contents · 29 simple harmonic motion 453 29.1 oscillating motion 453 29.2 sine waves 456 29.3...

Copyrighted material – 9781137443236


Contents

Preface ix

How to use this book x

Acknowledgements xi

Units and Measurements 1

Philosophy and practice in science 1The S.I. system of units 1Symbols and equations in physics 3Making measurements in physics 4Uncertainty and accuracy 6

Summary 8Revision questions 8

PART 1 Mechanics 9

1 Forces in Equilibrium 11

1.1 Force as a vector 111.2 Turning effects 151.3 Stability 171.4 Friction 191.5 Equilibrium conditions 22


2 Dynamics 27

2.1 Speed and distance 272.2 Speed and velocity 292.3 Acceleration 302.4 The equations for uniform

acceleration 332.5 Acceleration due to gravity 352.6 Rates of change 38


3 Force and Motion 41

3.1 Newton’s laws of motion 413.2 Force and momentum 45

3.3 Conservation of momentum 47Summary 51Revision questions 51

4 Energy and Power 53

4.1 Work and energy 534.2 Power and energy 564.3 Efficiency 584.4 Energy resources 60


PART 2 Properties of Materials 67

5 Matter and Molecules 69

5.1 States of matter 695.2 Elements and compounds 715.3 The Avogadro constant, NA 745.4 Intermolecular forces 75


6 Thermal Properties of Materials 79

6.1 Thermal expansion 796.2 Specific heat capacity 816.3 Specific latent heat 846.4 Heat transfer 866.5 More about thermal conduction 89


7 Strength of Solids 94

7.1 Measuring force 947.2 Force and materials 967.3 Stress and strain 977.4 Stress versus strain curves 1007.5 Elastic energy 103


v




CONTENTSvi

8 Pressure 106

8.1 Pressure and force 1068.2 Hydraulics 1078.3 Pressure in a fluid at rest 1098.4 Measurement of pressure 1108.5 Flotation 112


PART 3 Waves 117

9 Properties of Waves 119

9.1 Types of waves 1199.2 Measuring waves 1209.3 Properties of waves 1229.4 Longitudinal and transverse waves 1269.5 Polarised light 128


10 Sound 131

10.1 The nature and properties of sound 13110.2 The human ear 13310.3 Ultrasonics 13510.4 Vibrating strings 13710.5 Acoustic resonance 139


11 Optics 145

11.1 Interference and the nature of light 14511.2 Reflection and refraction of light 14811.3 Lenses 15111.4 Optical instruments 155


12 Electromagnetic Waves 160

12.1 The visible spectrum 16012.2 Types of spectra 16112.3 Infra-red and beyond 16612.4 Ultraviolet radiation, X-radiation and

gamma radiation 170Summary 172Revision questions 173

PART 4 Electricity 175

13 Introduction to Electricity 177

13.1 Static electricity 17713.2 Current and charge 18013.3 Potential difference 18513.4 Resistance 188


14 Electric Circuits 194

14.1 Cells and batteries 19414.2 The potentiometer 19814.3 The Wheatstone bridge 20114.4 Resistivity 20414.5 Electrical measurements 205


15 Capacitors 211

15.1 Storing charge 21115.2 Capacitor combinations 21415.3 Energy stored in a charged cell 21715.4 Capacitor design factors 21915.5 Capacitor discharge 221


16 Electronics 226

16.1 The systems approach 22616.2 Electronic logic 22716.3 Electronics at work 23116.4 Operational amplifiers 23416.5 Multivibrators 241


PART 5 Fields 244

17 Electric Fields 247

17.1 Electrostatic forces 24717.2 Electric field patterns 24917.3 Electric field strength 25317.4 Electric potential 258





CONTENTS vii

18 Magnetic Fields 262

18.1 Magnetic field patterns 26218.2 Electromagnets 26518.3 The motor effect 26618.4 Magnetic flux density 26918.5 Magnetic field formulae 27218.6 Magnetic materials 275


19 Electromagnetic Induction 280

19.1 The dynamo effect 28019.2 Magnetic flux 28419.3 The alternating current generator 28719.4 The transformer 29019.5 Self-inductance 294


20 Alternating Current 299

20.1 Measurement of alternating currents

and voltages 29920.2 Rectifier circuits 30220.3 Alternating current and power 30420.4 Capacitors in a.c. circuits 30720.5 Coils in a.c. circuits 31120.6 Resonant circuits 313


PART 6 Atomic and NuclearPhysics 319

21 Electrons and Photons 321

21.1 Electron beams 32121.2 The charge of the electron 32621.3 Photoelectricity 33021.4 Electrons in the atom 33421.5 X-rays 33821.6 Wave mechanics 342


22 Radioactivity 349

22.1 Inside the atom 34922.2 Radiation from radioactive

substances 35222.3 The range and penetrating power of

alpha, beta and gamma radiation 356

22.4 Radioactive decay 36022.5 The mathematics of radioactive

decay 363Summary 365Revision questions 366

23 Energy from the Nucleus 367

23.1 The nature of force 36723.2 Binding energy 37023.3 Nuclear power 37523.4 Probing the nucleus 380


PART 7 Further Physics 387

24 Fluid Flow 389

24.1 Flow patterns 38924.2 Flow rates 39124.3 Viscous flow 39424.4 Non-viscous flow 398


25 Gases 402

25.1 The gas laws 40225.2 The ideal gas equation 40725.3 The kinetic theory of gases 408


25 Thermodynamics 415

26.1 Temperature 41526.2 Heat and work 41826.3 The thermodynamics of ideal gases 42026.4 The Second Law of Thermodynamics 426


27 Uniform Circular Motion 431

27.1 Circular measures 43127.2 Centripetal acceleration 43327.3 Reactions and rides 435


28 Gravitation 440

28.1 Newton’s theory of gravity 44028.2 Gravitational field strength 440




CONTENTSviii

28.3 Gravitational potential energy 44628.4 Satellite motion 448


29 Simple Harmonic Motion 453

29.1 Oscillating motion 45329.2 Sine waves 45629.3 Forces in oscillating systems 45829.4 Resonance 462


30 Rotational Dynamics 466

30.1 Angular motion 46630.2 Moment of inertia 46930.3 Rotational kinetic energy 473

30.4 Angular momentum 477Summary 481Revision questions 481

Further Questions 482

Using Spreadsheets 494

List of Experiments in the Book 497

Location Guide to Mathematical Skills 499

Summary of Equations 500

Useful Data 504

Answers to In-text Questions andRevision Questions 505

Answers to Further Questions 534

Glossary 535

Index 543




Forces in Equilibrium

OBJECTIVES

After working through this unit, you should be able to:

. represent a force geometrically or numerically

. combine two or more forces

. resolve a force into perpendicular components

. describe the condition for a point object to be in equilibrium

. draw a free-body diagram of the forces acting on a body

. understand and use the concept of centre of gravity

Force as a vector

Vectors and scalars

An air traffic controller needs to know the position, height, speed and direction ofmotion of an aircraft in order to monitor its flight path. Each piece of informationis important, including the direction of motion. The position and height of anaircraft gives its displacement, which is its distance and direction from the airtraffic controller. Its speed and direction of motion define its velocity. See Fig. 1.1.

Displacement and velocity are examples of vector quantities because they havea direction as well as a magnitude. Distance and speed are examples of scalarquantities because they have a magnitude only. Any vector may be represented byan arrow of length in proportion to the magnitude of the vector and in theappropriate direction.

. A vector is defined as any physical quantity that has a direction. Examplesinclude weight, force, displacement (i.e. distance in a given direction), velocity,acceleration and momentum.

. A scalar is any physical quantity that has no direction. Examples include mass,energy and speed.

1.1

UNIT

1CONTENTS

1 Force as a vector

2 Turning effects

3 Stability

4 Friction

5 Equilibriumconditions

Summary

Revision questions

11

N

SMAP

0EW

Kilometre grid

Velocity = 60 ms–1 south-eastDisplacement from 0 = 3.5 km36°E of due North (height not shown)

Fig. 1.1 Vectors and scalars




MECHANICS12

Force as a vector

Force is measured in units called newtons (N).The weight of a mass of 1 kg isapproximately 10 N on the surface of the Earth. An object acted on by two forceswill be at rest if the two forces are equal and opposite, as in Fig. 1.2a. However, ifone of the forces is larger than the other, their combined effect is the differencebetween the two forces, as in Fig. 1.2b.

Each force in Fig. 1.2 can be represented by a vector (i.e. an arrow of lengthproportional to the force in the appropriate direction). From now on in this book, abold symbol will denote a vector. For example, in Fig. 1.2b, F1 denotes force vectorF1 and F2 denotes force vector F2.

The parallelogram of forces

Fig. 1.3 shows how to work out the effect of two forces, A and B, acting on a pointobject but not along the same line. Each force is represented by a vector, such thatthe two vectors form adjacent sides of a parallelogram. The combined effect of thetwo forces, the resultant, is the diagonal of the parallelogram between the twovectors. The resultant is therefore given by force vector B added onto force vector A.Fig. 1.4 shows how to balance out the resultant of A and B with an equal andopposite force, C.

1.1A QUESTIONS

1 A point object is acted on by a force of 5.0 N acting dueEast and a force of 12.0 N. Use the parallelogram methodto determine the magnitude and direction of theresultant force when the 12.0 N force actsa) due East,b) due West,c) due North,

d) 608 North of due East,e) 608 North of due West.

2 A point object is acted on by forces of 6.0 N and 8.0 N.Determine the magnitude of the resultant of these twoforces if the angle between them isa) 908,b) 458.

F1 = 20 N F2 = 20 N

Object

(a) F1 = F2 so object is at rest

F1 = 20 N F2 = 30 N

Object

(b) F1 < F2 so object moves towards F2. The resultant force is 10 N

Fig. 1.2 Forces in opposite directions

A = 4.0 N

A + B = 6.1

N

B = 3.0 N

Fig. 1.3 The parallelogram of forces

A

C

A + B

B0

Fig. 1.4 Equilibrium




FORCES IN EQUILIBRIUM 13

The condition for equilibrium of a point object

In general, a point object acted on by two or more forces is in equilibrium (i.e. atrest) if the resultant of the forces is zero.

1 For equilibrium of a point object acted on only by two forces, A and B, the twoforces must be equal and opposite to each other. The resultant of the two forcesmust be zero.

Aþ B ¼ 0

2 For equilibrium of a point object acted on by three forces, A, B and C, theresultant of any two of the three forces is equal and opposite to the third force.For example, Aþ B ¼ �C. Rearranging this equation gives

Aþ Bþ C ¼ 0

The three force vectors add together to give a zero resultant if the object is inequilibrium. This can be represented as a triangle, as in Fig. 1.5.

3 In general, a point object is in equilibrium if the forces acting on it form a vectordiagram which is a closed polygon. This rule is called the closed polygon rule.

Resolving a force into perpendicular components

This is a mathematical technique which enables equilibrium situations to beanalysed without scale diagrams. Sketch diagrams are nevertheless useful to visualisesituations.

Consider a force, A, acting at point, O, of an x–y coordinate system, as in Fig. 1.6.The magnitude at A is represented by A and the direction of A is at angle � to thex-axis. This force may be resolved into two perpendicular components.

1 Ax ¼ A cos � along the x-axis.2 Ay ¼ A sin � along the y-axis.

Force A may be written in terms of its components in the form

A ¼ A cos � iþ A sin � j

where i and j are vectors of unit length along the x-axis and the y-axis respectively.Using Pythagoras’ theorem gives

A ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAx

2 þ Ay2

� �q

and using the rules of trigonometry gives

tan � ¼ Ay

Ax

AC

A + B + C = 0

B

Fig. 1.5 Equilibrium of a pointobject

j

i

A

Ax = A cos O

Ay = A sin

A = Ax2+ Ay

2

Ay

Ax

tan =

x

y

Fig. 1.6 Resolving a force

Notes

1 Pythagoras’ theorem states that for a right-angled triangle ABC,

AB2 þ BC2 ¼ AC2.

2 The following trigonometric functions are defined from this triangle

sin � ¼ AB

AC

�¼ o

h

�cos � ¼ BC

AC

�¼ a

h

�tan � ¼ AB

BC

�¼ o

a

�

where o is the opposite side and a is the adjacent side to �, and h is the hypotenuse.aC B

A

oh




MECHANICS14

How to calculate the resultant of two or more forces

Consider a point object, O, acted on by two or more forces, A, B, C, etc, as shown inFig. 1.7. The resultant of these forces can be calculated by following these steps:

1 Resolve each force into perpendicular components along the x-axis and they-axis.

2 For each axis, add the components, taking account of þ or � directions, to givethe component of the resultant along each axis.

3 Use Pythagoras’ equation to calculate the magnitude of the resultant, and use thetrigonometry equations to calculate the direction of the resultant.

1.1 WORKED EXAMPLE

A point object, O, is acted on by three forces, A, B and C, as shownin Fig. 1.8. Calculate (a) the magnitude and (b) the direction of theresultant of these three forces.

Solution

Resolving the three forces into componentsalong the i-axis and the j-axis gives:

A ¼ 10 cos 45iþ 10 sin 45j

B ¼ �8 sin 30iþ 8 cos 30j

C ¼ �5j

Therefore the resultant is

R ¼ Aþ Bþ C

¼ ð10 cos 45� 8 sin 30Þiþ ð10 sin 45þ 8 cos 30� 5Þjthus R ¼ 3:1iþ 1:0j

a) The magnitude of the resultant, R ¼ pð3:12 þ 1:02Þ ¼ 9:5 Nb) The angle between the resultant and the x-axis, �, is given by

tan � ¼ Ry

Rx¼ 9:0

3:1¼ 2:90

Hence � ¼ 718.

A R = A

+ B

B

O Ax

By

Ay

RxBx +x

+y

R = Rx2+ Ry

2

where Rx = Ax + Bx

and Ry = Ay + By

Fig. 1.7 Using a calculator

j

i

A

C

RB

0

A = 10

N

C = 5 N

B = 8 N

45°

30°

+x–x

+y

–y

Fig. 1.8





1.1B QUESTIONS

1 Calculate the magnitude and direction of theresultant of two forces, A and B, acting on a pointobject for each of the arrangements shown inFig. 1.9.

2 For each arrangement shown in Fig. 1.9, state themagnitude and direction of a third force, C, actingon O which would cancel out the resultant of Aand B.

Turning effects

When you need to use a spanner to unscrew a nut, the longer the handle of thespanner, the easier the task will be. The same applies to a claw hammer if ever youneed to remove a nail from a piece of wood. The longer the handle, the greater theleverage about the turning point. See Fig. 1.10.

The moment of a force about a point is defined as the magnitude of theforce the perpendicular distance from its line of action to the point (seeFig. 1.11).

The unit of a moment is the newton metre (Nm). The term torque is used todescribe the moment of a force about an axis.

For example, if a force of 40 N is applied to a spanner at a perpendicular distanceof 0.20 m from the turning point, the moment of the force about that point is equalto 8.0 Nm (¼ 40 N� 0:20 m). The same moment could be achieved by applying aforce of 80 N at a perpendicular distance of 0.1 m from the pivot (¼ 80 N� 0:1 m).Now you can see why a lesser force gives the same leverage if it acts at a greaterdistance. Prove for yourself that a force of 16 N acting at a perpendicular distance of0.5 m from the turning point gives the same moment as 40 N at 0.20 m.

The principle of momentsAny object that is not a point object can be turned when one or more forces act onit. For example, a door turns on its hinges when it is given a push. The term body isused for any object that is not a point object.

. A body acted on by only one force cannot be in equilibrium and will turn if theforce does not act through its centre of gravity.

. A body acted on by two or more forces may or may not turn, depending on theposition and direction of the forces acting on it. For example, a balanced see-saw,as shown in Fig. 1.12 carrying a child either side of the pivot will becomeunbalanced if one of the children climbs off. For balance, a child of weight 250 Nwould need to be nearer the pivot than a child of weight 300 N. The condition fora balanced see-saw is that the moment of the child on one side about the pivotshould equal the moment of the other child about the same pivot. For example, ifthe 250 N child is 1.20 m from the pivot (moment ¼ 250� 1:20 ¼ 300 Nm), theother child would need to be 1.0 m from the pivot (moment ¼ 300 N� 1:0 m)for balance.

1.2

A = 3

N

B = 2 NO

45°x

y(a)

A = 4 N

B = 2.5 N O30°

x

y(b)

Fig. 1.9

Pull onhandle

Claw hammerForceon nail

Pivot

Fig. 1.10 Applying leverage

F

Moment about P = Fd

PPull onhandle

d

Fig. 1.11 Moment = force �perpendicular distance




MECHANICS16

The balanced see-saw is an example of a more general rule, the Principle ofMoments, which applies to any body in equilibrium.

The Principle of Moments states that for a body in equilibrium, the sum of theclockwise moments about any point is equal to the sum of the anticlockwisemoments.

1.2 WORKED EXAMPLE

A uniform beam of length 4.0 m pivoted horizontally about its centresupports a 5.0 N weight at a distance of 1.5 m from the centre, and a6.0 N weight at the other side of the centre. Calculate the distancefrom the 6.0 N weight to the centre of the beam.

Solution

Let d represent the distance from the centre to the 6.0 N weight.

Applying the principle of moments about the centre gives 6:0d ¼ 5:0� 1:5.

Hence d ¼ 5:0� 1:5

6:0¼ 1:25 m

1.2 QUESTIONS

1 The uniform beam in Fig. 1.14 is pivoted at its centre andsupports three weights, W1, W2 and W3, at distances d1,d2 and d3 as shown.

For each set of weights and distances in the table,calculate the value of the missing quantity necessary tomaintain the beam in equilibrium.

W1=N d1=m W2=N d2=m W3=N d3=m6.0 2.0 4.0 1.0 8.0 (a)4.0 (b) 3.0 2.0 8.0 1.54.0 1.5 6.0 (c) 4.5 2.0(d) 1.0 2.0 2.0 4.0 1.5

2 A simple beam balance is shown in Fig. 1.15. The scalepan is suspended from one end of a metre rule which ispivoted at its centre. The rule is balanced by adjusting theposition of a 2.0 N weight suspended from the rule at theother side of the pivot to the scale pan.

a) When the scale pan is empty, the 2.0 N weight mustbe positioned 150 mm from the centre of the rule tokeep the rule horizontal. Calculate the weight of thescale pan.

b) An object, X, of unknown weight is placed on thescale pan and the 2.0 N weight is moved to a distanceof 360 mm from the centre to keep the rulehorizontal. Calculate the weight of X.

1.0 m1.2 m

250 N 300 N

Fig. 1.12 A balanced see-saw

6.0 N 5.0 N

1.5 md

Fig. 1.13

W2

d3d2

d1

PivotW3W1

Fig. 1.14 Scale pan

2 N

Pivot

Fig. 1.15





Stability

Mass and weight

If you want to lose weight, go to the Moon where the force of gravity is one-sixth ofthe Earth’s gravity. Unfortunately, you won’t become slimmer because your masswill be unchanged.

. The mass of an object is the amount of matter it possesses. The unit of mass isthe kilogram (kg), defined by means of a standard kilogram at BIPM (BureauInternational des Poids et Mesures), Paris.

. The weight of an object is the force of gravity acting on it. The unit of weight isthe newton (N).

. The force of gravity per unit mass, g, at the surface of the Earth, is 9.8 N kg�1.The value of g changes slightly with position on the Earth’s surface, ranging from9.78 N kg�1 at the equator to 9.81 N kg�1 at the poles. The cause of this variationis due partly to the shape of the Earth not being exactly spherical and partly tothe effect of the Earth’s rotation. Strictly, this latter effect is not due to the force ofgravity but arises from the circular motion of an object at the equator. The forceof gravity on an object on the Moon, at 1.6 N kg�1, is much smaller than that onan object on the Earth because the Moon is smaller in size than the Earth.

For an object of mass m, its weight, W, can be calculated from the equationW ¼ mg

Stable and unstable equilibrium

At a bowling alley, have you noticed how easily a pin falls over? Each pin is designedto be top-heavy with a small base. Fig. 1.16 shows a bowling pin in comparison with‘Wobbly Walter’, a bottom-heavy child’s toy that rights itself when knocked over.

. The child’s toy is an example of an object in stable equilibrium – it returns toequilibrium when knocked over because its centre of gravity is always over its base.

. The standing bowling pin is an example of an object in unstable equilibrium – itmoves away from equilibrium when released from a tilted position.

. The bowling pin lying on its side is an example of an object in neutralequilibrium – it stays wherever it is moved to, neither returning to nor movingaway from where it was.

Centre of gravity

The centre of gravity of an object is the point where its weight can beconsidered to act.

. An object freely suspended from a point and then released will come to rest withits centre of gravity directly beneath the point. Fig. 1.17 shows how to find thecentre of gravity of a flat object.

. A tall object tilted too far will topple over if released. This happens if it is tiltedbeyond the point where its centre of gravity is directly above the point aboutwhich it turns, as in Fig. 1.18. If released beyond this position, the moment of theweight about the point of turning causes the object to overbalance.

1.3

A bowlingalley pin

High centreof gravity

Weight

A wobbly toy

Low centreof gravity

Weight

Fig. 1.16 Equilibrium




See www.palgrave.com/foundations/breithaupt for aproof that the centre ofgravity of a uniform beam is atits midpoint.

MECHANICS18

. The moment of an object due to its weight, W, about any point = Wd, where d isthe perpendicular distance from the point to the vertical line through its centre ofgravity. For example, Fig. 1.19 shows a rule pivoted at one end. The rule can beheld horizontal by a vertical string attached to the other end. The moment of therule’s weight about the pivot can be proved to be equal to WL/2, where L is itslength. Therefore its centre of gravity is at a distance L/2 from the pivot.

. An object may be balanced by a single vertical force applied at its centre ofgravity. For example, it ought to be possible to support a plate on the end of avertical rod, provided the plate is placed with its centre on the end of the rod.Another example is when someone carries a ladder in a horizontal position; thetask is much easier if the ladder is supported at its centre of gravity, because theladder is balanced at this point.

1.3 WORKED EXAMPLE

A road gate consists of a 4.5 m uniform steel tube ofweight 120 N which has a 400 N counterweight fixedto one end, as shown in Fig. 1.20. It is pivoted about ahorizontal axis which passes through the beam 0.55 mfrom the centre of the counterweight.a) Calculate the position of the centre of gravity of the

road gate.b) Calculate the magnitude and direction of the force

that must be applied to the counterweight to keepthe beam horizontal.

EXERCISE

Locating the centre of gravity of a flat card

Use a plumbline to mark a vertical line through the pivot on thecard as in Fig. 1.17.Repeat for a different pivot.The centre of gravity is where the lines intersect.

Pivot P

Card freelypivoted at P

Fixed rod

Marker

Centre ofgravityis here

Plumbline

Fig. 1.17

(b)(a)

Pivot

Fig. 1.18 Stability (a) tilting without toppling,(b) on the point of toppling

Pivot P

L

W

Fig. 1.19 Centre of gravity of arule

1.7 m

Cg

(Cg = centre of gravity)

CounterweightPivot

d

0.55 m

Fig. 1.20





1.3 WORKED EXAMPLE continued

Solution

a) Let d ¼ the distance from the centre of gravity Cg of the road gate to the counterweight. The distance fromthe centre of gravity of the counterweight to the centre of gravity of the tube ¼ 2:25 m. The moment of thetube about the counterweight ¼ 120 N� 2:25 m ¼ 270 Nm anticlockwise. This is the same as the momentof the whole gate about the counterweight ¼ ð400þ 120Þd anticlockwise.

Hence 520d ¼ 270 Nm ; d ¼ 270� 520 ¼ 0:52 m.

b) Because Cg is between the counterweight and the pivot, the road gate will turn clockwise if no additionalforce is applied to it. Let F ¼ the upward vertical force on the counterweight needed to keep the road gatehorizontal.

Applying the principle of moments about the pivot, the moment of the road gate about the pivot¼ ð400þ 120Þ � 0:03 ¼ 16 Nm clockwise.

The moment of force F about the pivot ¼ 0:55 F anticlockwise.

Hence 0.55 F ¼ 30 ; : F ¼ 16� 0:55 ¼ 28 N

1.3 QUESTIONS

1 A placard consists of a uniform pole of length 4.0 m and of weight 30 Nwhich has a square board of weight 20 N fixed to one end, as shown inFig. 1.21. Calculate the distance from the other end of the pole to thecentre of gravity of the placard.

2 An advertising sign consists of a uniform board as in Fig. 1.22. The totalmass of the board is 15 kg.a) Calculate the weight of the rectangular section of the board.b) Calculate the weight of the square section of the board.c) Calculate how high above the base the centre of gravity of the whole

board is.

Friction

Friction exists between any two solid surfaces that slide over one another. Walkingand running would be very difficult without friction (e.g. on ice). See Fig. 1.23.However, friction causes undesirable wear and heating in machines and engines.Friction always acts on a surface in the opposite direction to the movement of thesurface. Oil between two solid surfaces reduces the friction because it keeps themapart and reduces the points of direct contact.

1.4

4.0 m

Fig. 1.21

0.4 m

2.0 m

0.4 m

0.2 m

Fig. 1.22

Push on

shoefrom foot

Friction on shoe

Fig. 1.23 Forces on a runningshoe




MECHANICS20

Measuring friction

The force of friction between two flat surfaces can be measured by:

. measuring the force needed to pull a block across a fixed horizontal surface. Oneof the surfaces to be tested is fixed to the underside of the block. The othersurface is the fixed surface. If the applied force is gradually increased from zerousing a spring balance, as in Fig. 1.24, the block does not slide until the appliedforce reaches a certain value. Once the block starts to move, the applied forcebecomes slightly less. At the point of sliding, the force needed to make the blockmove is equal to the maximum possible frictional force between the two surfaces,referred to as the limiting value of the frictional force

. using an inclined plane as in Fig. 1.25. The angle of the incline is increased untilthe block on the plane is at the point of sliding down the incline. The limitingvalue of the frictional force is equal to the component of the block’s weight,W sin �, acting down the incline.

The coefficient of static friction,

The arrangement in Fig. 1.24 may be used to prove that the limiting value of thefrictional force, F, is proportional to the weight of the block. Since the weight of theblock on a horizontal surface is equal and opposite to the normal reaction, N, of thesurface on the block, the frictional force F is proportional to N. In other words, theratio F=N is a constant for the two surfaces. This ratio is referred to as thecoefficient of static friction, �.

FN

In Fig. 1.25, the normal reaction on the block is equal to W cos �, the componentof the block’s weight normal to the surface. If the plane is made steeper, the blockwill slip if its component of weight parallel to the slope, W sin �, exceeds thefrictional force. At the point of sliding, the frictional force is equal to W sin �.Therefore the coefficient of static friction is

� ¼ F

N¼ W sin �

W cos �¼ tan �, since

sin �

cos �¼ tan �.

1.4 WORKED EXAMPLE

A cupboard of weight 350 N is pushed at steady speed across a horizontal floor, by a force of 150 N appliedhorizontally near its base, as in Fig. 1.26. Calculatea) the coefficient of static friction between the two surfaces that slide over each other,b) the force needed if the weight of the cupboard is reduced to 200 N by removing some of its contents.

m

Pulled inthis direction

Pull onthe block

10N

0Frictionalforce F

Block Fig. 1.24 Measuring friction on ahorizontal surface

BlockF

Centre ofgravity Normal

reaction N

W cos

W sin

W

Fig. 1.25 Measuring frictionusing an inclined plane




Index

A page number followed by N indicates that relevant information on that page is given only in a boxed note.

Aabsolute permittivity of free

space 220, 248, 254–6absolute temperature

scale 80, 405, 406, 417absolute zero of

temperature 405acceleration 30, 31, 34N,

38–9centripetal 433–6due to gravity 35–7, 43–4,

460equations for

uniform 33–4of oscillating objects 454,

458–62relation to force 41–8

accelerators see particleaccelerators

acoustic resonance 137–40adiabatic changes 419N

of ideal gas 422–4advanced gas cooled

reactor 377, 378aircraft, banking 438alpha (a) decay, Q values 374alpha (a) radiation 171,

352–60, 374cloud chamber tracks 356ionising power 354range and penetrating

power 357scattering by nucleus 359

alternating current 299–317measuring 299–301, 305–7rectification 302–4root mean square value 305

alternating currentgenerator 287

alternating voltage 288ammeters 183, 205

digital 209extending range of 206–7

amorphous solids 70, 101,102

Ampere, Andre 181ampere (unit) 181, 274Ampere’s rule 273amplifiers 234–40

operational 236–40amplitude 120, 454amplitude modulation 168–9analogue circuits 227AND gates 228Anderson, Carl 381aneroid barometer 111angles 431–2angular acceleration 467angular frequency 457Nangular momentum 477angular speed 432–3angular velocity 467annihilation (particles) 381antimatter 380–1antineutrinos 369Archimedes’ Principle 113arcs 431area, units 3astable multivibrators 241–2astronomical unit 450Natomic mass unit 72N, 351,

371Natomic number 72N, 351atomicity of gases 421–2atoms 71–2

electrons in 334–8energy levels 335–6nuclear model 359structure 178, 319–20,

349–50see also nucleus (atomic)

Avogadro constant (NA) 74,352, 407

Avogadro’s hypothesis 413

Bback e.m.f. 290bandwidth (amplifiers) 235banked curves 437–8barometers 111

baryons 383batteries 194–5Becquerel, Henri 352becquerel (unit) 362bell, electric 265Bernoulli effect 399Bernoulli equation 399–402beta (b) decay 368, 374

Q value 374beta radiation 352–60

cloud chamber tracks 356ionising power 353–4range and penetrating

power 357, 358bicycle dynamo 280–9bimetallic strip 81binding energy 370–5black bodies 88black holes 447–9blood pressure,

measurement 112boiling 71bond energy 77bonds 75–7Bourdon gauge 111Boyle’s law 402–4brakes, hydraulic 108breaking stress 97, 100bridge rectifier 302–4brittleness 96Brownian motion 408bubble chambers 382

Ccalculator watch 227calculators 4N

displays (liquid crystal) 129exponential function

button 223calculus see differentiation;

rates of changecamera 155–6capacitance 213capacitor smoothing

(a.c.) 304

capacitors 211–24in a.c. circuits 307–10,

313–16combinations 214–16design factors 219–20discharging 221–4energy stored in charged

capacitor 217–18reactance 307–11, 313–16

carsbatteries 194–5engine power and

speed 57hydraulic brakes 108seat-belt warning

light 229–30cathode rays 319–23Cavendish, Henry 441Ncells (electrical) 194–6

internal resistance 195–6,201N

standard 206Celsius temperature scale 79,

405, 417centigrade temperature

scale 417Ncentre of gravity 17–18centripetal

acceleration 433–5centripetal force 434Chadwick, James 381chain reactions (nuclear) 376changes of state 69, 425NCharles’ law 404–7chemical energy 370Chernobyl nuclear

accident 379chromatic aberration 155circuit breaker 266circuits see electric circuitscircular motion 431–9

and simple harmonicmotion 456–7

closed polygon rule 12, 21cloud chamber 356, 381

543




INDEX544

coefficient of staticfriction 20

coefficient of thermalconductivity 89–90

coefficient of thermalexpansion 80

coherent light sources 146coils, in a.c. circuits 307,

311–18collisions 47, 48colours of light 160comets 450communications

microwaves in 168radio waves in 168–9

commutator 267–8compass 263compounds 71, 72computers, capacitors in 221concave lens 153conduction see electrical

conductivity; electricalconductors; thermalconduction

conduction electrons 76, 180conservation of angular

momentum 478conservation of energy 54,

282–3conservation of

momentum 47–50continuity equation 392–4continuous spectra 161–2convection 86–7convex lens 124, 152, 154

focal length 152–4cooling curves 87Copernicus, Nicolas 1corkscrew rule 264cosmic radiation 369, 381Coulomb, Charles 247–8Coulomb’s law 248, 257coulomb (unit) 183couples 23covalent bonds 76–7critical angle 150–1critical damping 463crystalline solids 70, 76, 101Curie, Marie 352

Ddamped oscillations 462–3decay constant 363deceleration 30decibel scale 134degree

unit of phasedifference 121

unit of temperature 79degrees of freedom 421–4density

of elements 74measuring 5–6, 111units 3, 6

deuterium 350dielectric substances 212

relative permittivity 220differentiation 222

sine function 310diffraction 124diffraction grating 162–4diffusion 70digital circuits 227digital meters 208diodes 189–90

in rectifier circuits 302–4Dirac, Paul 381direct current 181discharge tubes 322, 337dislocations 102dispersion 160–1displacement 11, 29

oscillating object 454displacement–time curves 38dissolving 70distance–time graphs 31domain theory of

ferromagnetism 275–7double slits

experiment 145–7drag 57–8dynamic pressure 400dynamics 27–39

spreadsheet 494–6dynamo effect 280–2

Eear 133–5Earth, magnetic field 263echoes 132eddy currents 293Edison, Thomas 323efficiency 58–9

of heat engines 426–8of transformer 292

Einstein, Albertmass–energy equation 55,

371and photoelectric

effect 330–3relativistic formula 381

elastic energy 103elastic limit 96, 100elasticity 96–7

see also Young modulus ofelasticity

electric bell 265electric charge 177–8, 183

forces between 247–9quantum of 327storage 211–15unit 183

electric circuits 181, 183,184–6

characteristics ofcomponents 188–90

diagrams 188resistor combinations

in 190–2electric current 180–7

growth, effect ofself-inductance 294–7

measuring see ammetersunit 1, 181, 274see also alternating current;

direct currentelectric fields 247–60

between charged parallelplates 254–5

near charged sphere 257patterns 249–52strength 253–7unit 253N

electric motorsdirect current 267–8, 290light-operated 233

electric potential 251, 258–9electric relay 266electrical conductivity 204Nelectrical conductors 180electrical insulators 180

see also dielectricsubstances

electrical power 186in a.c. circuits 309, 312,

electricity, static 177–9electrodes 182electrolysis 182electromagnetic force 367electromagnetic

induction 280–97electromagnetic

waves 119–20, 127,160–72

speed 166electromagnetism 264electromagnets 182, 265–6electromotive force 196–7

back 288–90induced see

electromagneticinduction

measuring 197, 200, 205unit 195

electron beams 321–6, 339effect of magnetic field 270

electron diffraction 342–3electron gun 324electron shells 72, 75–6, 178,

334–6electron volt 324N, 370electronic pressure gauge 111electronics 226–42

logic circuits 227–30systems approach 226–7

electrons 72, 75, 178, 321–6,349–50

cathode rays 321charge of 326–30conduction 76, 180specific charge of 325–6valence 180see also beta (b) particles;

photoelectric emission;thermionic emission

electroscope, gold leaf 178–9electrostatic forces 247–9,

367electroweak force 368elements 71e.m.f. see electromotive forceemission spectra 161–2, 336energy 54

conservation 54, 282forms 54–5and power 56–8spreading out 59unit 81, 54useful 58

energy level diagrams 335–7energy resources 60–3enthalpy 425equations and formulae 3–4,

33list 504

equilibriumconditions for 22–3of point object 13stable, unstable and

neutral 17equilibrium separation

(atoms/molecules) 77equipotentials 251–2errors in measurements 6N, 7excitation (atoms) 335–6experimental evidence 1explosions 49exponential decay

capacitor discharge 221–4radioactive decay 360–4

exponential function 222–3,363–4




INDEX 545

Ffairground rides 435–7falling objects 35–7, 43,fan-out 228farad (unit) 213Faraday’s law of

electromagneticinduction 284–6

fast breeder reactor 377feedback (amplifiers) 235ferromagnetism 275–6fields see electric fields;

gravitational field strength;magnetic fields

film badges 341, 379flotation 112–14flow line 390focal length

concave lens 154convex lens 152–4

force carriers 368–9force diagrams 21, 23force–distance graphs 103forced oscillations 463forces

and acceleration 41–5centripetal 433–4frictional 19–21fundamental 367–8impulse 48measuring 95moment of 15and momentum 45–7parallelogram of 12pressure 106–7resolving into

components 13resultant 12, 13turning 15–16as vector quantities 12–13and work 53–4

Fortin barometer 111fossil fuels 60, 61four-stroke petrol engine 418free oscillations 462free-body force diagrams 21,

23frequency 120

angular 457Nmeasuring (sound

waves) 132resonant 463fundamental 137–8,

139–42frequency modulation 169friction 19–21, 58, 59fuels, supply and

demand 60–1

full-wave rectification 303–4fundamental

frequency 137–8, 139–42fuses 187fusion, latent heat of 84

GGalileo Galilei 1gamma (g) radiation 171,

353ionising power 356range and penetrating

power 356–8gas laws 402–7

ideal gas equation 407–8kinetic theory 408–11

gas thermometer 417–18gases 69, 77, 402–14Gauss’s law 257Geiger–Muller tube 355geostationary satellites 451geothermal power 63glasses 70gold leaf electroscope 178–9gradient of straight line 35grains (metals) 70, 101–3graphs 35gravitation 440–52gravitational field

strength 443–5gravitational potential

energy 54, 446–8gravity

acceleration due to 35–7,43–4, 461

force of 17, 43, 367, 441gravity wheel 436grid system 293ground state of atom 335–6

Hhalf-life of radioactive

isotope 361–4half-value thickness (radiation

absorbers) 358half-wave rectification 303Hall effect 270–1Hall probe 271, 272hardness 96hearing 133–5heat 79, 418heat engines 418, 426–8heat transfer 86–91helium nuclei 353, 372

see also alpha (a) radiationhenry (unit) 295hertz (unit) 120, 300, 432Hooke’s law 95, 459

Huygens, Christiaan 145hydraulics 107–9hydroelectric power 63hydrogen atom 337

emission spectrum 337isotopes 350

hydrometer 114hysteresis

ferromagnetic 276, 292mechanical 96

Iice, measuring specific latent

heat of fusion 84ideal gas equation 407–8ideal gas temperatures 417ideal gases 402–6

thermodynamics 420–6impacts see collisionsimpedance 313–14impulse of force 48incompressible fluid 391–2,

393inertia 470infra-red radiation 86, 88,

166–7instruments 4–5

electrical 205–9insulators see electrical

insulatorsinterference 125

light waves 145–8intermolecular forces 75–7internal energy 418internal resistance 196–7

measuring 197interstitial atoms 102ionic bonds 76ionisation 334ionisation chamber 354ionisation energy 334–5ionising radiation 171, 353

detectors 355–6range and penetrating

power 356–8see also X-rays

ions 76isothermal curves 403, 423isotopes 72N, 350

Jjet engine 419joule (unit) 54, 81, 425joulemeter 81

Kkelvin, unit of

temperature 79–80, 405,417

Kepler’s laws of planetarymotion 449–50

kilogram (unit) 17kilowatt hour (unit) 81, 187Nkinetic energy 55kinetic theory of

gases 408–12

Llaminar flow 391, 396laser experiments 147, 164

safety in 164Nlatent heat 71, 84–6, 425Nlaw of reflection 148laws of motion see Newton’s

laws of motionlaws of planetary motion see

Kepler’s laws of planetarymotion

laws of thermodynamicsfirst law 419–20, 425second law 426–9zeroth law 418

LDRs see light-dependentresistors

lead–acid batteries 195LEDs see light-emitting

diodesleft-hand rule 266, 269Nlength

measuring 5units 1, 3

lens formula 153lenses 151–4

aberrations 155concave 153convex 124, 151–4in optical instruments 155–7

Lenz’s law 282–3, 285Nleptons 381, 383leverage 15lifts 43–4

hydraulic 107–9light

colours 161interference 155–8measuring

wavelength 146–7,164–5

photon theory 331polarisation 126–9reflection 148refraction 148–9speed 382total internal

reflection 150–1visible spectrum 160–1wave nature 120, 142




INDEX546

light-dependent resistors(LDRs) 199, 203, 231–2

light-emitting diodes (LEDs)190, 228N

light-operated electricmotor 233

light sensors 231, 232lightning conductor 253–4line emission spectra 162,

337lines of force

electric field 249–251gravitational field 444magnetic field 263–4, 267,

274, 284liquid drop model (atomic

nucleus) 375liquid-in-glass

thermometer 415liquids 69–71, 77

measuring density 5,110–11

measuring specific heatcapacity 83

measuring specificlatent heat ofvaporisation 85

logarithms see naturallogarithm function

logic circuits 229–31logic gates 228–9long sight 151longitudinal waves 126loudspeaker 126, 267

Mmagnetic compass 263magnetic fields 262–79

formulae 272–4patterns 262–4in solenoid 272–3strength see magnetic flux

densityin toroidal solenoid 276

magnetic flux 284–6unit 284

magnetic fluxdensity 269–72, 284,325N

unit 269magnetic flux linkage 284N,

287, 295magnetic forces 367–8magnetic materials 262,

275–6magnetic poles 263

forces between 263magnification (lenses) 153N

magnifying power(telescope) 157

manometer 110mass 17

measuring 4units 1, 3, 16

mass defect 372mass number 72N, 350mean value 6measurements 4–6

uncertainty andaccuracy 6–7

mechanical hysteresis 96melting 70–1,

latent heat of 84mesons 383–4metallic bonding 75–7metals

crystals 76dislocations 102electrical conduction 180measuring specific heat

capacity 82–3thermal conduction 86,

89–90micrometer 5microscope (optical) 156microwave radiation 120,

167–8Millikan, Robert 323, 326mirrors, plane 148molar gas constant 407molar heat

capacities 420–2ratio (g) 421–3

molar mass 74, 352, 407molarity 407molecular bonds 75–7molecules 72

estimating size of oil 73moles 74, 351, 407moment of force 15

of couples 23due to weight 18

momentum 45–7moment of inertia 471

conservation ofmomentum 47–50

monostablemultivibrators 241

motor effect 266–8moving coil meters 268

adapting for alternatingcurrent/voltage 302–4

extending range of 207multimeters 205–6multivibrators 241–2musical instruments 137–9

NNAND gates 228natural logarithm

function 223neutral point (magnetic

field) 264neutrons 71, 349–51

discovery 380-1Newton, Isaac 41, 145,

law of gravitation 441–3,449

theory of gravity 441Newton’s laws of motion

first law 41second law 42, 46third law 47

newton (unit) 12, 17, 42, 91nodes and antinodes 138non-newtonian fluid 395nuclear fission 374

induced 375–9nuclear fusion 374nuclear power 61–2, 375–80nuclear reactors

fast breeder 377thermal 377–8, 379

nuclear waste 380nucleons 372

see also neutrons; protonsnucleus (atomic) 70–1, 178,

349–50, 359binding energy 370–5liquid drop model 375mass 372Nmass defect 372structure 380–4see also strong nuclear force;

weak nuclear forcenumbers

prefixes 2significant figures 2–3standard form 2

Oohm (unit) 188, 308, 312oil, estimating size of

molecules 72–073omega minus (O�)

particle 383operational

amplifiers 234–41inverting 238, 240non-inverting 237–8summing 239

optical fibres 150optical instruments 155–7optics 142–59OR gates 228–9

oscillating systems 453–5Forces in 458–62resonating 463–4

oscilloscope experimentscomparing waveforms 235investigating

ferromagnetism 275–6measuring alternating

voltage 299–301measuring reactance 309measuring sound

waves 132–3output transducer 203, 232overtones 137–9

Ppair production

(particles) 381parallel circuits 185–6,

191–2, 215parallelogram of forces 12particle accelerators 382pascal (unit) 97N, 99N, 106pendulums, oscillating 453,

454–5, 460–1, 462Periodic Table 75, 76permeability

of free space (�0) 273–4relative (�r) 277

permittivity see absolutepermittivity of free space

phase difference 121phasor diagrams 308, 312,

314photocells 170,photoelectric emission 330–3photon theory of light 331–2photons

energies 331, 336, 339virtual 368–9see also gamma (g) radiation

pions 346, 383–4Pitot-static tube 400Planck constant 331–2planets 449–50plastic behaviour 96, 101, 102plutonium, induced nuclear

fission 377Poiseuille’s equation 396polarisation 127–9

light 128–9polymers 97, 101, 102potential difference 185–7

across capacitor 213–17measuring 205–6; see also

voltmeterssupplying of variable 199unit 185




INDEX 547

potential dividers 198–9potential energy 54

gravitational 54, 446–8potential gradient 255potentiometers 199–201powder volume,

determination 404power 56, 81

see also electrical powerpower stations

alternators 289grid system 293

pressure 106–15in fluid at rest 109of gas 402, 408; see also

Boyle’s lawhydraulic 107–9of liquid column 110measuring 110–11

pressure sensors 231pressurised water

reactor 377, 378primary cells 194–6primary colours 160principal quantum

number 337principle of moments 15proton number 72N, 350protons 72, 350pulse code modulation 169

QQ values 374

fission reactions 375quanta

of electric charge 327virtual 368

quantum mechanics 337quarks 382–4

Rradian

unit of angle 431unit of phase

difference 121radiation (heat transfer) 86,

88–9radio waves 120, 169–70radioactive decay 171, 360–4radioactivity 349–66random errors 7rates of change 38–9, 222–3ray diagrams 152–3reactance

of capacitors 307–9, 314of inductors 311–13

reactive components(a.c. circuits) 307

real image 151rechargeable

cells/batteries 194–6rectifier circuits 302–4reflection 123

light 148sound waves 132total internal 150–1waves on string 137

refraction 124light 148–9

refractive index 148–50dependence on colour 160

relative atomic mass 72Nrelative permeability (�r) 277relative permittivity ("0) 220relay switches 232, 266remanence 276renewable energy

resources 60–3resistance 188–91

comparison 201measuring unknown 201,

206and temperature 189

resistive components(a.c. circuits) 304, 305,313–15

resistivity 204–5resonance 136, 139–42, 315,

462–3resonant circuits 313–15resultant force 12, 14reversible engines 427ripple tank

experiments 122–3rockets

escape speed 447launch 43

roller coaster 435–7root mean square values

alternating current 305molecular speeds 412N

rubber 97Rutherford, Ernest 352, 359,

381

Ssalt crystals 70, 76satellites

geostationary 451motion 448–51

saturation (amplifiers) 234saturation

(ferromagnetism) 276scalar quantities 11, 29scanning tunnelling

microscope 345

Searle’s apparatus 90seat-belt warning

light 229–30secondary cells 194–5secondary colours 161seismic waves 120

primary 126secondary 127surface 126N

self-inductance 294–7semiconductors 180

Hall effect in 270–1sensor circuits 199, 229,

231–3series circuits 184, 186,

190–91, 214–15LCR 313–15

shape of solids 69, 70shuttling ball experiment 183significant figures 2–3simple harmonic

motion 453–65sinusoidal curves 288–9, 456

equation 301‘slinky’ 126

magnetic flux densityin 272–3

small angleapproximation 431

Snell’s law 148, 150solar energy 62–6solenoid rule 265solidification 71, 84–5solids 69–70,sound 131–44

acoustic resonance 139–42loudness 133–5sound waves 119, 126,

131–2measuring 131speed 131–2, 139transverse representation

119Nspecific heat capacity 81–4specific latent heat 84–5spectra

continuous 161–2of electromagnetic

waves 120line emission 162, 336, 338visible 160–1

spectrometer 165speed 27–8

of object in circularmotion 432, 433

speed limits 27–8speed–time graphs 31–2spherical aberration 155

sphygmomanometer 112,391

spreadsheet exercises 38–9,58N

spring balance 95, 443Nspring constant 95, 459springs 95

energy stored in 103oscillating 454, 456, 458

stability 17–18standard form (numbers) 2stars, emission spectra 162states of matter 69–70

changes 70–1static electricity 178–9

hazards due to 179stationary waves 137–42steam turbine 427Stefan’s law of radiation 88stiffness 96Stokes’ Law 329, 397stopping potential

(photoelectricemission) 332

stopwatch 5straight line graphs 35Nstrain 98

see also stress–strainrelationships

strange particles 383streamline 390–1strength of materials 96stress 98

breaking 97, 101stress–strain relationships

98–103strings, waves on 127, 137–9strong nuclear force 368,

369–70sunglasses, polaroid 129surfaces 69–70swing (fairground) 437sensors 231, 232symbols 3

circuit diagrams 188, 211,291

compounds 72electronics circuit

diagrams 227elements 71isotopes 72N, 351

systematic errors 7Systeme International

(units) 1–2

TTacoma bridge 464telescope (refracting) 157–8




INDEX548

temperature 79–80and gas pressure 406and gas volume 404–5and kinetic energy 411scales 79, 405, 415, 417units 1

temperature sensors 232temperature-dependent

resistors see thermistorstensile strength,

ultimate 102–3tensile stress, ultimate 101tensometer 100terminal speed 38, 58terminal velocity 38, 328, 397ternary form (numbers) 2tesla (unit) 269, 325Nthermal conduction 86,

89–91thermal expansion 79–80thermal nuclear

reactor 376–80thermal radiation 86, 88thermionic emission 323–4thermistors 188, 203, 232thermocouple

thermometer 416thermodynamics 415–28thermometers 415–16thermopile engine 427thermostat (radiator) 81Thomson, J.J. 323threshold frequency

(photoelectricemission) 330

tidal power 63time, unit 1time constant of capacitor

discharge circuit 223time period 119N, 300, 454,

457Noscillating spring 458–9simple pendulum 460–1

top-pan balance 4torque 15total internal

reflection 150–1toughness 96transducer 203transformers 290–3, 303transistors 233transmission electron

microscope 344transverse waves 123, 126–7

travelling waves 120trigonometry 149N, 13Ntrip switches 266triple point temperature

(water) 417tritium 350truth tables 228, 229tunnelling 345turbulent flow 390–1turning forces 14–15

UU-tube manometer 110U-value 90ultimate tensile

strength 102–3ultimate tensile stress 101ultrasonic scanner 119,

135–6ultrasonics 119, 135–6

echo sounder 131ultraviolet radiation 170–1,

330, 333uncertainty in

measurements 6–7units 1–2

acceleration 30activity of radioactive

isotope 362angle 431angular frequency 457Nangular speed 432Natomic mass 72N, 351

371Ncapacitance 213coefficient of thermal

expansion 80density 3electric charge 183electric current 1, 181, 274electric field 253Nelectrical

conductivity 204Nelectrical energy 81, 187Nelectromotive force 196energy 54, 81enthalpy 425force 12, 42frequency 120, 300, 432gravitational

constant 441Ngravitational field

strength 443Nlength 1, 3

magnetic flux 284magnetic flux density 269,

325Nmass 1, 3, 16molar gas constant 407molar mass 74, 352, 407molarity 407moment 15momentum 45phase difference 121planetary distance 450Npotential difference 185power 56, 81,pressure 106, 111Nquantity of matter 351reactance 307, 311resistance 188resistivity 204Nself-inductance 294specific heat capacity 81specific latent heat 84speed 27–8stress 97Ntemperature 1, 79–80, 405time 1weight 17, 94work 54Young modulus 99N

universal constant ofgravitation 441

universal (molar) gasconstant 407

uraniuminduced nuclear

fission 373, 375–8radioactivity 352

useful energy 58

Vvalence electrons 180van der Waals bonds 76vaporisation 71, 85vector quantities 11–12, 29velocity 29, 30, 38–9, 41–5

gradient in a fluid 395of object in circular

motion 433velocity–time graphs 38

oscillating objects 454–5vernier calipers 5virtual image 148, 153virtual quanta 368–9viscosity 57, 328–9, 394–7viscous drag 57–8

volt (unit) 185, 196Volta, Alessandro 194voltage see potential

differencevoltmeters 185–6, 205–6

digital 206, 207extending range of 207

volumeformulae 5units 3, 6N

WW-bosons 368–9warning indicators 228–9,

232water waves 120, 122–3

see also ripple tankexperiments

watt (unit) 56, 81wave particle duality 342–5wave power 63wave speed 121wavelength 120

of light, measuring 145–7,164–5

waveslongitudinal 126measuring 120properties 122–5transverse 126–7types 119–20

weak nuclear force 368see also electroweak force

weber (unit) 284weight 17, 43, 94, 440‘weightlessness’ 43Wheatstone bridge 201–3Wien’s law of radiation 88Nwind power 63work 53–4, 103, 418

done by expanding gas 420work function of metal

(�) 331–2

XX-rays 171–2, 338–42

Yyield point 101Young, Thomas 145Young modulus of

elasticity 99–100

Zzero gravity 442–3


contents · 29 simple harmonic motion 453 29.1 oscillating motion 453 29.2 sine waves 456 29.3...

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