Physics for Geologists, Second edition

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Kinetic energy Force 21 Newton's First and Third Laws of Motion imply that any body in motion has energy because of that motion; and that work is required to stop its motion. The dimensions of kinetic energy are the same as for other energy, ML~T-~, but it is more usefully regarded as a mass times the square of a speed or velocity (rather than as a weight times a distance, as for potential energy). For a body of mass m moving at velocity V the kinetic energy is mv2/2. In a frictionless process, this amount of work could be performed. Why the half? If you drop a mass m from a height h above the ground, the potential energy before dropping is equal to the kinetic energy at impact in a frictionless process. (See Note 2 on page 140 if you need to.) The kinetic energy of the hammer drives the nail; that of the golf club drives the ball. In billiards, snooker and croquet, most of the kinetic energy of the ball that is struck is transferred to any other ball it hits - and so on. Energy is conserved, and one form of energy can change to another. When a volcano erupts, kinetic energy can do work in throwing volcanic bombs into the air, where they acquire potential energy due to their elevation. When an aeroplane crashes and bursts into flame, the cause may be the conversion of kinetic energy into heat. When a volcanic eruption, such as that of Mount St Helens on 18 May 1980, throws ash and dust into the air, the energy that elevates the fine dust is kinetic and thermal, and this combination may be large enough to put material into the stratosphere (about 10-50 km altitude). The ash-plume of Mount St Helens reached an altitude of 25 km, and ash and tephra were spread out 100 km to the NE. The initial velocity required to put a mass of lop3 kg to an altitude of 25 km by kinetic energy alone, ignoring friction, can be found by equating kinetic energy to the potential energy of the mass at an elevation of 25 km: and m v2 - = mgh 2 The initial velocity required to raise any mass to 25 km would therefore be at least 700 m sP1 - about twice the speed of sound - and this is inde- pendent of the mass of the piece in the absence of friction. It is therefore probably safe to conclude that only dust-size particles reached 25 km, and that they were carried there largely by thermal convection currents generated by the heat of the volcano. If 100 m s-' is a likely maximum launch velocity, 500 m is a likely maximum altitude from kinetic energy alone (if 200 m s-l, 2 000 m). A similar argument precludes kinetic energy as the sole mechanism for spreading ash and tephra over 100 km to the NE. Copyright 2002 by Richard E. Chapman
22 Force How does momentum differ from kinetic energy? Momentum has the dimensions of mass x velocity [MLT-'1 while kinetic energy has the dimensions of mass x velocity squared [ML~T-~]. Both are conserved, and both can be transferred to other bodies, but kinetic energy can be converted to other forms of energy, as we have seen. Momentum is a property of a moving mass that can be imparted to other bodies on impact. Earlier we asked why pieces of artificial satellites return to Earth from time to time when Equation 2.5 seems to suggest that as a satellite slows down its height h above the Earth will increase. It is a matter of energy. The satellite has energy due to its motion in orbit and due to its position in the gravitational field of the Earth. Its kinetic energy is where o is the angular velocity (in rads-l: the right hand side uses Equation 2.5). The potential energy is found by considering the work required to move the mass m in the gravitational field from a distance x from the earth's centre of gravity to x + 6x. This, from Equation 2.2, is The work done in moving the mass m from x to oo, where the potential energy is zero, is Hence the potential energy at (RE + h) is and the total energy is the sum of the kinetic and potential energies, This is negative, so as the kinetic energy decreases and the total energy becomes a larger negative number, h also decreases; and as h decreases, its speed increases until it enters the atmosphere, where frictional resistance slows it down and it returns to Earth. Why is the potential energy negative, and what meaning is to be attached to negative potential energy? If a satellite is considered to have zero potential energy when effectively iso- lated from the gravitational field of its planet, and you have to do work on it to get it there from its orbit, then its potential energy in its orbit is negative (Ep + work = 0). Let us now gather all those quantities together in one table (Table 2.1). 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 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: 20 Force Figure 2.3 Torque is the p
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
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
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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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Physics for Geologists, Second edition

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