2. air 3. both": 4exp=3:egc=3:return=458:getans "Polarised light is": U"1. at all angles 2. at 90 degrees 3. in one plane": 4exp=3:egc=3:return=465:getans 2n$=c$:start=500:return=498:endsec    t and v waves  %"Transverse & longitudinal waves": "Sound and light are both waves, but are different in many ways. Most of these differences are due to light being a transverse wave and sound being longitudinal.": scrhdr "A longitudinal wave transmits energy by a succession of compressions and rarefactions through a medium, eg. air. Because there must be something to compress to transmit the wavea longitudinal wave cannot travel through a vacuum.": *15,502:0,25:25,502:0,25:37%,502:0,25:557,502:0,25:75K,502:0,25:93],502:0,25:105i,502:0,25:115s,502:0,25 z15+110n,502:0,25:25+110n,502:0,25:37%+110n,502:0,25:557+110n,502:0,25:75K+110n,502:0,25:93]+110n,502:0,25:105i+110n,502:0,25:115s+110n,502:0,25 817,2;"C R C R C":scrhdr "A transverse wave is harder to imagine. It is not a compressionwave,and so needs nothing to compress. It can therefore travel through a vacuum.":  \"The vibration is electromagneticand is at right angles to the direction of movement.":  scrhdr R"Radiation consisting of transverse waves can be ""polarised""." e"This means that the energy can be transmitted in one plane, eg. horizontally or vertically.": ^"Normally, light consists of radiation with the energy transmitted at all angles." scrhdr qsthdr  442 ""Refractive index is given by": !V"1. sin i / sin r 2. sin r / sin i 3. cos i / cos r": $4exp=1:egc=3:return=550&:getans &"Red is refracted": (["1. more than violet 2. less than violet 3. the same as violet": +4exp=2:egc=3:return=558.:getans 0."Compared with a vacuum, light travels ": 2W"1. slower in glass 2. faster in glass 3. the same speed": 54exp=1:egc=3:return=5688:getans U2n$=c$:start=300,:return=598V:endsec V W X Z ] diffraction ` b"Diffraction": c"If a light consisting of a single wavelength is shone through a grating, patches of light and dark can be seen at regular intervals. This is caused by two effects- diffraction and interference.": dy"Diffraction causes the light to spread out. The narrower the spacing in the grating, the greater the spread.": escrhdr g"Interference is the addition of the waves that go to make up thelight beam. Where they cancel, no light is seen; where they adda bright dot is produced.": jzy=0:anti=0:5500|:y=30:anti=0:5500|:17,0;"Constructive interference" kscrhdr:y=0:anti=0:5500|:y=45-:anti=1:5500|:17,0;"Destructive interference":scrhdr lz"There is a formula for calculating the angle of diffraction for different wavelengths. It is :": n"n x Lambda = d sin Theta": q"where n is the order Lambda is the wavelength d is the grating spacing Theta is the angle of diffraction.": rscrhdr t"eg. what is the angle that the first beam of light is diffracted by if the wavelength is 700nm and the grating spacing is 100 lines to the millimetre ?": u "(nm=nanometres=10^-9m)": vV"sin Theta = n x Lambda / d = 7 x 10^-7 / 10^-5 = 0.07": x&"so Theta = sin 0.07 = 4 degrees": {N"Note that unlike refraction, red is diffracted more than blueor violet." ~scrhdr qsthdr "Red light is diffracted": ["1. less than violet 2. more than violet 3. the same as violet": 4exp=2:egc=3:return=650:getans ("The formula used in diffraction is": a"1. n x Lambda = d sin Theta 2. n / Lambda = d sin Theta 3. n x Lambda = d cos Theta": 4exp=1:egc=3:return=697:getans 2n$=c$:start=600X:return=698:endsec       " ( z;start=600X:return=898:n$="matrix arithmetic" endsec     forms of energy  "Forms of energy": ="Energy can take various forms. Some are listed below :": ~"1. K.E. ":"2.Potential energy":"3. Heat":"4. electromagnetic radiation 5. chemical 6. electrical" :"All of these can be converted from one to another.": scrhdr "eg. an electric car": $"chemical -> electrical -> K.E.": "eg. a light bulb": !"electrical -> heat -> light": scrhdr 2n$=c$:start=900:return=998:endsec      N T    x z     @ B H   scalars and vectors  :"Scalars and vectors": }"Quantities such as mass, volume and length are called SCALAR quantities. Scalar quanties havesize but not direction.": z"Quantities such as velocity and acceleration have both size and direction. Thistype of quantity is called a vector.": D"The general propertyof a vector is that it has two components.": scrhdr qsthdr 1:"Which of these is a vector quantity ? " S:"1. length 2. time 3. velocity": 5exp=3:egc=3:return=1760:getans 3start=1700:return=1798:n$="vectors" endsec      vector arith. & laws  ":"Vector arithmetic and laws": ^"Vector arithmetic is very simpleand follows the laws of conventional arithmetic.": "Addition": <"Two vectors a and b add to make a vector c as follows:": ""a = 2 b = 3":" 1 4" 8i=12 :x=29:y=63?:br:x=93]:br &:"c = 2+3 = 5":" 1+4 = 5" x=101e:y=39':br  x=39':i=24:br !scrhdr $""a = 2 b = 3":" 1 4" &&:"c = 2+3 = 5":" 1+4 = 5" '9i=12 :x=29:y=151:br:x=93]:br (n:"Vector addition is commutative since it makes no difference which way round the vectors are added.": )&x=101e:y=39'+88X:br *x=39':i=24:br +"a + b = b + a = c": ."This is easy to see if you thinkof the vectors as position vectors. It makes no difference which one is taken first - the final position is the same." 0scrhdr 2"vector addition is also associative. Three vectors a, b and c add to make the same result in both of the following ways:": 54" d = a + (b + c) d = (a + b) + c" 8_:"Again, this can be easily understood if the vectors are thought of as positional." :3:"Vector subtraction is also conventional." <scrhdr ?"Vector multiplication": B/"A vector can be multiplied by a scalar:": D1" eg. a = 2 1": F:" eg. 2a = 2 x 2 = 4 2 x 1 = 2" GFi=12 :x=165:y=87W:br:x=77M:y=111o:br H(i=44,:x=85U:y=87W:br Iscrhdr Lqsthdr N/:"Is vector addition commutative ?":a$:a$ P;a$="No"a$="no""Yes it is ! Read the section again." Sa$="yes"a$="Yes"praise V(:"Is vector addition associative ?": X a$:a$ Z;a$="No"a$="no""Yes it is ! Read the section again." ]a$="yes"a$="Yes"praise b=n$="vector arithmetic":start=1800:return=1898j gendsec j k l n qvelocity triangles t v:"Velocity triangles"::"Sometimes it is necessary to know the length of a vector rather than its individual components.": x"Since the two components of a positional vector are at right angles to each other, the lengthof a vector can be calculated using Pythagoras' theorem." yscrhdr {:"For example, the length of a vector:"::" 4":" 3":::::::::"is 5. This can be seen in the triangle above." }1x=14-1:y=119w:i=12 :br ~label=0:triangle O"AB represent a the x component and BC the y component. AC is the length." scrhdr "The length of the vector can represent quantites such as speed. If an aircraft is flying at right angles to the wind its ground speed can be calculated using vectors:":  triangle q"AB represents the aircraft's airspeed, BC represents the wind velocity and AC represents the ground speed." 8,17;"air speed=150":10 ,17;"wind speed=80":12 ,17;"AC=150+80":12 +1,20;"AC=28900":14,21;"AC=170"  :::: scrhdr "Sometimes velocities will not be at right angles. In these cases Puthagorus cannot be used as the resultant triangle is not right angled." d:"The length can be calculated in these cases by drawing the triangle and measuring length." >n$="velocity triangles":start=1900l:return=1998 endsec   x$="": o=1̱x$ n=18 #w(o,n):x$(oo)+n-1,w(o,n) n o  H24,16,16,32 ,16,16,24,0 C24,8,8,4,8,8,24,0 F0,0,62>,64@,64@,64@,62>,0 E0,0,124|,2,2,2,124|,0 G0,66B,66B,66B,66B,66B,44,,0 G0,44,,66B,66B,66B,66B,66B,0  G0,0,60<,64@,124|,64@,60<,0 I240,8,120x,128,248,0,0,0 C0,0,0,4,126~,4,0,0 I248,136,136,136,0,0,0,0 C4,4,228,4,0,0,0,0 G240,8,240,8,240,0,0,0 G28,20,16,16,8,8,40(,568  E4,68D,228,68D,0,0,0,0 "G16,16,16,0,0,480,72H,480 %E12 ,18,18,12 ,0,0,0,0 (E7,4,4,8,8,144,80P,32 *G4,8,16,16,16,32 ,32 ,32 ,G32 ,32 ,32 ,16,16,16,8,4 /C32 ,16,8,8,8,4,4,4 2C4,4,4,8,8,8,16,32 4 )::(40(*3.14159Iρ/180)  z=31000 %v=((z^2-(z-1)^2)) u=v^0.5 C((u)-(u+0.5))<0.01z# =z;":";z-1;":";v^0.5 z  z=07 z:7-z 7x=13:"" c=110 :c x z 0::" G C E TUTORING"::" Orders"  |"15,502+y:old=0 ~Xz=16*0.09}8Q:new=((z+*anti))-old:1,2*new:old=new:z  @"A geometric figure can be rotated by multiplying the individual coordinates by one ofthree different transformation matrices, depending on whether rotation through 90,180 or 270 is required.": B&"For a 90 rotation, multiply by:": E" 0 -1":" 1 0": H,"A 90 rotation is shoen in the diagram." I J:"The coordinates of the corners of the triangle are:": L&" 2 2 3":" 2 1 1": MM"which when multiplied by the matrix for a 90 rotation become:": N?" 0 -1 2 0-3 -3 1 0 3 2+0 2": O?" 0 -1 2 0-1 -1 1 0 1 2+0 2": P=" 0 -1 3 0-1 -1 1 0 1 3-0 3" R scrhdr:  Gx,y:0,16,-/3:x+i,y:0,16,/3: "There is a special matrix calledthe UNIT or identity matrix. If another matrix is multiplied by it there is no effect, rather like multiplying a number by 1 in ordinary arithmetic." $:"This is the 2x2 unit matrix:": " 1 0":" 0 1": 'x=8:i=24:y=80P:br scrhdr  " "square + rectangle "]27,568:502,0:0,502:-502,0:0,-502 "_27,568:100d,0:0,502:-100d,0:0,-502 "$7,2;"A D F" "%15,2;"B C E" " " "square + parallelogram "]27,568:75K,0:0,502:-75K,0:0,-502 "`27,568:75K,0:25,502:-75K,0:-25,-502 "#7,3;"A E D F" "!15,3;"B C" " " #K27,568:110n,0:568,41):0,557 #f15,7;"0":15,9 ;"2":15,11 ;"4":15,12 +1;"6" #E14,6;"0":12 ,6;"2":10 ,6;"4" #K27,568:110n,0:568,41):0,557 # [568+16,568+8:0,16:8,-16:-8,0 # ^568+32 ,568+16:0,32 :16,-32 :-16,0 #\568-10 ,568+16:-16,0:16,8:0,-8 #11 ,9 ;"A" #9 ,12 ;"B" #11 ,4;"C" #& #' #( #2K27,41):110n,0:27,41):0,557 #:]17,3;"0":17,6;"2":17,9 ;"4":17,12 ;"6" #<17,15;"8" #>\16,2;"0":14,2;"2":12 ,2;"4":10 ,2;"6" #A #Fi579+x,513+y:20,20:-20,20:-20,-20:20,-20: #Hc72H+x,568+y:0,30:-30,0:0,-30:30,0: #P'"Here is an example of ";n$ #R #Z #\ #_noises #b #d-z=120:0.01z# =,-24:z #f #h #i&z=15:0.3,t(z):z #l #mz=15:t(z):z: #n*7,9 ,5,-7,0 # # # #axes # #_30,90Z:210,0:30,90Z:0,557:0,-110n #10 ,2;"0" #f11 ,9 ;"90":11 ,15;"180":11 ,22;"270":11 ,29;"360" #atype=09124# #atype=19130# #.4,2;"1":16,1;"-1" #07,1;".5":13 ,0;"-.5" # #.7,2;"1":13 ,1;"-1" #.4,2;"2":16,1;"-2" # # # #draw triangle # #N30,60<:100d,0:0,60<:-100d,-60< #label=09175# #15,6;"adjacent" # 8,1;"hypoteneuse" #11 ,18;"opposite" #6123{,60<:0,7:7,0 #H41),60<:0,2:-3,2:-2,0 #14,2;"A" #14,17;"B" #6,17;"C" #::::::::: # # #)::9200#+((*6)+1): #"Berk ! What's ";c$;" ?": #'"Wally ! ";c$;" isn't on the tape.": ##"Moron ! Try spelling straight": #"sorry, ";n$;" ? ": #"Are you tired, ";n$;" ?": #"Don't wind me up, ";n$: $T $V scrhdr() $Y $\9900&:: $ $ qsthdr() $ $'9600%:9900&:egc=0: $ $ $endsec(start,n$) $ $5"That finishes ";n$:"Hit r to repeat this section" $ 9900& $a$="r"start $return $ $ $getans(loop,exp) $ $?dp=0:err=0:u$:u$:(u$)>10 err=1 $(u$)=09460$ $[j=1̱(u$):(u$(jj))<45-ů(u$(jj))>579ů(u$(jj))=47/err=1 $%9480%:j:u$="-."err=1 $Cerr=1dp>1"type the answer as a number":9460$ $=ans=(u$):(exp-ans)>0.005y# ="No, the answer is ";exp $$(ans-exp)0.005y# =9720% $return $ % %$(u$(jj))=46.dp=dp+1 % ,j>1Ư(u$(jj))=45-err=1 %  %k9800H&:d1=r(1)/10 +r(2)/100d+r(3)/1000:dec=d1:int=1000*dec %& %A"See if you understand this by trying the following examples" % 9800H& % %"True or false ?" %a$ %a$ %a$"t"a$"f"9650% % %n:n;"/";:d:d: % 9630% %h"No. Don't add the numbers together. It's just the second number, so the answer is ";r(2) % %K"No, its the second number, not the first, so the answer is ";r(2) % %%9720%+((*9 )+1): % "Good": % "Correct": %"Right again": %"OK": %"That's it": %"Brilliant !": %"Well done": &"Very good": &"Genius !": &HWz=110 :r(z)=(*9 )+1:z:r(1)r(2)9800H&: &R#r(1)r(2)9800H& &\ &z "trap": & &"Hit C to continue" &a$= &a$="c"9950& &a$="r"9950& & 9920& & &z=1502:z & 5  lȅ}8Q녞crhdT$sthd$ndse$etan$ig"iF#xes(#P#xe#riangl#iagrarais%qure"qupa"gxetur*r$nU1tarNAcSwavCwavl䀧S~e}ဗ >@@@>||BBBBB,,BBBBBXph2 ^i6:6:0:  G C E Tutoring  June 1984 Zk(3,500):j$(3,500):w(25,8):5000:2000 r(10 ) t(5):9069m# Lscrhdr=9300T$:qsthdr=9350$:endsec=9400$:getans=9450$ fig2=8950":fig=9030F#:axes2=9000(#:eg=9040P#:axes=9100#:triangle=9150#:diagram=218:praise=9720% 5br=8100:squrec=8850":squpar=8900" .::" PHYSICS help ph2":" Optics" #:"  G C E Tutoring June 1984" 2t:"Hello, what's your name ?":n$:n$:"OK, ";n$;",":"I'll begin by telling you how touse this physics program." 4P:"This tape covers 6 subjects which all come under the headingof optics." :>:"Press the key marked C so I can type the next screenfull" <a$=:a$="c"62> = 60< >:z=1100d:z AF:"Thanks. From now on when I want you to press the C key, I'll say" D:" Hit C to continue" F4:"Here's the list of subjects on this program": H"lenses refraction colour ray diagrams optical devices the eye and its defects" K2:"Which subject do you want to try ?":s$: Lc$=s$ N'(s$)>3s$=s$(13) Os$="len"100d Ps$="ref"300, Qs$="col" 200 Rs$="ray"400 Ss$="opt"500 Ts$="the"900 ^Cs$"len"s$"ref"s$"col"s$"ray"s$"opt"s$"the"9200# _ 70F c d f ilenses l n "Lenses": p."There are two main types of lenses :": s/"1. concave 2. convex": tscrhdr vM"Concave lenses diverge parallel light, as shown on the next screen:": x#scrhdr:dgnum=2:3500 z="Concave lenses are used in correcting short sight.": }scrhdr e"Convex lenses focus parallel rays of light to a point. They are known as converging lenses.": scrhdr:3500 scrhdr @"Convex lenses are used in any device when a ""real image""" "is needed." "A real image is one which can beprojected on to a screen. Devices using convex lenses include cameras and slide projectors.": ?"Another use for convex lenses isin correcting long sight.": scrhdr qsthdr 958 ?"The light sensitive area at the back of the eye is called": O"1. the retina 2. pupil 3. cornea": 4exp=1:egc=3:return=158:getans "Myopia is corrected using ": T"1. convex lens 2. concave lens 3. astigmatism": 4exp=2:egc=3:return=162:getans 0"Astigmatism is caused by the lens being": "1. too powerful 2. too weak 3. having different focal lengths in different planes": 4exp=3:egc=3:return=170:getans 2start=900:return=198:n$=c$:endsec     colour  "Colour": R"The eye perceives colour as being composed of three components :": M"1. red 2. green 3. blue": scrhdr "This is because there are three different types of colour receptive cells inside the eye. Each one is most receptive to one of the colours above. Their sensitivity extends outside these exact colours.": scrhdr \"Differing wavelengths of light stimulate different cones or combinations of cones.": "These are shown below": "red R yellow R+G green G cyan G+B blue B magenta R + B white R+G+B" scrhdr qsthdr 8"The eye perceives colour as being composed of ": \"1. red, yellow and blue 2. red, yellow and green 3. red, blue and green": 4exp=3:egc=3:return=240:getans ?"The light sensitive area at the back of the eye is called": O"1. cones 2. rods 3. retina": ,exp=3:egc=3:return=250 getans scrhdr )2start=200:return=298*:n$=c$:endsec * + , . 1 refraction 4 6"Refraction": 8"The velocity of light changes according to the medium it travels through. It is highest through a vacuum, and only very slightly slower through air, butthrough plastic or glass it travels at as little as 2/3rds its velocity through a vacuum.": 9scrhdr ;"When light travels from one medium to another, the ratio of the speed of light through one to the speed of light through the other is very important. It is called the refractive index. The higher the refractive index,the more the light's path is deviated.": ?scrhdr @"The deviation is called refraction. Notice that violet is refracted more than red. Thisis because there is a slightly different refractive index for each wavelength.": Bscrhdr E5"The refractive index of a mediumis defined as :": H "ref. index = sin i / sin r": JK"where"::"i is the angle of incidence and r is the angle of refraction" Rscrhdr TC"For further details about this topic please refraction on ph1." Vscrhdr 2start=300,:return=398:n$=c$:endsec     ray diagrams  "Ray diagrams":: "Lenses produce images of objectsplaced in front of them. There are a number of terms used to describe the image produced and the apparatus that produced it.": #"Here are some important terms": scrhdr "Principle axis :": c"This is an imaginary line drawn through the centre of the lens perpendicularly to the plane.": "A converging lens focuses rays of light parallel to the principle axis to a point. The point is the principle focus.": scrhdr "Optical centre": Y"This is the point at the centre of the lens where light passes through undeviated.": scrhdr "Focal length": B"The distance from the principle focus to the optical centre.": scrhdr "Real image": M"A real image can be projected on to a screen, eg. a cinema screen.": scrhdr "Virtual image": "A virtual image cannot be projected, but can be viewed directly, for example looking through a magnifying glass.": scrhdr "Magnification :": "Image size/object size": scrhdr ^"Real images are produced if the object is outside the focal length of a convex lens.": dž"Virtual images are produced if the object is inside the focal length of a convex lens, or in any position with a convex lens.": scrhdr qsthdr !"Magnification is defined as": a"1. image size/object size 2. object size/ image size 3. object size x image size": 4exp=1:egc=3:return=472:getans "A virtual image can": d"1. be projected 2. not be projected 3. only be projected virtually": 4exp=2:egc=3:return=480:getans !"A real image is produced by": "1. an object within the focal length of a concave lens 2. an object outside the focal length of a convex lens 3. an object outside the focal length of a concave lens": 4exp=2:egc=3:return=488:getans 2start=400:return=498:n$=c$:endsec     optical devices  "Optical devices": "A microscope is an instrument with a number of lenses placed in such a way as to give a much greater magnification than is possible with one alone. This iscalled a compound arrangement.": a"magnification = Me x Mo => magnification of eyepiece x magnification of object.": scrhdr "A telescope allows the viewing of distant objects with considerable magnification. There are two main types :":  2"1. Reflecting 2. Refracting":  scrhdr  :"A refracting telescope has a powerful (short focal length) eyepiece, and a weak (long focallength) objective lens.": "magnification = Fob / Feye eg. if Fob = 1000mm and Feye = 4mm then mag = 1000 / 4 = 250x": scrhdr "A reflecting telescope uses a concave mirror instead of the objective lens. A flat mirror then directs the light towards the eyepiece, which is at right angles to the rest of the telescope.": scrhdr qsthdr )"A telescope views objects that are": !M"1. near 2. far 3. both": $4exp=2:egc=3:return=550&:getans &)"The powerful lens in a telescopeis ": (M"1. in the eyepiece 2. at the objective 3. both": +4exp=1:egc=3:return=558.:getans .!"A reflecting telescope uses": 0M"1. two lenses 2. a lens and a mirror 3. both": 24exp=2:egc=3:return=5655:getans 5scrhdr U2start=500:return=598V:n$=c$:endsec V W X Z ] diffraction ` b"Diffraction": c"If a light consistion of a single wavelength is shone through a grating, patches of light and dark can be seen at regular intervals. This is caused by two effects- diffraction and interference.": dy"Diffraction causes the light to spread out. The narrower the spacing in the grating, the greater the spread.": escrhdr g"Interference is the addition of the waves that go to make up thelight beam. Where they cancel, no light is seen; where they adda bright dot is produced.": j:"":: kscrhdr lz"There is a formula for calcualting the angle of diffraction for different wavelengths. It is :": n"n=d sin ": q"where n is the order is the wavelength d is the grating spacing is the angle of diff.": rscrhdr t"eg. what is the angle that the first beam of light is diffracted by if the wavelength is 700nm and the grating spacing is 100 lines to the millimetre ?": vS"sin = n/d = 7 x 10^-7 / 10^-5 = 0.07": x"so =sin 0.07 = 4": {N"Note that unlike refraction, red is diffacted more than blue or violet." ~scrhdr 2start=600X:return=698:n$=c$:endsec      " ( z;start=600X:return=898:n$="matrix arithmetic" endsec     the eye + defects  "The eye and its defects": @"The eye consists of a convex lens focusing an image on a light sensitive surface called the retina. Focusing is achievedby cillary muscles surrounding the lens, and the eye is protected from damage by bright light by the pupil, which contracts to prevent too much light reaching the retina.": e"Sometimes the eye has a slight defect. This can be corrected with glasses or contact lenses.": #"There are three basic defects": scrhdr "1. Myopia": "If the lens is too powerful, or the cornea too curved, the imageis formed before the retina, making it out of focus when it reaches the back of the eye.": +scrhdr:dgnum=1:3500 :scrhdr "Myopia can be corrected by a concave lens which diverges the incoming light. The lens then has to deviate the path of the light more to produce a focussedimage." scrhdr "2. Hypermetropia": "If the lens is too weak, or the cornea not sufficiently curved, the image has not formed when the light strikes the retina. This is known as long sight.": scrhdr:3500 :scrhdr "Long sight can be corrected using a convex lens. This converges the incoming light to overcome the inadequate power of the eye. The image is broughtforward onto the retina." scrhdr "3. Astigmatism": "If the lens or cornea is unevenly curved, then the image may be in focus in one plane but not in another. This is corrected with a lens with differing characteristics in each plane.": scrhdr qsthdr  150 "A concave lens is": "1. thinner in the middle than at the edges 2. thicker in the middle than at the edges 3. the same thickness at all points": ,exp=1:egc=3:return=965 getans "A convex lens produces": Y"1. a real image 2. a virtual image 3. either of these": 4exp=3:egc=3:return=972:getans 2start=100d:return=998:n$=c$:endsec      N T    x z     @ B H   scalars and vectors  :"Scalars and vectors": }"Quantities such as mass, volume and length are called SCALAR quantities. Scalar quanties havesize but not direction.": z"Quantities such as velocity and acceleration have both size and direction. Thistype of quantity is called a vector.": D"The general propertyof a vector is that it has two components.": scrhdr qsthdr 1:"Which of these is a vector quantity ? " S:"1. length 2. time 3. velocity": 5exp=3:egc=3:return=1760:getans 3start=1700:return=1798:n$="vectors" endsec      vector arith. & laws  ":"Vector arithmetic and laws": ^"Vector arithmetic is very simpleand follows the laws of conventional arithmetic.": "Addition": <"Two vectors a and b add to make a vector c as follows:": ""a = 2 b = 3":" 1 4" 8i=12 :x=29:y=63?:br:x=93]:br &:"c = 2+3 = 5":" 1+4 = 5" x=101e:y=39':br  x=39':i=24:br !scrhdr $""a = 2 b = 3":" 1 4" &&:"c = 2+3 = 5":" 1+4 = 5" '9i=12 :x=29:y=151:br:x=93]:br (n:"Vector addition is commutative since it makes no difference which way round the vectors are added.": )&x=101e:y=39'+88X:br *x=39':i=24:br +"a + b = b + a = c": ."This is easy to see if you thinkof the vectors as position vectors. It makes no difference which one is taken first - the final position is the same." 0scrhdr 2"vector addition is also associative. Three vectors a, b and c add to make the same result in both of the following ways:": 54" d = a + (b + c) d = (a + b) + c" 8_:"Again, this can be easily understood if the vectors are thought of as positional." :3:"Vector subtraction is also conventional." <scrhdr ?"Vector multiplication": B/"A vector can be multiplied by a scalar:": D1" eg. a = 2 1": F:" eg. 2a = 2 x 2 = 4 2 x 1 = 2" GFi=12 :x=165:y=87W:br:x=77M:y=111o:br H(i=44,:x=85U:y=87W:br Iscrhdr Lqsthdr N/:"Is vector addition commutative ?":a$:a$ P;a$="No"a$="no""Yes it is ! Read the section again." Sa$="yes"a$="Yes"praise V(:"Is vector addition associative ?": X a$:a$ Z;a$="No"a$="no""Yes it is ! Read the section again." ]a$="yes"a$="Yes"praise b=n$="vector arithmetic":start=1800:return=1898j gendsec j k l n qvelocity triangles t v:"Velocity triangles"::"Sometimes it is necessary to know the length of a vector rather than its individual components.": x"Since the two components of a positional vector are at right angles to each other, the lengthof a vector can be calculated using Pythagoras' theorem." yscrhdr {:"For example, the length of a vector:"::" 4":" 3":::::::::"is 5. This can be seen in the triangle above." }1x=14-1:y=119w:i=12 :br ~label=0:triangle O"AB represent a the x component and BC the y component. AC is the length." scrhdr "The length of the vector can represent quantites such as speed. If an aircraft is flying at right angles to the wind its ground speed can be calculated using vectors:":  triangle q"AB represents the aircraft's airspeed, BC represents the wind velocity and AC represents the ground speed." 8,17;"air speed=150":10 ,17;"wind speed=80":12 ,17;"AC=150+80":12 +1,20;"AC=28900":14,21;"AC=170"  :::: scrhdr "Sometimes velocities will not be at right angles. In these cases Puthagorus cannot be used as the resultant triangle is not right angled." d:"The length can be calculated in these cases by drawing the triangle and measuring length." >n$="velocity triangles":start=1900l:return=1998 endsec   x$="": o=1̱x$ n=18 #w(o,n):x$(oo)+n-1,w(o,n) n o  H24,16,16,32 ,16,16,24,0 C24,8,8,4,8,8,24,0 F0,0,62>,64@,64@,64@,62>,0 E0,0,124|,2,2,2,124|,0 G0,66B,66B,66B,66B,66B,44,,0 G0,44,,66B,66B,66B,66B,66B,0  G0,0,60<,64@,124|,64@,60<,0 I240,8,120x,128,248,0,0,0 C0,0,0,4,126~,4,0,0 I248,136,136,136,0,0,0,0 C4,4,228,4,0,0,0,0 G240,8,240,8,240,0,0,0 G28,20,16,16,8,8,40(,568  E4,68D,228,68D,0,0,0,0 "G16,16,16,0,0,480,72H,480 %E12 ,18,18,12 ,0,0,0,0 (E7,4,4,8,8,144,80P,32 *G4,8,16,16,16,32 ,32 ,32 ,G32 ,32 ,32 ,16,16,16,8,4 /C32 ,16,8,8,8,4,4,4 2C4,4,4,8,8,8,16,32 4   save screen  ptr2=0 z=16384@22528X ptr=z-16383? data=(z) Jdata0ptr2=ptr2+1:j$(dgnum,ptr2)=(data):k(dgnum,ptr2)=z z    !fetch screen $ &z=16384@23296[ (ptr=z-16383? +data=(j$(dgnum,ptr)) 0z,data :z D N S fetch fast X 3200 Yx=16384@23296[ Z x,((addr)) ]addr=addr+1 `x b  fetch screen bits   z=1500 k(dgnum,z),(j$(dgnum,z)) z    save dg  "dgdata"j$() "dgaddr"k() r  z=31000 %v=((z^2-(z-1)^2)) u=v^0.5 C((u)-(u+0.5))<0.01z# =z;":";z-1;":";v^0.5 z    start  !7,10 ;"PLEASE WAIT" "dgdata"j$() "dgaddr"k()  41:7,9 ;"STOP THE TAPE":0   #( #2K27,41):110n,0:27,41):0,557 #:]17,3;"0":17,6;"2":17,9 ;"4":17,12 ;"6" #<17,15;"8" #>\16,2;"0":14,2;"2":12 ,2;"4":10 ,2;"6" #A #Fi579+x,513+y:20,20:-20,20:-20,-20:20,-20: #Hc72H+x,568+y:0,30:-30,0:0,-30:30,0: #P'"Here is an example of ";n$ #R #Z #\ #_noises #b #d-z=120:0.01z# =,-24:z #f #h #i&z=15:0.3,t(z):z #l #mz=15:t(z):z: #n*7,9 ,5,-7,0 # # # #axes # #_30,90Z:210,0:30,90Z:0,557:0,-110n #10 ,2;"0" #f11 ,9 ;"90":11 ,15;"180":11 ,22;"270":11 ,29;"360" #atype=09124# #atype=19130# #.4,2;"1":16,1;"-1" #07,1;".5":13 ,0;"-.5" # #.7,2;"1":13 ,1;"-1" #.4,2;"2":16,1;"-2" # # # #draw triangle # #N30,60<:100d,0:0,60<:-100d,-60< #label=09175# #15,6;"adjacent" # 8,1;"hypoteneuse" #11 ,18;"opposite" #6123{,60<:0,7:7,0 #H41),60<:0,2:-3,2:-2,0 #14,2;"A" #14,17;"B" #6,17;"C" #::::::::: # # #)::9200#+((*6)+1): #"Berk ! What's ";c$;" ?": #'"Wally ! ";c$;" isn't on the tape.": ##"Moron ! Try spelling straight": #"sorry, ";n$;" ? ": #"Are you tired, ";n$;" ?": #"Don't wind me up, ";n$: $T $V scrhdr() $Y $\9900&:: $ $ qsthdr() $ $'9600%:9900&:egc=0: $ $ $endsec(start,n$) $ $5"That finishes ";n$:"Hit r to repeat this section" $ 9900& $a$="r"start $return $ $ $getans(loop,exp) $ $?dp=0:err=0:u$:u$:(u$)>10 err=1 $(u$)=09460$ $[j=1̱(u$):(u$(jj))<45-ů(u$(jj))>579ů(u$(jj))=47/err=1 $%9480%:j:u$="-."err=1 $Cerr=1dp>1"type the answer as a number":9460$ $=ans=(u$):(exp-ans)>0.005y# ="No, the answer is ";exp $$(ans-exp)0.005y# =9720% $return $ % %$(u$(jj))=46.dp=dp+1 % ,j>1Ư(u$(jj))=45-err=1 %  %k9800H&:d1=r(1)/10 +r(2)/100d+r(3)/1000:dec=d1:int=1000*dec %& %A"See if you understand this by trying the following examples" % 9800H& % %"True or false ?" %a$ %a$ %a$"t"a$"f"9650% % %n:n;"/";:d:d: % 9630% %h"No. Don't add the numbers together. It's just the second number, so the answer is ";r(2) % %K"No, its the second number, not the first, so the answer is ";r(2) % %%9720%+((*9 )+1): % "Good": % "Correct": %"Right again": %"OK": %"That's it": %"Brilliant !": %"Well done": &"Very good": &"Genius !": &HWz=110 :r(z)=(*9 )+1:z:r(1)r(2)9800H&: &R#r(1)r(2)9800H& &\ &z "trap": & &"Hit C to continue" &a$= &a$="c"9950& &a$="r"9950& & 9920& & &z=1502:z & NNickAced>Q dgdata ?@ 8 < @x@ p8 `q@ 0 @ < `@9 |8|x@@@@@ @p<@ 0@>8p @  p8 @?8@888x< 0@xD DDD@ 8DD DDD@DD DD<`xD8 8D0 80  P@H@`@@`@@@@  @ `0 ` @   1   @` p& @ X 8@` @@p @0@0D  @ pH 0@pL (   0#`08x8D88xD8D DD DD DDDD( DD <(x DD(x DD D(@ DD(@(8D<<8D:"Press the key marked C so I can type the next screenfull" <a$=:a$="c"62> = 60< >:z=1100d:z AF:"Thanks. From now on when I want you to press the C key, I'll say" D:" Hit C to continue" F4:"Here's the list of subjects on this program": H"magnetism induction transformers galvonometers flux patterns force, motion and current motors and dynamos" K2:"Which subject do you want to try ?":s$: Lc$=s$ N'(s$)>3s$=s$(13) Os$="mag"100d Ps$="ind"200 Qs$="tra" 300, Rs$="gal"400 Ss$="flu"500 Ts$="for"900 Us$="mot"600X ^Cs$"len"s$"ref"s$"col"s$"ray"s$"opt"s$"the"9200# _ 70F c d f i magnetism l n"Magnetism": pu"A magnet has two poles called north and south. Like poles repel each other, and unlike poles attraact.": r*10 ,4;"-> N S N S <-" s0x=491:y=100d:mag:x=119w:mag t*14,4;"<- N S S N ->" u7x=491:y=68D:mag:x=119w:mag:scrhdr v"This principle is used in the magnetic compass. A very light bar magnet which is free to rotate will align itself so thatits north pole points towards the earth's south, and its southpole to the earth's north. This permits navigation.": wscrhdr x"An electromagnet consists of a coil of wire around a core of soft iron. When a current is passed through the coil, a magnetic field is generated.": yscrhdr z"The greater the current through an electromagnet, the greater the magnetic field. The field isalso increased if the number of turns of wire in the coil is large.": scrhdr qsthdr "Like poles :": T"1. attract 2. repel 3. are neutral": 4exp=2:egc=3:return=140:getans F"An electromagnet generates a magnetic field which is large if": v"1. the current is high 2. there are fewer turns in the coil 3. both of these": 4exp=1:egc=3:return=148:getans ;n$="magnetism":return=198:start=100d:endsec     induction  "Induction": ԟ"A changing magnetic field causes the flow of current in a coil by induction. The transformer relies on this effect for its operation.": "The changing magnetic field created by the AC applied to theprimary coil induces a current in the secondary. AC can therefore pass by mutual induction from one coil to another, but as DC does not produce a changing magnetic field, it cannot.": scrhdr @x=30:y=130:inv=1:coil:y=y-60<:coil 60<,20:0,110n:70F,20:0,110n:65A,20:0,110n:7,12 ;"The diagram shows":8,12 ;"inductive linking":9 ,12 ;"between two coils":19,0;" ":scrhdr |"Induction is improved by the addition of a magnetic material - eg. iron - into the path between the coils. " scrhdr qsthdr D"Which of these can pass from onecoil to another by induction :": V"1. AC 2. DC 3. both of these": 4exp=1:egc=3:return=240:getans );n$="induction":return=298*:start=200:endsec * + , . 1transformers 4 6"Transformers": 8w"A transformer converts AC at onevoltage to AC at another. It consists of two coils linked by a soft iron core.": :J60<,62>:0,45-:65A,62>:0,45- ;,x=30:y=110n:inv=1:coil <-x=95_:y=110n:inv=-1:coil =Az=110 ::z::"A general formula follows.":scrhdr >"The ratio of voltage in to the voltage out depends on the number of turns in the input coil (the primary) to the numberof turns in the output coil (the secondary).": ?scrhdr @"The output voltage can be higherthan the input voltage by havingmore turns in the secondary thanthe primary. This is NOT gettingsomething for nothing - the current is proportionately less,so the power is the same.": Ascrhdr B"Alternatively, the output voltage can be less than the input by having less turns. Thiscan be useful, as mains electricity is at too high a voltage to operate electronic equipment.": Cscrhdr E"eg. a transformer has a primary coil with 1200 turns, and a secondary coil with 30 turns. What is the output voltage ?": F"The formula to use is :": Gb"Vout = Vin x (no. of turns on the secondary /no. of turns on the primary)": HT"Vout = Vin x 30/1200 = 240 x 30/1200 = 6 volts": Iscrhdr J"A transformer which raises the voltage is called a step-up transformer. When electricity is transmitted from a power station, it is at a very high voltage, sometimes as much as 400 000v. This is to reduce losses.": Kscrhdr L"A generator produces 1 000 000W.If the power is transmitted at 1000v and the resistance of the pylon cable is 0.1 ohms, what power is lost ?": O" V = IR = I x 0.1 I = P/V = 1 000 000/1000 = 1000A V = 1000 x 0.1 =100v P = 100v x 1000A = 100 000W": Pscrhdr R"The generator is connected to a step up transformer before being connected to the pylon. Electricity is now transmitted at 100 000v. What is the new loss ?": T" V = IR = I x 0.1 I = P/V = 1 000 000/100 000 = 10A V = 10 x 0.1 = 1v P = 1v x 10A = 10W": V-"Which is 10 000 times less than before.": Wscrhdr Y"As well as less power lost in the line, the reduced current means that the pylon cables can be made from thinner wire, making them lighter and cheaper.": \ ^qsthdr `"A transformer with ";r(1)*120x;" turns on its primary has a secondary with ";r(2)*5;" turns. If the input voltage is 240v, what is the output ?": cKexp=10 *r(2)/r(1):egc=3:return=357e:getans emoreq hmore=1350^ ;start=300,:return=398:n$="K.E. and momentum" >n$="transformers":return=398:start=100d:endsec     galvanometers  "Galvanometers": "A galvanometer measures the flowof current. Unlike an ammeter, it reads zero at the centre. This means that it can display aflow of current in either direction.": Lx=30:y=75K:ptr=1:galv:x=130:ptr=-1:galv ::::::scrhdr "Inside a galvanometer there is asmall coil made of extremely fine wire. It is in the field ofa permanent magnet, so if current flows through it, the electromagnetic force produced either attracts or repels it.": "The coil is only free to rotate,so this is what it does. The movement of the coil is made more noticable by the addition of the pointer.": scrhdr qsthdr !"A galvanometer reads zero :": _"1. in the left had side 2. in the centre 3. on the right hand side": 4exp=2:egc=3:return=438:getans "A galvanometer measures": S"1. current 2. voltage 3. resistance": 4exp=1:egc=3:return=445:getans ?n$="galvanometers":return=498:start=400:endsec     flux patterns  "Flux patterns": o"A line whose direction at each point is that of the magnetic field is called a magnetic line of force.": 5"Lines of force can be plotted using a compass": scrhdr a"The lines of force from a bar magnet follow curves leading from one pole to the other.":  scrhdr  "A current flowing through a wirecreates a magnetic field,the lines of force of which radiate out in concentric circles from the wire.": scrhdr U?n$="flux patterns":return=598V:start=500:endsec V W X Z ]motors and dynamos ` b"Motors and dynamos": d^"An electric motor consists of a freely rotating coil of wire within a magnetic field.": hscrhdr j"Current flows through the brushes to the commutator, and then from the commutator to the coil. A magnetic field is created, causing the coil to be repelled from the magnet. This makes the armature, on which thecoil is mounted, rotate.": kscrhdr lJ"When the coil has rotated far enough, the current flows in theopposite direction through the coil. This is because the brushes now make contact with the opposite electrodes on the commutator to the ones before. Positive is now applied to the end of the coil which was previously negative, and vice versa." mscrhdr n"The magnetic field produced now repels the coil from the poles that it was previously attractedto. This causes another 1/2 turnof rotation.": qZ"The process then continues from the beginning, causing continuous rotation.": tscrhdr v"A dynamo generates electricity. Mechanically it is the same as an electric motor, but instead of current flowing through the coil causing rotation, the coil is rotated creating current to flow through it.": xscrhdr {qsthdr ~F"What changes the direction that current flows through the coil ?": V"1. the commutator 2. the brushes 3. none of these": 4exp=1:egc=3:return=645:getans 6"Electricity flows from the brushes to the :": O"1. commutator 2. permanent magnet 3. dynamo": 4exp=1:egc=3:return=652:getans O"A dynamo generates electricity when power is apllied in the form of :": k"1. passing current through the coil 2. rotating the armature 3. both" 4exp=2:egc=3:return=660:getans Dn$="motors and dynamos":return=698:start=600X:endsec       " ( z;start=600X:return=898:n$="matrix arithmetic" endsec     force, motion and current  "Force, motion and current": "When a magnetic field is appliedto a wire, a force is exerted at right angles to the field andthe current flowing through the wire. The direction of the forceis worked out using Fleming's left hand rule.": scrhdr "Fleming's left hand rule uses the fingers of left hand to represent the force, motion andcurrent. Force is on the thumb, direction of field is the fingerand current is the second finger": scrhdr A"A way to remember Fleming's lefthand rule is as follows :":: ["First Finger = field seCond finger = current thuMb = motion" scrhdr "Using Fleming's left hand rule, the direction of force in the example below can be worked out."::"The vertical arrows are the current, the arrow from left to right the field, and the other two arrows show the force." 14,7;">" %36$,59;:22,0 70F,45-:0,30:-4,-4:4,4:4,-4:80P,45-:-4,4:4,-4:4,4:-4,-4:0,30 90Z,65A:15,15:-3,0:3,0:0,-3:557,502:-15,-15:0,3:0,-3:3,0 ::: scrhdr:qsthdr d"Fleming's left hand rule uses the fingers of the left hand. The second finger represents :": N"1. motion 2. current 3. field": 4exp=2:egc=3:return=938:getans D"When a magnetic field is aplied to a wire, a force is exerted:": "1. at right angles to to the field 2. at right angles to the current 3. at right angles to both": 4exp=3:egc=3:return=945:getans Kn$="force, motion and current":return=998:start=900:endsec      N T    x z     @ B H   scalars and vectors  :"Scalars and vectors": }"Quantities such as mass, volume and length are called SCALAR quantities. Scalar quanties havesize but not direction.": z"Quantities such as velocity and acceleration have both size and direction. Thistype of quantity is called a vector.": D"The general propertyof a vector is that it has two components.": scrhdr qsthdr 1:"Which of these is a vector quantity ? " S:"1. length 2. time 3. velocity": 5exp=3:egc=3:return=1760:getans 3start=1700:return=1798:n$="vectors" endsec      vector arith. & laws  ":"Vector arithmetic and laws": ^"Vector arithmetic is very simpleand follows the laws of conventional arithmetic.": "Addition": <"Two vectors a and b add to make a vector c as follows:": ""a = 2 b = 3":" 1 4" 8i=12 :x=29:y=63?:br:x=93]:br &:"c = 2+3 = 5":" 1+4 = 5" x=101e:y=39':br  x=39':i=24:br !scrhdr $""a = 2 b = 3":" 1 4" &&:"c = 2+3 = 5":" 1+4 = 5" '9i=12 :x=29:y=151:br:x=93]:br (n:"Vector addition is commutative since it makes no difference which way round the vectors are added.": )&x=101e:y=39'+88X:br *x=39':i=24:br +"a + b = b + a = c": ."This is easy to see if you thinkof the vectors as position vectors. It makes no difference which one is taken first - the final position is the same." 0scrhdr 2"vector addition is also associative. Three vectors a, b and c add to make the same result in both of the following ways:": 54" d = a + (b + c) d = (a + b) + c" 8_:"Again, this can be easily understood if the vectors are thought of as positional." :3:"Vector subtraction is also conventional." <scrhdr ?"Vector multiplication": B/"A vector can be multiplied by a scalar:": D1" eg. a = 2 1": F:" eg. 2a = 2 x 2 = 4 2 x 1 = 2" GFi=12 :x=165:y=87W:br:x=77M:y=111o:br H(i=44,:x=85U:y=87W:br Iscrhdr Lqsthdr N/:"Is vector addition commutative ?":a$:a$ P;a$="No"a$="no""Yes it is ! Read the section again." Sa$="yes"a$="Yes"praise V(:"Is vector addition associative ?": X a$:a$ Z;a$="No"a$="no""Yes it is ! Read the section again." ]a$="yes"a$="Yes"praise b=n$="vector arithmetic":start=1800:return=1898j gendsec j k l n qvelocity triangles t v:"Velocity triangles"::"Sometimes it is necessary to know the length of a vector rather than its individual components.": x"Since the two components of a positional vector are at right angles to each other, the lengthof a vector can be calculated using Pythagoras' theorem." yscrhdr {:"For example, the length of a vector:"::" 4":" 3":::::::::"is 5. This can be seen in the triangle above." }1x=14-1:y=119w:i=12 :br ~label=0:triangle O"AB represent a the x component and BC the y component. AC is the length." scrhdr "The length of the vector can represent quantites such as speed. If an aircraft is flying at right angles to the wind its ground speed can be calculated using vectors:":  triangle q"AB represents the aircraft's airspeed, BC represents the wind velocity and AC represents the ground speed." 8,17;"air speed=150":10 ,17;"wind speed=80":12 ,17;"AC=150+80":12 +1,20;"AC=28900":14,21;"AC=170"  :::: scrhdr "Sometimes velocities will not be at right angles. In these cases Puthagorus cannot be used as the resultant triangle is not right angled." d:"The length can be calculated in these cases by drawing the triangle and measuring length." >n$="velocity triangles":start=1900l:return=1998 endsec   x$="": o=1̱x$ n=18 #w(o,n):x$(oo)+n-1,w(o,n) n o  H24,16,16,32 ,16,16,24,0 C24,8,8,4,8,8,24,0 F0,0,62>,64@,64@,64@,62>,0 E0,0,124|,2,2,2,124|,0 G0,66B,66B,66B,66B,66B,44,,0 G0,44,,66B,66B,66B,66B,66B,0  G0,0,60<,64@,124|,64@,60<,0 I240,8,120x,128,248,0,0,0 C0,0,0,4,126~,4,0,0 I248,136,136,136,0,0,0,0 C4,4,228,4,0,0,0,0 G240,8,240,8,240,0,0,0 G28,20,16,16,8,8,40(,568  E4,68D,228,68D,0,0,0,0 "G16,16,16,0,0,480,72H,480 %E12 ,18,18,12 ,0,0,0,0 (E7,4,4,8,8,144,80P,32 *G4,8,16,16,16,32 ,32 ,32 ,G32 ,32 ,32 ,16,16,16,8,4 /C32 ,16,8,8,8,4,4,4 2C4,4,4,8,8,8,16,32 4 )::(40(*3.14159Iρ/180)  z=31000 %v=((z^2-(z-1)^2)) u=v^0.5 C((u)-(u+0.5))<0.01z# =z;":";z-1;":";v^0.5 z  z=07 z:7-z 7x=13:"" c=110 :c x z 0::" G C E TUTORING"::" Orders"  p r ucoil (x,y,inv) x zKx,y:20*inv,0:z=15:0,-10 ,-*inv:z |-20*inv,0    galv (x,y,ptr)  x,y 20,0 35#,0,- -35#,0,-  x+557,y:20,0 3x+27,y+7:20,0,-/2 x+38&,y-7 ptr*7,12 7 8 : =mag @ Bx,y D%502,0:0,-15 G%-502,0:0,15  @"A geometric figure can be rotated by multiplying the individual coordinates by one ofthree different transformation matrices, depending on whether rotation through 90,180 or 270 is required.": B&"For a 90 rotation, multiply by:": E" 0 -1":" 1 0": H,"A 90 rotation is shoen in the diagram." I J:"The coordinates of the corners of the triangle are:": L&" 2 2 3":" 2 1 1": MM"which when multiplied by the matrix for a 90 rotation become:": N?" 0 -1 2 0-3 -3 1 0 3 2+0 2": O?" 0 -1 2 0-1 -1 1 0 1 2+0 2": P=" 0 -1 3 0-1 -1 1 0 1 3-0 3" R scrhdr:  Gx,y:0,16,-/3:x+i,y:0,16,/3: "There is a special matrix calledthe UNIT or identity matrix. If another matrix is multiplied by it there is no effect, rather like multiplying a number by 1 in ordinary arithmetic." $:"This is the 2x2 unit matrix:": " 1 0":" 0 1": 'x=8:i=24:y=80P:br scrhdr  " "square + rectangle "]27,568:502,0:0,502:-502,0:0,-502 "_27,568:100d,0:0,502:-100d,0:0,-502 "$7,2;"A D F" "%15,2;"B C E" " " "square + parallelogram "]27,568:75K,0:0,502:-75K,0:0,-502 "`27,568:75K,0:25,502:-75K,0:-25,-502 "#7,3;"A E D F" "!15,3;"B C" " " #K27,568:110n,0:568,41):0,557 #f15,7;"0":15,9 ;"2":15,11 ;"4":15,12 +1;"6" #E14,6;"0":12 ,6;"2":10 ,6;"4" #K27,568:110n,0:568,41):0,557 # [568+16,568+8:0,16:8,-16:-8,0 # ^568+32 ,568+16:0,32 :16,-32 :-16,0 #\568-10 ,568+16:-16,0:16,8:0,-8 #11 ,9 ;"A" #9 ,12 ;"B" #11 ,4;"C" #& #' #( #2K27,41):110n,0:27,41):0,557 #:]17,3;"0":17,6;"2":17,9 ;"4":17,12 ;"6" #<17,15;"8" #>\16,2;"0":14,2;"2":12 ,2;"4":10 ,2;"6" #A #Fi579+x,513+y:20,20:-20,20:-20,-20:20,-20: #Hc72H+x,568+y:0,30:-30,0:0,-30:30,0: #P'"Here is an example of ";n$ #R #Z #\ #_noises #b #d-z=120:0.01z# =,-24:z #f #h #i&z=15:0.3,t(z):z #l #mz=15:t(z):z: #n*7,9 ,5,-7,0 # # # #axes # #_30,90Z:210,0:30,90Z:0,557:0,-110n #10 ,2;"0" #f11 ,9 ;"90":11 ,15;"180":11 ,22;"270":11 ,29;"360" #atype=09124# #atype=19130# #.4,2;"1":16,1;"-1" #07,1;".5":13 ,0;"-.5" # #.7,2;"1":13 ,1;"-1" #.4,2;"2":16,1;"-2" # # # #draw triangle # #N30,60<:100d,0:0,60<:-100d,-60< #label=09175# #15,6;"adjacent" # 8,1;"hypoteneuse" #11 ,18;"opposite" #6123{,60<:0,7:7,0 #H41),60<:0,2:-3,2:-2,0 #14,2;"A" #14,17;"B" #6,17;"C" #::::::::: # # # #"Berk ! What's ";c$;" ?": #'"Wally ! ";c$;" isn't on the tape.": ##"Moron ! Try spelling straight": #"sorry, ";m$;" ? ": #"Are you tired, ";m$;" ?": #"Don't wind me up, ";m$: $T $V scrhdr() $Y $\9900&:: $ $ qsthdr() $ $'9600%:9900&:egc=0: $ $ $endsec(start,n$) $ $5"That finishes ";n$:"Hit r to repeat this section" $ 9900& $a$="r"start $return $ $ $getans(loop,exp) $ $?dp=0:err=0:u$:u$:(u$)>10 err=1 $(u$)=09460$ $[j=1̱(u$):(u$(jj))<45-ů(u$(jj))>579ů(u$(jj))=47/err=1 $%9480%:j:u$="-."err=1 $Cerr=1dp>1"type the answer as a number":9460$ $=ans=(u$):(exp-ans)>0.005y# ="No, the answer is ";exp $$(ans-exp)0.005y# =9720% $return $ % %$(u$(jj))=46.dp=dp+1 % ,j>1Ư(u$(jj))=45-err=1 %  %k9800H&:d1=r(1)/10 +r(2)/100d+r(3)/1000:dec=d1:int=1000*dec %& %A"See if you understand this by trying the following examples" % 9800H& % %"True or false ?" %a$ %a$ %a$"t"a$"f"9650% % %n:n;"/";:d:d: % 9630% %h"No. Don't add the numbers together. It's just the second number, so the answer is ";r(2) % %K"No, its the second number, not the first, so the answer is ";r(2) % %%9720%+((*9 )+1): % "Good": % "Correct": %"Right again": %"OK": %"That's it": %"Brilliant !": %"Well done": &"Very good": &"Genius !": &HWz=110 :r(z)=(*9 )+1:z:r(1)r(2)9800H&: &R#r(1)r(2)9800H& &\ &z "trap": & &"Hit C to continue" &a$= &a$="c"9950& &a$="r"9950& &a$="q"9950& & 9920& & &z=1502:z & &more=0 &"More questions ?": & d$:d$ &d$=d$(11) &d$="y"more=1 &  m#crhdT$sthd$ndse$etan$ig"iF#xes(#P#xe#riangl#iagrarais%ore&oipala8qure"qupa"xyKgxeturr$ntarXnorDntSmotCmotU1Nmotors and dynamos >@@@>||BBBBB,,BBBBB<@|@<x~(8DD0H0  P    X5  M A @