module 2

Part 66 Syllabus Module 2 Physics

For B1 & B2 Categories

Part 66 Training Syllabus Module 2 Physics

Part 66 Module 2

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Table of Contents

Matter .................................................................................................................................................................. 5 The Nature of Matter ....................................................................................................................................... 5 The Components of Atoms ............................................................................................................................. 5 Periodic Table of the Elements ....................................................................................................................... 6 Chemical Definitions ....................................................................................................................................... 6

Elements ..................................................................................................................................................... 6 Mixtures ....................................................................................................................................................... 6 Compounds ................................................................................................................................................. 7 Atomic Number ............................................................................................................................................ 7 Mass Number .............................................................................................................................................. 7 Molecules .................................................................................................................................................... 7 Isotopes ....................................................................................................................................................... 7 lonization ..................................................................................................................................................... 8

The Electronic Structure of Atoms .................................................................................................................. 8 Valency ...................................................................................................................................................... 10

Chemical Bonding ......................................................................................................................................... 13 Cohesion and Adhesion ............................................................................................................................ 13 Noble Gases .............................................................................................................................................. 13 Covalent and Ionic Bonding ...................................................................................................................... 13

Covalent Bonding ................................................................................................................................. 13

The Properties of Small Covalent Molecules ............................................................................................ 15 Large Covalent Molecules and their Properties ........................................................................................ 15

Ionic Bonding ................................................................................................................................................ 15 The properties of Ionic Compounds .............................................................................................................. 17 States of Matter ............................................................................................................................................. 17

Solids ......................................................................................................................................................... 17 Liquids ....................................................................................................................................................... 18 Gases ........................................................................................................................................................ 18 Plasma ...................................................................................................................................................... 18

Changes between States .............................................................................................................................. 18 Mass ................................................................................................................................................................. 19 Force ................................................................................................................................................................. 19 Weight ............................................................................................................................................................... 19 Distinction between Mass and Weight ............................................................................................................. 19 Stress, Strain and Hooke's Law ....................................................................................................................... 22 Introduction ....................................................................................................................................................... 22 Types of Structural Stress ................................................................................................................................ 22 Stress, Strain and Young's Modulus ................................................................................................................ 23 Related Definitions ........................................................................................................................................... 25 Bulk Modulus .................................................................................................................................................... 25 Poisson's Ratio ................................................................................................................................................. 25 Cantilever.......................................................................................................................................................... 25 Materials Behaviour .......................................................................................................................................... 26 Elastic ............................................................................................................................................................... 26 Brittle ................................................................................................................................................................. 26 Ductile ............................................................................................................................................................... 26 Viscous ............................................................................................................................................................. 26 Nature and Properties of Solids, Liquids and Gas ........................................................................................... 28 Solid .................................................................................................................................................................. 28 Liquid ................................................................................................................................................................ 28 Gas ................................................................................................................................................................... 29 Changes of State .............................................................................................................................................. 29 Evaporation and Boiling (liquid to gas) ............................................................................................................. 29 Condensing (gas to liquid) ................................................................................................................................ 30 Melting (solid to liquid) ...................................................................................................................................... 30 Freezing (liquid to solid) ................................................................................................................................... 30 Summary .......................................................................................................................................................... 31 Pressure and Force .......................................................................................................................................... 31 Computing Force, Pressure, and Area ............................................................................................................. 31 Atmospheric Pressure ...................................................................................................................................... 31

Transmission of Forces Through Liquids ...................................................................................................... 32 Pressure and Force in Fluid Power Systems ................................................................................................ 34


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The Hydraulic Ram Principle ........................................................................................................................ 35 Differential Areas ...................................................................................................................................... 36 Volume and Distance Factors .................................................................................................................. 37

Relationship between Force, Pressure, and Head ...................................................................................... 37 Static and Dynamic Factors ......................................................................................................................... 37 Operation of Hydraulic Components ............................................................................................................ 38 Hydraulic Jack .............................................................................................................................................. 38

Hydraulic Brakes ...................................................................................................................................... 39 Accumulators ............................................................................................................................................ 40

Barometers ................................................................................................................................................... 42 Mercury barometers ................................................................................................................................. 42 Aneroid barometers .................................................................................................................................. 43

Buoyancy ...................................................................................................................................................... 43 Archimedes Principle ................................................................................................................................ 43 Archimedes' Principle Applied to Bodies that Float .................................................................................. 44 Archimedes' Principles as Applied to Airships and Balloons ................................................................... 45

Kinetics ......................................................................................................................................................... 48 Linear Motion ............................................................................................................................................ 48 The Equations of Motion ........................................................................................................................... 48

Accelerated Motion of a "Freely Falling" Body ............................................................................................. 50 Rotational Motion ......................................................................................................................................... 53 Degrees and Radians .................................................................................................................................. 53 Periodic Motion............................................................................................................................................. 58 Mass and Spring .......................................................................................................................................... 59 Simple Harmonic Motion (SHM) ................................................................................................................... 59 Properties of SHM ........................................................................................................................................ 60 Vibration ....................................................................................................................................................... 60 Types of vibration ......................................................................................................................................... 61 Resonance ................................................................................................................................................... 61 Examples of Resonance .............................................................................................................................. 61 What Causes Resonance? .......................................................................................................................... 61 Design Implications of Resonance ............................................................................................................... 62 Harmonics .................................................................................................................................................... 62 Simple Machines and the Principle of Work ................................................................................................ 63 General Theory of All Machines ................................................................................................................... 63 The Lever ..................................................................................................................................................... 65 The Wheel and Axle ..................................................................................................................................... 67 The Screw Jack ............................................................................................................................................ 67 Dynamics ...................................................................................................................................................... 70 Newton's First Law ....................................................................................................................................... 70 Newton's Second Law .................................................................................................................................. 70 Newton's Third Law ...................................................................................................................................... 72 Every action has an equal and opposite reaction ........................................................................................ 72 Motion in a Circle ......................................................................................................................................... 76 Units of Force ............................................................................................................................................... 77 Friction .......................................................................................................................................................... 79 Static Friction................................................................................................................................................ 79 Rolling Friction.............................................................................................................................................. 79 Kinetic Friction .............................................................................................................................................. 79 Calculating Friction ....................................................................................................................................... 80 Work, Energy and Power ............................................................................................................................. 81 Gravitational Potential Energy...................................................................................................................... 82 Power ........................................................................................................................................................... 83 Alternate Form for Power ............................................................................................................................. 84 Momentum ................................................................................................................................................... 86 Momentum - mV ........................................................................................................................................... 86 Conservation of Momentum ......................................................................................................................... 86 Recoil Problems ........................................................................................................................................... 86 Collision Problems ....................................................................................................................................... 87 Inelastic Collisions ........................................................................................................................................ 87 Elastic Collisions .......................................................................................................................................... 88 Torque .......................................................................................................................................................... 92 Extensions .................................................................................................................................................... 93 Couples ........................................................................................................................................................ 94


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The Gyroscope ............................................................................................................................................. 94 Apparent Drift (or Wander)............................................................................................................................ 95 Transport Drift (or Wander) ........................................................................................................................... 96 Fluid Dynamics ............................................................................................................................................. 97 Cabin Altitude ................................................................................................................................................ 98 Humidity ...................................................................................................................................................... 101 Definitions ................................................................................................................................................... 101 Density and Specific Gravity ....................................................................................................................... 102 Specific Gravity ........................................................................................................................................... 104 Compressibility in Fluids ............................................................................................................................. 104 Viscosity ...................................................................................................................................................... 105 Viscosity Measurement ............................................................................................................................... 105 Units of Measure ......................................................................................................................................... 106 Kinematic viscosity ...................................................................................................................................... 106 Viscosity of air ............................................................................................................................................. 106 Viscosity of water ........................................................................................................................................ 106 Drag and Streamlining ................................................................................................................................ 106 Stokes's Drag .............................................................................................................................................. 107 Viscous resistance = - bv ............................................................................................................................ 107 Drag Coefficient .......................................................................................................................................... 107 Streamlining ................................................................................................................................................ 108 Bernoulli's Principle ..................................................................................................................................... 109 The Venturi Tube ........................................................................................................................................ 111 Application of Bernoulli's Principle to Aerofoil Sections .............................................................................. 112 Temperature ............................................................................................................................................... 115 The Gas Laws ............................................................................................................................................. 116 Boyle's Law ................................................................................................................................................. 117 Charles' Law ............................................................................................................................................... 117 Gay-Lussac's Law ....................................................................................................................................... 118 The General (Ideal) Gas Law...................................................................................................................... 119 Alternate Form of the General (Ideal) Gas Law .......................................................................................... 120 Application of the General Gas Law to Compressors ................................................................................. 121 Thermal Expansion ..................................................................................................................................... 122 Linear Expansion ........................................................................................................................................ 123 Area Expansion ........................................................................................................................................... 123 Volume Expansion ...................................................................................................................................... 124 Expansion of Liquids and Gases ................................................................................................................ 124 The Interesting Case of Water .................................................................................................................... 124 Heat ............................................................................................................................................................. 126 Heat Exchange ........................................................................................................................................... 129 Latent Heat of Fusion and Vaporisation ..................................................................................................... 130 Further Discussion on Latent Heat ............................................................................................................. 131 Heat Transfer .............................................................................................................................................. 133 Refrigeration and Heat Pumps ................................................................................................................... 134 How do things get colder? .......................................................................................................................... 134 The States of Matter ................................................................................................................................... 135 The Magic of Latent Heat............................................................................................................................ 135 So what is a refrigerant? ............................................................................................................................. 136 So is water a refrigerant? ............................................................................................................................ 137 Heat Pumps ................................................................................................................................................ 138 Thermodynamics and the 1st and 2nd Laws .............................................................................................. 139 Boyle's Law ................................................................................................................................................. 139 Charles' Law ............................................................................................................................................... 139 Gay Lussac's Law ....................................................................................................................................... 139 An Adiabatic Process .................................................................................................................................. 139 Thermodynamic Work ................................................................................................................................. 140 Work = PV ................................................................................................................................................... 141 Internal Energy ............................................................................................................................................ 141 Enthalpy ...................................................................................................................................................... 141 The First Law of Thermodynamics ............................................................................................................. 141 The Second Law of Thermodynamics ........................................................................................................ 142 Wavelength, Frequency and Speed ........................................................................................................... 144 The Speed of Light in Various Substances................................................................................................. 146 Light Waves in Matter ................................................................................................................................. 147


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Refraction and the speed of light waves .................................................................................................... 147 Refractive Index Varies with Wavelengthe speed of light in a given transparent medium is also likely to vary with frequency - the refractive index is different for different frequencies. The diagram below shows how the refractive index of fused quartz and crown glass varies with the vacuum wavelength of radiation between short ultraviolet wavelengths ( ~200nm) and near infrared ( ~750nm). Fused quartz is widely used in optical devices as it is transparent over a wide range of wavelengths. ........................................ 148 Dispersion and Chromatic Aberration ........................................................................................................ 148 Lenses ........................................................................................................................................................ 149 Predicting the image .................................................................................................................................. 151 Drawing to find the image .......................................................................................................................... 151 Finding the image by formula ..................................................................................................................... 152 The Diverging Lens .................................................................................................................................... 153 The sign convention ................................................................................................................................... 153 The Power of a Lens .................................................................................................................................. 154 Lens Power = ........................................................................................................................................ 154 Mirrors ........................................................................................................................................................ 154 The angle of incidence equals the angle of reflection. ............................................................................... 154 Front-silvered mirrors ................................................................................................................................. 156 Reflecting Prisms ....................................................................................................................................... 156 Concave Mirrors ......................................................................................................................................... 157 Convex Mirrors ........................................................................................................................................... 158 Fibre Optics ................................................................................................................................................ 158 Fibre Optic Data Links ................................................................................................................................ 158 History of Fibre Optic Technology .............................................................................................................. 159 Advantages and Disadvantages of Fibre Optics ........................................................................................ 160 Frequency and Bandwidth ......................................................................................................................... 161 Basic Structure of an Optical Fibre ............................................................................................................ 162 Propagation of Light along a Fibre ............................................................................................................. 163 Ray Theory ................................................................................................................................................. 163 Mode Theory .............................................................................................................................................. 165 Optical Fibre Types .................................................................................................................................... 168 Single Mode Fibres .................................................................................................................................... 169 Multimode Fibres ........................................................................................................................................ 169 Properties of Optical Fibre Transmission ................................................................................................... 169 Attenuation ................................................................................................................................................. 170 Dispersion .................................................................................................................................................. 173 Intermodal Dispersion ................................................................................................................................ 173 The Transmission of Signals ...................................................................................................................... 174 Analogue Transmission .............................................................................................................................. 174 Digital Transmission ................................................................................................................................... 174 Optical Fibres and Cables .......................................................................................................................... 174 Optical Fibre and Cable Design ................................................................................................................. 174 Optical Fibres ............................................................................................................................................. 175 Multimode Step-Index Fibres ..................................................................................................................... 176 Multimode Graded-lndex Fibres ................................................................................................................. 177 Optical Time-Domain Reflectometry .......................................................................................................... 180 Power Meter ............................................................................................................................................... 182 Wave Motion .............................................................................................................................................. 183 Progressive and Stationary Waves ............................................................................................................ 183 The Wave Formula ..................................................................................................................................... 183 Resonance ................................................................................................................................................. 186 Sound ......................................................................................................................................................... 186 Intensity of Sound ...................................................................................................................................... 187 Sound Waves and Resonant Vibrations .................................................................................................... 188 Constructive and Destructive Interference ................................................................................................. 188 Noise Cancelling Headphones ................................................................................................................... 188 Reflected Waves ........................................................................................................................................ 189 Producing Stationary Waves ...................................................................................................................... 190 Beats .......................................................................................................................................................... 191 Supersonic Speed and Mach Number ....................................................................................................... 191 The Doppler Effect ..................................................................................................................................... 191


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Matter

Matter

The Nature of Matter Scientists for a long time suspected that all substances were composed of small particles which they called atoms. However, it wasn't until the beginning of this century that the existence of atoms was demonstrated to everyone's satisfaction. The size of the atom was found to be so small that a few hundred million, if placed side by side in a row, would form a line less than an inch long. All atoms are, crudely speaking, the same size and can be thought to consist of two main parts. The outer part is composed of 1 or more orbits of electrons. These orbits makes up most of the volume of the atom yet contributes practically nothing to its substance. The other part, located at the centre, is extremely small compared to the atom as a whole, yet essentially all of the real substance of the atom can be attributed to this small speck. We call this speck the nucleus. Further investigation revealed that the nucleus is actually composed of two kinds of particles of roughly equal size and substance packed closely together. These nuclear particles are the proton and neutron. When we refer to the amount of material or substance in an object, we are really talking about the number of protons and neutrons in that object. Also, what we perceive as the mass of an object is related directly to the number of protons and neutrons contained it. The simplest atom is hydrogen which has a single proton for a nucleus. An atom of lead, on the other hand, has 82 protons and 125 neutrons in its nucleus and so has 207 (125 + 82) times as much material or substance as an atom of hydrogen. The size of an atom bears no simple relation to the number of particles in its nucleus. A sodium atom, for example, with 11 protons and 12 neutrons is approximately the same size as an atom of mercury with 80 protons and 121 neutrons. In general, we can say that the size of an atom is determined by its electron orbits, its substance is determined by the total number of protons and neutrons in its nucleus.

The Components of Atoms Atoms are the smallest particles of matter whose properties we study in Chemistry. However from experiments done in the late 19

th and early 20

th century it was deduced that atoms were made up of three

fundamental sub-atomic particles (Table 0-1).

Particle Relative mass Electrical charge Comments

Neutron 1 0 (zero) In the nucleus

Proton 1 +1 (positive) In the nucleus

Electron 1/1850 -1 (negative) Arranged in energy levels or shells around the nucleus

Table 0-1 The sub-atomic components of atoms

Figure 1.1 gives some idea on the structure of an atom.

Figure 0-1 The structure of an atom.


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Periodic Table of the Elements

Figure 0-2 The Periodic Table of the Elements

The elements are laid out in order of Atomic Number. Hydrogen 1, H, does not readily fit into any Group.

A Group is a vertical column of like elements e.g. Group IA, The Alkali Metals (Li, Na, K etc.), Group VIIB, The Halogens (F, Cl, Br, I etc.) and Group VIII (or 0), The Noble Gases (He, Ne, Ar etc.). The Group number equals the number of electrons in the outer shell (e.g. chlorine's electron arrangement is 2.8.7, the second element down, in Group 7). A Period is a horizontal row of elements with a variety of properties. The Period number equals the number of shells (1-7).

Chemical Definitions

Elements Pure substances, made up of atoms with the same number of protons. Note that an element:

consists of only one kind of atom, cannot be broken down into a simpler type of matter by either physical or chemical means, and can exist as either atoms (e.g. argon) or molecules (e.g., nitrogen).

Mixtures Mixtures are of pure substances. Mixtures have the properties of the different substances that make it up. Mixtures melt at a range of temperatures and are easy to separate. Note that a mixture:

consists of two or more different elements and/or compounds physically intermingled, can be separated into its components by physical means, and often retains many of the properties of its components.


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Compounds Pure substances made up more than 1 element which have been joined together by a chemical reaction therefore the atoms are difficult to separate. The properties of a compound are different from the atoms that make it up. Splitting of a compound is called chemical analysis. Note that a compound:

consists of atoms of two or more different elements bound together, can be broken down into a simpler type of matter (elements) by chemical means (but not by physical

means), has properties that are different from its component elements, and always contains the same ratio of its component atoms.

Atomic Number The atomic number (also known as the proton number) is the number of protons found in the nucleus of an atom. It is traditionally represented by the symbol Z. The atomic number uniquely identifies a chemical element. In an atom of neutral charge, atomic number is equal to the number of electrons.

Mass Number The mass number (A), also called atomic mass number or nucleon number, is the number of protons and neutrons (also defined as a less commonly known term, nucleons) in an atomic nucleus. The mass number is unique for each isotope of an element and is written either after the element name or as a superscript to the left of an element's symbol. For example: Carbon-12 (12C) has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (Z) as a subscript to the left of the element symbol directly below the mass number, thus:

The difference between the mass number and the atomic number gives the number of neutrons (N) in a given nucleus: N=A-Z. For example: Carbon-14 is created from Nitrogen-14 with seven protons (p) and seven neutrons via a cosmic ray interaction which transmutes 1 proton into 1 neutron. Thus the atomic number decreases by 1 (Z: 76) and the mass number remains the same (A = 14), however the number of neutrons increases by 1 (n: 78). Before:

Nitrogen-14 (7p, 7n) After:

Carbon-14 (6p, 8n).

Molecules A pure substance which results when two or more atoms of a single element share electrons, for example O2. It can also more loosely refer to a compound, which is a combination of two or more atoms of two or more different elements, for example: H2O. Atoms combine to form more complex structures which we call molecules. Like building blocks, these molecules organize to form all of the materials, solid, liquid and gas, which we encounter in our daily lives. Solids and liquids are materials in which the molecules attract one another so strongly that their relative motion is severely restricted. In a gas, the freedom of motion of the molecules is only slightly influenced by their mutual attraction. This is why gases fill the entire space to which they are confined, They spread out unconstrained until they encounter the walls of their container.

Isotopes Isotopes are atoms of the same element with different numbers of neutrons. This gives each isotope of the element a different mass or nucleon number but being the same element they have the same atomic or proton number. There are small physical differences between the isotopes e.g. the heavier isotope has a greater density and boiling point. However, because they have the same number of protons they have the same electronic structure and are identical chemically. Examples are illustrated below. Do not assume the word isotope means it is radioactive, this depends on the stability of the nucleus i.e. unstable atoms might be referred to as radioisotopes.


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Figure 0-3 The three isotopes of hydrogen

Figure 1-3 shows the three isotopes of hydrogen. They are called hydrogen, deuterium, and tritium respectively. How do we distinguish between them? They each have one single proton (Z = 1), but differ in the number of their neutrons. Hydrogen has no neutron, deuterium has one, and tritium has two neutrons. The isotopes of hydrogen have, respectively, mass numbers of one, two, and three. Hydrogen-1 is the most common, there is a trace of hydrogen-2 naturally but hydrogen-3 is very unstable and is used in atomic fusion weapons.

Figure 0-4 The two isotopes of helium

Figure 1-4 shows the two isotopes of helium with mass numbers of 3 and 4, with 1 and 2 neutrons respectively but both have 2 protons. Helium-3 is formed in the Sun by the initial nuclear fusion process. Helium-4 is also formed in the Sun and as a product of radioactive alpha decay of an unstable nucleus. An alpha particle is a helium nucleus, it picks up two electrons and becomes the atoms of the gas helium.

Figure 0-5 The two isotopes of sodium

Figure 1-5 shows the two isotopes of sodium with mass numbers of 23 and 24, with 12 and 13 neutrons respectively but both have 11 protons. Sodium-23 is quite stable e.g. in common salt (NaCI, sodium chloride) but sodium-24 is a radio-isotope and is a gamma emitter used in medicine as a radioactive tracer e.g. to examine organs and the blood system.

lonization When the atom loses electrons or gains electrons in this process of electron exchange, it is said to be ionised. For ionisation to take place, there must be a transfer of energy which results in a change in the internal energy of the atom. An atom having more than its normal amount of electrons acquires a negative charge, and is called a negative ion (or 'anion'). The atom that gives up some of its normal electrons is left with less negative charges than positive charges and is called a positive ion (or 'cation'). Thus, ionisation is the process by which an atom loses or gains electrons.

Cation - A cation is a positively charged ion. Metals typically form cations. Anion - An anion is a negatively charged ion. Non-metals typically form anions.

The Electronic Structure of Atoms The electrons are arranged in energy levels or shells around the nucleus and with increasing distance from the nucleus. The shells are lettered from the innermost shell outwards from K to Q. There are rules about the maximum number of electrons allowed in each shell.

The 1st shell (K) has a maximum of 2 electrons The 2nd shell (L) has a maximum of 8 electrons The 3rd shell (M) has a maximum of 18 electrons The 4th shell (N) has a maximum of 32 electrons

Our knowledge about the structure of atoms depends on the mathematical formulations predicted by Neils Bohr. He suggested that electrons are distributed in orbits and the number of electrons held in the orbit


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depends on the number of the orbit. The orbits are counted outwards from the nucleus. Higher the orbit number, farther are the electrons in that orbit from the nucleus. If the orbit number is "n", then the maximum electrons held in the orbit is given as 2n

2. The first orbit has n=1, and will hold maximum of 2 electrons, the

second orbit has n=2 and is capable of holding a total of 8 electrons; similarly the third orbit will be able to contain 18 electrons and so on.

Electrons within an atom have definite energies. The electrons closest to the nucleus (n=1) are most tightly bound; the reason is because of stronger electrostatic attraction with the nucleus. Electrons in the highest orbit are least tightly bound. Electrons in the same orbit have same energies. The electron orbits are also called as electron energy levels or shells. Electronic shells are known as K shell, L shell, M shell, N shell corresponding to orbit number n=1, 2, 3 and 4 respectively. Higher number orbits are assigned shell names in alphabetical order after N. Figure 0-6 The atomic

structure of Helium and Neon

Figure 0-7 Electron shell (orbit) designation

Examples: diagram, symbol or name of element (Atomic Number = number of electrons in a neutral atom), shorthand electron arrangement:

On Period 1

Figure 0-8 Electron arrangement of Hydrogen and Helium

On Period 2

Figure 0-9 Electron arrangement of Lithium, Carbon and Neon

On Period 3

to Figure 0-10 Electron arrangement of Sodium, Chlorine and Argon


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On Period 4

Figure 0-11 Electron arrangement of Potassium and Calcium

Valency Hydrogen is the simplest element. It has one electron. Its outer shell only holds two electrons. Let us use Hydrogen as a standard to see how other atoms combine with it. Table 1-2 lists the simplest compound of selected elements with Hydrogen. Valency can be simply defined as the number of Hydrogen atoms that an element can combine with. In the above table, Helium, Neon and Argon have a valency of 0. They do not normally form compounds. Lithium, Sodium and Potassium have a valency of 1 because they combine with one Hydrogen atom. Beryllium, Magnesium and Calcium all have a valency of 2: they combine with two Hydrogen atoms. Note that the valences of all these atoms are equal to the number of outer electrons that these elements have. Boron and Aluminium combine with three Hydrogen atoms - their valences are 3 - and they have three outer electrons. Carbon and Silicon combine with four Hydrogen atoms. The valency of these elements is 4. It will come as no surprise that they both have four outer electrons. Any element with 4 electrons in its outer shell is known as a semiconductor

Atom Symbol Outer Shell Compound Helium He Full None Lithium Li 1 LiH Beryllium Be 2 BeH2 Boron B 3 BH3 Carbon C 4 CH4 Nitrogen N 5 NH3 Oxygen 6 H2O Fluorine F 7 HF Neon Ne Full None Sodium Na 1 NaH Magnesium Mg 2 MgH2 Aluminium Al 3 AIH3 Silicon Si 4 SiH4 Phosphorus P 5 PH3 Sulphur S 6 H2S Chlorine Cl 7 HCI Argon Ar Full None Potassium K 1 KH Calcium Ca 2 CaH2

Table 0-2 Electrons in outer shells of some common elements

What about Nitrogen and Phosphorus? They have five outer electrons. But they normally only combine with three Hydrogen atoms. Their valences are 3. Note that 3 is 5 less that 8. These atoms are three electrons short of a full shell. Please note that both Nitrogen and Phosphorus can also have a valency of 5. Some atoms are capable of having more than one valency. That will confuse the issue so we will talk of normal valency. Now to Oxygen and Sulphur. Both have six outer electrons. Six is two short of a full shell. Their normal valences are 2 and they combine with two atoms of Hydrogen. Water is H2O. Finally, Fluorine and Chlorine have seven outer electrons. This is one short of a full shell. They both combine with a single Hydrogen atom and their normal valences are 1.


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As a side note, Chlorine can also have valences of 3, 5 and 7. The reasons are well beyond the scope of these notes. The rules above can be summarised as follows:

The normal valency of an atom is equal to the number of outer electrons if that number is four or less. Otherwise, the valency is equal to 8 minus the number of outer electrons.

The atoms with full electron shells (Helium, Neon, Argon) are chemically inert forming few compounds. The atoms don't even interact with each other very much. These elements are gases with very low boiling points. The atoms with a single outer electron or a single missing electron are all highly reactive. Sodium is more reactive than Magnesium. Chlorine is more reactive than Oxygen. Generally speaking, the closer an atom is to having a full electron shell, the more reactive it is. Atoms with one outer electron are more reactive than those with two outer electrons, etc. Atoms that are one electron short of a full shell are more reactive than those that are two short. Atoms with only a few electrons in its outer shell are good electrical conductors. Atoms with 8, or close to 8 electrons in its outer shell are poor conductors (or good insulators). This is why atoms with 4 electrons in its outer shell are semi-conductors. When a semiconductor (such as silicon or germanium) atom bonds with another similar atom, it does so covalently. Each atom shares one electron with 4 neighbour atoms. Thus all its electrons are used up in what becomes a solid lattice of semiconductor atoms. The solid material has therefore no free electrons (and no holes for electrons to fit into). The following names are given to ions of the specific number of electron bindings (valence):

1 electron binding - monovalent 2 electron binding - divalent 3 electron binding - trivalent 4 electron binding - tetravalent 5 electron binding - pentavalent 6 electron binding hexavalent


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Atomic No.

Element Electrons per Shell Atomic

No. Element

Electrons per Shell

K L M N P Q K L M N P Q

1 Hydrogen 1 53 iodine 2 8 18 8 7

2 Helium 2 54 Xenon 2 8 18 18 8

3 Lithium 2 1 55 Caesium 2 8 18 8 8 1

4 Beryllium 2 2 56 Barium 2 8 18 8 8 2

5 Boron 2 3 57 Lanthanum 2 8 18 8 9 2

6 Carbon 2 4 58 Cerium 2 8 18 19 9 2

7 Nitrogen 2 5 59 Praseodymium 2 8 18 20 9 2

8 Oxygen 2 6 60 Neodymium 2 8 18 21 9 2

9 Fluorine 2 7 61 Promethium 2 8 18 22 9 2

10 Neon 2 8 62 Samarium 2 8 18 23 9 2

11 Sodium 2 8 1 63 Europium 2 8 18 24 9 2

12 Magnesium 2 8 2 64 Gadolinium 2 8 18 25 9 2

13 Aluminium 2 8 3 65 Terbium 2 8 18 26 9 2

14 Silicon 2 8 4 66 Dysprosium 2 8 18 27 9 2

15 Phosphorus 2 8 5 67 Holmium 2 8 18 28 9 2

16 Sulphur 2 8 6 68 Erbium 2 8 18 29 9 2

17 Chlorine 2 8 7 69 Thulium 2 8 18 30 9 2

18 Argon 2 8 8 70 Ytterbium 2 8 18 31 9 2

19 Potassium 2 8 8 1 71 Lutetium 2 8 18 32 9 2

20 Calcium 2 8 8 2 72 Halnium 2 8 18 32 10 2

21 Scandium 2 8 9 2 73 Tantalum 2 8 18 32 11 2

22 Titanium 2 8 10 2 74 Tungsten 2 8 18 32 12 2

23 Vanadium 2 8 11 2 75 Rhenium 2 8 18 32 13 2

24 Chromium 2 8 13 1 76 Osmium 2 8 18 32 14 2

25 Manganese 2 8 13 2 77 iridium 2 8 8 32 15 2

26 iron 2 8 14 2 78 Platinum 2 8 8 32 16 2

27 Cobalt 2 8 15 2 79 Gold 2 8 8 32 18 1

28 Nickel 2 8 16 2 80 Mercury 2 8 8 32 18 2

29 Copper 2 8 18 1 81 Thallium 2 8 8 32 18 3

30 Zinc 2 8 18 2 82 Lead 2 8 8 32 18 4

31 Gallium 2 8 18 3 83 Bismuth 2 8 8 32 18 5

32 Germanium 2 8 18 4 84 Polonium 2 8 8 32 18 6

33 Arsenic 2 8 18 5 85 Asatine 2 8 8 32 18 7

34 Selenium 2 8 18 6 86 Radon 2 8 8 32 18 8

35 Bromine 2 8 18 7 87 Francium 2 8 8 32 18 8 1

36 Krypton 2 8 18 8 88 Radium 2 8 8 32 18 8 2

37 Rubidium 2 8 18 8 1 89 Actinium 2 8 18 32 18 9 2

38 Strontium 2 8 18 8 2 90 Thorium 2 8 18 32 19 9 2

39 Yttrium 2 8 18 9 2 91 Proactinium 2 8 18 32 20 9 2

40 Zirconium 2 8 18 10 2 92 Uranium 2 8 18 32 21 9 2

41 Niobium 2 8 18 12 93 Neptunium 2 8 18 32 22 9 2

42 Molybdenum 2 8 18 13 94 Plutonium 2 8 18 32 23 9 2

43 Technetium 2 8 18 14 95 Americium 2 8 18 32 24 9 2

44 Ruthenium 2 8 18 15 96 Curium 2 8 8 32 25 9 2

45 Rhodium 2 8 18 16 97 Berkelium 2 8 8 32 26 9 2

46 Palladium 2 8 18 18 98 Californium 2 8 8 32 27 9 2

47 Silver 2 8 18 18 1 99 Einsteinium 2 8 8 32 28 9 2

48 Cadmium 2 8 18 18 2 100 Fermium 2 8 8 32 29 9 2

49 indium 2 8 18 18 3 101 Mendelevium 2 8 18 32 30 9 2

50 Tin 2 8 18 18 4 102 Nobelium 2 8 18 32 31 9 2

51 Antimony 2 8 18 18 5 103 Lawrencium 2 8 18 32 32 9 2

52 Tellurium 2 8 18 18 6

Table 0-3 Electrons per shell


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Chemical Bonding

Cohesion and Adhesion 'Cohesion' is the intermolecular force between liquid particle types (for example, it is what makes water molecules stick together, or 'cohere', to make a rain drop). 'Adhesion' is the intermolecular force between dissimilar atoms (for example, it is what makes the rain drops 'adhere' to a washing line). These types of bonding are temporary. Atomic bonding refers to the permanent bonding between atoms which holds all materials together.

Noble Gases Some atoms are very reluctant to combine with other atoms and exist in the air around us as single atoms. These are the Noble Gases and have very stable electron arrangements e.g. 2, 2.8 and 2.8.8 and are shown in the diagrams below.

Figure 0-12 (Atomic Number) and electron arrangement

Covalent and Ionic Bonding All other atoms therefore, bond to become electronically more stable, that is to become like Noble Gases in electron arrangement. Atoms can do this in two ways:

COVALENT BONDING - sharing electrons to form molecules with covalent bonds, the bond is usually formed between two non-metallic elements in a molecule.

or IONIC BONDING - By one atom transferring electrons to another atom. The atom losing electrons

forms a positive ion and is usually a metal. The atom gaining electrons forms a negative ion and is usually a non-metallic element.

The types of bonding and the resulting properties of the elements or compounds are described in detail below. In all the electronic diagrams ONLY the outer electrons are shown.

Covalent Bonding Covalent bonds are formed by atoms sharing electrons to form molecules. This type of bond usually formed between two non-metallic elements. The molecules might be that of an element i.e. one type of atom only OR from different elements chemically combined to form a compound. The covalent bonding is caused by the mutual electrical attraction between the two positive nuclei of the two atoms of the bond, and the electrons between them. One single covalent bond is a sharing of 1 pair of electrons, two pairs of shared electrons between the same two atoms gives a double bond and it is possible for two atoms to share 3 pairs of electrons and give a triple bond. The Bonding in Small Covalent Molecules The simplest molecules are formed from two atoms and examples of their formation are shown below. The electrons are shown as dots and crosses to indicate which atom the electrons come from, though all electrons are the same. The diagrams may only show the outer electron arrangements for atoms that use two or more electron shells. Examples of simple covalent molecules are... Example 1 - 2 hydrogen atoms (1) form the molecule of the element hydrogen H2:

and combine to form where both atoms have a pseudo helium structure of 2 outer electrons around each atom. Example 2 -2 chlorine atoms (2.8.7) form the molecule of the element chlorine:


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and combine to form where both atoms have a pseudo neon or argon structure of 8 outer electrons around each atom. Example 3 - 1 atom of hydrogen (1) combines with 1 atom of chlorine (2.8.7) to form the molecule of the compound hydrogen chloride HCI:

and combine to form where hydrogen is electronically like helium and chlorine like neon or argon. Example 4 - 2 atoms of hydrogen (1) combine with 1 atom of oxygen (2.6) to form the molecule of the compound we call water H2O

and and combine to form so that the hydrogen atoms are electronically like helium and the oxygen atom becomes like neon or argon. The molecule can be shown as:

with two hydrogen - oxygen single covalent bonds. Example 5 - 3 atoms of hydrogen (1) combine with 1 atom of nitrogen (2.5) to form the molecule of the compound we call ammonia NH3.

Three of and one combine to form so that the hydrogen atoms are electronically like helium and the nitrogen atom becomes like neon or argon. The molecule can be shown as:

with three nitrogen - hydrogen single covalent bonds. Example 6 - 4 atoms of hydrogen (1) combine with 1 atom of carbon (2.4) to form the molecule of the compound we call methane CH4.

Four of and one of combine to form so that the hydrogen atoms are electronically like helium and the nitrogen atom becomes like neon or argon. The molecule can be shown as

with four carbon - hydrogen single covalent bonds. All the bonds in the above examples are single covalent bonds. Below are three examples 7-9, where there is a double bond in the molecule, in order that the atoms have stable Noble Gas outer electron arrangements around each atom. Example 7 - Two atoms of oxygen (2.6) combine to form the molecules of the element oxygen O2.

The molecule has one double covalent bond . Example 8 - One atom of carbon (2.4) combines with two atoms of oxygen (2.6) to form carbon dioxide CO2. .

The molecule can be shown as with two carbon = oxygen double covalent bonds.


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Example 9 - Two atoms of carbon (2.4) combine with four atoms of hydrogen (1) to form ethane C2H4.

The molecule can be shown as with one carbon = carbon double bond and four carbon - hydrogen single covalent bonds.

The Properties of Small Covalent Molecules The electrical forces of attraction between atoms in a molecule are strong and most molecules do not change on heating. However the forces between molecules are weak and easily weakened further on heating. Consequently small covalent molecules have low melting and boiling points. They are also poor conductors of electricity because there are no free electrons or ions in any state to carry electric charge. Most small molecules will dissolve in a solvent to form a solution.

Large Covalent Molecules and their Properties It is possible for many atoms to link up to form a giant covalent structure. This produces a very strong 3-dimensional covalent bond network. This illustrated by carbon in the form of diamond. Carbon can form four single bonds to four other atoms etc. etc. This type of structure is thermally very stable and they have high melting and boiling points. They are usually poor conductors of electricity because the electrons are not usually free to move as they can in metallic structures. Also because of the strength of the bonding in the structure they are often very hard and will not dissolve in solvents like water.

Figure 1-12: A plane of Carbon atoms from a diamond crystal.

Ionic Bonding Ionic bonds are formed by one atom transferring electrons to another atom to form ions. Ions are atoms, or groups of atoms, which have lost or gained electrons. The atom losing electrons forms a positive ion (a cation) and is usually a metal. The overall charge on the ion is positive due to excess positive nuclear charge (protons do NOT change in chemical reactions). The atom gaining electrons forms a negative ion (an anion) and is usually a non-metallic element. The overall charge on the ion is negative because of the gain, and therefore excess, of negative electrons. The examples below combining a metal from Groups 1 (Alkali Metals), 2 or 3, with a non-metal from Group 6 or Group 7 (The Halogens). Example 1 - A Group 1 metal + a Group 7 non-metal e.g. sodium + chlorine sodium chloride NaCI or ionic formula Na

+CI

-.

In terms of electron arrangement, the sodium donates its outer electron to a chlorine atom forming a single positive sodium ion and a single negative chloride ion. The atoms have become stable ions, because electronically, sodium becomes like neon and chlorine like argon.

Na (2.8.1) + Cl (2.8.7) Na+ (2.8) Cl- (2.8.8)

One Na combines with one Cl to form:

Example 2 - A Group 2 metal + a Group 7 non-metal e.g. magnesium + chlorine magnesium chloride MgCI2 or ionic formula Mg

2+(CI

-)2.

In terms of electron arrangement, the magnesium donates its two outer electrons to two chlorine atoms forming a double positive magnesium ion and two single negative chloride ions. The atoms have become stable ions, because electronically, magnesium becomes like neon and chlorine like argon.

Mg (2.8.2) + 2CI (2.8.7) Mg2+ (2.8) 2Cl- (2.8.8)


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One Mg combines with two Cl to form:

* *NOTE: You can draw two separate chloride ions, but in these examples a number subscript has been

used, as in ordinary chemical formula. Example 3 - A Group 3 metal + a Group 7 non-metal e.g. aluminium + fluorine aluminium fluoride AIF3 or ionic formula AI

3+(F

-)3.

In terms of electron arrangement, the aluminium donates its three outer electrons to three fluorine atoms forming a triple positive aluminium ion and three single negative fluoride ions. The atoms have become stable ions, because electronically, aluminium becomes like neon and also fluorine.

Al (2.8.3) + 3F (2.8.7) AI3+ (2.8) 3F- (2.8)

One combines with three to form Example 4 - A Group 1 metal + a Group 6 non-metal e.g. potassium + oxygen potassium oxide K2O or ionic formula (K

+)2O

2-.

In terms of electron arrangement, the two potassium atoms donates their outer electrons to one oxygen atom. This results in two single positive potassium ions to one double negative oxide ion. All the ions have the stable electronic structures 2.8.8 (argon like) or 2.8 (neon like)

2K (2.8.8.1) + O (2.6) 2K+ (2.8.8) O2- (2.8)

Two combine with one to form Example 5 - A Group 2 metal + a Group 6 non-metal e.g. calcium + oxygen calcium oxide CaO or ionic formula Ca

2+O

2-.

In terms of electron arrangement, one calcium atom donates its two outer electrons to one oxygen atom. This results in a double positive calcium ion to one double negative oxide ion. All the ions have the stable electronic structures 2.8.8 (argon like) or 2.8 (neon like):

Ca (2.8.8.2) + O (2.6) => Ca2+

(2.8.8) O2-

(2.8)

ONE combines with ONE to form Example 6 - A Group 3 metal + a Group 6 non-metal e.g. aluminium + oxygen aluminium oxide Al2O3 or ionic formula (AI

3+)2(O

2-)3.

In terms of electron arrangement, two aluminium atoms donate their three outer electrons to three oxygen atoms. This results in two triple positive aluminium ions to three double negative oxide ions. All the ions have the stable electronic structure of neon 2.8

2AI (2.8.3) + 3O (2.6) => 2AI3+

(2.8) 3O2-

(2.8)

Two combine with three to form


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The properties of Ionic Compounds The ions in an ionic solid are arranged in an orderly way in a giant ionic lattice shown in the

diagram on the left. The ionic bond is the strong electrical attraction between the positive and negative ions next to each other in the lattice. Salts and metal oxides are typical ionic compounds.

This strong bonding force makes the structure hard (if brittle) and have high melting and boiling points. Unlike covalent molecules, ALL ionic compounds are crystalline solids at room temperature.

Many ionic compounds are soluble in water, but not all. The solid crystals DO NOT conduct electricity because the

ions are not free to move to carry an electric current. However, if the ionic compound is melted or dissolved in water, the liquid will now conduct electricity, as the ion particles are now free.

Figure 0-13 Sodium Chloride lattice structure

The crystal lattice of metals consists of ions, NOT atoms. The outer electrons (-) from the original metal atoms are free to move around between the positive metal ions formed (+). These free or 'delocalised

1

electrons are the 'electronic glue' holding the particles together. There is a strong electrical force of attraction between these mobile electrons and the immobile positive metal ions - this is the metallic bond.

Figure 0-14 'Electron cloud' formation of Ionic (or Metallic) Bonding

This strong bonding generally results in dense, strong materials with high melting and boiling points.

Metals are good conductors of electricity because these 'free' electrons carry the charge of an electric current when a potential difference (voltage!) is applied across a piece of metal.

Metals are also good conductors of heat. This is also due to the free moving electrons. Non-metallic solids conduct heat energy by hotter more strongly vibrating atoms, knocking against cooler less strongly vibrating atoms to pass the particle kinetic energy on. In metals, as well as this effect, the 'hot' high kinetic energy electrons move around freely to transfer the particle kinetic energy more efficiently to 'cooler' atoms.

Typical metals also have a silvery surface but remember this may be easily tarnished by corrosive oxidation in air and water.

States of Matter

Solids A solid object is characterized by its resistance to deformation and changes of volume. At the microscopic scale, a solid has these properties:

The atoms or molecules that comprise the solid are packed closely together. These constituent elements have fixed positions in space relative to each other. This accounts for

the solid's rigidity. In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a unit cell, a set of atoms arranged in a particular way; which is periodically repeated in three dimensions on a lattice. The spacing between unit cells in various directions is called its lattice parameters.

If sufficient force is applied, its lattice atomic structure can be disrupted, causing permanent deformation.


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Because any solid has some thermal energy, its atoms vibrate. However, this movement is very small, and cannot be observed or felt under ordinary conditions.

Liquids A liquid's shape is confined to, but not determined by, the container it fills. That is to say, liquid particles (normally molecules or clusters of molecules) are free to move within the volume, but they form a discrete surface that may not necessarily be the same as the vessel. The same cannot be said about a gas; it can also be considered a fluid, but it must conform to the shape of the container entirely.

Gases Gases consist of freely moving atoms or molecules without a definite shape and without a definite volume. Compared to the solid and liquid states of matter a gas has lower density and a lower viscosity. The volume of a gas will change with changes in temperature or pressure, as described by the ideal gas law. A gas also has the characteristic that it will diffuse readily, spreading apart in order to uniformly fill the space of any container.

Plasma A plasma is typically an ionized gas. Plasma is considered to be a distinct state of matter, apart from gases, because of its unique properties. 'Ionized' refers to presence of one or more free electrons, which are not bound to an atom or molecule. The free electric charges make the plasma electrically conductive so that it responds strongly to electromagnetic fields. Plasma typically takes the form of neutral gas-like clouds (e.g. stars) or charged ion beams, but may also include dust and grains (called dusty plasmas). They are typically formed by heating and ionizing a gas, stripping electrons away from atoms, thereby enabling the positive and negative charges to move more freely.

Changes between States Solids can melt and become liquids, and liquids can boil to become gases. Likewise, gases can condense to become liquids, and liquids can freeze to become solids. Sometimes solids can become gases without ever becoming liquids. This is called subliming.


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Mechanics

Mass In physics, the term for what we have up to now referred to as the amount of substance or matter is "mass". A natural unit for mass is the mass of a proton or neutron. This unit has a special name, the "atomic mass unit" (amu). This unit is useful in those sciences which deal with atomic and nuclear matter. In measuring the mass of objects which we encounter daily, this unit is much too small and therefore very inconvenient. For example, the mass of a bowling ball expressed in amu's would be about 4,390,000,000,000,000,000,000,000,000. One kilogram equals 602,000,000,000,000,000,000,000,000 amu. Since one amu is the mass of a proton or neutron we know immediately that a kilogram of anything has this combined number of protons and neutrons contained in it. The kilogram is the SI unit of mass. In the English system, the standard unit of mass is the slug. The conversion is:

1 slug = 14.59 kg = 8,789,000,000,000,000,000,000,000,000 amu

We will use the conveniently sized units, the slug in the English system and the kilogram in the metric system, for all of the problems that we will do in this course. Note that the above conversion, 1 slug = 14.59 kilogram, is listed with your conversion factors in the table of conversion factors (Table 1-1).

Force The physicist uses the word "force" to describe any push or pull. A force is one kind of vector. A vector is a quantity that has both size and direction. A force has a certain magnitude or size. Also, a force is always in a certain direction. To completely describe a force, it is necessary to specify both the size of the push or pull and its direction. The units in which force are measured are the pound (Ib.) in the English system and the Newton (N) in the metric system. The Newton is named for Sir Isaac Newton, a famous British physicist who lived in the 17th century. The relationship between the metric and English units is given by the conversion factor:

1 Ib. = 4.448 N

Weight A weight is one kind of force. It is defined as the gravitational pull of the earth on a given body. The direction of this force is toward the geometrical centre of the earth.

Distinction between Mass and Weight The physicist very carefully distinguishes between "mass" and "weight". As we have seen, mass is the quantity of matter, determined by the number of protons and neutrons in the body, and weight is a measure of the gravitational pull of the earth on this quantity of matter. It may seem that this is an unimportant distinction. However, there is one important difference. The mass of an object is the same wherever this object is in the universe. The mass of a stone is the same if the stone is on the earth, on Mars, in a space ship, or some place in the Milky Way Galaxy. If the stone is not on the earth but is in a space station orbiting the earth some distance from the earth's surface, the weight of this stone is different from its weight on the earth's surface. If the stone is on the planet Mars, we speak of its "weight on Mars", the gravitational pull of Mars on the stone. As you have probably figured out, the greater the mass of an object on the surface of the earth, the greater is the weight of this object. These two quantities are approximately proportional to each other as long as the body remains on the surface of the earth. The word "approximately" in the previous sentence refers to the fact that the pull of the earth on a body of a given mass varies slightly with the position of the body on the earth's surface. For example, a body that weighs 57.3 Ibs. at the North Pole would weigh 57.0 Ibs. at a place on the equator. This occurs because a body at either pole is slightly closer to the centre of the earth than it is


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at the equator. Thus, the pull of the earth on the body is greater at the poles and slightly smaller at other places on the earth. However, we usually neglect this slight difference. Physicists and engineers measure masses of bodies in slugs or kilograms and weights in pounds or Newtons. The equation relating mass and weight is:

w = mg

In this equation, g has a definite numerical value. We will use the following relations:

g = 32

or g = 9.8

There is a great source of confusion in British marketing practices. For example, we often see on a packet of sugar the information regarding the contents:

1 kg or 2.2 Ibs

We note that 2.2 Ibs. equals 1 kg. We have just learned that 2.2 Ibs. is the weight of the sugar and that 1 kg is the mass of the sugar. In other words, British packaging practices list the weight of the product if we deal with the English system and list the mass of the product if we are in the metric system.

For example, suppose the weight of a piece of cheese is marked 32 oz. and we wish to know the number of grams. First we convert the weight in ounces to 2 Ibs. Then we convert from pounds to Newtons.

W = 2lbs x

= 8.9 N

Next, we use the relation:

w = mg or m =

Therefore, we write:

m =

= 0.908 kg = 908 grams

Note that we can convert from pounds to Newtons since both are units of weight and we can convert from kilograms to slugs since both are units of mass. However, if we want to find a mass if we know a weight or a weight if we know a mass we must use the equation:

m =

or w = mg

In summary, let us note that mass is a measure of the quantity of matter - ultimately, a measure of the number of protons and neutrons in the body and weight is the force with which the earth pulls on a body. These are related but not identical concepts. The units of mass are slugs and kilograms. The units of weight are pounds and Newtons. A mass can be changed from slugs to kilograms and vice versa. A weight can be changed from Newtons to pounds or vice versa. However, one cannot say that one pound equals 454 grams. The only correct statement is that a body having a weight of one pound has a mass of 454 grams. The equation relating mass and weight is:

m =

or w = mg

Problems 1. What is the mass of a body having a weight of 45 N?

2. What is the weight of a body having a mass of 23 kg?

3. What is the mass of a body having a weight of 350 Ibs.?

4. What is the weight of a body having a mass of 23.6 slugs?

5. What is the weight (in Ibs.) of the corn flakes in a box where the mass is listed as 680 g?

6. What is the mass in grams of 2.5 Ibs. of bologna?


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Answers All answers are to 3 significant figures. 1. 4.59kg

2. 225 N

3. 10.9 slugs

4. 755 Ibs.

5. 1.45 Ibs.

6. 1140g


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Stress, Strain and Hooke's Law

Introduction Structural integrity is a major factor in aircraft design and construction. No production aeroplane leaves the ground before undergoing extensive analysis of how it will fly, the stresses it will tolerate and its maximum safe capability. Every aircraft is subject to structural stress. Stress acts on an aeroplane whether on the ground or in flight. Stress is defined as a load applied to a unit area of material. Stress produces a deflection or deformation in the material called strain. Stress is always accompanied by strain. Current production general aviation aircraft are constructed of various materials, the primary being aluminium alloys. Rivets, bolts, screws and special bonding adhesives are used to hold the sheet metal in place. Regardless of the method of attachment of the material, every part of the fuselage must carry a load, or resist a stress placed on it. Design of interior supporting and forming pieces, and the outside metal skin all have a role to play in assuring an overall safe structure capable of withstanding expected loads and stresses. The stress a particular part must withstand is carefully calculated by engineers. Also, the material a part is made from is extremely important and is selected by designers based on its known properties. Aluminium alloy is the primary material for the exterior skin on modern aircraft. This material possesses a good strength to weight ratio, is easy to form, resists corrosion, and is relatively inexpensive.

Types of Structural Stress The five basic structural stresses to which aircraft are subject are:

1. Tension 2. Compression 3. Torsion 4. Shear 5. Bending

While there are many other ways to describe the actual stresses which an aircraft undergoes in normal (or abnormal) operation, they are special arrangements of these basic ones.

Tension - is the stress acting against another force that is trying to pull something apart. For example, while in straight and level flight the engine power and propeller are pulling the aeroplane forward. The wings, tail section and fuselage, however, resist that movement because of the airflow around them. The result is a stretching effect on the airframe. Bracing wires in an aircraft are usually in tension.

Compression - is a squeezing or crushing force that tries to make parts smaller. Anti-compression design resists an inward or crushing force applied to a piece or assembly. Aircraft wings are subjected to compression stresses. The ability of a material to meet compression requirements is measured in pounds per square inch (PSI).

Torsion - is a twisting force. Because aluminium is used almost exclusively for the outside, and, to a

large extent, inside fabrication of parts and covering, its tensile strength (capability of being stretched) under torsion is very important. Tensile strength refers to the measure of strength in pounds per square inch (PSI) of the metal. Torque (also a twisting force) works against torsion. The torsional strength of a material is its ability to resist torque. While in flight, the engine power and propeller twist the forward fuselage. The force, however, is resisted by the assemblies of the fuselage. The airframe is subjected to variable torsional stresses during turns and other manoeuvres.

Shear - stress tends to slide one piece of material over another. Consider the aircraft fuselage. The

aluminium skin panels are riveted to one another. Shear forces try to make the rivets fail under flight loads; therefore, selection of rivets with adequate shear resistance is critical. Bolts and other fasteners are often loaded in shear, an example being bolts that fasten the wing to the spar or carry-through structure. Although other forces may also be present, shear forces try to rip the bolt in two. Generally, shear strength is less than tensile or compressive strength in a particular material.


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Bending - is a combination of two forces, compression and tension. During bending stress, the material on the inside of the bend is compressed and the outside material is stretched in tension. An example of this is the G-loading an aeroplane structure experiences during manoeuvring. During an abrupt pull-up, the aeroplane's wing spars, wing skin and fuselage undergo positive loading and the upper surfaces are subject to compression, while the lower wing skin experiences tension loads. There are many other areas of the airframe structure that experience bending forces during normal flight.

An aircraft structure in flight is subjected to many and varying stresses due to the varying loads that may be imposed. The designer's problem is trying to anticipate the possible stresses that the structure will have to endure, and to build it sufficiently strong to withstand these. The problem is complicated by the fact that an aeroplane structure must be light as well as strong.

Stress, Strain and Young's Modulus What is known as Axial (or Normal) Stress, is defined as the force perpendicular to the cross sectional area of the member divided by the cross sectional area. Or:

Stress =

(units Ib/in

2 or N/m

2)

In figure 2-1, a solid rod of length L, is under simple tension due to force F, as shown. If we divide that axial force, F, by the cross sectional area of the rod (A), this would be the axial stress in the member. Axial stress is the equivalent of pressure in a gas or liquid. As you remember, pressure is the force/unit area. So axial stress is really the 'pressure' in a solid member. Now the question becomes, how much 'pressure' can a material bear before it fails.

Figure 0-1Tensile Stress

In fact, if we look at a metal rod in simple tension as shown in figure 2.1, we see that there will be an elongation (or deformation) due to the tension. If we then graph the tension (force) verses the deformation we obtain a result as shown in figure 2.2.

Figure

module 2

Documents

covalent bonding

chemical bonding

training syllabus module

ionic bonding

table of contents matter

periodic table

nature of matter

components of atoms