Physics for Geologists, Second edition

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Force 17 Consider two dimensions first. If you want to walk in a straight line radially on a revolving stage (that is, the path drawn on the stage would be a straight line), one of the forces acting on you gives you an acceleration as the distance from the centre increases. Your angular velocity remains constant, but your speed increases as the radius increases. So if the stage were rotating to the right as you look out from the centre, the acceleration in that direction means that you would have to lean over to the right to counteract it. Failing that, your path will deviate to the left of the straight line. What about bowling a ball along the stage from the centre? Assuming a frictionless process, the ball would indeed travel in a straight line out from the centre, but its path over the stage would be curved. If you had a very-long-distance gun and wished to fire a shell from Brisbane to Canberra (which is south of Brisbane), you would miss if you pointed the gun directly at Canberra because Brisbane is travelling a greater distance around the world's axis in a day than Canberra does. Both have an angular velocity of 15" an hour, but this is a speed of 1480 km h-l in the latitude of Brisbane (27:"s) and 1365 kmh-l in the latitude of Canberra (35"s). The Brisbane component of the shell's velocity would carry it to the east of Canberra - to the left. If Canberra returned the fire, its component of the shell's velocity due to latitude would be less than the velocity of Brisbane, and so the shell would fail to keep up with Brisbane and land to the west of Brisbane - again, missing to the 1eft.l So for any longitudinal motion in the Southern Hemisphere there is a tendency for the path to deviate to the left. This is why the winds blowing out of a high-pressure area are deflected to the left, giving an anti-clockwise rotation. Winds blowing into the centre of a cyclone in the Southern Hemisphere also deviate to the left and give rise to a clockwise motion. In the Northern Hemisphere, the deviation is to the right. Centrifugal and centripetal forces: motor cycles and space craft When a motorcyclist takes a bend in the road, the rider and machine have to bank. If they did not bank, Newton's First Law of Motion would ensure that it went straight ahead. A force is needed to make it change direction. Similarly, when you swing a stone around on a string, a force exists in the string that makes the stone travel in a circular orbit. Again, Newton's First Law of Motion asserts that the stone will fly off at a tangent to that circle the moment you let the string go - or it breaks. The force that keeps the object in its orbit is the centripetal force (the equal and opposite reaction being the centrifugal force). Dimensional analysis at the end of the previous chapter revealed that this force, F,, is equal to rnv2/r, for a circular orbit (or an acceleration of v2/r towards the centre of the circular orbit). 1 There is another element to the trajectory of long-range missiles - the value of g. Apart from the latitude effect, there may be other changes that would have to be taken into account. Copyright 2002 by Richard E. Chapman
18 Force When a motorcycle takes a bend of radius xm, it requires a centripetal force of mv2/x. The machine will have to bank to provide this force, and bank at an angle such that the lateral component of weight of the machine and its rider provides the centripetal force required.2 The vertical component is the weight of the machine and rider, mg, so the lateral component is mg tan 0 and Similar considerations apply to the orbits of planets around the sun and satellites around their planets. A spacecraft in a circular orbit requires an acceleration towards the Earth that is provided by gravity, so, denoting the Earth's radius by RE, its mass by ME, and the gravitational constant by G (as usual), from which and the relationship between a spacecraft's elevation above the surface of the Earth, h, and its required velocity can be determined. Note again that the mass of the object does not come into the equation. That is why an astro- naut feels 'weightless', and everything in the spacecraft, even the smallest thing, appears to be weightless. They are not weightless, because they have mass and there is a force of mutual attraction between their masses and the Earth's. They are all accelerating towards the Earth at the same rate. This equation does not mean that no force acts on the spacecraft, for if that were true, Newton's first law of motion would come into play and the spacecraft would travel in a straight line and fly off into space. The force, the only significant force, acting on it is gravitational and centripetal, giving it an acceleration towards the Earth. It is this unbalanced force that gives rise to the forward motion and this acceleration that gives it its orbit. Why do pieces of artificial satellites return to Earth from time to time? Surely Equation 2.5 suggests that as a satellite slows down, its height h above the Earth will increase? We shall consider that when we have considered potential and kinetic energy. 2 The racing motorcyclist shifts his weight inwards on the bends so that the machine will be more upright. The angle is measured from the points of contact with the road through the centre of gravity of bike and rider as a whole. 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: 16 Force Figure 2.1 The sum of the
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
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
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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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Physics for Geologists, Second edition

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