Physics for Geologists, Second edition

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Gravity 29 g being a vector, the negative sign indicating that it acts downwards. The gravity field is -g and the force acting on any mass in the field is simply that mass multiplied by the value of the field in that position. Regionally, it may be sufficient to consider the gravity field as being every- where -9.8 m s-2 directed towards the centre of the Earth, approximately; but in detail, -g is constant neither in quantity nor direction. We have noted earlier that there is a latitude effect. A formula for the sea-level value for g in latitude 4 is which is not considered to be quite correct but was nevertheless the standard until artificial satellites led to the better formula The discrepancy is very small, and of no significance over the limited area of many surveys. Indeed, merely changing the equatorial value of g in the old formula would have given results within about 1$ parts in 10 000 of the new. But the more we learn about the earth, the better we can and must describe it. As we have already noted, the acceleration on the Equator due to the centrifugal force, v~/R, is about 34 x loF3 m s-~. The practical unit of g is the gal, which is acceleration in units of cm sP2, so multiply Equation 3.3 by 100 if you want to use gals - but beware! The milligal is the common unit. The SI unit is the Gravity Unit, or g.u. One milligal equals 10 g.u. The rotation of the Earth about the Sun also affects the value of g, as does the Moon's rotation about the Earth, both of which we see in tides (which will be examined more closely below). On a local scale, the topography and elevation above sea level must also be taken into account because hills distort the local gravitational field, as do valleys, and elevation implies extra mass beneath a gravimeter - the instrument for measuring the value of g. When all these effects have been taken into account, there are still local variations that Copyright 2002 by Richard E. Chapman
30 Gravity are significant to geologists owing to the variations of mass density in the rocks below the surface. The field has to be mapped by careful measurement, and anomalies in the field may indicate geological features of interest. This is easier said than done because of the need to be able to measure differences of about one millionth of the value of g. Of great interest in this regard is the Falcon system of airborne gravity surveys that will be mentioned briefly when other aspects of global gravity have been considered. Tides The waters of the Earth are subject to various forces: centrifugal forces from the Earth's rotation in orbit, rotation about its axis and rotation with the Moon; and gravitational attraction to the Earth, the Moon and the Sun. When the Moon is new, and it is pulling in the same direction as the Sun, tides are higher than when there is a half-Moon. That is fairly straight- forward; but why are there very high tides soon after the Moon is full, on the opposite side of the Earth from the Sun? Indeed, why are there two tides a day in most places, and not just one? The centre of mass of the Earth-Moon system, called the barycentre, is not at the centre of the Earth, but displaced towards the Moon - still within the Earth, at about 0.74 RE from the centre, RE being 6 371 km (Figure 3.1). The Moon and the Earth rotate around their barycentre, and at the centre of the Earth the centrifugal force due to rotation about the barycentre exactly equals the gravitational attraction between the Earth and the Moon - indeed, there is a circle around the Earth on which the Moon is on the horizon and in which these two forces balance each other. Away from that circle, the balance is not found, and this imbalance gives rise to tide-generating forces Copyright 2002 by Richard E. Chapman Figure 3.1 Tide-generating forces or accelerations on the surface of the Earth due to the attraction of the Moon. CM is the centre of mass of the Moon-Earth system, called the barycentre.
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 and 18: xx Symbols mass refractive index bu
Page 19 and 20: 2 Basic concepts Table 1.1 Dimensio
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: 3 Gravity Universal gravity When di
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
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
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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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Physics for Geologists, Second edition

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