LONGMAN PHYSICS TOPICS General Editor: John L. Lewis

IFORCESIR. D. Harrison B.Sc., A.Inst.P.

Senior Lecturer in PhysicsNewcastle upon Tyne PolytechnicN.E. Co-ordinator for Nujjield O-Level Physics School Trials

Illustrated by T. H. McArthur

LONGMAN

LONGMAN GROUP LTDLondonAssociated companies, branches and representatives throughout the world

© Longman Group Ltd (formerly Longmans, Green & Co Ltd) 1968

All rights reserved. No part of this publication may be reproduced, stored in aretrieval system or transmitted in any form or by any means - electronic.mechanical. photocopying. recording or otherwise - without the prior permissionof the copyright owner

First published 1968Reprinted with corrections 1970SBN 582 32174 3

Printed in Great Britain by Butler & Tanner Ltd. London and Frome

IACKNOWLEDGEMENTS IThe author and publisher are grateful to the following forpermission to use photographs: frontispiece R. W. Evans;figures 5 Dr H. E. Edgerton, Massachusetts Institute ofTechnology; 6 Philip Harris Ltd; 7 Wakeman FarranceEngineering Ltd, photograph by Cecil H. Greville Ltd;9 Societe Encyclopedique Universelle ; 10 Mount Wilsonand Palomar Observatories; 14Barnaby's Picture Library,photograph by F. J. Armes; 20 Fogg & Young Engineer­ing Ltd, photograph by E. John Wells Ltd; 27 ShellPhotographic Unit; 28 Barnaby's Picture Library; 29bCentral Electricity Generating Board; 30 M-O Valve CoLtd; 31 Crown Copyright, Science Museum, London; 32Radio Times Hulton Picture Library; 36 General ElectricCo Ltd, photograph by Lewis & Randall Ltd; 38 Educa­tional Services Inc (still from the film The Pressure ofLight); 39 Royal Greenwich Observatory; 40 SamuelDenison & Son Ltd; 41 Camera Press, photograph byA. G. Hutchinson; 43 Barnaby's Picture Library, photo­graph by A. L. Hunter; 44 Cement and Concrete Associa­tion, photograph by Leonard G. Alsford; 45 KeystonePress Agency. Photographs for figures 13, 18, 19, 26,27and 35 were taken by J. Cummins. Figure 34 isreproducedfrom William Gilbert, De Magnete, Dover Publications,Inc, New York, 1940, by permission of the publisher.Cover photographs by courtesy of Keystone Press Agency(front) and NASA (back).

NOTETO THETEACHER

This book is one in a series of physics background booksintended primarily for use with the Nuffield O-Level PhysicsProject. The team of writers who have contributed to the serieswere all associated with that project. It was always intendedthat the Nuffield teachers' materials should be accompaniedby background books for pupils to read, and a number of suchbooks is being produced under the Foundation's auspices.This series is intended as a supplement to the Nuffield pupils'materials: not books giving the answers to all the investigationspupils will be doing in the laboratory, certainly not textbooksin the conventional sense, but books that are easy to read andcopiously illustrated, and which show how the principlesstudied in school are applied in the outside world.

The books are such that they can be used with a conven­tional as well as a modern physics programme. Whatevercourse pupils are following, they often need straightforwardbooks to help clarify their knowledge, and sometimes to helpthem catch up on any topic they have missed in their schoolcourse. It is hoped that this series will meet that need.

This background series will provide suitable material forreading in homework. This volume is divided into sections,and the teacher may feel that one section at a time is suitablefor each homework session for which he wishes to use thebook.

This particular book is written as a background book for theForces section of Years I and, more particularly, II. It is hopedthat the examples given, which range rather beyond the Nuffieldcourse, will help pupils to appreciate the importance of forcesin everyday life and begin to explain how they come about,thus laying the foundation for more formal studies later. Atthe same time, some attention is paid to the role of forces intechnology and engineering. This is essentially a book forpupils to browse in, taking up points which catch their interestand possibly pursuing them further.

INTRODUCINGTHIS BOOK

There are many different ways of looking at the thingsaround us. Some people are impressed by their beauty orugliness. Other people, looking at the same things, willwonder how they were made or what their history hasbeen. I sometimes find it fun to think about all the forcesthat are involved. I hope you will find this fun too.

ICONTENTSWhat is a force?Elastic forcesGravitational forcesImpact forces and pressureCohesive forcesElectric and magnetic forcesMuscular forcesForces due to light pressureSummary and conclusions

69

12182432363840

WHAT ISA FORCE?

6

If a stone lying in the middle of a level path suddenlystarted to move, would you be surprised? Probably youwould, unless you believe in magic. Most people, if theyobserved such a thing happening, would look for a cause.

The scientific name for a cause of motion is force. Aforce is anything which can cause a body to start movingwhen it is at rest, or stop it when it is moving, or deflect itonce it is moving. This is basically how a force is defined,although you will learn a more precise definition later.

The only sure test for a force is to ask oneself, 'Can itmake a body start or stop moving?' That is how we recog­nise the existence of forces. Once it is started, the bodycan keep going by itself without the help of any force, butanother force is needed to stop it.

You may be surprised to learn that a body could go onmoving for ever without any force acting upon it. Mostthings obviously come to rest rather quickly. This is be­cause they are acted upon by aforce offriction which slowsthem down. If the friction is small, for example when astone slides over smooth ice, then the body will go further.We find that the smaller the friction, the further the bodywill go. If we try to imagine what would happen if therewere no friction at all, we can see that the body wouldprobably go on and on for ever without stopping (unlessit bumped into something). We can never test this conclu­sion exactly, since there is always some friction. Neverthe­less, we have every reason to suppose it is true. The Earth,for instance, has gone on revolving round the Sun for hun­dreds of millions of years because there are almost noforces to slow it down.

A force cannot exist by itself - it can only be exerted byone body on another. The Earth pulls you and me andapples and stones towards itself. You can push a pram andmake it start moving. A magnet can attract a piece of irontoward itself. The wind can whisk a leaf into the air.

Something to think about1. When an arrow is shot into the air, what force makes it start?2. Once it is going, what forces are acting upon it?3. If the ground or the target did not get in the way, would it go on movingat the same speed for ever? If not, why not?4. What makes it stop at the end of its flight?

WHAT IS AFORCE?

5. In which direction do these forces act?We are not going to tell you the answers to these straight away, because weexpect you will have no difficulty in guessing them. But you will find clueslater on, which will help you to decide whether you are right or wrong. Or youcan discuss it with your friends or your teacher.

Something to doThere are many different ways in which one body can exert a force on another.Make a list of as many examples as you can think of and try to invent a namefor the kind of force involved in each case. Looking up books on physics orengineering in the library may suggest some examples you had not thought offor yourself. If you want to be very systematic, make your list with threecolumns:

Body exerting force Body acted upon Type of force

but it does not matter if you decide to be less formal.

EQUILIBRIUM

In everyday life the most familiar forces are those we exertourselves through the action of our own muscles. Throw­ing, kicking and catching a ball, propelling a pellet with apea shooter, lifting food to our mouths. These and manyother similar activities, depend on muscular forces to setthings in motion or to stop them.

But what happens when we stretch a spring or a pieceof elastic? Motion ceases, yet our nerves tell us that weare still exerting a force - often quite a large one. Why dowe get no more starting or stopping?

The answer is probably obvious to you, but in case itis not, think what happens when you tie your shoe. Youare pulling on each lace and thus exerting a force on yourfoot, yet your foot does not begin to move.

Of course you are exerting several forces on your foot ­one in each lace, and one from your leg - and they cancelout. The total force is zero.

When we add up forces in this way to get zero, we haveto take into account not only the size of the forces, butalso the directions in which they act. A body tries to startmoving in the direction of the force. If two equal forcesact in opposite directions they just balance and produceno motion. Things like forces, which have direction aswell as strength, are called vectors. You will learn moreabout them in your mathematics course.

7

WHAT IS AFORCE?

1 Forces on afiagstafJ. How do the guyropes stop the flagstaff falling over?What happens to the tensions in A. Band C when the wind blows as shown?

2 Forces on a seated person.

A set of forces which just balance and produce nomotion is said to be in equilibrium. The world is liter­ally full of forces in equilibrium. As you sit reading thisbook, the force of gravity pulling you towards the earthis just balanced by the support of the chair on your body.The chair itself is held steady by an upward push of thefloor. A flagstaff is held steady by the pull of its guy ropesand, again, by an upthrust from the ground. The tensionin the strings of a piano is maintained by the counterforces in the piano frame. The pull of all the strings in apiano amounts to several tens of thousands of newtons, sothe frame has to be a very strong one.

We soon lose count of all the different forces aroundus. Luckily we can forget about most of them, since theysimply cancel each other out and produce no motion.

1Wind)

upthrustfrom ground

8

2

Tthrust ofchair upwards

ELASTICFORCES

3 Equal and opposite pulls ofthe springon the left and right just cancel out sothat the bit of spring at A remains atrest.4 A plank bent by a weight.5 A ball struck by a bat.

4

Consider the stretching of a spring. Can you rememberwhat it feels like to pull out a spring or a piece of wire?

At first when we apply a small force using our muscles,there is a slight movement and the spring begins to get abit longer. Very soon this motion stops. We become awareof the tension in the spring. Each part of the spring is inequilibrium with this tension acting in opposite directionson each side of it. If we pull a bit harder the spring movesa little more until the tension again balances each part.The greater the pull, the greater the stretch and thegreater the tension. (We must not let the pull be too greator it will spoil the spring or even break it.) Ifwe let go, thetension sets the parts of the spring in motion again until itgets back to its original length. The tension is a real force,according to our definition that a force is somethingwhich causes motion.

Forces produced by stretching, or bending, or twistinga body, that is, by deforming it, are called elastic forces.Whenever a body is deformed in any way, so that its shapeor size is altered, elastic forces will be brought into playwhich try to restore the original size or shape. Conversely,when a body is subjected to a force it will be deformed.What happens to a football when you kick it? Whathappens to the floor when you stand on it? Luckily thesedeformations are often so small that we can forget aboutthem, but they are always there.

5

9

ELASTICFORCES

10

Something to doSee if you can detect the deformation in a thick plank or bar of metal sup­ported at each end when a weight is put on to the middle. You might find amirror and a beam of light from a torch useful.

Elastic deformation is generally the most convenientmethod available for detecting and measuring forces. Itis also useful for producing forces of known strength. Ifwe want to know how big a force we have acting, wemeasure the amount of stretching or twisting it produces.Is it safe to assume that if we have twice the stretch wehave twice the force without checking to make sure thatthis is so?

Something to doTry to find out if the stretch in a rubber band is proportional to the numberof forces acting on it, so that twice the force gives twice the stretch, and so on.You will need a number of identical forces. How can you arrange this? (Youcan use as many rubber bands as you like and might find a paper clip, a rulerand a pencil and paper useful. Or perhaps you can find a completely differentway of doing it.)

HOOKE'S LAW

Probably you will find that if you double the force youget more or less double the stretch - provided you do notstretch it too far. Nearly all materials behave in this way.If they do they are said to obey Hooke's Law, which isnamed after Robert Hooke, who first studied the stretch­ing of springs about three hundred years ago.

Hooke's Law is a delightfully simple relationship be­tween force and stretch. We could hardly have anythingsimpler. Life is very much easier for engineers and physi­cists when their materials obey this law. But it is not afundamental law of nature. There is no theory to provethat all substances must obey it. It is just an experimentalfact that most substances obey it up to a point. Do youthink plasticine or crepe paper or even ordinary elasticobey Hooke's Law? Perhaps you had better have anotherlook at the stretching of your rubber bands.

In any case, ordinary materials only obey Hooke's Law

ELASTICFORCES

6 A spring balance used for measuringforce in newtons.

7 An Engineer's Proving Ring used formeasuring forces up to 1800 N. Thedial gauge in the middle will measurevery small deformations ofthe ringfroma true circleand these indicate the force.

up to a certain point. If they are stretched too far beyondthe elastic limit an extra force produces more extra stretchthan it should and a little more force still will break thematerial. We must always be very careful not to assumethat Hooke's Law holds when it does not.

Something to doStretch a number of different substances until they break. or bend them if thatis easier. Do they break suddenly, or tear, or give gradually? Do they seem toobey Hooke's Law at all, or is their elastic limit very small? If you have to bendthem, do they break suddenly (that is, are they brittle?) or do you have to keepbending them backwards and forwards until they are fatigued?

When a spring or a piece of metal does obey Hooke'sLaw, we can use it to measure forces. The amount ofstretch or deformation tells us what the force is. A springbalance calibrated in force units is generally the most con­venient method of measuring forces.

6 7

II

GRAVITA­TIONALFORCES

8 A weight of I kg. A cube of waterof side 10 em has a mass of I kg anda weight of 9·8 N or I kg[.

12

WEIGHT

Perhaps the most familiar force of all is that of gravity ­the force which pulls things towards the Earth. It certainlyis a force, because if you let something go, it starts tomove - to fall. But even when a body is not free to fall,it is still acted upon by gravity and a counter-force isneeded to keep it still.

The gravitational force on a body is called its weight.The weight of one kilogramme of material near the

surface of the Earth is about 9·8 newtons, which is alsoknown as a kilogramme force (kgf). We have to be verycareful not to confuse mass (quantity of matter) withweight (gravitational force on that matter). In everydaylife we talk about weighing when we mean measuring themass, which is sometimes very confusing.

WEIGHING FORCES

Another method of measuring forces is to weigh them,that is, to balance them against a known weight.

Something to doSee if you can devise a method of weighing forces to enable you to measure aforce without using a spring balance. You need some weights and a balancebeam or a pulley.

If you like, you could try to use this arrangement to see how stronglyyou can pull in different directions; up, down and horizontally. Besides yourbalance. you will need another pulley (or a smooth rod) fixed to the groundand a piece of clothes line. Bricks in a bucket might make suitable weights.A brick has a mass of about 3·5 kg and weighs 35 N.

Something to think aboutDo you think the weight of a body will be the same everywhere on the Earth'ssurface? Will it be the same if we go up a mountain or down a coal-mine? Onthe Moon? Way out in space? Would your force-weighing apparatus be anyuse in these other places? If not, what other sort of apparatus would you haveto take with you on a space journey to be able to measure forces?

WEIGHTLESSNESS

The force of gravity is the most universal of all forces ofnature and probably the most mysterious. It acts upon useverywhere all the time. No one can ever get away from it.

GRAVITATIONALFORCES

Suppose, however, that you were in a lift falling freelywithout a rope to restrain it. Do you think you would stillfeel the floor of the lift pressing against your feet? Wouldyou feel any gravity at all? Would you have any weight?

When one is falling freely under gravity, one is said tobe in a weightless state. Near the surface of the Earth, suchan experience will come to a sudden and unpleasant endwhen one hits the ground, but astronauts travelling roundthe Earth are often weightless for very long periods.

Something to think aboutWould it be pleasant to be weightless? Could you move around very easily?Would you know where you were, what is up and what is down? Could youmake things stay put? Would it be good for you to be weightless? What doyou think happens to muscles which are not used?

The Earth may be regarded as being in free fall as it travels round the Sun,but it is still possible to detect the Sun's gravitational attraction, for examplein 'Spring' tides. Can you explain why? Which part of the Earth do you thinkis in free fall?

UNIVERSAL GRAVITATION

One of the most mysterious features of gravity is the factthat, unlike the other forces we have considered so far, itacts across space - across a perfectly empty vacuum. Thereis nothing connecting the body attracting and the bodyattracted - nothing between the Earth and the fallingapple. This feature is termed action at a distance and theearly scientists were very puzzled about it. Eventually SirIsaac Newton avoided the problem by pointing out that,even if we do not know how it happens, there is no doubtthat it does and it is more profitable to concentrate on find­ing out as much as we can about how gravity behaves ­that is, to describe the laws of gravitation - than to wonderhow it works. Newton himself found out most of what weknow on the subject and published it in 1687in one of thegreatest books on physics, his Principia. It is only in thepresent century that we have learned a little more aboutit, and even now we do not know how it acts. Gravitationis regarded as one of the fundamental forces of naturewhich cannot be explained in terms of anything simpler.

Perhaps the most surprising of Newton's conclusions13

GRAVITATIONALFORCES

9 Gravitational attraction betweenJupiter and its 'moons' causes them togo round Jupiter just as the Moon goesround the Earth. Jupiter's moons can beseen in a small telescope or binoculars.Why do you think Jupiter itself is flat­tened?

10 The Andromeda Nebula, just visibleto the naked eye on a clear, dark night,is a collection of about JOOOOOOOOOOOstars 2·5 million light years (2·4 XJO" m) from the Earth. The stars whirlaround the centre and the galaxy is heldtogether by gravitational forces. Thereare millions of galaxies in the universe.(Photograph from the Mount Wilsonand Palomar Observatories.)

14

was that all bodies attract each other gravitationally. Itis not only that the Earth attracts small objects on its sur­face. It also attracts the Moon and deflects its path intoa more or less circular orbit around the Earth. The Sunattracts the Earth and deflects its path into a more or lesscircular orbit around the Sun. Also the Moon attracts theEarth and moves the oceans over its surface, causing thetides. Distant stars attract each other so that they clusterin huge galaxies, like the Milky Way. Even insignificantobjects like two apples attract each other, but the forcebetween them is far too small to be detected. Only thetheory tells us it is there.

There is a very famous story that when Newton wastrying to explain why the Moon goes round the Earth,

GRAVITATIONALFORCES

he sat under an apple tree and was hit on the head bya falling apple. Suddenly he realised that the Moon fallsround the Earth under the force of gravity, which stretchesall that way out into space. No one is quite sure whetherthis story is true or not; it is apocryphal.

Nobody quite knows how people get new ideas. Cer­tainly one has to think very hard about a problem for along time before one can solve it. Then very often thesolution comes quite suddenly, when one is thinking ofsomething else. A chance happening, like an apple falling,may provide the vital clue. So even if the story of Newtonand the apple is not true, it could be true. It tells us some­thing about how men think.

,.Nowadays, when physicists need to measure very small twists. they attach a smallmirror to the moving part. The light reflected from this mirrorforms a bright spoton a scale. When the mirror twists slightly, the spot moves along the scale andmagnifies the movement. The modern versionis illustrated in the photographbelow.

When Newton put forward his theory, he was able toaccount for so many different phenomena that nearlyeveryone agreed that it must be correct. Nevertheless,there were doubters who needed to be convinced that itwas true. About fifty years after Newton, Bouguer was ableto show that a small lead weight was attracted by a moun­tain, so that a plumb line on the side of a mountain did notpoint quite to the centre of the Earth.

In 1798 Cavendish performed a celebrated experimentto measure the force between two sets of metal spheres.

As the force is so small, he hung two of his spheres ona very fine wire which could be twisted by a very smallforce. ':' When he brought two heavy lead spheres up tothe sides of the suspended spheres they moved slightly,although the movement was very small and difficult todetect, showing that they were indeed being attractedgravitationally. No one could have any more doubt. Fromthe size of the deflection Cavendish was able to work outthe size of the force between any two bodies, and thisknowledge has enabled astronomers and astro-physicists

TWO IMPORTANT EXPERIMENTS

IIIIIIIII-,IIIIIIIII

1G

'IiIIIIIIII

Chimborazo

II,IIIII: parallel beams of lightV from a distant starIIIIIIIII

elfi\I

11 Bouguer's experiment (1740). Themountain Chimborazo, in SouthAmerica. attracts a plumb-line towardsitself by gravity. Measuring the anglesthat the plumb-line makes to the lightfrom a distant star on each side of themountain shows the existence of thisattraction. The angles in the diagramare very much exaggerated and thecurvature of the Earth has beenneglected. (A similar experiment wascarried out by Maskelyne, the Astro­nomer Royal. in 1774. on Schiehallionin Scotland.)

15

GRAVITATIONALFORCES

12

13

lamp

fine thread

A'

A and A' are large fixedlead spheres.

Band B' are suspendedlead spheres.

The arrows show thedirection of theattraction on Band B'

reflectedlight

position of spotof light showshow far rodhas twisted

12 & 13 Diagram and photograph ofamodern version of Cavendish's experi­ment.

16

GRAVITATIONALFORCES

to measure many properties of the stars and planets, in­cluding the mass of the Earth. Cavendish's experimentwas undoubtedly one of the most important (and diffi­cult) experiments ever carried out in the whole history ofscience.

Bouguer and Cavendish and other physicists were ableto show by direct experiment that Universal Gravitationreally does exist. But even if these experiments had neverbeen carried out we should probably still believe in itbecause it enables us to explain a very large number ofdifferent natural phenomena. Perhaps the greatest triumphof the theory came in 1846. The planet Uranus, which hadbeen found in 1781 by Sir William Herschel, was found tofalter slightly in its journey round the Sun, sometimesgoing a little too fast and sometimes a little too slow. Twomathematicians, Adams and Leverrier, thought this mightbe because it was being attracted by another planetmoving even further from the Sun. They worked outwhere this should be and, sure enough, when the astro­nomers looked in this direction in the sky, they found anew planet, Neptune. No scientific theory can achieve agreater success than this - to predict something com­pletely new.

THE INVERSE SQUARE LAWThe force of gravity depends on the distance betweenthe gravitating bodies, becoming rapidly smaller as theyget further apart. That is one reason why we are moreconscious of the pull of the Earth than that of the Sun,although the Sun is many times bigger than the Earth.

If the distance between two bodies is doubled, the gravi­tational attraction between them is one-quarter, that is

-1, of its previous value. If the distance is trebled, the force22

is only one-ninth, or -1, and so on. A law of this type is32

called an inverse square law. Later on, you will studyseveral other inverse square laws in physics.

The inverse square law is probably a result of the factthat we live in a three-dimensional world, with three dis­tinct directions, for example, North, East and Up.

17

IMPACTFORCESANDPRESSURE

18

COLLISIONS

A moving body colliding with a stationary one can set itin motion, so it must exert a force on it. Such a force maybe termed an impact force.

Something to doTry to find out what happens when two Dinky cars or, better, two trolleysmade of Meccano collide. Let one collide with the other at rest. What is theeffect of making the moving car move faster') What happens if one car is madeheavier by putting a weight on it? What happens if two cars moving in thesame direction collide? What happens in a head-on collision? Then try all thisagain using marbles or ball bearings. Do these make it easier or more difficultto see what is happening?

Something to think aboutFor how long do you think an impact force lasts? What would happen if youkept on throwing things at a body one after another? For example, a stream ofpeas from a pea-shooter hitting a piece of cardboard hanging from a string?What would be the effect of shooting the peas twice as often or making themmove twice as fast or making them twice as heavy?

Impact forces arise in all sorts of different ways whichoften get very complicated, so that it is difficult to seeexactly what is going on. The simplest cases occur whensmooth hard spheres, like marbles or billiard balls, collide.Then there are no complications due to the shape or mate­rial of the colliding bodies, and the effects of friction arevery small. When physicists understand what happens withbilliard balls, it helps them to explain the behaviour bothof tiny things like atoms and enormous things like stars. Itis good science to study simple things first and then go onto more complicated situations.

In all impacts, one body hits another and exerts a forceon it which causes it to move. If the first body movestwice as fast the forces are (usually) twice as great, andif the moving body is made twice as heavy, other thingsbeing the same, the force will be twice as great.

WINDS AND WATER JETS

If a stream of particles, like peas from a pea-shooter, allhit the same target, each tiny impact produces a very small

IMPACT FORCESAND PRESSURES

14

force for a very short time one after the other. This isalmost the same as exerting a steady force. In fact, thesmaller the impacts and the faster they arrive, the morelike a steady force it gets. This is how jets of water andgusts of air exert a force. Each molecule of water or airexerts an impact force one after the other.

wind

Something to think aboutHow does wind propel a yacht? Probably you will have no great difficulty inseeing what happens when the wind is blowing from behind, but what happenswhen the wind is blowing from the front? Here is a diagram to help.The keel plays two very important parts. Can you see what they are? Why doesa sailor have to tack (that is, to go first in one direction and then in another)when he wants to sail against the wind?

/

direction of netforce on sails

cleat

mainsail

tiller

rudder

mainsheet15

wind~deflectedby sails

14 and 15 How a yacht sails closehauled against the wind. The burgee onthe masthead shows the wind direction.Why do the crew have to lean so farout of the boat? Sheet is the nauticalterm for the rope, attached to the clewof the sail, which must be held tight bythe helmsman or crew.

FLIGHT

The forces concerned with making an aeroplane fly arerather interesting and basically very simple. There is apropeller, or jet engine, which moves the aeroplanethrough the air and a wing which supports it againstgravity.

In trying to understand how an aeroplane wing works, itdoes not matter whether the wing moves through the air,or the air moves past the wing. Both situations produce alift. This is why it is useful for aeronautical engineers to beable to test an aeroplane in a wind tunnel before trying tomake it fly. (If you have any difficulty in seeing that the

19

IMPACT FORCESAND PRESSURES

two situations are equivalent in producing lift, get hold ofa toy celluloid windmill. First blow on it and then sweep itthrough the air.)

In explaining an aeroplane wing, we will make thingseasier for ourselves by supposing that the air is blowingpast the wing.

net force

16 How an aeroplane wing works.Part of the force supports the aeroplaneand part produces a backward 'drag'.

deflectedwater stream

net force

-----~;:;;;:;;;;;;~~L--reduced pressure

deflectedair stream

20

One way in which lift might be produced would be fora stream of air to strike the underside of the wing and bedeflected downwards. This would produce an upwardimpact force on the underside of the wing which wouldsupport the aeroplane against gravity. This is in fact themechanism of the water ski. It would not, however, bevery suitable for an aeroplane because the backward dragwould be too great. Instead, the air stream is deflectedover the top of the wing in such a manner that the mole­cules are less likely to bombard the upper surface of thewing, i.e., the pressure is reduced there. This is known asthe Bernouilli effect. The normal pressure beneath thewing now provides the necessary upward force. The air­flow is still deflected downwards after passing over thewing (can you see why this must be so?), so that if anaeroplane flew very close above your head, you wouldfeel the downdraught of air as it went past. Now can yousee how a propeller works? It is rather like a little wingbeing rotated through the air, which deflects a stream ofair backwards. Perhaps you have seen this when an aero­plane is 'revving up' on the ground.

The art of designing an aeroplane wing is to make surethat the drag it exerts on the forward motion of the planeis as small as possible, and also that the machine can bemanceuvred safely when it is flying. The design of a modernaeroplane demands great mathematical skill, the use of

IMPACT FORCESAND PRESSURES

vast computers and large-scale experiments. It may costhundreds of millions of pounds.

Jet and rocket engines also throw a jet of air or gasbackwards and are themselves pushed forward by thereaction. Perhaps you have seen the same thing happeningwhen you blow up a balloon and let it go, or let go a hose­pipe when the water is full on. If enough gas is pushed outvery fast, enormous thrusts can be generated. Some rocketmotors can produce a force of millions of newtons.

PRESSURE

When the individual molecules of a gas or liquid collidewith the walls of a container or with each other, they exertimpact forces. These all add up to a steady force orpressure.If we try to compress a fluid, the molecules beat againstthe walls more frequently and increase the pressure.

In gases, the increase in pressure for a small compres­sion is quite small. Gases can be compressed easily. Butliquids resist compression very strongly indeed. An enor­mous pressure is needed to compress them even slightly.Liquids are almost incompressible. Pressure in liquids isone of the most convenient ways of exerting very largeforces in the laboratory, in manufacturing industry and invarious pieces of moving machinery.

The basic idea is very simple. The liquid is compressedby a little piston of area a, which is connected by a strongtube (why must it be strong?) to a cylinder in which a largepiston of area A can move. It does not require a very largeforce to move the little piston slightly and impart alarge pressure to the liquid. But since pressure is, bydefinition, force/area and is the same throughout a liquid,

large force F Ata

little movement

piston area A

piston area a

forc,,-et'-7-r-jI==J:::::::::::::::::::::::::::::::::::::::::~:::::::::::::::::-J

17 Diagram ofa simple hydraulicsystem.

small force large movement(may be replaced by a pump)

narrow tube(may be flexible)

21

IMPACT FORCESAND PRESSURES

18 A simple manometer measuring anexcess pressure of16·6 em of(coloured)water by 'weighing' it against the gravi­

tational pull on the water.

19 A Bourdon gauge used to measure

pressure by the deformation of thecoiled tube.

20 An industrial hydraulic press whichcan exert a maximum of 500 000 N.

The oil tank and the pump jar com­

pressing the oil can be seen at the top.The large cylinders are at the bottom.

the force exerted on the large piston will be A / a times as

large as the force on the small piston.

Thus a hydraulic system acts as a device which can

magnify a force, transmit it over a distance and make it

turn round a corner. A familiar example is the hydraulic

brake system of a car. For continuous operation, the small

piston may be replaced by a pump. Hydraulic car lifts

used in garages work on this principle.When it comes to measuring pressure, there are two

main types of pressure gauge - the Bourdon type, which

depends on the deformation produced by pressure forces,

and the manometer, which weighs a pressure against

gravity. These are examples of the two basic methods of

measuring forces which were described earlier.

1"I

18

22

IMPACT FORCESAND PRESSURES

PRESSURE IN THE EARTH

Although the Earth is mainly composed of solid rocks, itis interesting to guess the pressure at its centre as thoughit were a liquid. This is actually quite a sensible thing to dobecause over the enormous distances of the Earth therigidity or strength of the rocks is not nearly enough tosupport their weight. They rely on the pressure of therocks underneath them to keep them from falling to thecentre of the Earth.

We can use the formula P = pgh, which gives the pres­sure in a liquid of density p at a distance h below the sur­face. g is the strength of gravity. The average density ofrocks in the Earth is about 5 500 kilogramme per cubicmetre and the depth is the radius of the Earth, 6 400000 m.We have to be a bit more careful about g. The strengthof gravity on the surface of the Earth is about 9.8 Njkg.But the strength of gravity right at the centre of the Earthis zero. Can you see why? Let us take the average value,say 5 Njkg. This may not be quite correct, but at least itlets us make a guess to find out about how big the pressurewill be. A scientist would say he was 'making an order ofmagnitude estimate to the first approximation'. That israther a pompous way of saying he is making a guess tosee about how big it might be, which will tell him whetheranything is likely to happen as a consequence. Thus weget the pressure at the centre of the Earth:

P = 5 500 X 5 X6 400 000 = 180000 000 000 N jm 2

or 1·8x101 1 Njm 2

This is a truly enormous pressure, much bigger than wecan conceive of in everyday terms.

Something to think aboutWhat sort of effect do you think such an enormous pressure will have on therocks which make the Earth? Remember that any force will produce somedeformation and that things usually break if the force on them gets too big.

You can read a lot more about pressure in the bookPressures in this series, but pressure provides such an im­portant way of exerting forces that it could not have beenleft out of this book altogether.

23

COHESIVEFORCES

A less obvious type of force is exerted whenever you pickup one end of a stick, and the other end comes too. Haveyou ever thought how surprising it is that this happens?The far end of the stick can only begin to move if somesort of force is exerted on it, so there must be a very com­plicated set of forces acting right through the stick. Theremust be similar forces through any other piece of solidmatter. These forces are called 'cohesive' forces.

Cohesive forces are the forces which hold pieces ofmatter together and give them strength. All matter tendsto stick together to some extent - some substances, such asiron and diamond, do so much more strongly than others.Gas molecules have so little cohesion that they justflyaway from each other. A great many physicists andchemists and other scientists devote themselves to findingout how different substances stick together, particularlythose which have some use.

There must be two sorts of force in a solid or a liquid:one which attracts the molecules and makes them tend tocome together, and another which keeps them apart, thetwo being in balance. If there were no repulsive forces,the atoms would just collapse in on each other until somesort of force prevented them going any further.

These balanced attractive and repulsive forces are alsoresponsible for the elasticity of a body, that is, its resist­ance to having its size and shape changed by the applica­tion of a force. If the force applied is too big, however, itwill overcome the forces between the molecules, and the

21 The forces between the atoms in asolid. The atoms arrange themselvessothat the two sets of forces are just inequilibrium. There is also attractionbetween atoms which are not 'nextdoor' to each other.

24

~force of repulsion

~

force of attraction

both sets of forcesact through thecentres of atoms

COHESIVEFORCES

material will break or collapse. Under the enormous pres­sures at the centre of the Earth the atoms themselvesbreak down to some extent and occupy a much smallervolume than normally. One consequence of this is thatbelow a depth of about 3000 km rocks do, in fact, behavelike a liquid. Convection currents in the liquid rock arenow believed to cause the Earth's magnetism and also,over millions of years, to raise mountains.

FRICTION

If we try to make one body slide over another, we findthat a force acts between them which tries to prevent themotion. This force is called friction and it is a very familiarkind of force. It is peculiar because it cannot start a bodymoving - it can only stop it once it is moving, or preventit from ever starting to move. Very often we regard fric­tion as a nuisance because it makes it more difficult tobicycle, or slows down our car, but in fact life withoutfriction would be almost impossible. Think what wouldhappen if there were no friction between our feet and thefloor.

Something to think aboutMake a list of examples of useful friction and another of harmful friction. Canyou suggest ways of increasing friction when we want it and of decreasing itwhen we need to keep it as small as possible?

Something to doSee if you can devise a simple way of finding out how much friction there isbetween two flat surfaces of various materials. The rubber bands might beuseful again for measuring the forces. You could try things like wood, paper,cloth, glass, sandpaper and so on. Does it matter how big the surfaces are?Does it matter how strongly they are pressed together? Which pair 'of surfacesgives the greatest friction? Which pair gives the least? Is the friction the sameeverywhere on the surface? Is it the same when the surfaces are sliding overeach other, and when they are not?

You should have no great difficulty in getting the answers to these questions,but your answers will not be very precise. They are qualitative rather thanquantitative - they can answer the question, 'What happens?' but not thequestion, 'How big?'

25

COHESIVEFORCES

In fact, friction has always been regarded as rather adifficult field for scientific investigation, because littlethings like a greasy fingerprint can upset all the results.It is only in the last twenty years that really reliable andreproducible results have been obtained, that is, resultswhich can be obtained by different people without dis­agreement. This is, of course, very important if somethingis to be regarded as properly scientific.

Nevertheless, some work was done on friction a longtime ago and led to some rather important conclusions.The friction between two bodies can never be greater thana certain amount called the limiting friction. When thebodies are sliding over each other, the friction is a littleless than this. Did you find this in your experiment?

If the normal or perpendicular force pressing the twosurfaces together is doubled, the limiting friction is alsodoubled.

If the force pressing the surfaces together is kept con­stant, but the area of the surfaces in contact is doubled,the limiting friction is unchanged. Do you think this isreally surprising? What do we call a force divided by anarea?

22 Illustration of the Laws ofFriction.(i) Double the normal force - doublethe friction. (ii) Double the area incontact - friction remains the same.

normal

~orce friction

force

moving

force I I

f

~orma l

force frictionforce

moving

force I ]ii f

normalforce

moving ~_~

force r------'===-------'------,

normalforce

moving ~-;::C=::=:J:tforce "'"

f

26

The actual value of the limiting friction depends onwhat two materials are pressed together. Smooth surfaceslike glass and polished metal have very little friction.

COHESIVEFORCES

23 A theory of friction. As the forcepressing the surfaces together increases,the high spots in (i] like A, Band Csquash fiat until the area in contact islarge enough to support the force asin Iii).

Rough surfaces like sawn wood or sandpaper have a lotof friction. In nearly every case the limiting friction is lessthan the force pressing the surfaces together.

A THEORY OF FRICTION

Quite recently it has become possible to explain theseeffects as a result of cohesive forces between atoms in thetwo surfaces. We must remember that even the smoothestsurface would look very rough and, indeed, mountainousif we were only about the size of an atom. So when wepress two surfaces together It will be something likeFigure 23.

Only high spots like A, Band C will actually touch. Soof course the pressure at these points will be quite enor­mous, and the tiny 'hills' which are in contact will tend tosquash flat. The harder we push the surfaces together, themore these points squash. They will go on squashing untilthe area in contact has become big enough to support theforce. This squashing under pressure is really quite drastic(almost as bad as the squashing of the atoms at the centreof the Earth). The two bits in contact become almostliquid and flow into each other and stick together - thisprocess is known as cold welding and is sometimes usedby engineers to stick things together.

Now, if we want to make the surfaces slide past eachother we have got to break all these tiny little welds, andas fast as we do so, new points will come into contact andweld together.

Something to think aboutCan you see how this model explains why we get friction and why the laws offriction are what they are'? If you have any difficulty, you might find it helpsto try pressing two rough pieces of plasticine together and then trying to makeone slide past the other.

There is, unfortunately, no space to describe the in­genious experiments which have been carried out to showthat this is the correct explanation of friction, but beforeleaving this topic we must show why it is a useful, as wellas an interesting, theory.

If we want to make friction as small as possible, the27

COHESIVEFORCES

28

theory tells us that we must either prevent the high spotsfrom sticking together or make sure that it is very easy totear them apart again after they have stuck.

A film of oil can prevent the two surfaces ever quitesticking together. That is why lubrication is so importantin all the moving parts of a machine. It not only reducesfriction, but also wear, which may be even more serious.Nowadays a very thin layer of air at high pressure is some­times used for lubrication instead of oil. It serves the samepurpose of keeping the surfaces apart, and allows slidingto take place even more easily than oil. The same prin­ciple is used on a big scale in hovercraft.

Another way of reducing friction is to make one of thesurfaces of quite a soft material, so that even if they dostick together, they can easily be pulled apart again. Thisis the principle used by engineers in white metal bearingswhich are used in motor-car engines and other pieces ofmachinery.

Yet another way is to look for a material whose atomsare so strongly joined to one another that they do noteasily join up to the atoms of a different material. Poly­tetrafluorethylene, or PTFE for short, is such a material.It slides over almost all other substances with very littlefriction and is used, among other things, for the best andmost expensive skis.

The theory of friction is a valuable guide when it comesto looking for new materials which will give low friction.

SURFACE TENSION

Things to doMake a needle float on water. You will need a very steady hand and cleanfingers. It may help to float the needle on a piece of paper which will eventuallysink. The important thing is to avoid getting the top of the needle wet.

Make a boat of paper and put a little piece of camphor in the stern so that itjust touches the water. The boat should dart about over the water.

Watch carefully what happens to a drop of water placed on a greasy surfaceand another on a clean surface. What effect does adding a little detergent haveon the drop placed on a greasy surface? Watch carefully what happens whena drop of water drips off a tap.

Try to waterproof a piece of blotting paper by dipping it in melted wax (becareful not to start a fire) or a waterproofing solution.

Blow some bubbles with soap solution and a piece of tubing. See if you can

COHESIVEFORCES

blow a big bubble on one tube and a little one on another. What happens whenyou join up the two tubes with rubber tubing? What does this tell you aboutthe pressure inside different sizes of soap bubble?

glass tubes

littlebubble

rubber tubes

bigbubble

Something to think aboutWhy does a piece of blotting paper soak up water, but a raincoat or a piece ofcanvas repel water, "atleast until it becomes really wet?

Can you see any connection between the various things you have just beenasked to do?

Some of the most striking results of the cohesive forcesbetween atoms are seen in liquids. All liquids appear tohave an invisible 'skin' round them which pulls them intodrops. This 'skin' behaves as though it were in tension,like an elastic sheet, and can exert forces on other bodies;for instance, to make a piece of camphor move, or to sup­port a needle.

net force

Figure 25(a) is very similar to Figure21 representing a solid. This does notmean that liquids are the same as solidsinside. Such diagrams are intended onlyto illustrate symbolically a single point- in this case the balance betweenattractive and repulsiveforces.

both sets of forcesact through thecentres of atoms

~force of repu Ision

------7force of attraction

Figure 25(a) shows some of the atoms near the surfaceof a liquid. The molecules in the body of the liquid areattracted by other molecules all round them and there isno force on them in any particular direction. But at A we

29

stretchedskin

25(b)

25(a) (right) How cohesiveforces causesurface tension. The attractive forceson a molecule in the surface of a liquidtend to pull it back into the liquid. Ifanelastic skin is stretched and deformed:the net force it exerts is perpendicularto the skin. Thus a liquid behaves as ifit were covered with an elastic skin.

have a molecule trying to get out of the liquid. The attrac­tions of the other molecules tend to pull it back. Can yousee how this will have an effect like that of an elastic skin?

The first effect of surface tension is to make a liquid'curl up' so as to reduce its surface area to the smallestpossible value - thus small drops left to themselves be­come spheres. What would happen to these spheres ifthere were not repulsive forces, as well as attractive forces,between the atoms?

When a liquid is in contact with a solid, a great dealdepends on whether or not it wets the solid. If the attrac­tive forces between the solid and the liquid are greaterthan those between the molecules of the liquid, then theliquid wets the solid, and it tries to spread out all overthe solid to make the area of contact as large as possible.But if the forces of attraction between the molecules ofthe liquid are greater than those between the liquid andthe solid, the liquid wants to have nothing to do with thesolid and retreats so that the area of contact is as small aspossible. Water will wet a clean surface but not a greasyone.

26(a) Water wets glass and rises in acapillary tube. On the right is a drop ofwater.

26(b) Mercury does not wet glass andfalls in a capillary tube. On the right isa drop ofmercury.

26(a) 26(h)

30

Sometimes wetting is a good thing, and to help it comeabout we can add something to the liquid to reduce thesurface tension. Soap has this effect with water. If the

COHESIVEFORCES

stuff which is added does not mix with the liquid, but sitson the surface, a very small quantity will spread out overa large area, like oil on water. Such substances makeeconomical wetting agents.

27 The addition of a little of thewetting agent 'Teepol' reduces surfacetension and enables the water to wetthe card.

water and 'Teepol' pure water

28 Mosquito larva floating in water.

Sometimes we want to prevent wetting - then it mayhelp to cover the solid with something which does notattract the liquid. Grease and wax and 'silicone' all havethis effect with water.

Something to think aboutWhat must you do to waterproof a fabric or a tent? How could you preventwater soaking through the brickwork of a house?

When a photograph is developed, it must be soaked in a special solution.How could you make sure that the developing solution can get to all parts ofthe photograph?

What effect do you think camphor has on the surface tension of water?(Think of your camphor boat.)

Surface tension plays a part in quite a lot of every­day activities; in washing up and keeping dry, for example.It is important to the workman who wants to solder twopieces of metal together, because he must make sure thesolder 'wets' the metal. It is also important in Nature.Very small organisms like water boatmen and mosquitolarvae make use of it to keep themselves floating on thesurface of a pond. What do you think we should do to thewater to get rid of mosquitoes?

31

ELECTRICANDMAGNETICFORCES

29(a)

29(8) Dust sticks to the wall by electro­static attraction.

29(b) Model of electrostatic dust preci­pitator used to remove dust from thesmoke emitted by power stations. High­voltage equipment is shown above. Dustis attracted to charged wires and shakenoff mechanically to fall through thehoppers below.

30 Cathode-ray oscilloscope, in whichelectrons which produce a picture aremoved by electrical forces.

31 Early electroscope. The gold leafmoves under the influence of electricalforces and reveals the presence ofelec­tric charges.

32 William Gilbert.

32

Have you ever played with a magnet, or better still, withtwo magnets? Magnetic forces are very striking and quitedifferent from the forces we have considered so far. Prob­ably, too, you will have picked up little pieces of dust witha plastic comb rubbed on your handkerchief or heard anylon garment crackle as you take it off. These are ex­amples of electric force. The ancient Greeks knew aboutelectric and magnetic forces more than two thousand yearsago, although it is only in the last hundred years that man­kind has really made use of them. Our word 'electricity'comes from a Greek word 'electron', which means amber.Amber is a hard fossil resin, from prehistoric trees. It isa natural plastic which was used by the Greeks for makingornaments, and they noticed that when it was rubbed itattracted small objects to itself.

29(b)

30

31

32

The forces produced by permanent magnets are rathersmall. Can you think of any uses for them, apart from themagnetic compass? There are a few, but they are not veryimportant. Electrical forces are also very small and notvery obvious, and they do not have very many direct uses.A few are illustrated in the pictures.

Points to think aboutIn what sort of ways are electrical and magnetic forces alike? How are theydifferent? Are they like gravity? Can you think of two important differencesbetween them and gravity?

Can any material, or only plastics and insulators, be electrified by rubbing?What about a piece of metal if you hold it with a piece of plastic? Why do wenot usually notice electrical forces unless we look for them specially?

Can electrical forces act through a piece of paper? Can magnetic forces?Can gravitational forces? Can a magnet placed inside a 'tin' box produce aforce outside the box?

MAGNETIC FORCES

It is sometimes said that William Gilbert, who lived from1540 to 1603 and was Queen Elizabeth's doctor, was thefirst modern scientist. He became famous for the experi­ments he did on electricity and magnetism. This was thetime when sailors were making great voyages of discoveryto unknown parts of the world. One of their great diffi­culties was to know where they were and in what directionthey should go. The magnetic compass was a great help tothem in all this. William Gilbert listened to stories of theirexperiences and tried to find out more about how a com­pass worked, to help them find their way more accurately.Do you think he did all this mainly because he wanted tobe useful, or because he was curious about magnets andcompasses? These are both powerful reasons for studyingscience and no one knows which is the most important.

When William Gilbert did these experiments, and manyothers like them, he did not have strong permanentmagnets to work with, only lumps of lodestone, that is,lumps of iron ore which happened to be magnetised.Lodestones are only slightly magnetised, and this madehis experiments very difficult to carry out successfully.Some of his most important experiments were carried outwith a sphere of lodestone, which he called a 'Terrella',or 'Little Earth'.

33

33

N

®N

33 (a) Compass direction finding onTerrel/a. (b) Compass needle on its sidenear Terrella. (c) Magnetising a knit­ting needle.

34 Diagram from Gilbert's book, 'DeMagnete', published in 1600, showingthe direction taken up by a compassneedle at different points on the Ter­rella.

34

Something to doYou can try some of William Gilbert's experiments for yourself. You need astrong magnet, some nails, a steel knitting needle, some cotton, a plottingcompass, a small magnet and some plasticine.

See how many nails you can hang from your magnet in a long chain. Doesit help to join the chain up to the other pole of the magnet? What happens tothe nails when they are in contact with the magnet?

In which direction does the compass needle point when it is a long wayaway from all magnets? What happens to it when a magnet is fairly near?How does the direction of the compass depend on whereabouts it is near themagnet?

Hang up the knitting needle from its centre. Does it hang horizontally? Ifnecessary, move the cotton until it is horizontal. Now magnetise it by strokingwith the magnet. Move the magnet gently along the needle, just touching it.Do not disturb the cotton. How can you make sure it is magnetised? Hang itup again. What happens now? What sort of a force is acting on it?

You can make a Terrella as follows. Put the small magnet in the middleof a lump of plasticine and roll it into a sphere. Now see what happens to thedirection of the compass needle when you place it at various positions on yoursphere. Is it anything like what happens to a compass needle at various placeson the Earth?

Turn the compass on its side so that the edge of its case just touches theplasticine. What is its direction now? Is it anything like the hanging knittingneedle?

Do you think you now know what the Earth's magnetic field, which makes acompass point North and South, is like? The ends of a magnet, where themagnetism appears to be, are called its poles. The pole of a compass needlewhich points towards the North is called a North pole. Do two North polesattract or repel each other? If the Earth has a magnet inside it, what sort ofpole must it have at its geographical North end?

ELECTROMAGNETIC FORCES

Although electrical and magnetic forces occurring natur­ally are very small, the magnetic forces produced by anelectric current - electromagnetic forces - can be verylarge. Have you ever made a magnet by winding some in­sulated wire round a nail and connecting the ends to abattery? How do we know that this is a magnetic force?

The pictures show some of the uses made of electro­magnetic forces.

Electrical and electromagnetic forces are perhaps themost important forces of all. We now know that all matterconsists of atoms and that atoms are composed of electri­cally charged particles. A complete atom has as muchnegative charge as positive charge, so the two kinds ofcharge very nearly cancel out. That is why electric forcesusually seem so small. It is only when a few atoms have

ELECTRIC ANDMAGNETICFORCES

35

35 The electric motor, the loudspeakerand the relay represent three commonuses oj electromagneticforces. Electricmotors of all shapes and sizes are verywidely used in industry, in transport, inthe home and many other places.

36 Electromagnet in use in a scrap-metal yardfor crushing purposes. 36

been partly broken up and lost some of their electriccharge that electric forces can come into play on a scalelarge enough for us to see.

But the electrical forces between one atom and its next­door neighbour can be very large. These forces enableatoms to join together to form molecules and chemicalcompounds. The whole of chemistry depends on electricalforces. They also stick the atoms in a solid or liquidtogether, so cohesive forces are really electrical innature; if atoms are squeezed too tightly together, otherelectrical forces try to push them apart again. Rememberthat electrical forces can repel as well as attract. So mostof the forces we have talked about so far, except gravita­tional forces, are really electrical.

Understanding how these electrical forces can causecohesion, elasticity and friction helps engineers andscientists to control these forces and make them performuseful functions. A great deal of modern scientific researchis devoted to this.

Something to think aboutWhat happens when two bodies collide? Do they really come in contact? Ordo the electrical forces between them really produce an action at a distancelike gravity?

35

MUSCULARFORCES

When we think about forces, we probably think first of allof the forces we can exert with our own bodies - by ourmuscles. Let us think what happens when we contract thebiceps muscle in the arm to raise a weight and then holdit steady, We can do this quite automatically withoutthinking about it at all, but it is really quite a complicatedprocess.

37 Diagram of biceps and tricepsmuscles.

triceps musclelowers arm

upper arm

~~don attachingmuscle to bone

36

To understand what happens, it may help first of all tofind out how a muscle differs from some of the otherforce-producing devices we have looked at. A stretchedspring can pick up a weight, so perhaps a muscle is some­thing like a spring. But there is one very important differ­ence. We can lower our arms again at will, but once aspring has raised a weight, it cannot be 'turned off' again.A muscle contraction can be released at will.

Or again, a weight can be held up at the end of a rodby tying it in place, so perhaps when we hold up a weightour biceps muscle is something like a string tying the fore­arm to the shoulder. But a string can go on holding aweight (that is, exerting a force against gravity) for everwithout getting tired. We quickly want to put down aheavy weight. A muscle is evidently doing something allthe time it is contracted even if it is not moving.

Clearly there are important differences between amuscle and a spring or a string, although both theseanalogies may occasionally be useful. To find out moreabout muscles, we have to look at their detailed structure.

MUSCULARFORCES

This has been done by physiologists, who find that everymuscle consists of a bundle of individual fibres, each withits own nerve. You can see these fibres in the meat you eat.Normally a fibre is relaxed and quite straight, but when anerve impulse arrives it produces a chemical change with­in the fibre, which causes it to try to contract and becomemuch shorter. In doing so, it can exert a small force. Themore fibres that contract together, the greater the totalforce exerted by the whole muscle. By balancing the forcesin two opposed muscles, like the biceps and the triceps(which straightens the arm), we can hold our hand steadywherever we want it. This balancing is done automaticallyby our nervous system, so we do not have to think about it.

This is not the whole story. Before long the chemicalsproduced by the nerve diffuse, or drift, out of the fibre,allowing the fibre to relax until another nerve impulsearrives, when it suddenly contracts again. So our nervoussystem can adjust the average force exerted by the wholemuscle, not only by varying the number of fibres whichcontract, but also by varying the frequency with whichthey contract. The faster they do it (up to about five timesa second, which is as fast as the mechanism will work) thegreater the force. Muscle force is not a static force, likethat in a spring, which requires nothing to maintain it. Itis a dynamic force rather like that produced by a streamof particles impinging on a surface. No wonder we gettired when we try to keep up a steady pull for a long time!

Because more fibres contract together at some instantsthan at others, the force is not quite steady and we trembleslightly when we really exert ourselves (don't confuse thiswith the shake of your hand produced by the beating ofyour heart).

This knowledge of how a muscle works makes it easierfor doctors to find out how to treat muscular disease.

37

FORCESDUE TOLIGHTPRESSURE

38 Apparatus to demonstrate lightpressure. If the light is switched on andoff with the right period, it can set thefoil suspended in a very high vacuumswinging like a pendulum.

38

The last method of exerting a force which we will discussis one which has probably not occurred to you, since it isfar too small to feel or to produce any visible effects in theeveryday world. It is the force exerted by light falling ona body.

You will probably be surprised to learn that light canexert a force. Yet there were strong theoretical reasonsfor believing this long before it was shown to happen ex­perimentally. Light is a form of wave motion and all wavescan exert forces. This is fairly obvious in the case of waveson water, since they can make a floating cork go up anddown. Similarly, a sound wave can make our eardrumsvibrate - or a tin tray vibrate on the piano when it isplayed. It is reasonable to suppose light waves should alsoexert a force - sometimes called radiation pressure - in thesame sort of way.

Although the force exerted by light is so very small on

FORCES DUETO LIGHTPRESSURE

39 Without radiation pressure to sup­port it against gravity, the Sun wouldshrink until it would appear no biggerthan the circle in the centre.

Earth, so that we are quite unconscious of it, it is veryimportant in the Sun and other stars. The centre of a staris very, very hot and gives out intense radiation whichpresses upwards on the outer layers. If there were no suchforce, all the stars would collapse under their own gravita­tion to a very small fraction of their present size. TheUniverse would then be a very different sort of place andthere would almost certainly be no life anywhere.

At the beginning of this book we said that forces canonly be exerted by one body, or piece of matter, acting onanother. Now we have found that light can exert a force.Perhaps this means that light is a form of matter too,although a very different form from the 'billiard balls' weare used to.

39

SUMMARYANDCONCLUSIONS

40

In the first chapter of this book we saw how forces areresponsible for making bodies start to move, for stoppingthem once they are moving and for deflecting them fromone direction to another when they are moving.

Very often, however, several different forces can act ona body in different directions so that they cancel out, andthen there is no starting or stopping, although very strongforces are acting. Forces which cancel out in this way aresaid to be in equilibrium.

Once a body has started to move, it can keep on goingin a straight line at the same speed without the aid of anyforce. The only forces on an arrow once it has left the boware the resistance of the air and gravity. The former slowsit down slightly. The latter pulls it out of a straight pathbut does not alter its speed very much unless it is shotstraight up into the air. There is no force to keep it goingand none is needed.

Whenever we see a body moving at a constant speed ina straight line, we can be sure that there are no forcesacting on it - or, if there are, that they are in equilibrium.In fact, because all bodies on Earth are subject to gravityand almost always to friction, we practically never seebodies move with truly constant speed in an exact straightline, but fast-moving bodies like bullets and arrows comequite close to it. Even so, we must take the pull of gravityinto account when aiming, if we are to hit a distant target.

Something to doI. Find out how the sights of a rifle work.2. Watch a ball bearing drop through a viscous liquid like glycerine or treacle.This is one of the very few situations where the ideal case of constant speeddoes occur. Can you see what happens to the forces?

In the rest of the book we talked about the differentkinds of force which occur in nature. Basically, there areonly two':' distinct kinds of force: first, gravity, whichmakes every piece of matter in the universe attract everyother piece according to the inverse square law; secondly,electrical forces, which make electrically charged bodies

"There are actually two more fundamental kinds of force which are concernedwith the nuclei inside atoms, but these have no effect on everyday life, so we canforget about them unless we are nuclear physicists.

SUMMARY ANDCONCLUSIONS

attract each other if they have unlike charges, or repeleach other if they both have the same kind of charge,again according to the inverse square law. Both theseforces act across empty space without any material con­tact between the bodies.

It is much too difficult, however, to work out all themyriad forces of the world around us just in terms of thesetwo. It is much simpler to think in terms of several othertypes of force.

First, there are the cohesive forces which hold solidsand liquids together and which are the result of equili­brium between forces of attraction and repulsion betweenatoms. These include elastic forces, which come into playwhen a body is stretched or compressed or twisted andwhich often obey the very convenient Hooke's Law; fric­tional forces, which occur when one body moves over orthrough another; and surface tension, which makes aliquid appear to be covered with an invisible skin.

Secondly, there are the impact forces, which arise whena moving body collides with another body and which canproduce the 'rocket' effect. Besides the direct impact ofmacroscopic bodies - that is, bodies which are largeenough to be seen or felt - there is the effect of the impactof innumerable small particles (molecules) which producethe effects of pressure in a liquid or gas. High pressurecan arise either because the fluid is very hot and thereforethe molecules are moving very fast, or because the fluidis compressed by a very great weight of other material ontop of it. Towards the centre of the Earth, the pressurebecomes so great that even solid rocks become like aliquid.

Thirdly, there is the magnetic force which arises be­tween magnetised pieces of iron and the much more im­portant electromagnetic force which arises from an electriccurrent, particularly when it flows through a coil of wire.A very special case of this type of force is radiation pres­sure, which is so slight that no human being will ever feelit, but which, in the fiery furnace of the Sun, is strongenough to prevent the Sun collapsing under its own weight.

Lastly, there are the forces exerted by living creatures­muscular forces. They are weak and puny on the cosmic

41

SUMMARY ANDCONCLUSIONS

42

scale, yet vitally important to us and, like almost every­thing in the biological world, extremely complicated inthe way they work.

There are many ways of measuring forces, but almostall of them depend on one of two basic principles. We canweigh a force by balancing it against gravity, or we canmeasure the extension it produces in a spring.

WHY WE NEED TO UNDERSTAND FORCES

You may possibly have wondered, from time to time,why it is worth knowing about all these different kindsof force. Some people find them interesting in themselvesand are fascinated by working out how the different sortsof force come about and the consequences of the interplayof the forces in a complex situation. Most people, how­ever, want to know what benefit they can get from a pieceof knowledge. There are innumerable benefits to begained from a study of forces. If we know the forces act­ing, then we know how things will move - that is, howthey work and what will happen to them in the future. Ifwe want to make things happen in a certain way, we muststudy the forces involved and adjust them to bring aboutour aims. Before we can get a man to the Moon, we needto know, very precisely, the force of gravity everywherealong his path, so that we can fire the rocket at just theright time, and with just the right speed and direction toget him there safely.

FORCES AND THE ENGINEER

Knowledge and understanding of forces are particularlyimportant for engineers, and we will conclude by takinga very brief look at a few of the places where they arisein engineering.

The first duty of an engineer is to make sure that thethings he builds are strong enough to stand up to theforces they will experience in normal working without

40 A tensile testing machine, capableof exerting up to 50 tons force. tomeasure the breaking strength ofpiecesof metal. Can you see how the force isproduced?

breaking or falling down. So the first thing the engineermust do is to measure or calculate these forces. Thisimmediately poses a problem: what is normal working?This is something which can be decided only by carefuljudgement in the light of past experience. There is noexact answer. In Great Britain, for instance, we wouldnot normally need to make a building strong enough towithstand the force of a 45 m/s wind, because such windsoccur very rarely - perhaps once in a century at anyoneplace - and it may seem reasonable to risk the buildingfailing if such an abnormal hurricane should occur. Butwe must build strongly enough to withstand 35 m/s winds,which do happen every few years.

Once he knows the forces involved, the engineer mustmake sure the materials he proposes to use will be strongenough - or rather, find out what thickness of materialwill be strong enough. For this, it is necessary to placea sample of the material in a testing machine, which willkeep increasing the force until the sample breaks. Thepicture shows such a machine. Why do the parts of themachine have to be so thick?

Another important consideration is to use the smallestamount of material which will do the job adequately - inother words, to make the construction as cheap as pos­sible. This means designing the shape very carefully, sothat the forces are spread out through the whole of thestructure and not concentrated at a few points whichwould become especially liable to break. Hundreds, orthousands, of calculations are needed to find the bestdesign - a job for a computer. The result is often not onlyeconomical, but strikingly beautiful. The pictures on thenext two pages show a few examples of modern structuresdesigned to equalise the stresses.

Many of the recent improvements in design have beenmade possible by the use of materials which have beeninvented in the last few years by pure scientists. It is nowpossible to produce 'tailor-made' materials which willstand up to large forces under arduous conditions, with­out needing great thickness. You can read about some ofthese in the companion volume in this series on Materials.Notice, in particular, how much stronger reinforced or

43

41 Flying buttresses at Westminster 41A bbey. These add much to the appear­ance ofthe building. but they are mainlythere for a purpose. Without them theroof would collapse. Can you see why?

42 Roman Catholic Cathedral, Liver­pool, opened 1967. This is an outstand-ing example ofa modern building madepossible by new materials. Notice howcleverly the reinforced concrete ribs haveheen used, hoth to support the buildingand to lead the eye up to the crown.

43 The Forth Road Bridge, Scotland,opened 1966. Can you see how theweight of the bridge is supported? Thedesigners also had to make sure thebridge will not blow down in a highwind. Models were tested in a windtunnel.

44

44

44 Prestressed concrete beams beingused in bridge construction. Can yousee the reinforcing wires, which havebeen stretched so as to keep the wholebeam in compression? Why does thismake the beams stronger, and why areno wires needed in the middle of thebeam? What are the loops at the endsof the beams/or?

45 Wagondrifi Dam, Natal, built 1965.Can you see how the shape ofthe dam,which is 30 m high, helps to supportthe weight oftne water?

45

prestressed concrete is than plain concrete, because thereinforcing bars can take up the forces where the concreteis weak and vice versa.

These examples are taken from civil engineering,where the forces involved are static forces, due to theweight of the structure. It becomes much more difficultto calculate the forces when movement is involved, be­cause all sorts of dynamic forces, due to the starting, stop­ping or deflection of the parts, come into play.

As an example, consider the forces acting in and on abicycle. Besides the weight of the rider and the upthrustof the road, there is one set of forces which keeps thebicycle going along a straight road, another set whichenables it to turn a corner and yet another set to stop it.

Something to doSee if you can make a list of the various forces acting in a bicycle.

45

SUMMARY ANDCONCLUSIONS

46 Some of the forces involvedin ridinga bicycle. Why is the horizontal forceon the front tyre in the opposite direc­tion to that on the back tyre?

gravity on rider

tensionin chain

chainonwheel

1hand on handlebar

bike on wheel

46

The rider presses down on the pedals, and the force onthe pedals is transmitted through the chain wheel and thechain to the back wheel. This force, together with frictionbetween the tyre and the ground, pushes the bicyclealong.

When he wants to turn, the rider applies a force to thehandlebars, which causes the front wheel to turn and thebicycle follows in the new direction. But this is not all. Alot of the steering is brought about by the rider leaninginwards, so that part of his weight makes him 'fall' roundthe circle. Dynamic forces can be quite complicated.

When he wants to stop, the rider applies a force to thebrake lever, which is transmitted through the cable to thebrake blocks, which squeeze the wheel and cause friction.The friction between wheel and brake blocks, plus thefriction between tyre and road, brings the bicycle to rest.

Designing a bicycle which will stand up to all theseforces, even with a heavy rider, and still be light and easyto propel, as well as good-looking, is no easy task, andthere are other problems as well. The bicycle must rideeasily over bumps in the road and the gear ratio must beright - both of which involve forces again. Probably theideal bicycle has yet to be designed. There is a prize onoffer, which has not yet been won, for a really good bicycledesign.

.J,~

tyre on ground

~1'ground on tvre

twist inshaft

pressure in brake fluidpresses brake shoesagainst brake drums

force onbrake pedalSUMMARY AND

CONCLUSIONS

47 Some of the forces involved indriving a car.

Something to doMake a list of some of the forces involved in a motor car or a boat or anaeroplane. What do you think are the most important points the designers ofthese vehicles have to take care of?

Luckily, when it comes to designing complicatedmachinery it is possible to deal with each part separately,so that one man can concentrate on the engine, anotheron the clutch, another on the gearbox and another on theseats (yes, even everyday things like seats need carefuldesign if they are to be efficient). Without this division oflabour, it is unlikely that engineering design would everget very far.

Something to think aboutWould you rather be a pure scientist who finds out how things work and howto make new materials, or an engineer who designs and builds the equipmentneeded by other people? Both are important in the modern world, but mostpeople are better suited to be one of these rather than the other.

CONCLUSION

I hope you have enjoyed this little book on Forces andnow find that there is more to the world than you hadrealised before. When you see things moving, or come

47

SUMMARY ANDCONCLUSIONS

48

across great engineering structures, ask yourself, 'Whatare the forces involved in this?' The answer will some­times surprise you.

Here is a little conundrum. Which twin is pulling which?Do all forces act both ways like this?