Physics for Geologists, Second edition

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1 Basic concepts Those of us who are not professional physicists, and those who last did some physics many years ago, may have forgotten some of the things that physicists take for granted. We start, therefore, with most of the basic concepts that will be used throughout this book. Dimensions and units When we write an equation, such as that relating pressure to vertical depth below the surface of a body of static water, where p is the mass density of the water (see page xx for the Greek alphabet), g is the acceleration due to gravity (or the acceleration of free fall) and z is the depth below the free surface, two aspects are involved: the dimensions of the constituent parts, and the units we are to use. It is not at all clear that multiplying a density by an acceleration and by a length has any real meaning; but if we use the 'right' units, we can evaluate the equation and determine the pressure at any depth in any liquid. All valid equations must be dimensionally homogeneous, that is, the dimensions must be the same on each side of the equation, and true constants are dimensionless. Units must be consistent for reliable evaluation. Inconsistent units are those in which components vary from one unit to another, such as pounds per square inch (psi) with lengths measured in feet. The requirement of dimensional homogeneity is used in dimensional analy- sis in order to find the form of an equation when all the quantities involved can be listed. This could be a powerful tool in Earth Sciences in which ana- lytical solutions to problems are not always possible (or are beyond our abilities). Many physical quantities have one or more of the dimensions of mass, length and time, or are dimensionless. An angle is dimensionless, being the ratio of a length to a length. Dimensions are indicated by the initial capital or lower case letter with its exponent (if other than 1). So an area has the Copyright 2002 by Richard E. Chapman
2 Basic concepts Table 1.1 Dimensions of some physical quantities Acceleration Bulk (and other) moduli Compressibility Density, mass Density, weight Energy Force Frequency Hydraulic conductivity Inertia Moment of inertia Torque Momentum Permeability, coefficient of (fluid) Permeability, intrinsic (fluid) Potential (fluid) Pressure, stress Specific discharge Surface tension Velocity Viscosity, absolute or dynamic Viscosity, kinematic Weight Work Temperature Quantity of heat Thermal conductivity dimensions of a length multiplied by a length, or L2; a velocity, a length divided by time, or LT-l. Dimensions may be put in square brackets after a quantity, for example, mass density [ML-3], and for a dimensionless quantity [0], or written out. It is essential for clear thinking in science to consider the dimensions of quantities. Table 1.1 lists the common quantities. Dimensions are quantified using arbitrary units such as metres for length. To be valid, Equation 1.1 must also balance dimensionally, that is, the sum of the exponents of M, the sum of the exponents of L, and the sum of the exponents of T must be equal on both sides of the equation. Pressure is a force (mass times acceleration) on an area and therefore has dimensions MLT-~/L~ = ML-~T-~; mass density is mass per unit of volume and has the dimensions ML-~; acceleration has the dimensions LTP2; depth has the dimension of length. So, Equation 1.1, written as Copyright 2002 by Richard E. Chapman
Page 1 and 2: Physics for Geologists Second editi
Page 3 and 4: Copyright 2002 by Richard E. Chapma
Page 5 and 6: ... vlii Contents Polarization 47 L
Page 7 and 8: Figures Copyright 2002 by Richard E
Page 9 and 10: Tables Copyright 2002 by Richard E.
Page 11 and 12: xiv Preface waves diminishes with d
Page 13 and 14: xvi Preface provides. This book is
Page 15 and 16: xviii Acknowledgements to K. Whaler
Page 17: xx Symbols mass refractive index bu
Page 21 and 22: 4 Basic concepts Table 1.2 Basic SI
Page 23 and 24: 6 Basic concepts pascal (Pa) and si
Page 25 and 26: 8 Basic concepts all the relevant d
Page 27 and 28: 10 Basic concepts relating them by
Page 29 and 30: 2 Force The dimensions of force are
Page 31 and 32: 14 Force The ratio of the Moon's ac
Page 33 and 34: 16 Force Figure 2.1 The sum of the
Page 35 and 36: 18 Force When a motorcycle takes a
Page 37 and 38: 20 Force Figure 2.3 Torque is the p
Page 39 and 40: 22 Force How does momentum differ f
Page 41 and 42: 24 Force the weights - that is, the
Page 43 and 44: 26 Force Figure 2.6 Wall-sticking i
Page 45 and 46: 3 Gravity Universal gravity When di
Page 47 and 48: 30 Gravity are significant to geolo
Page 49 and 50: 32 Gravity Figure 3.2 The tractive,
Page 51 and 52: 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
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52 Optics Diffraction If you shine
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54 Optics Figure 4.7 Geometrical op
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56 Optics Figure 4.9 The mirrors in
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5 Atomic structure and age-dating P
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60 Atomic structure and age-dating
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66 Electromagnetic radiation radiat
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68 Electromagnetic radiation Source
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Heat and heat flow The noun heat ha
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72 Heat and heat flow Second Law: A
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8 Electricity and magnetism Electri
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Electricity and magnetism 77 Figure
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Electricity and magnetism 79 rivett
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Electricity and magnetism 8 1 defin
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Electricity and magnetism 83 is kno
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9 Stress and strain Pressure, p, is
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Stress and strain 87 than some natu
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These three elastic constants are r
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Stress and strain 91 Figure 9.1 New
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Stress and strain 93 Figure 9.2 Com
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Stress and strain 95 Figure 9.3 Ide
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Fracture Stress and strain 97 We fo
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Stress and strain 99 from which we
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10 Sea waves The nature of water wa
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Sea waves 103 Figure 10.1 Wave moti
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Sea waves 105 refraction by islands
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Acoustics: sound and other waves 10
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Acoustics: sound and other waves 10
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12 Fluids and fluid flow Introducti
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Fluids and fluid flow 1 13 Figure 1
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Fluids and fluid flow 115 Figure 22
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Fluids and fluid flow 117 and the f
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water above a vertical thickness h
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Fluids and fluid flow 121 where V i
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Fluids and fluid flow 123 ardentes,
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Fluids and fluid flow 125 Figure 12
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- 14 $ 12 E 10 K .- 3 8 r cll + 6 0
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Fluids and fluid flow 129 the liqui
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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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