ZXTape! 0Created with Ramsoft MakeTZXb1 ,I,F, :n=79 :n,8;"STOP THE TAPE!":n:502:18,3;"Press any key to continue":0 :502:2000 d&:n=015:b:"f"+n,b:n ]g$="against":a$="Acceleration":s$="Distance":p$="Displacement":v$="Velocity":t$="Time" ,:"We have already used graphs to"'"illustrate moving bodies.":200:''"We will now look at graphs in"'"more detail, to see what can be"'"discovered from them." 6300,:''"We will look at graphs of:":100d:12 ,4;s$;" (";p$;")";13 ,4;g$;" ";t$;15,4;v$;" ";g$;" ";t$ @R8000@::502:s$;" (";p$;")/";t$:0,166:223,0 J502:502:14,0;"A body moving at uniform";15,0;v$;" will travel equal"'s$;"s in equal intervals of"'t$;" (in a constant direction)." TD150:'"A graph of ";p$;" ";g$'t$;" will be a straight line." ^#100d:7000X:6000p hF502:88X,80P:40(,71G:502:8000@ rzw$="14000630":9000(#:15,0;"Take any point on the graph and"'"drop a perpendicular to the ";t$'"axis." |150:12 ,10 ;"A";4,14;"B":502:119w,135:0,-546:502:12 ,15;"C" &502:8000@:w$="15000231":9000(#:15,0;"BC is the ";p$;" (";s$'"moved) in ";t$;" interval AC.":100d:18,1;v$;" = ";p$;" = BC";18,12 ;1;"____________ __";19,16;t$;19,27;"AC" j100d:21,10 ;"= the gradient of AB.":100d:21,16;1;"gradient" 1502:8000@:w$="15000631":9000(# 15,0;"Imagine the graph is of a man"'"going to buy a paper.":150:'"We will assume he walks at a"'"uniform ";v$;" from his house"'"to the shop, a ";s$;" of BC,"'"in ";t$;" interval AC." <100d:w$="03150101":9000(#:502:8000@ w$="15000630":9000(#:15,0;"When he reaches the shop he buys"'"the paper. This takes a ";t$'"interval of BD." M100d:120x,135:31,0:4,19;"D" ̉100d:19,0;"He is (more or less) standing"'"still, so his ";v$;" is zero."'"(The gradient of BD is zero.)" 1502:8000@:w$="15000631":9000(# 16,0;"Then he walks home again (DE).":502:31,-557:12 ,23;"E":502:151,135:0,-557:502:12 ,19;"F" 502:18,0;"He is now going in the opposite"'"direction. His ";p$;" and"'"his ";v$;" are both negative."'"(Remember they are Vectors.)" 150:w$="16000029":9000(#:15,1;v$;" = -DF = gradient of DE";15,13 ;1;"__";16,13 ;"FE":502:8000@ <:s$;" (";p$;")/";t$:0,166:223,0 f502:15,0;"Now consider a body moving at"'"variable ";v$;".":502:7000X G6010z:502:u=0:a=.01z# =:l=120x:7100 8000@:w$="15000128":9000(#:15,0;"To find the ";v$;" at any"'"instant I,":502:7,20;"I" &t502:16,11 ;"imagine a triangle"'"whose hypotenuse is small enough"'"to coincide with the curve." 0100d:2:160,104h:15,15:0,-15:-15,0:8,22;"s";9 ,21;"t" :0:100d:20,0;v$;" at I = s";20,16;1;"_";21,16;"t":502:8000@ Dw$="15000331":9000(#:15,0;"But this is the same as finding"'"the gradient of a tangent to the"'"curve at point I. So we can draw"'"a bigger triangle." Na150:2:136,80P:63?,63?:0,-63?:-63?,0 XZ0:12 ,16;"A";3,25;"B";12 ,25;"C" bk100d:20,18;"= BC";20,20;1;"__";21,20;"AC" l502:8000@ <:s$;" (";p$;")/";t$:0,166:223,0 502:15,0;"Now think of a ball thrown up inthe air.":502:7000X:6010z:6020:502:18,0;"On the way up it will decelerateat a uniform rate under the"'"effect of gravity." K100d:a=-.02{# =:l=140:u=1.43333:h=12 :7200   5000:6000p *`502:15,0;"Imagine a car travelling at a"'"uniform ";v$;" v for a ";t$;" t." 4w100d:89Y,127:94^,0:100d:18,0;p$;19,0;"(";s$;"), s = vt" >100d:12 ,10 ;"A";5,10 ;"B";5,23;"C":502:0,-46.:502:12 ,23;"D" H3100d:19,19;"= AB x AD" R200:w$="06110511":1:5:9000(#:7:0:100d:21,14;"= Area of ABCD" \18000@:w$="15000631":9000(#:502 f15,0;s$;" (";p$;") is"'"therefore represented by the"'"area between the ";v$;"/";t$'"curve and the ";t$;" axis." pP200:20,0;"This applies whatever the shape"'"of the curve." z100d:5000 ]100d:16,0;"Now consider a body moving with"'"uniform ";a$;".":100d ?6010z:6020:89Y,127:62>,31 100d:12 ,10 ;"A";5,10 ;"B";1,19;"C":502:0,-78N:502:12 ,19;"D" 502:19,0;"During ";t$;" AD, ";p$;" s"'"is equal to the area of the"'"trapezium ABCD.":150:8000@ w$="16000130":9000(#:502:15,8;"s = (AB + CD) x AD";1;15,13 ;"_______";16,16;2 2100d:8000@:w$="15000631":9000(# [502:15,0;"Since ";a$;" is the rate"'"of change of ";v$;" with ";t$;"," V100d:90Z,127:60<,0:502:5,19;"E" K100d:18,0;a$;" = CE in ";t$;" AD":100d x8000@:502:18,18;" ";18,15;1;"__";19,15;"AD" 7100d:21,13 ;"= gradient of BC." L502:5000 Vz15,0;"Finally, consider a body moving"'"with variable ";a$;".":502:6010z:6030:100d `J88X,81Q:480,480,1:32 ,32 ,-1 jX502:18,0;"At any point I,":502:8,14;"I" te502:18,16;a$;" is"'"equal to the gradient of a"'"tangent to the curve at I." ~100d:2:104h,81Q:513,63?:100d:8000@:502:0,-63?:0:502:12 ,12 ;"A";3,19;"B";12 ,19;"C" /502:w$="15000130":9000(#:502 a15,0;a$;" = BC";15,15;1;"__";16,15;"AC" 502:8000@ ܪ:502:3,0;"Press:";5,6;"1 to repeat this program";7,6;"2 to load the next program";9 ,6;"3 to stop" J+n=10 :17,3;"think" T.n:w$="tank":18,3;5;w$ YMn:23,44,:0,-21:41),0:0,21 c(n:23,40(:41),0 hfm=63-1:n/502,24+2*m:5;18,m;"";w$(m-2):m r'2*n:18,3;"t" |]m=36:n/502,21+3*m:5;18,m;w$(m-2);"":m '2*n:18,6;"k" ="1"20  ="3" B="2":502:8,8;"START THE TAPE":""  1640h 410 ,0;"" >5n=11 20:2:n,0;"":n H1n=020:2:21,n;"":n R;n=2011 -1:2:n,20;"":n \10 ,20;"" 5:1 m=2013 -1  m,0; &n=020:1:" ";:n m 7:0 12 ,0;"" 5n=119:2:12 ,n;"":n 12 ,20;"" `5:1 j13 ,0; o 5 t)"     " y 5 ~3"     " 5 5"       " 5 " " 5 &"   " 5 5"     " 5 7"       " 5 "  " 10 40:7:19,21;"Educational" 20,21;"Software" (@200::502:2,1;"GRAPHS of MOTION" 2r100d:5,2;" 1983";7,2;"CP Lawrence";8,2;"MA (Cantab.), MA (London)" F200:: S8000@::502:v$;"/";t$:0,166:103g,0:502 88X,159:0,-79O:159,0:3,1;v$;",";4,8;"v";13 ,25;t$;", t": pK7,1;"Uniform ";8,1;"Velocity": zK7,1;"Variable";8,1;"Velocity": q9 ,1;"Uniform ";10 ,1;"Acceler-";11 ,1;"ation ": q9 ,1;"Variable";10 ,1;"Acceler-";11 ,1;"ation ": X88X,159:0,-79O:159,0:3,1;"Displace-";4,1;"ment, s";13 ,25;t$;", t": Gt=0l:s=u*t+a*(t^2/2):88X+t,80P+s:t:  Bt=0l:s=u*t+a*(t^2/2):88X+t,80P+s *t=70Fh=10 :w$="15000531":9000(#:15,00;"For a split second it will reach"'"a standstill.":200:18,0;"Then it will fall back to where"'"it started, accelerating this"'"time under the effect of"'"gravity." 4D11 -s/8,30;"0";h-s/8,30;" " Rt: @""press ENTER to continue ";w$: #(z=w$(2)̰w$(2)+w$(56):m=w$(34)̰w$(34)+w$(7):z,m;" ":m:z: %&0,480,122z,188,252,122z,480,0,0,12 ,94^,61=,63?,94^,12 ,0 d bGagainstA AccelerationSDistanceP DisplacementVVelocityTTimeWh b2 AAQbA :n=79 :n,8;"STOP THE TAPE!":n:502:18,3;"Press any key to continue":0  :502 d10 ,0;"" n5n=11 20:2:n,0;"":n x1n=020:2:21,n;"":n ;n=2011 -1:2:n,20;"":n 10 ,20;"" 5:1 m=2013 -1 m,0; &n=020:1:" ";:n m 7:0 ,12 ,0;"" 65n=119:2:12 ,n;"":n @12 ,20;"" 5:1 13 ,0;  5 )"     "  5 3"     "  5 5"       "  5 " "  5 &"   "  5 5"     "  5 7"       "  5 "  "  10 40:7:19,21;"Educational" 20,21;"Software" XN200::502:2,1;"GRAVITY, WEIGHT and FRICTION" br100d:5,2;" 1983";7,2;"CP Lawrence";8,2;"MA (Cantab.), MA (London)" v 200: ):n=07:usr:"b"+n,usr:n 'n=07:usr:"s"+n,usr:n 'n=07:usr:"k"+n,usr:n 'n=07:usr:"l"+n,usr:n 'n=07:usr:"r"+n,usr:n 'n=07:usr:"m"+n,usr:n 'n=07:usr:"i"+n,usr:n 'n=07:usr:"f"+n,usr:n  'n=07:usr:"g"+n,usr:n w:"GRAVITY":502:3,0;"What is gravity?":100d:5,2;"Gravity is a force." 100d:8,0;"What is a force?":100d:11 ,0;"We cannot really say what a"'"force is, but only what it can"'"do." %502:9950&::"FORCE" Z502:2,0;"A force acting on a static body"'"could make the body move." T100d:10 ,14;"":502:10 ,8;"FORCE":9940& $D10 :n=08:10 ,14+n;" ":5:n .502:9950&:w$="02000130":9960&:10 ,23;" ":502:2,0;"A force acting on a moving body"'"could make the body change"'"direction" 8]150:n=08:18-n,14;"";19-n,14;" ":2:n BVn=15:10 -n,14+n;"";11 -n,13 +n;" ":2:n L502:9950&:5,19;" ":502:w$="04000008":1:9960&:0:502:4,10 ;"or speed;" VG502:n=116:10 ,30-n;" ":n*2:n `X4,13 ;1;" ";4,20;"or stop it"'"moving altogether." j/502:9950&::"FORCE":502 t2,0;"So force can be defined as"'"whatever changes a body's":100d:5,6;"state of rest":502:7,3;"or uniform motion";8,6;"in a straight line." ~B150:w$="05060317":1:9960&:0:502 D12 ,0;"A force therefore causes a body to accelerate." 3n=015:18,n;" ":10 :n 18,10 ;"FORCE" 2:76L,35#:40(,0:0,5:8,-12 :-8,-12 :0,5:-40(,0:0,13 :0 An=1630:18,n;" ":16-(n/2):n %502:9950&::"FORCE" Č502:2,0;"The unit of force is defined in terms of the acceleration"'"produced when a force acts on a unit of mass." 5200:5,0;1;" " N502:8,0;"The unit of force is the newton.":100d q11 ,0;"It was named in honour of the"'"great 17th Century physicist"'"Sir Isaac Newton.":200 16,0;" One newton (1N) is the force needed to accelerate a mass of one kilogram by one metre per second. " 2100d:9950&::502:"GRAVITY" f502:3,0;"What is gravity?":100d:5,2;"Gravity is a force."  2502:8,0;"What sort of force?" U502:12 ,0;"Gravity is the"'"force which keeps"'"us on the earth." 100d:152,68D:87W,0,-/2:8,24;"o":195,104h:0,-8:191,88X:4,8:4,-8:191,102f:1:9 ,0:0 (E502:16,0;"Gravity pulls us towards"'"the earth." 2&502:12 ,24;"" :39',0:0,-10 :15,0:-35#,-20:-35#,20:15,0:0,10 d~100d:19,0;"But there are instruments"'"sensitive enough to measure thisattraction.":502:9950& ni:"GRAVITY":502:2,8;"Newton's Law of";3,5;"Universal Gravitation" x502:5,0;"Two bodies attract each other with a force proportional to theproduct of their masses, and inversely proportional to the square of their distance apart. " 200:64@,63?,20:502:168,63?,24:502:12 ,7;"M1";12 ,20;"M2":502:64@,63?:103g,0:502:13 ,14;"d" s502:19,5;"F varies with M1 x M2";19,19;1;"_______";20,22;"d" '502:9950&::"GRAVITY" 502:2,0;"Gravity holds the moon in its"'"orbit around the earth, and the earth in its orbit around the"'"sun." _200:8,0;"A body moving in a circle is"'"changing direction all the time." H100d:12 ,0;"Newton's First Law of Motion:":502 14,0;"A body continues in its state ofrest or uniform motion in a straight line, unless acted on by some external force. " C200:20,0;"Therefore...":502:9950& :"GRAVITY":502 ܐ2,0;"...if the earth is constantly"'"changing direction, a force mustbe acting on it in the directionof the centre of its orbit." =200:176,480:0,71G,/2.5 _502:11 ,23;"";8,23;"^":502:11 ,20;"" 502:17,0;"This force, which is called a"'"centripetal force, is of course supplied by the gravitational"'"pull of the sun." /502:2;80P,84T,24 0502:9950&::502:"WEIGHT" [502:1,28;"":502:216,15:23,0:502 "o3,0;"One newton will accelerate"'"a mass of one kilogram by"'"one metre per second.":150 ,8,0;"A mass of one kilogram"'"falling freely to the"'"ground through a vacuum"'"(to eliminate air"'"resistance) will accel-"'"erate by about 9.8 m/sec"'"under the effect of"'"gravity." 6W300,:n=119:n,28;"";n-1,28;" ":20-n:n @502:18,0;"The force of gravity on a"'"mass of 1 kg is therefore"'"approximately 9.8 N.":150:21,28;"" J;502:9950&:w$="03001825":9960&:502 T^2,0;"The kilogram will press down on the earth's surface with a forceof 9.8 N." h_200:6,0;"Therefore the weight of one"'"kilogram is 9.8 N.":200 r{10 ,0;"The weight of a body will vary slightly depending on where it is on the earth's surface.":300, |@14,0;"There are two reasons for this:":100d R16,2;"1 The earth is not a perfect";17,4;"sphere." 9100d:19,2;"2 The earth rotates." q502:9950&::"WEIGHT":502:2,0;"1 The earth is not a perfect"'" sphere." V502:176,112p:63?,0,-3:-63?,0,-3 _502:6,0;"The poles are nearer"'"the earth's centre"'"than the equator is." 200:10 ,0;"The gravitational"'"force between two"'"bodies varies inversely"'"with the square of the distance"'"between them (ie between their"'"centres)." ~300,:17,0;"Therefore a unit of mass will"'"weigh more at one of the poles"'"than it will at the equator." &502:9950&::"WEIGHT" J502:2,0;"2 The earth rotates about its"'" axis." V502:176,112p:63?,0,-3:-63?,0,-3 2502:208,146:0,-70F f502:6,0;"So a body on the"'"surface of the earth"'"will be moving in a"'"circle." 200:'"Part of the earth's"'"gravitational force"'"provides a centripetal force"'"which keeps the body moving in acircle - just like the earth"'"around the sun." m300,:'"The remaining gravitational"'"force pulls the body towards theearth, and provides its weight." M100d:9950&:w$="06000619":9960&:w$="13000731":9960& W502:6,0;"The size of the"'"circle depends on"'"where the body is." &m200:'"Since the earth's"'"axis passes North"'"to South, there is no"'"circular motion at the poles." 0\300,:'"At the poles the entire gravita-tional force provides the weightof the body." :p300,:'"However the variation in weight between poles and equator (from both causes) is only about 0.5%." D2502:9950&::502:"FRICTION" Nk502:'"Friction is a force which"'"opposes the sliding motion of"'"one surface relative to another." XA300,:'"A simple experiment can show its"'"main features." b_200:'"Attach a spring balance to a"'"block of wood, and stand the"'"block on a table." lh200:80P,20:0,27:557,0:0,-27:-557,0 v:502:136,34":15,0:502 *2;17,20;" " &2;18,20;"" 17,19;"" 215,33!,6 /502:64@,19:95_,0 1502:9950&:w$="02000931":9960& =502:2,0;"Gradually pull on the balance." $100d:17,28;"" j502:4,0;"This will apply a gradually"'"increasing horizontal force (P) to the block." #100d:17,30;"P" 100d:8,0;"At first the block will not movesince an equal and opposite"'"frictional force F will act at"'"the undersurface of the block." %300,:19,6;"F" ;502:9950&:w$="02000931":9960&:502 _2,0;"As long as the block stays"'"static, F will increase as P"'"increases."  W200:'"P (and therefore F) can be read from the value on the spring"'"balance." S300,:'"We can say that F and P are in"'"equilibrium.":502:9950&  %w$="02000930":9960&:502 *2,0;"Sooner or later the block will"'"start to slip. The friction"'"between the two surfaces has"'"just reached its maximum." 4D300,:'"This maximum value is called thestatic friction." >1502:9950&:w$="02000631":9960& Ht502:2,0;"If the block is pulled along at a steady speed, the balance willshow a lower reading." RB300,:'"This is sliding or kinetic"'"friction." \u200:''"Both static and sliding/kinetic friction act in a direction"'"parallel to the surfaces in"'"contact." f2100d:9950&:w$="02001131":9960& pX502:2,0;"Repeat the experiment with"'"weights on top of the block." zR200:14,11 ;"   ";15,11 ;"   " 502:5,0;"This will increase the force R"'"which is the reaction of the"'"table to the weight of the block(+ weights), W." 300,:108l,40(:-3,-3:6,0:-3,3:0,-30:-3,3:6,0:-3,-3 9502:17,14;"R";20,14;"W" x502:10 ,0;"R is the force which is pressingthe surfaces together, and is"'"equal and opposite to W." 2200:9950&:w$="02001031":9960& 502:2,0;"You will find that both static"'"and kinetic friction will"'"increase roughly in proportion"'"to R." 2100d:9950&:w$="02000329":9960& x502:2,1;"If F = force of friction,"''"and R = force pressing surfaces";5,8;"together," q200:'"then the coefficient of friction"''" = F";9 ,8;1;"_";10 ,8;"R" :200:9 ,15;"Since F (kinetic)";10 ,15;"is slightly less";11 ,15;"than F (static),";12 ,15;"so (kinetic) is";13 ,21;"less than";14,21;" (static)." )100d:9950&::"FRICTION" C502:'"These coefficients are only"'"approximate constants." i200:'"They will vary especially if thesliding motion is fast, or the contact pressure is high." 300,:'"The main function of lubricants (grease, oil, graphite etc) is to reduce the coefficients of"'"friction between surfaces." 100d:9950& :502:3,0;"Press:";5,6;"1 to repeat this program";7,6;"2 to load the next program";9 ,6;"3 to stop" +n=10 :17,3;"think" $.n:t$="tank":18,3;5;t$ )Mn:23,44,:0,-21:41),0:0,21 3(n:23,40(:41),0 8fm=63-1:n/502,24+2*m:5;18,m;"";t$(m-2):m B'2*n:18,3;"t" L]m=36:n/502,21+3*m:5;18,m;t$(m-2);"":m V'2*n:18,6;"k" t="1"20 ~ ="3" B="2":502:8,8;"START THE TAPE":""  36408 & &ԧ2:60<,99c:40(,0:0,5:8,-12 :-8,-12 :0,5:-40(,0:0,13 :0: &""press ENTER to continue ";q$: &vi=w$(2):j=w$(34):k=w$(56):l=w$(7):z=ii+k:m=jj+l:z,m;" ":m:z: &O60<,126~,255,255,255,255,126~,60< &J96`,144,16,96`,128,240,0,0 &L126~,98b,94^,82R,90Z,227,126~,60< &E3,7,15,31,31,15,7,3 &Q192,224,240,248,248,240,224,192 &I0,0,255,255,255,255,0,0 &G0,36$,36$,524,42*,32 ,64@,0 'K0,480,122z,188,252,122z,480,0 'G0,12 ,94^,61=,63?,94^,12 ,0  b3 }<}:1;n+1,5;"";0;n,5;" " 3n:.08}# =,40(:2:.2~L,36$ G502:14,0;"The coin should fall into the"'"bottle." d100d:'"(Friction between the card and the coin is too short-lived to displace the coin.)" 502:9950&::n$ N502:'"A body in a state of uniform"'"motion in a straight line: " 100d:''"An object moving":502:8,5;"* unimpeded;":502:10 ,5;"* at a uniform velocity;":502:12 ,5;"* in a constant direction;"  q502:14,0;"will carry on forever.":100d:14,14;1;1;"forever" r502:16,14;"?":502:16,17;"?":502:16,20;"?" ,502:14,14;"forever" (7502:19,0;"This is not so obvious!" 2502:9950&::n$ <=502:'"Push a trolley along the floor and let it go." F0100d:0,94^:255,0 PK502:n=020:8,n;"  ";9 ,n;"  " Z'(n+1)/502,-(n+14):n d:502:5,0;"It will slow down and stop." n\100d:11 ,0;"But this is because there are"'"forces working against it:" x100d:14,0;"* friction between the wheels";15,2;"and the floor, and between the";16,2;"axles and their bearings;" #200:9 ,19;"" 1502:18,0;"* air resistance." "502:8,24;"" \502:20,0;"Remove all these forces, and thetrolley would go on forever." 100d:9950&::n$ x502:0,94^:192,0:0,32 :15,0:0,-32 :47/,0 C502:8,0;"  ";9 ,0;"  " R502:2,0;"Put an object on the trolley to represent a driver," !150:7,1;"" Q502:3,20;"and push thetrolley hard against an obstruc-tion." [502:n=020:7,n;" ";8,n;"  ";9 ,n;"  " +.5+n/10 :n:.1}L,28 !7,21;" ":3 ,7,22;" ":.06|u\,16 #7,22;" ":3.2L #7,21;" ":3.3S333 "#7,20;" ":3.5` ,#7,19;" ":3.7l 698,18;" ";7,19;" ":3.9y @D9 ,17;" ";8,18;" ":.084},1&,-32 J,9 ,16;" ":.4L,-32 T502:11 ,0;"An external force (the obstruc- tion) stops the trolley and the driver, but not simultaneously." ^200:'"The driver obeys Newton's first law and continues in motion -"'"until opposing forces bring him to a standstill." h@300,:'"This is why a seat belt can savea driver's life." r502:9950&::n$ |7502:''"This tendency for a body to stayeither": 100d:6,7;"* at rest;":502:8,4;"or * in uniform motion";9 ,9 ;"in a straight line;" 7100d:12 ,0;"is called inertia." 502:9950&::502:n$="NEWTON'S SECOND LAW of MOTION":n$:502:0,9 ;"SECOND":1700:1770 7502:w$="02000129":1:1:9960& D502:2,0;"When a body is acted on by a"'"force," &100d:w$="04000229":9960& C502:5,0;"the rate of change of its"'"momentum" &100d:w$="07000529":9960& Y502:8,5;"* is proportional to the";9 ,7;"applied force;" l100d:11 ,1;"and * takes place in the same";12 ,7;"direction as the force.": 150:0:6,0;1;"momentum":502:0:15,0;"What is momentum?":502:9950& a:n$:502:''"A body's momentum is, quite"'"simply, its mass multiplied by its velocity:" -200:7,4;"momentum = mv" Q502:''"Momentum is also sometimes"'"described as quantity of motion." 502:9950&::n$ j502:'"A trolley loaded with weights"'"will need a larger force to get it going than an empty one." &>200:8,3;" ";9 ,3;" " 0X502:n=76-1:m=35:n,m;n-m;" ":30:m:n ::n=86-1:502:n,1;"":n D502:n=016:6,n;"    ";7,n;"    ";8,n;"  ";9 ,n+2;" ":(17-n)/502,n-36$:n N502:12 ,0;"Similarly a heavy vehicle needs a greater force to slow it down or stop it than a lighter"'"vehicle travelling at the same speed." X@300,:'"A train needs more powerful"'"brakes than a car." b502:9950&::n$ l502:''"A heavy body has a greater"'"quantity of motion or momentum than a lighter body moving at"'"the same velocity." v250:'"If an equal force is applied to two bodies of different mass forequal lengths of time, the"'"lighter body will build up a"'"higher velocity than the heavierone." 7350^:'"But each will gain the same"'"momentum." >100d:''"Which brings us back to Newton'ssecond law..." 502:9950&::n$ 1700:0:0 502:9950&::n$ >502:'"A force F acts for a time t on abody of mass m." F200:'"Its velocity increases (or dec-"'"reases) from u to v." J200:'"Its momentum will change in timet uniformly from mu to mv." И250:'" the rate of change of momentum":100d:13 ,10 ;"= mv-mu";13 ,12 ;1;"_____";14,14;"t" M200:'"By Newton's second law, this"'"varies with the force applied:" e200:19,8;"F mv-mu";19,12 ;1;"_____";20,14;"t" 502:9950&::n$ W2,8;"F mv-mu";2,12 ;1;"_____";3,14;"t" f100d:5,6;" F m(v-u)";5,12 ;1;"______";6,14;"t"  300,:'"But (v-u) = change in velocity";8,4;1;"_____":96`,104h:143,0:9 ,6;"t";9 ,18;"time" 4300,:11 ,10 ;"= acceleration (a)"  150:13 ,6;" F ma":250:15,6;" F = kma (where k is";16,19;"a constant)." *502:9950&::n$ 4&502:2,8;"F = kma" >C100d:'"An absolute unit of force can"'"now be defined:" H+200:7,5;"If m = 1 kg" R1100d:8,4;"and a = 1 m/sec," \7150:'"then our unit should be defined so that" fW200:12 ,8;"F = 1 unit":100d:13 ,3;"when k = 1." p4150:'"This unit is the newton (N)." zH150:'"One newton will accelerate a"'"mass of 1 kg by 1 m/sec." A200:w$="17000431":1:6:1:9960& I100d:20,6;" F = ma";:100d:" (because k = 1)" 10:7:0:502:9950& c:502:n$="NEWTON'S THIRD LAW of MOTION":n$:502:0,9 ;"THIRD" .502:w$="02000231":1:9960& o502:2,0;"When a force acts on a body, an equal and opposite force acts onsome other body." :0:300,:''"This is sometimes summarised as:" /100d:w$="09000131":1:9960& Y502:9 ,0;"To every action there is an"'"equal and opposite reaction." v250:0:''"But it is important to remember that the action and the reactionoperate on different bodies." p300,:15,11 ;1;" ":100d:4,5;1;" " 502:9950&::n$ t502:'"Right now your Sinclair Spectrumis probably standing on a table or a desktop.":2310 :2340$ :300,:0,79O:255,0:502 Y10 ,4;"";:n=19 :"";:n:"" ?11 ,4;" ";:n=122:" ";:n: $g502:125},80P:0,-24:-4,4:8,0:-4,-4 .J502:13 ,2;"Weight of";14,2;"the Spectrum" 8n100d:13 ,19;"acting on";14,19;"the table":2370B :2400` By100d:1;123{,79O:1;0,39':-4,-4:8,0:-4,4 LG502:7,2;"Reaction of";8,2;"the table" V\100d:7,18;"acting on ";8,18;"the Spectrum": `502:9950&::n$ jy502:'"Action and reaction forces must not be confused with forces in equilibrium - which act on the same body." t 2310 ~y502:1:125},85U:0,-28:0:-4,4:8,0:-4,-4 D502:13 ,2;"Force of";14,2;"gravity" \100d:13 ,18;"acting on ";14,18;"the Spectrum" 2370B 502:17,0;"It is of course the acceleratingforce of gravity which acts on the Spectrum's mass, and causes its weight." 300,:9950& x:502:3,0;"Press:";5,6;"1 to repeat this program";7,6;"2 to stop" +n=10 :17,3;"think" $.n:t$="tank":18,3;5;t$ )Mn:23,44,:0,-21:41),0:0,21 3(n:23,40(:41),0 8fm=63-1:n/502,24+2*m:5;18,m;"";t$(m-2):m B'2*n:18,3;"t" L]m=36:n/502,21+3*m:5;18,m;t$(m-2);"":m V'2*n:18,6;"k" t="1"20 ~ ="2"  36408 #(O60<,126~,255,255,255,255,126~,60< #2K12 ,24,480,127,127,480,24,12 #