Physics for Geologists, Second edition

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88 Stress and strain Equations 9.2a above can be written as The co-ordinate system may not be parallel to the principal stresses and strains. It can be shown that Since these are not necessarily principal stresses, there will be three possible shear stresses: where y is the shear strain. Adding Equations 9.3a and using the dilatation term above, There are other material constants of a similar nature. Consider a wire that is not coiled supporting a weight mg that is not so large that the proportional or elastic limit will be exceeded. The ratio of stress to strain is constant, so mg/A = E/(61/1), where A is the cross-sectional area of the wire. E is called Young's modulus. It is a special case of Hooke's law and is sometimes called the modulus of elasticity. The dimensions of Young's modulus are those of a force on an area (a pressure), ML-~T-~, and the units are pascals (N mP2). It is essentially uniaxial. The ratio of shear stress to shear strain, t/y, is called the modulus of rigidity or shear modulus (G). Strain is dimensionless, being 6111, so the dimensions are also those of a pressure, and the units, pascals. The wire also suffers a loss of radius when extended. The modulus that relates the loss of radius to the increase of length, is called Poisson's ratio: v = (6r/r)/(61/1). This is dimensionless. When an elastic body is submerged and a pressure is applied to the fluid enveloping the body, there is a change of volume. The strain is defined as a change of volume per unit of volume, so the ratio of the change of pressure and the strain it causes is 6p/(6V/V). This is the bulk modulus (K), and it has the dimensions of pressure. Compressibility is the inverse of K. Copyright 2002 by Richard E. Chapman
These three elastic constants are related by and each can be expressed in terms of LamC's parameters: Stress and strain 89 51 (331 + 2G) ,ML-~T-~l Young's modulus of elasticity: E = - = El (1 + G) t Modulus of rigidity, or shear modulus: G = - [ML-~T-~] Y E2 X Poisson's ratio: v = - = [dimensionless] or [0] El 2(X + G) Bulk modulus: K = See Jaeger and Cook (1979) for a full analysis of these constants and their derivation, and the propagation of elastic waves through rocks; and Ramsay (1967, pp. 283f.). Friction The laws of thermodynamics were once wittily as You cannot win: at best you can draw. You can only draw if you can get to Absolute Zero (0 K). You cannot get to Absolute Zero. Friction is a force that dissipates all forms of kinetic energy, transforming some of it to heat. Even in space (but not in a perfect vacuum) artificial satellites lose their kinetic energy very slowly, and eventually will return to Earth. The frictional resistance on return to the atmosphere slows the satellite down and generates spectacular heat against which passengers and sensitive equipment must be shielded. The total energy is conserved. Friction is involved in the flow of fluids, gases to a lesser extent than liquids. This is the practical meaning of viscosity. Friction is critical in the design of aeroplanes because that is the main cause of loss of energy in flight. It is also important in the design of motor cars for similar reasons. In both cases, the changing fuel consumption with speed, per unit of distance travelled, is a measure of the increasing losses due to frictional resistance of the air. Curiously, air resistance, whatever the shape of the solid, generally increases as the square of the speed or velocity. 1 I regret having been unable to trace the author of this. Copyright 2002 by Richard E. Chapman
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
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xviii Acknowledgements to K. Whaler
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xx Symbols mass refractive index bu
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2 Basic concepts Table 1.1 Dimensio
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4 Basic concepts Table 1.2 Basic SI
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6 Basic concepts pascal (Pa) and si
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8 Basic concepts all the relevant d
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10 Basic concepts relating them by
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2 Force The dimensions of force are
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14 Force The ratio of the Moon's ac
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16 Force Figure 2.1 The sum of the
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18 Force When a motorcycle takes a
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20 Force Figure 2.3 Torque is the p
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22 Force How does momentum differ f
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24 Force the weights - that is, the
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26 Force Figure 2.6 Wall-sticking i
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3 Gravity Universal gravity When di
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30 Gravity are significant to geolo
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32 Gravity Figure 3.2 The tractive,
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34 Gravity Mean sea level It might
Page 53 and 54: 36 Gravity The benefits of space fl
Page 55 and 56: 38 Gravity Figure 3.6 Profile of th
Page 57 and 58: 40 Gravity Figure 3.8 The siphon at
Page 59 and 60: 4 Optics Light is an electromagneti
Page 61 and 62: 44 Optics Figure 4.2 Refraction. (a
Page 63 and 64: 46 Optics The coeficient of reflect
Page 65 and 66: 48 Optics only the light oscillatin
Page 67 and 68: 50 Optics called Iceland Spar. Two
Page 69 and 70: 52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103: Stress and strain 87 than some natu
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119 and 120: Sea waves 103 Figure 10.1 Wave moti
Page 121 and 122: Sea waves 105 refraction by islands
Page 123 and 124: Acoustics: sound and other waves 10
Page 125 and 126: Acoustics: sound and other waves 10
Page 127 and 128: 12 Fluids and fluid flow Introducti
Page 129 and 130: Fluids and fluid flow 1 13 Figure 1
Page 131 and 132: Fluids and fluid flow 115 Figure 22
Page 133 and 134: Fluids and fluid flow 117 and the f
Page 135 and 136: water above a vertical thickness h
Page 137 and 138: Fluids and fluid flow 121 where V i
Page 139 and 140: Fluids and fluid flow 123 ardentes,
Page 141 and 142: Fluids and fluid flow 125 Figure 12
Page 143 and 144: - 14 $ 12 E 10 K .- 3 8 r cll + 6 0
Page 145 and 146: Fluids and fluid flow 129 the liqui
Page 147 and 148: Some dangers of mathematical statis
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Appendix 139 What would happen if y
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Notes 141 and since x is very large
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References Allum, J. A. E. (1966) P
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References 145 -(1950) 'Mechanism o
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Further reading 147 Trigg, G. L. an
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Physics for Geologists, Second edition

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