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4 w$="15000631":
3 s$;" (";p$;")/";t$:
3 STOP THE TAPE!
3 ;"Software"
3 ;"Press:";
3 ;"Press any key to continue":
3 ;"MA (Cantab.), MA (London)"
3 ;"Educational"
3 ;"CP Lawrence";
3 "press ENTER to continue ";
3 to repeat this program";
3
2 w$="02000931":
2 quantity of motion
2 acting on
2 START THE TAPE
2 ;t$;", t":
2 ;"What is gravity?":
2 ;"Gravity is a
2 "s"+n,usr:
2 "r"+n,usr:
2 "m"+n,usr:
2 "l"+n,usr:
2 "g"+n,usr:
2 "f"+n,usr:
2 "b"+n,usr:
2 to load the next program";
1 w$="17000431":
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1 w$="15000630":
1 w$="15000531":
1 w$="15000331":
1 w$="15000231":
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1 w$="14000630":
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1 w$="09000131":
1 w$="07000529":
1 w$="06110511":
1 w$="06000619":
1 w$="05060317":
1 w$="04000229":
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1 w$="03150101":
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1 w$="02001131":
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1 w$="02000631":
1 w$="02000329":
1 w$="02000231":
1 w$="02000130":
1 w$="02000129":
1 v$="Velocity":
1 v$;"/";t$:
1 unit of mass
1 uniform motion
1 static friction
1 state of rest
1 s$="Distance":
1 rate of change of momentum
1 principia mathematica.
1 p$="Displacement":
1 of natural philosophy.
1 in a straight line
1 g$="against":
1 frictional
1 centripetal force
1 centripetal
1 b3 }<
1 b2
1 b1
1 absolute unit of force
1 a$="Acceleration":
1 Two bodies attract each other with a force proportional to theproduct of their masses, and inversely proportional to the square of their distance apart.
1 The mathematical principles
1 Philosophiae naturalis
1 NEWTON'S THIRD LAW of MOTION
1 NEWTON'S SECOND LAW of MOTION
1 NEWTON'S LAWS of MOTION
1 NEWTON'S FIRST LAW of MOTION
1 GRAVITY, WEIGHT and FRICTION
1 GRAPHS of MOTION
1 DisplacementV
1 Created with Ramsoft MakeTZX
1 AccelerationS
1 A body in a state of uniform"'"motion in a straight line:
1 A body in a state of rest:
1 A body continues in its state ofrest or uniform motion in a straight line, unless acted on by some external force.
1 A body continues in its state ofrest or of uniform motion in a straight line unless compelled to do otherwise by some externalforce.
1 ;v$;" will travel equal"'s$;"s in equal intervals of"'t$;" (in a constant direction)."
1 ;v$;" = ";p$;" =
1 ;v$;" ";g$;" ";t$
1 ;s$;" (";p$;")";
1 ;s$;" (";p$;") is"'"therefore represented by the"'"area between the ";v$;"/";t$'"curve and the ";t$;" axis."
1 ;g$;" ";t$;
1 ;a$;" is"'"equal to the gradient of a"'"tangent to the curve at
1 ;a$;" = BC
1 ;"zontal movement."
1 ;"with a quick, hori-";
1 ;"will carry on forever.":
1 ;"when k = 1."
1 ;"together,"
1 ;"the table"
1 ;"the rate of change of its"'"momentum"
1 ;"the Spectrum"
1 ;"than F (static),";
1 ;"sphere."
1 ;"s = (AB + CD) x
1 ;"over the mouth."
1 ;"or stop it"'"moving altogether."
1 ;"or * in uniform motion";
1 ;"on the card directly";
1 ;"mouth of a bottle,";
1 ;"momentum":
1 ;"momentum = mv"
1 ;"ment, s";
1 ;"less than";
1 ;"is slightly less";
1 ;"is called
1 ;"in a straight line;"
1 ;"imagine a triangle"'"whose hypotenuse is small enough"'"to coincide with the curve."
1 ;"gravity"
1 ;"gradient"
1 ;"forever"
1 ;"direction as the force.":
1 ;"axles and their bearings;"
1 ;"applied force;"
1 ;"and then place a coin";
1 ;"and the floor, and between the";
1 ;"and push thetrolley hard against an obstruc-tion."
1 ;"and a = 1 m/sec
1 ;"and * takes place in the same";
1 ;"a constant)."
1 ;"____________
1 ;"_______";
1 ;"______";
1 ;"You will find that both static"'"and kinetic friction will"'"increase roughly in proportion"'"to R."
1 ;"When he reaches the shop he buys"'"the paper. This takes a ";t$'"interval of
1 ;"When a force acts on a body, an equal and opposite force acts onsome other body."
1 ;"When a body is acted on by a"'"force,"
1 ;"What sort of force?"
1 ;"What is momentum?":
1 ;"What is a force?":
1 ;"Weight of";
1 ;"We do not notice that, for"'"example, two billiard balls"'"attract each other, because the force is tiny compared to the"'"earth's gravitational force."
1 ;"We cannot really say what a"'"force is, but only what it can"'"do."
1 ;"Universal Gravitation"
1 ;"Translated from latin, the titlemeans:"
1 ;"To find the ";v$;" at any"'"instant
1 ;"To every action there is an"'"equal and opposite reaction."
1 ;"This will increase the force R"'"which is the reaction of the"'"table to the weight of the block(+ weights), W."
1 ;"This will apply a gradually"'"increasing horizontal force (P) to the block."
1 ;"This is not so obvious!"
1 ;"This force, which is called a"'"
1 ;"This applies whatever the shape"'"of the curve."
1 ;"Therefore...":
1 ;"Therefore the
1 ;"Therefore a unit of mass will"'"weigh more at one of the poles"'"than it will at the equator."
1 ;"There are two reasons for this:":
1 ;"Then it will fall back to where"'"it started, accelerating this"'"time under the effect of"'"gravity."
1 ;"Then he walks home again (
1 ;"The weight of a body will vary slightly depending on where it is on the earth's surface.":
1 ;"The unit of force is the
1 ;"The unit of force is defined in terms of the acceleration"'"produced when a force acts on a
1 ;"The size of the"'"circle depends on"'"where the body is."
1 ;"The poles are nearer"'"the earth's centre"'"than the equator is."
1 ;"The kilogram will press down on the earth's surface with a forceof 9.8 N."
1 ;"The gravitational"'"force between two"'"bodies varies inversely"'"with the square of the distance"'"between them (ie between their"'"centres)."
1 ;"The force of gravity on a"'"mass of 1 kg is therefore"'"approximately 9.8 N.":
1 ;"The coin should fall into the"'"bottle."
1 ;"Take any point on the graph and"'"drop a perpendicular to the ";t$'"axis."
1 ;"Sooner or later the block will"'"start to slip. The friction"'"between the two surfaces has"'"just reached its maximum."
1 ;"So force can be defined as"'"whatever changes a body's":
1 ;"So a body on the"'"surface of the earth"'"will be moving in a"'"circle."
1 ;"Sir Isaac Newton discovered thatgravity, or gravitational force,exists between all bodies."
1 ;"Since F (kinetic)";
1 ;"Since ";a$;" is the rate"'"of change of ";v$;" with ";t$;","
1 ;"Similarly a heavy vehicle needs a greater force to slow it down or stop it than a lighter"'"vehicle travelling at the same speed."
1 ;"Repeat the experiment with"'"weights on top of the block."
1 ;"Remove all these forces, and thetrolley would go on forever."
1 ;"Reaction of";
1 ;"R is the force which is pressingthe surfaces together, and is"'"equal and opposite to W."
1 ;"Put an object on the trolley to represent a driver,"
1 ;"Put a card over the";
1 ;"One newton will accelerate"'"a mass of one kilogram by"'"one metre per second
1 ;"On the way up it will decelerateat a uniform rate under the"'"effect of gravity."
1 ;"Now think of a ball thrown up inthe air.":
1 ;"Now consider a body moving with"'"uniform ";a$;".":
1 ;"Now consider a body moving at"'"variable ";v$;".":
1 ;"Newton's Law of";
1 ;"Newton's First Law of Motion:":
1 ;"It will slow down and stop."
1 ;"It was named in honour of the"'"great 17th Century physicist"'"Sir Isaac Newton.":
1 ;"It is of course the acceleratingforce of gravity which acts on the Spectrum's mass, and causes its weight."
1 ;"Imagine the graph is of a man"'"going to buy a paper.":
1 ;"Imagine a car travelling at a"'"uniform ";v$;" v for a ";t$;" t."
1 ;"If the block is pulled along at a steady speed, the balance willshow a lower reading."
1 ;"If m = 1 kg"
1 ;"If F = force of friction,"''"and R = force pressing surfaces";
1 ;"He is now going in the opposite"'"direction. His ";p$;" and"'"his ";v$;" are both negative."'"(Remember they are Vectors.)"
1 ;"He is (more or less) standing"'"still, so his ";v$;" is zero."'"(The gradient of
1 ;"Gravity pulls us towards"'"the earth."
1 ;"Gravity is the"'"force which keeps"'"us on the earth."
1 ;"Gravity holds the moon in its"'"orbit around the earth, and the earth in its orbit around the"'"sun."
1 ;"Gradually pull on the balance."
1 ;"Force of";
1 ;"For a split second it will reach"'"a standstill.":
1 ;"Flick the card away";
1 ;"Finally, consider a body moving"'"with variable ";a$;".":
1 ;"F varies with M1 x M2";
1 ;"F = kma"
1 ;"F = 1 unit":
1 ;"During ";t$;"
1 ;"Displace-";
1 ;"But this is the same as finding"'"the gradient of a tangent to the"'"curve at point
1 ;"But this is because there are"'"forces working against it:"
1 ;"But there are instruments"'"sensitive enough to measure thisattraction.":
1 ;"But that is not all...":
1 ;"At first the block will not movesince an equal and opposite"'"
1 ;"At any point
1 ;"As long as the block stays"'"
1 ;"An external force (the obstruc- tion) stops the trolley and the driver, but not simultaneously."
1 ;"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
1 ;"A force therefore causes a body to accelerate."
1 ;"A force acting on a static body"'"could make the body move."
1 ;"A force acting on a moving body"'"could make the body change"'"
1 ;"A body moving in a circle is"'"changing direction all the time."
1 ;"A body moving at uniform";
1 ;"= the gradient of AB.":
1 ;"= mv-mu";
1 ;"= gradient of
1 ;"= acceleration (a)"
1 ;"= Area of
1 ;"...if the earth is constantly"'"changing direction, a force mustbe acting on it in the directionof the centre of its orbit."
1 ;"* unimpeded;":
1 ;"* is proportional to the";
1 ;"* in a constant direction;"
1 ;"* friction between the wheels";
1 ;"* at rest;":
1 ;"* at a uniform velocity;":
1 ;"* air resistance."
1 ;"(";s$;"), s = vt"
1 ;" ";
1 ;" "
1 . So we can draw"'"a bigger triangle."
1 .
1 ,"'"in ";t$;" interval
1 , as it is usually known, was written in 1687."
1 , F will increase as P"'"increases."
1 , ";p$;" s"'"is equal to the area of the"'"trapezium
1 ''"Which brings us back to Newton'ssecond law..."
1 ''"We will now look at graphs in"'"more detail, to see what can be"'"discovered from them."
1 ''"We will look at graphs of:":
1 ''"This tendency for a body to stayeither":
1 ''"This is sometimes summarised as:"
1 ''"Static objects do not suddenly start moving of their own"'"accord."
1 ''"Momentum is also sometimes"'"described as
1 ''"But it is important to remember that the action and the reactionoperate on different bodies."
1 ''"Both static and sliding/kinetic friction act in a direction"'"parallel to the surfaces in"'"contact."
1 ''"An old trick demonstrates this quite neatly..."
1 ''"An object moving":
1 ''"A heavy body has a greater"'"
1 ''"A body's momentum is, quite"'"simply, its mass multiplied by its velocity:"
1 '"then the coefficient of friction"''"
1 '"then our unit should be defined so that"
1 '"We will assume he walks at a"'"uniform ";v$;" from his house"'"to the shop, a ";s$;" of
1 '"We can say that F and P are in"'"equilibrium.":
1 '"This unit is the
1 '"This maximum value is called the
1 '"This is why a seat belt can savea driver's life."
1 '"This is
1 '"They will vary especially if thesliding motion is fast, or the contact pressure is high."
1 '"These coefficients are only"'"approximate constants."
1 '"The remaining gravitational"'"force pulls the body towards theearth, and provides its weight."
1 '"The main function of lubricants (grease, oil, graphite etc) is to reduce the coefficients of"'"friction between surfaces."
1 '"The driver obeys Newton's first law and continues in motion -"'"until opposing forces bring him to a standstill."
1 '"Since the earth's"'"axis passes North"'"to South, there is no"'"circular motion at the poles."
1 '"Right now your Sinclair Spectrumis probably standing on a table or a desktop.":
1 '"Push a trolley along the floor and let it go."
1 '"Part of the earth's"'"gravitational force"'"provides a
1 '"P (and therefore F) can be read from the value on the spring"'"balance."
1 '"One newton will accelerate a"'"mass of 1 kg by 1 m/sec
1 '"Newton's three laws of motion"'"are found in the first part of"'"his book:"
1 '"Its velocity increases (or dec-"'"reases) from u to v."
1 '"Its momentum will change in timet uniformly from mu to mv."
1 '"It is one of the most important scientific works ever written."
1 '"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."
1 '"However the variation in weight between poles and equator (from both causes) is only about 0.5%."
1 '"Friction is a force which"'"opposes the sliding motion of"'"one surface relative to another."
1 '"By Newton's second law, this"'"varies with the force applied:"
1 '"But each will gain the same"'"momentum."
1 '"But (v-u) = change in velocity";
1 '"Attach a spring balance to a"'"block of wood, and stand the"'"block on a table."
1 '"At the poles the entire gravita-tional force provides the weightof the body."
1 '"Action and reaction forces must not be confused with forces in equilibrium - which act on the same body."
1 '"A trolley loaded with weights"'"will need a larger force to get it going than an empty one."
1 '"A train needs more powerful"'"brakes than a car."
1 '"A simple experiment can show its"'"main features."
1 '"A graph of ";p$;" ";g$'t$;" will be a straight line."
1 '"A force F acts for a time t on abody of mass m."
1 '"(Friction between the card and the coin is too short-lived to displace the coin.)"
1 "t"+n,usr:
1 "n"+n,usr:
1 "k"+n,usr:
1 "i"+n,usr:
1 "a"+n,usr:
1 "We have already used graphs to"'"illustrate moving bodies.":
1 "'"which keeps the body moving in acircle - just like the earth"'"around the sun."
1 "'"under the effect of"'"gravity."
1 " (because k = 1)"
1 of one"'"kilogram is 9.8 N.":
1 is the ";p$;" (";s$'"moved) in ";t$;" interval
1 in ";t$;"
1 force, is of course supplied by the gravitational"'"pull of the sun."
1 force F will act at"'"the undersurface of the block."
1 can"'"now be defined:"
1 The earth rotates."
1 The earth rotates about its"'" axis."
1 The earth is not a perfect";
1 The earth is not a perfect"'" sphere."
1 One newton (1N) is the force needed to accelerate a mass of one kilogram by one metre per second
1 F = ma";:
1 F = kma (where k is";
1 = gradient of
1 (static)."
1 (kinetic) is";
1 than a lighter body moving at"'"the same velocity."