Forces (Longman Physics Topics)

LONGMAN PHYSICS TOPICS

General Editor: John L. Lewis

IFORCESI R. D. Harrison

B.Sc., A.Inst.P.

Senior Lecturer in Physics Newcastle upon Tyne Polytechnic N.E. Co-ordinator for Nujjield O-Level Physics School Trials

Illustrated by T. H. McArthur

LONGMAN

LONGMAN GROUP LTD

London Associated 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 a retrieval system or transmitted in any form or by any means - electronic. mechanical. photocopying. recording or otherwise - without the prior permission of the copyright owner First published 1968 Reprinted with corrections 1970 SBN 582 32174 3 Printed in Great Britain by Butler & Tanner Ltd. London and Frome

I ACKNOWLEDGEMENTS I The author and publisher are grateful to the following for permission to use photographs: frontispiece R. W. Evans; figures 5 Dr H. E. Edgerton, Massachusetts Institute of Technology; 6 Philip Harris Ltd; 7 Wakeman Farrance Engineering Ltd, photograph by Cecil H. Greville Ltd; 9 Societe Encyclopedique Universelle ; 10 Mount Wilson and Palomar Observatories; 14 Barnaby's Picture Library, photograph by F. J. Armes; 20 Fogg & Young Engineering Ltd, photograph by E. John Wells Ltd; 27 Shell Photographic Unit; 28 Barnaby's Picture Library; 29b Central Electricity Generating Board; 30 M-O Valve Co Ltd; 31 Crown Copyright, Science Museum, London; 32 Radio Times Hulton Picture Library; 36 General Electric Co Ltd, photograph by Lewis & Randall Ltd; 38 Educational Services Inc (still from the film The Pressure of Light); 39 Royal Greenwich Observatory; 40 Samuel Denison & Son Ltd; 41 Camera Press, photograph by A. G. Hutchinson; 43 Barnaby's Picture Library, photograph by A. L. Hunter; 44 Cement and Concrete Association, photograph by Leonard G. Alsford; 45 Keystone Press Agency. Photographs for figures 13, 18, 19, 26,27 and 35 were taken by J. Cummins. Figure 34 is reproduced from 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).

NOTE TO THE TEACHER

This book is one in a series of physics background books intended primarily for use with the Nuffield O-Level Physics Project. The team of writers who have contributed to the series were all associated with that project. It was always intended that the Nuffield teachers' materials should be accompanied by background books for pupils to read, and a number of such books 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 investigations pupils will be doing in the laboratory, certainly not textbooks in the conventional sense, but books that are easy to read and copiously illustrated, and which show how the principles studied 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. Whatever course pupils are following, they often need straightforward books to help clarify their knowledge, and sometimes to help them catch up on any topic they have missed in their school course. It is hoped that this series will meet that need. This background series will provide suitable material for reading in homework. This volume is divided into sections, and the teacher may feel that one section at a time is suitable for each homework session for which he wishes to use the book. This particular book is written as a background book for the Forces section of Years I and, more particularly, II. It is hoped that the examples given, which range rather beyond the Nuffield course, will help pupils to appreciate the importance of forces in everyday life and begin to explain how they come about, thus laying the foundation for more formal studies later. At the same time, some attention is paid to the role of forces in technology and engineering. This is essentially a book for pupils to browse in, taking up points which catch their interest and possibly pursuing them further.

INTRODUCING THIS BOOK

ICONTENTS

There are many different ways of looking at the things around us. Some people are impressed by their beauty or ugliness. Other people, looking at the same things, will wonder how they were made or what their history has been. I sometimes find it fun to think about all the forces that are involved. I hope you will find this fun too.

What is a force? Elastic forces Gravitational forces Impact forces and pressure Cohesive forces Electric and magnetic forces Muscular forces Forces due to light pressure Summary and conclusions

6 9

12 18 24 32

36 38 40

WHAT IS A FORCE?

If a stone lying in the middle of a level path suddenly started to move, would you be surprised? Probably you would, unless you believe in magic. Most people, if they observed such a thing happening, would look for a cause. The scientific name for a cause of motion is force. A force is anything which can cause a body to start moving when it is at rest, or stop it when it is moving, or deflect it once 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 it make a body start or stop moving?' That is how we recognise the existence of forces. Once it is started, the body can keep going by itself without the help of any force, but another force is needed to stop it. You may be surprised to learn that a body could go on moving for ever without any force acting upon it. Most things obviously come to rest rather quickly. This is because they are acted upon by aforce offriction which slows them down. If the friction is small, for example when a stone slides over smooth ice, then the body will go further. We find that the smaller the friction, the further the body will go. If we try to imagine what would happen if there were no friction at all, we can see that the body would probably go on and on for ever without stopping (unless it 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 no forces to slow it down. A force cannot exist by itself - it can only be exerted by one body on another. The Earth pulls you and me and apples and stones towards itself. You can push a pram and make it start moving. A magnet can attract a piece of iron toward itself. The wind can whisk a leaf into the air. Something to think about 1. 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 moving at the same speed for ever? If not, why not? 4. What makes it stop at the end of its flight?

6

WHAT IS A FORCE?

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

Something to do There 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 name for the kind of force involved in each case. Looking up books on physics or engineering in the library may suggest some examples you had not thought of for yourself. If you want to be very systematic, make your list with three columns: 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 exert ourselves through the action of our own muscles. Throwing, kicking and catching a ball, propelling a pellet with a pea shooter, lifting food to our mouths. These and many other similar activities, depend on muscular forces to set things in motion or to stop them. But what happens when we stretch a spring or a piece of elastic? Motion ceases, yet our nerves tell us that we are still exerting a force - often quite a large one. Why do we get no more starting or stopping? The answer is probably obvious to you, but in case it is not, think what happens when you tie your shoe. You are pulling on each lace and thus exerting a force on your foot, 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 cancel out. The total force is zero. When we add up forces in this way to get zero, we have to take into account not only the size of the forces, but also the directions in which they act. A body tries to start moving in the direction of the force. If two equal forces act in opposite directions they just balance and produce no motion. Things like forces, which have direction as well as strength, are called vectors. You will learn more about them in your mathematics course. 7

WHAT IS A FORCE?

1 Forces on afiagstafJ. How do the guy ropes stop the flagstaff falling over? What happens to the tensions in A. B and C when the wind blows as shown? 2 Forces on a seated person.

1

A set of forces which just balance and produce no motion is said to be in equilibrium. The world is literally full of forces in equilibrium. As you sit reading this book, the force of gravity pulling you towards the earth is just balanced by the support of the chair on your body. The chair itself is held steady by an upward push of the floor. A flagstaff is held steady by the pull of its guy ropes and, again, by an upthrust from the ground. The tension in the strings of a piano is maintained by the counter forces in the piano frame. The pull of all the strings in a piano amounts to several tens of thousands of newtons, so the frame has to be a very strong one. We soon lose count of all the different forces around us. Luckily we can forget about most of them, since they simply cancel each other out and produce no motion.

2 Wind)

T

thrust of

chair upwards

upthrust from ground

8

ELASTIC FORCES

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

4

Consider the stretching of a spring. Can you remember what 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 a bit longer. Very soon this motion stops. We become aware of the tension in the spring. Each part of the spring is in equilibrium with this tension acting in opposite directions on each side of it. If we pull a bit harder the spring moves a little more until the tension again balances each part. The greater the pull, the greater the stretch and the greater the tension. (We must not let the pull be too great or it will spoil the spring or even break it.) If we let go, the tension sets the parts of the spring in motion again until it gets back to its original length. The tension is a real force, according to our definition that a force is something which causes motion. Forces produced by stretching, or bending, or twisting a body, that is, by deforming it, are called elastic forces. Whenever a body is deformed in any way, so that its shape or size is altered, elastic forces will be brought into play which 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? What happens to the floor when you stand on it? Luckily these deformations are often so small that we can forget about them, but they are always there.

5

9

ELASTIC FORCES

Something to do See 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 a mirror and a beam of light from a torch useful.

Elastic deformation is generally the most convenient method available for detecting and measuring forces. It is also useful for producing forces of known strength. If we want to know how big a force we have acting, we measure the amount of stretching or twisting it produces. Is it safe to assume that if we have twice the stretch we have twice the force without checking to make sure that this is so? Something to do Try to find out if the stretch in a rubber band is proportional to the number of 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? (You can use as many rubber bands as you like and might find a paper clip, a ruler and a pencil and paper useful. Or perhaps you can find a completely different way of doing it.)

HOOKE'S LAW Probably you will find that if you double the force you get more or less double the stretch - provided you do not stretch it too far. Nearly all materials behave in this way. If they do they are said to obey Hooke's Law, which is named 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 anything simpler. Life is very much easier for engineers and physicists when their materials obey this law. But it is not a fundamental law of nature. There is no theory to prove that all substances must obey it. It is just an experimental fact that most substances obey it up to a point. Do you think plasticine or crepe paper or even ordinary elastic obey Hooke's Law? Perhaps you had better have another look at the stretching of your rubber bands. In any case, ordinary materials only obey Hooke's Law 10

up to a certain point. If they are stretched too far beyond the elastic limit an extra force produces more extra stretch than it should and a little more force still will break the material. We must always be very careful not to assume that Hooke's Law holds when it does not.

ELASTIC FORCES

Something to do Stretch a number of different substances until they break. or bend them if that is easier. Do they break suddenly, or tear, or give gradually? Do they seem to obey Hooke's Law at all, or is their elastic limit very small? If you have to bend them, do they break suddenly (that is, are they brittle?) or do you have to keep bending them backwards and forwards until they are fatigued? 6 A spring balance used for measuring force in newtons.

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

7 An Engineer's Proving Ring used for measuring forces up to 1800 N. The dial gauge in the middle will measure very small deformations ofthe ringfrom a true circleand these indicate the force.

6

7

II

GRAVITATIONAL FORCES

WEIGHT Perhaps the most familiar force of all is that of gravity the force which pulls things towards the Earth. It certainly is a force, because if you let something go, it starts to move - to fall. But even when a body is not free to fall, it is still acted upon by gravity and a counter-force is needed 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 also known as a kilogramme force (kgf). We have to be very careful not to confuse mass (quantity of matter) with weight (gravitational force on that matter). In everyday life we talk about weighing when we mean measuring the mass, which is sometimes very confusing.

WEIGHING FORCES 8 A weight of I kg. A cube of water

of side 10 em has a mass of I kg and a weight of 9·8 N or I kg[.

Another method of measuring forces is to weigh them, that is, to balance them against a known weight. Something to do See if you can devise a method of weighing forces to enable you to measure a force without using a spring balance. You need some weights and a balance beam or a pulley. If you like, you could try to use this arrangement to see how strongly you can pull in different directions; up, down and horizontally. Besides your balance. you will need another pulley (or a smooth rod) fixed to the ground and 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 about Do you think the weight of a body will be the same everywhere on the Earth's surface? Will it be the same if we go up a mountain or down a coal-mine? On the Moon? Way out in space? Would your force-weighing apparatus be any use in these other places? If not, what other sort of apparatus would you have to 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 of nature and probably the most mysterious. It acts upon us everywhere all the time. No one can ever get away from it. 12

GRAVITATIONAL FORCES

Suppose, however, that you were in a lift falling freely without a rope to restrain it. Do you think you would still feel the floor of the lift pressing against your feet? Would you feel any gravity at all? Would you have any weight? When one is falling freely under gravity, one is said to be in a weightless state. Near the surface of the Earth, such an experience will come to a sudden and unpleasant end when one hits the ground, but astronauts travelling round the Earth are often weightless for very long periods. Something to think about Would 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 you make things stay put? Would it be good for you to be weightless? What do you 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 example in 'Spring' tides. Can you explain why? Which part of the Earth do you think is in free fall?

UNIVERSAL GRAVITATION One of the most mysterious features of gravity is the fact that, unlike the other forces we have considered so far, it acts across space - across a perfectly empty vacuum. There is nothing connecting the body attracting and the body attracted - nothing between the Earth and the falling apple. This feature is termed action at a distance and the early scientists were very puzzled about it. Eventually Sir Isaac Newton avoided the problem by pointing out that, even if we do not know how it happens, there is no doubt that 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 wonder how it works. Newton himself found out most of what we know on the subject and published it in 1687 in one of the greatest books on physics, his Principia. It is only in the present century that we have learned a little more about it, and even now we do not know how it acts. Gravitation is regarded as one of the fundamental forces of nature which cannot be explained in terms of anything simpler. Perhaps the most surprising of Newton's conclusions 13

GRAVITATIONAL FORCES

9 Gravitational attraction between Jupiter and its 'moons' causes them to go round Jupiter just as the Moon goes round the Earth. Jupiter's moons can be seen in a small telescope or binoculars. Why do you think Jupiter itself is flattened?

10 The Andromeda Nebula, just visible to the naked eye on a clear, dark night, is a collection of about JOOOOOOOOOOO stars 2·5 million light years (2·4 X JO" m) from the Earth. The stars whirl around the centre and the galaxy is held together by gravitational forces. There are millions of galaxies in the universe. (Photograph from the Mount Wilson and Palomar Observatories.)

14

was that all bodies attract each other gravitationally. It is not only that the Earth attracts small objects on its surface. It also attracts the Moon and deflects its path into a more or less circular orbit around the Earth. The Sun attracts the Earth and deflects its path into a more or less circular orbit around the Sun. Also the Moon attracts the Earth and moves the oceans over its surface, causing the tides. Distant stars attract each other so that they cluster in huge galaxies, like the Milky Way. Even insignificant objects like two apples attract each other, but the force between them is far too small to be detected. Only the theory tells us it is there. There is a very famous story that when Newton was trying to explain why the Moon goes round the Earth,

he sat under an apple tree and was hit on the head by a falling apple. Suddenly he realised that the Moon falls round the Earth under the force of gravity, which stretches all that way out into space. No one is quite sure whether this 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 a long time before one can solve it. Then very often the solution comes quite suddenly, when one is thinking of something else. A chance happening, like an apple falling, may provide the vital clue. So even if the story of Newton and the apple is not true, it could be true. It tells us something about how men think.

GRAVITATIONAL FORCES

11 Bouguer's experiment (1740). The mountain Chimborazo, in South America. attracts a plumb-line towards itself by gravity. Measuring the angles that the plumb-line makes to the light from a distant star on each side of the mountain shows the existence of this attraction. The angles in the diagram are very much exaggerated and the curvature of the Earth has been neglected. (A similar experiment was carried out by Maskelyne, the Astronomer Royal. in 1774. on Schiehallion in Scotland.) I

I

,I

I I

I

I

I

I

I

I

I

I

I

:

V I I I I I I I

parallel beams of light from a distant star

I

-,

I

I I

I I

I I

I

I

I

elfi\ I

I

1 Ii G

I

I I

I I

'

TWO IMPORTANT EXPERIMENTS When Newton put forward his theory, he was able to account for so many different phenomena that nearly everyone agreed that it must be correct. Nevertheless, there were doubters who needed to be convinced that it was true. About fifty years after Newton, Bouguer was able to show that a small lead weight was attracted by a mountain, so that a plumb line on the side of a mountain did not point quite to the centre of the Earth. In 1798 Cavendish performed a celebrated experiment to measure the force between two sets of metal spheres. As the force is so small, he hung two of his spheres on a very fine wire which could be twisted by a very small force. ':' When he brought two heavy lead spheres up to the sides of the suspended spheres they moved slightly, although the movement was very small and difficult to detect, showing that they were indeed being attracted gravitationally. No one could have any more doubt. From the size of the deflection Cavendish was able to work out the size of the force between any two bodies, and this knowledge has enabled astronomers and astro-physicists

I

I I I

Chimborazo

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

15

GRAVITATIONAL FORCES

A and A' are large fixed lead spheres.

12 fine thread

Band B' are suspended lead spheres.

A'

The arrows show the direction of the attraction on Band B'

reflected light

position of spot of light shows how far rod has twisted

lamp

13

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

16

GRAVITATIONAL FORCES

to measure many properties of the stars and planets, including the mass of the Earth. Cavendish's experiment was undoubtedly one of the most important (and difficult) experiments ever carried out in the whole history of science. Bouguer and Cavendish and other physicists were able to show by direct experiment that Universal Gravitation really does exist. But even if these experiments had never been carried out we should probably still believe in it because it enables us to explain a very large number of different natural phenomena. Perhaps the greatest triumph of the theory came in 1846. The planet Uranus, which had been found in 1781 by Sir William Herschel, was found to falter slightly in its journey round the Sun, sometimes going a little too fast and sometimes a little too slow. Two mathematicians, Adams and Leverrier, thought this might be because it was being attracted by another planet moving even further from the Sun. They worked out where this should be and, sure enough, when the astronomers looked in this direction in the sky, they found a new planet, Neptune. No scientific theory can achieve a greater success than this - to predict something completely new.

THE INVERSE SQUARE LAW The force of gravity depends on the distance between the gravitating bodies, becoming rapidly smaller as they get further apart. That is one reason why we are more conscious 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 force 22

is only one-ninth, or

-1,2 and so on. A law of this type is

3 called an inverse square law. Later on, you will study several other inverse square laws in physics. The inverse square law is probably a result of the fact that we live in a three-dimensional world, with three distinct directions, for example, North, East and Up.

17

IMPACT FORCES AND

PRESSURE

COLLISIONS A moving body colliding with a stationary one can set it in motion, so it must exert a force on it. Such a force may be termed an impact force. Something to do Try to find out what happens when two Dinky cars or, better, two trolleys made of Meccano collide. Let one collide with the other at rest. What is the effect of making the moving car move faster') What happens if one car is made heavier by putting a weight on it? What happens if two cars moving in the same direction collide? What happens in a head-on collision? Then try all this again using marbles or ball bearings. Do these make it easier or more difficult to see what is happening?

Something to think about For how long do you think an impact force lasts? What would happen if you kept on throwing things at a body one after another? For example, a stream of peas 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 them move twice as fast or making them twice as heavy?

Impact forces arise in all sorts of different ways which often get very complicated, so that it is difficult to see exactly what is going on. The simplest cases occur when smooth 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 are very small. When physicists understand what happens with billiard balls, it helps them to explain the behaviour both of tiny things like atoms and enormous things like stars. It is good science to study simple things first and then go on to more complicated situations. In all impacts, one body hits another and exerts a force on it which causes it to move. If the first body moves twice as fast the forces are (usually) twice as great, and if the moving body is made twice as heavy, other things being the same, the force will be twice as great.

WINDS AND WATER JETS If a stream of particles, like peas from a pea-shooter, all hit the same target, each tiny impact produces a very small 18

IMPACT FORCES AND PRESSURES

14

force for a very short time one after the other. This is almost the same as exerting a steady force. In fact, the smaller the impacts and the faster they arrive, the more like a steady force it gets. This is how jets of water and gusts of air exert a force. Each molecule of water or air exerts an impact force one after the other. Something to think about How does wind propel a yacht? Probably you will have no great difficulty in seeing what happens when the wind is blowing from behind, but what happens when 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 does a sailor have to tack (that is, to go first in one direction and then in another) when he wants to sail against the wind?

wind

/ wind~ deflected by sails

tiller

rudder

mainsail

direction of net force on sails

15

14 and 15 How a yacht sails close hauled against the wind. The burgee on the masthead shows the wind direction. Why do the crew have to lean so far out of the boat? Sheet is the nautical term for the rope, attached to the clew of the sail, which must be held tight by the helmsman or crew.

mainsheet

cleat

FLIGHT The forces concerned with making an aeroplane fly are rather interesting and basically very simple. There is a propeller, or jet engine, which moves the aeroplane through the air and a wing which supports it against gravity. In trying to understand how an aeroplane wing works, it does not matter whether the wing moves through the air, or the air moves past the wing. Both situations produce a lift. This is why it is useful for aeronautical engineers to be able to test an aeroplane in a wind tunnel before trying to make it fly. (If you have any difficulty in seeing that the 19

IMPACT FORCES AND PRESSURES

two situations are equivalent in producing lift, get hold of a toy celluloid windmill. First blow on it and then sweep it through the air.) In explaining an aeroplane wing, we will make things easier for ourselves by supposing that the air is blowing past the wing. net force net force

-----~;:;;;:;;;;;;~~L--reduced 16 How an aeroplane wing works. Part of the force supports the aeroplane and part produces a backward 'drag'.

deflected water stream

pressure

deflected air stream

One way in which lift might be produced would be for a stream of air to strike the underside of the wing and be deflected downwards. This would produce an upward impact force on the underside of the wing which would support the aeroplane against gravity. This is in fact the mechanism of the water ski. It would not, however, be very suitable for an aeroplane because the backward drag would be too great. Instead, the air stream is deflected over the top of the wing in such a manner that the molecules are less likely to bombard the upper surface of the wing, i.e., the pressure is reduced there. This is known as the Bernouilli effect. The normal pressure beneath the wing now provides the necessary upward force. The airflow is still deflected downwards after passing over the wing (can you see why this must be so?), so that if an aeroplane flew very close above your head, you would feel the downdraught of air as it went past. Now can you see how a propeller works? It is rather like a little wing being rotated through the air, which deflects a stream of air 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 sure that the drag it exerts on the forward motion of the plane is as small as possible, and also that the machine can be manceuvred safely when it is flying. The design of a modern aeroplane demands great mathematical skill, the use of 20

IMPACT FORCES AND PRESSURES

vast computers and large-scale experiments. It may cost hundreds of millions of pounds. Jet and rocket engines also throw a jet of air or gas backwards and are themselves pushed forward by the reaction. Perhaps you have seen the same thing happening when 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 out very fast, enormous thrusts can be generated. Some rocket motors can produce a force of millions of newtons.

PRESSURE When the individual molecules of a gas or liquid collide with the walls of a container or with each other, they exert impact forces. These all add up to a steady force orpressure. If we try to compress a fluid, the molecules beat against the 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. But liquids resist compression very strongly indeed. An enormous pressure is needed to compress them even slightly. Liquids are almost incompressible. Pressure in liquids is one of the most convenient ways of exerting very large forces in the laboratory, in manufacturing industry and in various pieces of moving machinery. The basic idea is very simple. The liquid is compressed by a little piston of area a, which is connected by a strong tube (why must it be strong?) to a cylinder in which a large piston of area A can move. It does not require a very large force to move the little piston slightly and impart a large pressure to the liquid. But since pressure is, by definition, force/area and is the same throughout a liquid, large force F

At

a

little movement

piston area A

piston area a

t'-7-r-jI==J:::::::::::::::::::::::::::::::::::::::::~:::::::::::::::::-J

forc,,-e

17 Diagram ofa simple hydraulic system.

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

narrow tube (may be flexible)

21

IMPAC T FORCES AND PRESSURES

18 A simple manometer measuring an excess pressure of16·6 em of(coloured) water by 'weighing' it against the gravitational pull on the water. 19 A Bourdon gauge used to measure pressure by the deformation of the coiled tube.

20 An industrial hydraulic press which can exert a maximum of 500 000 N. The oil tank and the pump jar compressing the oil can be seen at the top. The large cylinders are at the bottom.

18

22

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, transm it it over a distance and make it turn round a corner. A familiar example is the hydraulic brake system of a car. For continuous operat ion, 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 pressu re gauge - the Bourdon type, which depends on the deform ation produc ed by pressure forces, and the manom eter, which weighs a pressure against gravity. These are examples of the two basic methods of measuring forces which were described earlier.

1

"I

IMPACT FORCES AND PRESSURES

PRESSURE IN THE EARTH Although the Earth is mainly composed of solid rocks, it is interesting to guess the pressure at its centre as though it were a liquid. This is actually quite a sensible thing to do because over the enormous distances of the Earth the rigidity or strength of the rocks is not nearly enough to support their weight. They rely on the pressure of the rocks underneath them to keep them from falling to the centre 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 of rocks in the Earth is about 5 500 kilogramme per cubic metre and the depth is the radius of the Earth, 6 400000 m. We have to be a bit more careful about g. The strength of gravity on the surface of the Earth is about 9.8 Njkg. But the strength of gravity right at the centre of the Earth is zero. Can you see why? Let us take the average value, say 5 Njkg. This may not be quite correct, but at least it lets us make a guess to find out about how big the pressure will be. A scientist would say he was 'making an order of magnitude estimate to the first approximation'. That is rather a pompous way of saying he is making a guess to see about how big it might be, which will tell him whether anything is likely to happen as a consequence. Thus we get the pressure at the centre of the Earth: P = 5 500 X 5 X 6 400 000

= 180000 000 000 N j m 2 or 1·8x10 1 1 Njm 2

This is a truly enormous pressure, much bigger than we can conceive of in everyday terms. Something to think about What sort of effect do you think such an enormous pressure will have on the rocks which make the Earth? Remember that any force will produce some deformation and that things usually break if the force on them gets too big.

You can read a lot more about pressure in the book

Pressures in this series, but pressure provides such an important way of exerting forces that it could not have been left out of this book altogether. 23

COHESIVE FORCES

A less obvious type of force is exerted whenever you pick up one end of a stick, and the other end comes too. Have you ever thought how surprising it is that this happens? The far end of the stick can only begin to move if some sort of force is exerted on it, so there must be a very complicated set of forces acting right through the stick. There must be similar forces through any other piece of solid matter. These forces are called 'cohesive' forces. Cohesive forces are the forces which hold pieces of matter together and give them strength. All matter tends to stick together to some extent - some substances, such as iron and diamond, do so much more strongly than others. Gas molecules have so little cohesion that they just flyaway from each other. A great many physicists and chemists and other scientists devote themselves to finding out how different substances stick together, particularly those 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 to come together, and another which keeps them apart, the two being in balance. If there were no repulsive forces, the atoms would just collapse in on each other until some sort of force prevented them going any further. These balanced attractive and repulsive forces are also responsible 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, it will overcome the forces between the molecules, and the

~ force of repulsion ~

21 The forces between the atoms in a solid. The atoms arrange themselves so that the two sets of forces are just in equilibrium. There is also attraction between atoms which are not 'next door' to each other.

24

force of attraction both sets of forces act through the centres of atoms

COHESIVE FORCES

material will break or collapse. Under the enormous pressures at the centre of the Earth the atoms themselves break down to some extent and occupy a much smaller volume than normally. One consequence of this is that below a depth of about 3000 km rocks do, in fact, behave like a liquid. Convection currents in the liquid rock are now 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 find that a force acts between them which tries to prevent the motion. This force is called friction and it is a very familiar kind of force. It is peculiar because it cannot start a body moving - it can only stop it once it is moving, or prevent it from ever starting to move. Very often we regard friction as a nuisance because it makes it more difficult to bicycle, or slows down our car, but in fact life without friction would be almost impossible. Think what would happen if there were no friction between our feet and the floor. Something to think about Make a list of examples of useful friction and another of harmful friction. Can you suggest ways of increasing friction when we want it and of decreasing it when we need to keep it as small as possible?

Something to do See if you can devise a simple way of finding out how much friction there is between two flat surfaces of various materials. The rubber bands might be useful 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 surfaces gives the greatest friction? Which pair gives the least? Is the friction the same everywhere on the surface? Is it the same when the surfaces are sliding over each 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 than quantitative - they can answer the question, 'What happens?' but not the question, 'How big?'

25

COHESIVE FORCES

In fact, friction has always been regarded as rather a difficult field for scientific investigation, because little things like a greasy fingerprint can upset all the results. It is only in the last twenty years that really reliable and reproducible results have been obtained, that is, results which can be obtained by different people without disagreement. This is, of course, very important if something is to be regarded as properly scientific. Nevertheless, some work was done on friction a long time ago and led to some rather important conclusions. The friction between two bodies can never be greater than a certain amount called the limiting friction. When the bodies are sliding over each other, the friction is a little less than this. Did you find this in your experiment? If the normal or perpendicular force pressing the two surfaces together is doubled, the limiting friction is also doubled. 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 is really surprising? What do we call a force divided by an area?

normal force

normal

o rce

moving

force

~ I

friction force

I

moving ~ _ ~ force r------'===-------'------,

f or m a l

~ I ] force

22 Illustration of the Laws of Friction. (i) Double the normal force - double the friction. (ii) Double the area in

contact - friction remains the same.

moving force

ii

normal force

friction force

f

moving

force

~-;::C=::=:J:t "'"

f

The actual value of the limiting friction depends on what two materials are pressed together. Smooth surfaces like glass and polished metal have very little friction. 26

COHESIVE FORCES

Rough surfaces like sawn wood or sandpaper have a lot of friction. In nearly every case the limiting friction is less than the force pressing the surfaces together.

A THEORY OF FRICTION

23 A theory of friction. As the force pressing the surfaces together increases, the high spots in (i] like A, Band C squash fiat until the area in contact is large enough to support the force as in Iii).

Quite recently it has become possible to explain these effects as a result of cohesive forces between atoms in the two surfaces. We must remember that even the smoothest surface would look very rough and, indeed, mountainous if we were only about the size of an atom. So when we press two surfaces together It will be something like Figure 23. Only high spots like A, Band C will actually touch. So of course the pressure at these points will be quite enormous, and the tiny 'hills' which are in contact will tend to squash flat. The harder we push the surfaces together, the more these points squash. They will go on squashing until the area in contact has become big enough to support the force. This squashing under pressure is really quite drastic (almost as bad as the squashing of the atoms at the centre of the Earth). The two bits in contact become almost liquid and flow into each other and stick together - this process is known as cold welding and is sometimes used by engineers to stick things together. Now, if we want to make the surfaces slide past each other we have got to break all these tiny little welds, and as fast as we do so, new points will come into contact and weld together. Something to think about Can you see how this model explains why we get friction and why the laws of friction are what they are'? If you have any difficulty, you might find it helps to try pressing two rough pieces of plasticine together and then trying to make one slide past the other.

There is, unfortunately, no space to describe the ingenious experiments which have been carried out to show that this is the correct explanation of friction, but before leaving this topic we must show why it is a useful, as well as an interesting, theory. If we want to make friction as small as possible, the 27

COHESIVE FORCES

theory tells us that we must either prevent the high spots from sticking together or make sure that it is very easy to tear them apart again after they have stuck. A film of oil can prevent the two surfaces ever quite sticking together. That is why lubrication is so important in all the moving parts of a machine. It not only reduces friction, 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 same purpose of keeping the surfaces apart, and allows sliding to 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 the surfaces of quite a soft material, so that even if they do stick together, they can easily be pulled apart again. This is the principle used by engineers in white metal bearings which are used in motor-car engines and other pieces of machinery. Yet another way is to look for a material whose atoms are so strongly joined to one another that they do not easily 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 little friction and is used, among other things, for the best and most expensive skis. The theory of friction is a valuable guide when it comes to looking for new materials which will give low friction.

SURFACE TENSION Things to do Make a needle float on water. You will need a very steady hand and clean fingers. It may help to float the needle on a piece of paper which will eventually sink. 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 it just touches the water. The boat should dart about over the water. Watch carefully what happens to a drop of water placed on a greasy surface and another on a clean surface. What effect does adding a little detergent have on the drop placed on a greasy surface? Watch carefully what happens when a drop of water drips off a tap. Try to waterproof a piece of blotting paper by dipping it in melted wax (be careful not to start a fire) or a waterproofing solution. Blow some bubbles with soap solution and a piece of tubing. See if you can

28

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

COHESIVE FORCES

glass tubes

little bubble

rubber tubes big bubble

Something to think about Why does a piece of blotting paper soak up water, but a raincoat or a piece of canvas repel water, "atleast until it becomes really wet? Can you see any connection between the various things you have just been asked to do?

Some of the most striking results of the cohesive forces between atoms are seen in liquids. All liquids appear to have an invisible 'skin' round them which pulls them into drops. 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. 25(a) (right) How cohesiveforces cause surface tension. The attractive forces on a molecule in the surface of a liquid tend to pull it back into the liquid. If an elastic skin is stretched and deformed: the net force it exerts is perpendicular to the skin. Thus a liquid behaves as if it were covered with an elastic skin. 25(b) stretched skin

~ force of repu Ision

------7 force of attraction

net force both sets of forces act through the centres of atoms

Figure 25(a) is very similar to Figure 21 representing a solid. This does not mean that liquids are the same as solids inside. Such diagrams are intended only to illustrate symbolically a single point - in this case the balance between attractive and repulsiveforces.

Figure 25(a) shows some of the atoms near the surface of a liquid. The molecules in the body of the liquid are attracted by other molecules all round them and there is no force on them in any particular direction. But at A we 29

have a molecule trying to get out of the liquid. The attractions of the other molecules tend to pull it back. Can you see 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 smallest possible value - thus small drops left to themselves become spheres. What would happen to these spheres if there were not repulsive forces, as well as attractive forces, between the atoms? When a liquid is in contact with a solid, a great deal depends on whether or not it wets the solid. If the attractive forces between the solid and the liquid are greater than those between the molecules of the liquid, then the liquid wets the solid, and it tries to spread out all over the solid to make the area of contact as large as possible. But if the forces of attraction between the molecules of the liquid are greater than those between the liquid and the solid, the liquid wants to have nothing to do with the solid and retreats so that the area of contact is as small as possible. Water will wet a clean surface but not a greasy one. 26(a)

26(h)

26(a) Water wets glass and rises in a capillary tube. On the right is a drop of water. 26(b) Mercury does not wet glass and falls in a capillary tube. On the right is a drop of mercury.

Sometimes wetting is a good thing, and to help it come about we can add something to the liquid to reduce the surface tension. Soap has this effect with water. If the 30

COHESIVE FORCES

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

27 The addition of a little of the wetting agent 'Teepol' reduces surface tension and enables the water to wet the card. water and 'Teepol'

pure water

Sometimes we want to prevent wetting - then it may help to cover the solid with something which does not attract the liquid. Grease and wax and 'silicone' all have this effect with water. 28 Mosquito larva floating in water.

Something to think about What must you do to waterproof a fabric or a tent? How water soaking through the brickwork of a house? When a photograph is developed, it must be soaked in How could you make sure that the developing solution can the photograph? What effect do you think camphor has on the surface (Think of your camphor boat.)

could you prevent a special solution. get to all parts of tension of water?

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 two pieces of metal together, because he must make sure the solder 'wets' the metal. It is also important in Nature. Very small organisms like water boatmen and mosquito larvae make use of it to keep themselves floating on the surface of a pond. What do you think we should do to the water to get rid of mosquitoes? 31

ELECTRIC AND MAGNETIC FORCES 29(a)

Have you ever played with a magnet, or better still, with two magnets? Magnetic forces are very striking and quite different from the forces we have considered so far. Probably, too, you will have picked up little pieces of dust with a plastic comb rubbed on your handkerchief or heard a nylon garment crackle as you take it off. These are examples of electric force. The ancient Greeks knew about electric and magnetic forces more than two thousand years ago, 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 is a natural plastic which was used by the Greeks for making ornaments, and they noticed that when it was rubbed it attracted small objects to itself. 29(b)

29(8) Dust sticks to the wall by electrostatic attraction. 29(b) Model of electrostatic dust precipitator used to remove dust from the smoke emitted by power stations. Highvoltage equipment is shown above. Dust is attracted to charged wires and shaken off mechanically to fall through the hoppers below. 30 Cathode-ray oscilloscope, in which electrons which produce a picture are moved by electrical forces. 31 Early electroscope. The gold leaf moves under the influence of electrical forces and reveals the presence ofelectric charges. 32 William Gilbert.

32

30

The forces produced by permanent magnets are rather small. Can you think of any uses for them, apart from the magnetic compass? There are a few, but they are not very important. Electrical forces are also very small and not very obvious, and they do not have very many direct uses. A few are illustrated in the pictures. Points to think about In what sort of ways are electrical and magnetic forces alike? How are they different? Are they like gravity? Can you think of two important differences between 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 we not 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 a force outside the box?

31

MAGNETIC FORCES

It is sometimes said that William Gilbert, who lived from

32

1540 to 1603 and was Queen Elizabeth's doctor, was the first modern scientist. He became famous for the experiments he did on electricity and magnetism. This was the time when sailors were making great voyages of discovery to unknown parts of the world. One of their great difficulties was to know where they were and in what direction they should go. The magnetic compass was a great help to them in all this. William Gilbert listened to stories of their experiences 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 to be useful, or because he was curious about magnets and compasses? These are both powerful reasons for studying science and no one knows which is the most important. When William Gilbert did these experiments, and many others like them, he did not have strong permanent magnets 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 made his experiments very difficult to carry out successfully. Some of his most important experiments were carried out with a sphere of lodestone, which he called a 'Terrella', or 'Little Earth'. 33

33

Something to do

N

® N

You can try some of William Gilbert's experiments for yourself. You need a strong magnet, some nails, a steel knitting needle, some cotton, a plotting compass, a small magnet and some plasticine. See how many nails you can hang from your magnet in a long chain. Does it help to join the chain up to the other pole of the magnet? What happens to the nails when they are in contact with the magnet? In which direction does the compass needle point when it is a long way away 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 the magnet? Hang up the knitting needle from its centre. Does it hang horizontally? If necessary, move the cotton until it is horizontal. Now magnetise it by stroking with 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 it up 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 middle of a lump of plasticine and roll it into a sphere. Now see what happens to the direction of the compass needle when you place it at various positions on your sphere. Is it anything like what happens to a compass needle at various places on the Earth? Turn the compass on its side so that the edge of its case just touches the plasticine. What is its direction now? Is it anything like the hanging knitting needle? Do you think you now know what the Earth's magnetic field, which makes a compass point North and South, is like? The ends of a magnet, where the magnetism appears to be, are called its poles. The pole of a compass needle which points towards the North is called a North pole. Do two North poles attract or repel each other? If the Earth has a magnet inside it, what sort of pole must it have at its geographical North end?

ELECTROMAGNETIC FORCES 33 (a) Compass direction finding on

Terrel/a. (b) Compass needle on its side near Terrella. (c) Magnetising a knitting needle. 34 Diagram from Gilbert's book, 'De Magnete', published in 1600, showing the direction taken up by a compass needle at different points on the Terrella.

34

Although electrical and magnetic forces occurring naturally are very small, the magnetic forces produced by an electric current - electromagnetic forces - can be very large. Have you ever made a magnet by winding some insulated wire round a nail and connecting the ends to a battery? 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 the most important forces of all. We now know that all matter consists of atoms and that atoms are composed of electrically charged particles. A complete atom has as much negative charge as positive charge, so the two kinds of charge very nearly cancel out. That is why electric forces usually seem so small. It is only when a few atoms have

ELECTRIC AND MAGNETIC FORCES

35

been partly broken up and lost some of their electric charge that electric forces can come into play on a scale large enough for us to see. But the electrical forces between one atom and its nextdoor neighbour can be very large. These forces enable atoms to join together to form molecules and chemical compounds. The whole of chemistry depends on electrical forces. They also stick the atoms in a solid or liquid together, so cohesive forces are really electrical in nature; if atoms are squeezed too tightly together, other electrical forces try to push them apart again. Remember that electrical forces can repel as well as attract. So most of the forces we have talked about so far, except gravitational forces, are really electrical. Understanding how these electrical forces can cause cohesion, elasticity and friction helps engineers and scientists to control these forces and make them perform useful functions. A great deal of modern scientific research is devoted to this. Something to think about What happens when two bodies collide? Do they really come in contact? Or do the electrical forces between them really produce an action at a distance like gravity?

35 The electric motor, the loudspeaker and the relay represent three common uses oj electromagneticforces. Electric motors of all shapes and sizes are very widely used in industry, in transport, in the home and many other places. 36 Electromagnet in use in a scrapmetal yardfor crushing purposes. 36

35

MUSCULAR FORCES

When we think about forces, we probably think first of all of the forces we can exert with our own bodies - by our muscles. Let us think what happens when we contract the biceps muscle in the arm to raise a weight and then hold it steady, We can do this quite automatically without thinking about it at all, but it is really quite a complicated process.

triceps muscle lowers arm

37 Diagram of biceps and triceps muscles.

~~don

attaching muscle to bone

upper arm

To understand what happens, it may help first of all to find out how a muscle differs from some of the other force-producing devices we have looked at. A stretched spring 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 a spring 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 rod by tying it in place, so perhaps when we hold up a weight our biceps muscle is something like a string tying the forearm to the shoulder. But a string can go on holding a weight (that is, exerting a force against gravity) for ever without getting tired. We quickly want to put down a heavy weight. A muscle is evidently doing something all the time it is contracted even if it is not moving. Clearly there are important differences between a muscle and a spring or a string, although both these analogies may occasionally be useful. To find out more about muscles, we have to look at their detailed structure. 36

MUSCULAR FORCES

This has been done by physiologists, who find that every muscle consists of a bundle of individual fibres, each with its own nerve. You can see these fibres in the meat you eat. Normally a fibre is relaxed and quite straight, but when a nerve impulse arrives it produces a chemical change within the fibre, which causes it to try to contract and become much shorter. In doing so, it can exert a small force. The more fibres that contract together, the greater the total force exerted by the whole muscle. By balancing the forces in two opposed muscles, like the biceps and the triceps (which straightens the arm), we can hold our hand steady wherever we want it. This balancing is done automatically by our nervous system, so we do not have to think about it. This is not the whole story. Before long the chemicals produced by the nerve diffuse, or drift, out of the fibre, allowing the fibre to relax until another nerve impulse arrives, when it suddenly contracts again. So our nervous system can adjust the average force exerted by the whole muscle, not only by varying the number of fibres which contract, but also by varying the frequency with which they contract. The faster they do it (up to about five times a second, which is as fast as the mechanism will work) the greater the force. Muscle force is not a static force, like that in a spring, which requires nothing to maintain it. It is a dynamic force rather like that produced by a stream of particles impinging on a surface. No wonder we get tired when we try to keep up a steady pull for a long time! Because more fibres contract together at some instants than at others, the force is not quite steady and we tremble slightly when we really exert ourselves (don't confuse this with the shake of your hand produced by the beating of your heart). This knowledge of how a muscle works makes it easier for doctors to find out how to treat muscular disease.

37

FORCES DUE TO LIGHT PRESSURE

38 Apparatus to demonstrate light pressure. If the light is switched on and off with the right period, it can set the foil suspended in a very high vacuum swinging like a pendulum.

38

The last method of exerting a force which we will discuss is one which has probably not occurred to you, since it is far too small to feel or to produce any visible effects in the everyday world. It is the force exerted by light falling on a body. You will probably be surprised to learn that light can exert a force. Yet there were strong theoretical reasons for believing this long before it was shown to happen experimentally. Light is a form of wave motion and all waves can exert forces. This is fairly obvious in the case of waves on water, since they can make a floating cork go up and down. Similarly, a sound wave can make our eardrums vibrate - or a tin tray vibrate on the piano when it is played. It is reasonable to suppose light waves should also exert a force - sometimes called radiation pressure - in the same sort of way. Although the force exerted by light is so very small on

FORCES DUE TO LIGHT PRESSURE

Earth, so that we are quite unconscious of it, it is very important in the Sun and other stars. The centre of a star is very, very hot and gives out intense radiation which presses upwards on the outer layers. If there were no such force, all the stars would collapse under their own gravitation to a very small fraction of their present size. The Universe would then be a very different sort of place and there would almost certainly be no life anywhere. At the beginning of this book we said that forces can only be exerted by one body, or piece of matter, acting on another. 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' we are used to.

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

39

SUMMARY AND CONCLUSIONS

In the first chapter of this book we saw how forces are responsible for making bodies start to move, for stopping them once they are moving and for deflecting them from one direction to another when they are moving. Very often, however, several different forces can act on a body in different directions so that they cancel out, and then there is no starting or stopping, although very strong forces are acting. Forces which cancel out in this way are said to be in equilibrium. Once a body has started to move, it can keep on going in a straight line at the same speed without the aid of any force. The only forces on an arrow once it has left the bow are the resistance of the air and gravity. The former slows it down slightly. The latter pulls it out of a straight path but does not alter its speed very much unless it is shot straight up into the air. There is no force to keep it going and none is needed. Whenever we see a body moving at a constant speed in a straight line, we can be sure that there are no forces acting on it - or, if there are, that they are in equilibrium. In fact, because all bodies on Earth are subject to gravity and almost always to friction, we practically never see bodies move with truly constant speed in an exact straight line, but fast-moving bodies like bullets and arrows come quite close to it. Even so, we must take the pull of gravity into account when aiming, if we are to hit a distant target. Something to do I. Find out 2. Watch a This is one does occur.

how the sights of a rifle work. ball bearing drop through a viscous liquid like glycerine or treacle. of the very few situations where the ideal case of constant speed Can you see what happens to the forces?

In the rest of the book we talked about the different kinds of force which occur in nature. Basically, there are only two':' distinct kinds of force: first, gravity, which makes every piece of matter in the universe attract every other 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 concerned with the nuclei inside atoms, but these have no effect on everyday life, so we can forget about them unless we are nuclear physicists.

40

SUMMARY AND CONCLUSIONS

attract each other if they have unlike charges, or repel each other if they both have the same kind of charge, again according to the inverse square law. Both these forces act across empty space without any material contact between the bodies. It is much too difficult, however, to work out all the myriad forces of the world around us just in terms of these two. It is much simpler to think in terms of several other types of force. First, there are the cohesive forces which hold solids and liquids together and which are the result of equilibrium between forces of attraction and repulsion between atoms. These include elastic forces, which come into play when a body is stretched or compressed or twisted and which often obey the very convenient Hooke's Law; frictional forces, which occur when one body moves over or through another; and surface tension, which makes a liquid appear to be covered with an invisible skin. Secondly, there are the impact forces, which arise when a moving body collides with another body and which can produce the 'rocket' effect. Besides the direct impact of macroscopic bodies - that is, bodies which are large enough to be seen or felt - there is the effect of the impact of innumerable small particles (molecules) which produce the effects of pressure in a liquid or gas. High pressure can arise either because the fluid is very hot and therefore the molecules are moving very fast, or because the fluid is compressed by a very great weight of other material on top of it. Towards the centre of the Earth, the pressure becomes so great that even solid rocks become like a liquid. Thirdly, there is the magnetic force which arises between magnetised pieces of iron and the much more important electromagnetic force which arises from an electric current, 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 feel it, but which, in the fiery furnace of the Sun, is strong enough 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 AND CONCLUSIONS

scale, yet vitally important to us and, like almost everything in the biological world, extremely complicated in the way they work. There are many ways of measuring forces, but almost all of them depend on one of two basic principles. We can weigh a force by balancing it against gravity, or we can measure 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 kinds of force. Some people find them interesting in themselves and are fascinated by working out how the different sorts of force come about and the consequences of the interplay of the forces in a complex situation. Most people, however, want to know what benefit they can get from a piece of knowledge. There are innumerable benefits to be gained from a study of forces. If we know the forces acting, then we know how things will move - that is, how they work and what will happen to them in the future. If we want to make things happen in a certain way, we must study the forces involved and adjust them to bring about our aims. Before we can get a man to the Moon, we need to know, very precisely, the force of gravity everywhere along his path, so that we can fire the rocket at just the right time, and with just the right speed and direction to get him there safely.

FORCES AND THE ENGINEER Knowledge and understanding of forces are particularly important for engineers, and we will conclude by taking a very brief look at a few of the places where they arise in engineering. The first duty of an engineer is to make sure that the things he builds are strong enough to stand up to the forces they will experience in normal working without 42

40 A tensile testing machine, capable of exerting up to 50 tons force. to measure the breaking strength ofpieces of metal. Can you see how the force is produced?

breaking or falling down. So the first thing the engineer must do is to measure or calculate these forces. This immediately poses a problem: what is normal working? This is something which can be decided only by careful judgement in the light of past experience. There is no exact answer. In Great Britain, for instance, we would not normally need to make a building strong enough to withstand the force of a 45 m/s wind, because such winds occur very rarely - perhaps once in a century at anyone place - and it may seem reasonable to risk the building failing if such an abnormal hurricane should occur. But we must build strongly enough to withstand 35 m/s winds, which do happen every few years. Once he knows the forces involved, the engineer must make sure the materials he proposes to use will be strong enough - or rather, find out what thickness of material will be strong enough. For this, it is necessary to place a sample of the material in a testing machine, which will keep increasing the force until the sample breaks. The picture shows such a machine. Why do the parts of the machine have to be so thick? Another important consideration is to use the smallest amount of material which will do the job adequately - in other words, to make the construction as cheap as possible. This means designing the shape very carefully, so that the forces are spread out through the whole of the structure and not concentrated at a few points which would become especially liable to break. Hundreds, or thousands, of calculations are needed to find the best design - a job for a computer. The result is often not only economical, but strikingly beautiful. The pictures on the next two pages show a few examples of modern structures designed to equalise the stresses. Many of the recent improvements in design have been made possible by the use of materials which have been invented in the last few years by pure scientists. It is now possible to produce 'tailor-made' materials which will stand up to large forces under arduous conditions, without needing great thickness. You can read about some of these in the companion volume in this series on Materials. Notice, in particular, how much stronger reinforced or 43

41 Flying buttresses at Westminster 41 A bbey. These add much to the appearance ofthe building. but they are mainly there for a purpose. Without them the roof would collapse. Can you see why? 42 Roman Catholic Cathedral, Liverpool, opened 1967. This is an outstanding example ofa modern building made possible by new materials. Notice how cleverly the reinforced concrete ribs have heen used, hoth to support the building and to lead the eye up to the crown.

43 The Forth Road Bridge, Scotland, opened 1966. Can you see how the weight of the bridge is supported? The designers also had to make sure the bridge will not blow down in a high wind. Models were tested in a wind tunnel.

44

44 44 Prestressed concrete beams being used in bridge construction. Can you see the reinforcing wires, which have been stretched so as to keep the whole beam in compression? Why does this make the beams stronger, and why are no wires needed in the middle of the beam? What are the loops at the ends of the beams/or? 45 Wagondrifi Dam, Natal, built 1965.

Can you see how the shape ofthe dam, which is 30 m high, helps to support the weight oftne water?

45

prestressed concrete is than plain concrete, because the reinforcing bars can take up the forces where the concrete is weak and vice versa. These examples are taken from civil engineering, where the forces involved are static forces, due to the weight of the structure. It becomes much more difficult to 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 a bicycle. Besides the weight of the rider and the upthrust of the road, there is one set of forces which keeps the bicycle going along a straight road, another set which enables it to turn a corner and yet another set to stop it. Something to do See if you can make a list of the various forces acting in a bicycle.

45

SUMMARY AND CONCLUSIONS gravity on rider

1

hand on handlebar

tension in chain

chain on wheel

bike on wheel

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

The rider presses down on the pedals, and the force on the pedals is transmitted through the chain wheel and the chain to the back wheel. This force, together with friction between the tyre and the ground, pushes the bicycle along. When he wants to turn, the rider applies a force to the handlebars, which causes the front wheel to turn and the bicycle follows in the new direction. But this is not all. A lot of the steering is brought about by the rider leaning inwards, so that part of his weight makes him 'fall' round the circle. Dynamic forces can be quite complicated. When he wants to stop, the rider applies a force to the brake lever, which is transmitted through the cable to the brake blocks, which squeeze the wheel and cause friction. The friction between wheel and brake blocks, plus the friction between tyre and road, brings the bicycle to rest. Designing a bicycle which will stand up to all these forces, even with a heavy rider, and still be light and easy to propel, as well as good-looking, is no easy task, and there are other problems as well. The bicycle must ride easily over bumps in the road and the gear ratio must be right - both of which involve forces again. Probably the ideal bicycle has yet to be designed. There is a prize on offer, which has not yet been won, for a really good bicycle design. 46

force on

SUMMARY AND CONCLUSIONS

brake pedal

twist in shaft

.J,~

47 Some of the forces involved in driving a car.

pressure in brake fluid presses brake shoes against brake drums

tyre on ground

~1'

ground on tvre

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

Luckily, when it comes to designing complicated machinery it is possible to deal with each part separately, so that one man can concentrate on the engine, another on the clutch, another on the gearbox and another on the seats (yes, even everyday things like seats need careful design if they are to be efficient). Without this division of labour, it is unlikely that engineering design would ever get very far. Something to think about Would you rather be a pure scientist who finds out how things work and how to make new materials, or an engineer who designs and builds the equipment needed by other people? Both are important in the modern world, but most people are better suited to be one of these rather than the other.

CONCLUSION I hope you have enjoyed this little book on Forces and now find that there is more to the world than you had realised before. When you see things moving, or come 47

SUMMARY AND CONCLUSIONS

48

across great engineering structures, ask yourself, 'What are 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?