Physics Module 2

AIRCRAFT MAINTENANCE ENGINEERING SERIES This page is intentionally left Blank

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EASA Part‐66 Module 2

Shahzad Khalil

2008

PAKISTAN

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PHYSICS

Shahzad Khalil M.Sc. Applied Physics specialization in Electronics (Gold medalist) University Of Karachi, Pakistan AME B737-300 CAA Pakistan. Instructor Engineering (Avionics) PIA Training Centre Karachi.

[email protected] Cell: +92 300 2428250


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PREFACE


CONTENTS MODULE 2. PHYSICS A 1

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2.2.1 Statics Forces, moments and couples, representation as vectors; Centre of gravity. Elements of theory of stress, strain and elasticity: tension, compression, shear and torsion; Nature and properties of solid, fluid and gas; Pressure and buoyancy in liquids (barometers).

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2.2.2 Kinetics Linear movement: uniform motion in a straight line, motion under constant acceleration (motion under gravity); Rotational movement: uniform circular motion (centrifugal/ centripetal forces); Periodic motion: pendulum movement; Simple theory of vibration, harmonics and resonance; Velocity ratio, mechanical advantage and efficiency.

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2.2.3 Dynamics (a) Mass, Force, inertia, work, power, energy (potential, kinetic and total energy), heat, efficiency;

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(b) Momentum, conservation of momentum; Impulse; Gyroscopic principles; Friction: nature and effects, coefficient of friction (rolling resistance).

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2.2.4 Fluid dynamics (a) Specific gravity and density;

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Page 2.0 Introduction, System of International units, FPS, Metric, Conversions between units, Prefixes. 2.1 Matter Nature of matter: the chemical elements, structure of atoms, molecules; Chemical compounds. States: solid, liquid and gaseous; Changes between states. 2.2 Mechanics

Contents Contd.; A 1

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2.3 Thermodynamics (a) Temperature: thermometers and temperature scales: Celsius, Fahrenheit and Kelvin; Heat definition.

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b) Heat capacity, specific heat; Heat transfer: convection, radiation and conduction; Volumetric expansion; First and second law of thermodynamics; Gases: ideal gases laws; specific heat at constant volume and constant pressure, work done by expanding gas; Isothermal, adiabatic expansion and compression, engine cycles, constant volume and constant pressure, refrigerators and heat pumps; Latent heats of fusion and evaporation, thermal energy, heat of combustion.

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(b) Viscosity, fluid resistance, effects of streamlining; effects of compressibility on fluids; Static, dynamic and total pressure: Bernoulli's Theorem, Venturi.

2.4 Optics (Light) Nature of light; speed of light; Laws of reflection and refraction: reflection at plane surfaces, reflection by spherical mirrors, refraction, lenses; Fiber optics. 2.5 Wave Motion and Sound Wave motion: mechanical waves, sinusoidal wave motion, interference phenomena, standing waves; Sound: speed of sound, production of sound, intensity, Pitch and quality, Doppler effect.

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PHYSICS The branch of science that deals with the study of matter, energy and their mutual relationships


Branches of physics Mechanics

Motion of the objects with or without reference of force.

Kinetics

Sub-branch of MechanicsÆ Motion without reference of force and mass

Dynamics

Sub-branch of MechanicsÆ Motion with reference of force

Static

Sub-branch of MechanicsÆ Static bodies, their mass and applied forces.

Thermodynamics

Heat, Energy and Work done Fundamentals

Optics

Light and its Fundamentals

Acoustics

Sound, Wave and their Propagation Quantities and Units

The System of International Unit: All systems of weights and measures are linked through a network of international agreements supporting the International System of Units. The SI is maintained by a small agency in Paris, the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures), and it is updated every few years by an international conference, the General Conference on Weights and Measures (CGPM, for Conférence Générale des Poids et Mesures), attended by representatives of all the industrial countries and international scientific and engineering organization


6. Mole: ¾ The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. ¾ When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. Note that this definition specifies at the same time the nature of the quantity whose unit is the mole. 7. Candela: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of ( 1/ 683) watt per steradian. 8. Radian: The radian is the plane angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius. 9. Steradian: The steradian is the solid angle that, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. Derived SI Units: All other quantities and units used in Physics can be expressed in terms of these seven base quantities and units. Derived quantity

Name

Symbol

Area

square meter

m2

Volume

cubic meter

m3

speed, velocity

meter per second

m/s

Acceleration

meter per second squared

m/s2

wave number

reciprocal meter

m-1

mass density

kilogram per cubic meter

kg/m3

specific volume

cubic meter per kilogram

m3/kg

current density

ampere per square meter

A/m2

magnetic field strength

ampere per meter

A/m

amount-of-substance concentration

mole per cubic meter

mol/m3

Luminance

candela per square meter

cd/m2

Foot-Pound-Second System of Units (British System, English System) The foot-pound-second (fps) system of units is a scheme for measuring dimensional and material quantities. The fundamental units are the foot for length, the pound for weight, and the second for time. The fps system has two variants, known as the American version and the Imperial version. Neither scheme is often used by scientists nowadays; the International System of Units (SI) is preferred. However, fps units are used to some extent by the general public, especially in the United States.


Foot: One foot (1 ft) represents a length of 12 inches. The inch was originally defined as the length of three typical barleycorns laid end-to-end. A foot was also approximately equal to three hand widths or 2/3 of a cubit (the distance from an average person's elbow to the tips of the fingers). Nowadays, a foot is considered to be 0.3048 meter, where the meter is the fundamental unit of displacement in the metric system and International System of Units (SI). Pound: One pound (1 lb) is the force that produces an acceleration of 32.1740 feet per second squared (32.1740 ft/sec2) when applied against a known standard mass. The acceleration of 32.1740 ft/sec2 is approximately the value of the earth's gravitational acceleration at 45 degrees north latitude. Second: One second (1 sec) is the time that elapses during 9.192631770 x 109 cycles of the radiation produced by the transition between two levels of Cesium 133. It is also 1/86,400 of a mean solar day. (There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day; 60 x 60 x 24 = 86,400) Metric System: Length: The standard unit of length in the metric system is the meter. Mass: The standard unit of mass in the metric system is the gram Time : The following conversions are useful when working with time: 1 minute = 60 seconds 1 hour = 60 minutes = 3600 seconds 1 day = 24 hours 1 week = 7 days 1 year = 365 1/4 days (for the Earth to travel once around the sun) In practice, every three calendar years will have 365 days, and every fourth year is a "leap year", which has 366 days, to make up for the extra quarter day over four years. The years 1992, 1996, 2000, and 2004 are all leap years. This gives us a total of 52 complete 7 day weeks in each calendar year, with 1 day left over (or 2 in a leap year). The year is divided into 12 months, each of which has 30 or 31 days, except for February, which has 28 days (or 29 days in a leap year) Temperature: Temperature is expressed in degrees Celsius in the metric system. The boiling point of water (at sea level) is 100°Celsius, or 100°C.


Conversion between Different Quantities Length Unit Abbreviation Number of Meters Approximate U.S. Equivalent kilometer km 1,000 0.62 mile hectometer hm 100 328.08 feet dekameter dam 10 32.81 feet meter m 1 39.37 inches centimeter cm 0.01 0.39 inch millimeter mm 0.001 0.039 inch Area Unit Abbreviation Number of Square Meters Approximate U.S. Equivalent 2 square kilometer km 1,000,000 0.3861 square miles hectare ha 10,000 2.47 acres acre a 100 119.60 square yards square cm2 0.0001 0.155 square inch centimeter Capacity Number of Approximate U.S. Equivalent Unit Abbreviation Liters cubic dry liquid kiloliter kl 1,000 1.31 cubic yards hectoliter hl 100 3.53 cubic feet 2.84 bushels dekaliter dal 10 0.35 cubic foot 1.14 pecks 2.64 gallons liter l 1 61.02 cubic inches 0.908 quart 1.057 quarts 3 cubic decimeter dm 1 61.02 cubic inches 0.908 quart 1.057 quarts deciliter dl 0.10 6.1 cubic inches 0.18 pint 0.21 pint 0.338 fluid centiliter cl 0.01 0.61 cubic inch ounce Mass and weight Number of Approximate U.S. Equivalent Unit Abbreviation Grams metric ton t 1,000,000 1.102 short tons kilogram kg 1,000 2.2046 pounds hectogram hg 100 3.527 ounces dekagram dag 10 0.353 ounce gram g 1 0.035 ounce decigram dg 0.10 1.543 grains centigram cg 0.01 0.154 grain milligram mg 0.001 0.015 grain microgram µg 0.000001 0.000015 grain


Other units used in Aviation Industry: Universal Time (UTC) is a time standard based on International Atomic Time (TAI) with leap seconds added at irregular intervals to compensate for the Earth's slowing rotation. Leap seconds are used to allow UTC to closely track UT1, which is mean solar time at the Royal Observatory, Greenwich. A nautical mile or sea mile is a unit of length. It corresponds approximately to one minute of latitude along any meridian at equator. It is a non-SI unit used especially by navigators in the shipping and aviation industries. One nautical mile converts to: ¾ ¾ ¾ ¾

1,852 metres 1.150779 mile (statute) 2,025.372 yards 6,076.1155 feet

The knot is a unit of speed equal to one nautical mile per hour. Multiples and Sub-multiples The range of multiples and submultiples is shown in the table. Name

Symbol

Yotta Zetta Exa Peta Tera Giga Mega Kilo Hecto Deca

Y Z E P T G M k H D

Multiplication Factor 1024 1021 1018 1015 1012 109 106 103 102 10

Name

Symbol

deci centi milli micro nano pico femto atto zepto yocto

d c m µ n p f a z y

Multiplication Factor 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 10-21 10-24


2.1-MATTER matter is anything that has both mass and volume (takes up space)


MATTER “Anything which occupies space and has some mass is called as matter”. Scientific name for all materials is Matter. Nature of Matter All matter is made up of small particles called molecules. A molecule is defined as the smallest particle that any substance can be reduced to and still retain the unique properties of the original substance. Matter can be classified into three states known as solid, liquid and gaseous states. Matter itself cannot be destroyed, but it can be changed from one state into another state by chemical or physical means. The Nature of matter depends upon Temperature and Pressure directly. For example, ice, water and steam are the three states of the same matter. When Heated Ice changes into Water which on heating changes into Steam. When Cooled Steam converts into Water which then converts into Ice. Solids: the state of matter which has a specific shape and a definite volume. Liquid: the state of matter which has a no specific shape but has a definite volume. Gas: the state of matter which has a no specific shape and no definite volume. In a solid the particles are close-packed; they vibrate at high frequency about fixed positions. Attractive forces between the particles give a solid its fixed shape. When the solid melts, the mean particle spacing increases slightly causing a decrease in the attractive forces between the particles. Liquids are amorphous; they have no regular structure or fixed shape. The particles in a liquid jostle and change positions. The particles in a gas are much more widespread and attractive forces are negligible; they move freely in a random direction, exerting pressure due to collisions with the walls of the container.

Evaporation from liquids takes place at all temperatures; it occurs when particles at the surface gain enough energy to move away from the attractive forces of neighboring particles. Boiling in a liquid only takes place at the boiling point; when a liquid boils, bubbles of vapor form in the body of liquid and rise to the surface, where they collapse and release the vapor into the atmosphere.


When molecules of a substance consist of only one type of atom, the substance is classified as an element e.g. Carbon, gold, oxygen hydrogen etc. there exists more than hundred natural or artificial elements some of which are unstable and change spontaneously into other known elements. The mass of the nucleus is due to the mass of Protons and Neutrons. The size of the protons and neutrons is very smaller. The theory suggests that binding forces hold the nucleus together. These forces are very strong but of short range and act only within nucleus. The positive charge of the protons is being cancelled by negative charge of revolving electrons. It suggests that there are as many electrons as protons within the nucleus so as to keep the atom electrically neutral.

Atomic Number: Number of Protons in an atom. Mass Number (Nucleon Number): Sum of the number of protons and neutrons in an atom. Isotopes: These are elements with same Atomic number but different mass number.

Shells: The electron shells are labeled K, L, M, N, O, P, and Q; or 1, 2, 3, 4, 5, 6, and 7; going from innermost shell outwards. Electrons in outer shells have higher average energy and travel further from the nucleus than those in inner shells, making them more important in determining how the atom reacts chemically and behaves as a conductor, etc, because the pull of the atom's nucleus upon them is weaker and more easily broken. Subshells: Each shell is composed of one or more Subshells, which themselves are composed of atomic orbital. For example, the first (K) shell has one subshell, called "1s"; the second (L) shell has two subshells, called "2s" and "2p"; the third shell has "3s", "3p", and "3d"; and so on. Number of electrons in each shell is determined by 2n2, where n is the number of shell. Therefore, the K shell, which contains only an s subshell, can hold up to 2 electrons; the L shell, which contains an s and a p, can hold up to 2+6=8 electrons; and so forth. The general formula is that the nth shell can in principle hold up to 2n2 electrons.


Hydrogen atom

Helium Atom

Silicon Atom

The chemical Elements A chemical element is a type of atom that is distinguished by its atomic number; that is, by the number of protons in its nucleus. The term is also used to refer to a pure chemical substance composed of atoms with the same number of protons.


Metalloids are the elements found along the stair-step line that distinguishes metals from non-metals. This line is drawn from between Boron and Aluminum to the border between Polonium and Astatine. The only exception to this is Aluminum, which is classified under "Other Metals". Metalloids have properties of both metals and non-metals. Some of the metalloids, such as silicon and germanium, are semi-conductors. This means that they can carry an electrical charge under special conditions. This property makes metalloids useful in computers and calculators. The halogens are five non-metallic elements found in group 17 of the periodic table. The term "halogen" means "salt-former" and compounds containing halogens are called "salts". All halogens have 7 electrons in their outer shells, giving them an oxidation number of -1. The halogens exist, at room temperature, in all three states of matter. The six noble gases are found in group 18 of the periodic table. These elements were considered to be inert gases until the 1960's, because their oxidation number of 0 prevents the noble gases from forming compounds readily. All noble gases have the maximum number of electrons possible in their outer shell (2 for Helium, 8 for all others), making them stable. The thirty rare earth elements are composed of the lanthanide and actinide series. One element of the lanthanide series and most of the elements in the actinide series are called trans-uranium, which means synthetic or man-made. All of the rare earth metals are found in group 3 of the periodic table, and the 6th and 7th periods. The Rare Earth Elements are made up of two series of elements, the Lanthanide and Actinide Series The 7 elements classified as "other metals" are located in groups 13, 14, and 15. While these elements are ductile and malleable, they are not the same as the transition elements. These elements, unlike the transition elements, do not exhibit variable oxidation states, and their valence electrons are only present in their outer shell. All of these elements are solid, have a relatively high density, and are opaque. They have oxidation numbers of +3, ±4, and -3. Molecule: Larger particle formed by combining atoms. They are the smallest particle of a compound. Matter exists in the shape of Molecules. Molecules are stable form of Matter. Chemical Compounds: Chemical compound is a substance consisting of two or more different elements chemically bonded together in a fixed proportion by mass and it is a substance that can be split up into simpler substances. Atoms combine to form molecules, releases energy to create inter molecular force. Molecules are more stable than Atoms. Intermolecular forces or attractive force that holds atoms together is called Chemical bond. IONIC BOND Complete Transfer of Electron High boiling and Melting Point

COVALENT BOND Sharing of Electron Low Boiling and Melting Point

An Ion is an atom or molecule which has lost or gained one or more electrons, giving it a positive or negative electrical charge.

2.2-MECHANICS Motion of the objects with or without reference of force

2.2.1-STATICS Branch of mechanics that deals with the study of object which are at rest and remain at rest when the force is applied is called Statics.


Scalars and Vectors Quantities such as mass, speed and temperature only have a size; these are scalar quantities. A scalar quantity is described by its magnitude and unit. Force, momentum and acceleration also have a direction; these are vector quantities. A complete description of a vector quantity must also include its direction as well as magnitude and unit. (Scalar is one dimensional and vector is two dimensional.) A vector quantity can be represented on a diagram by an arrow, drawn to scale, in the direction that the vector quantity acts. The ordinary rules of number apply to the addition of scalar quantities; if 3 kg of iron is added to 2 kg of iron the result can only be 5 kg of iron, i.e. 2 kg + 3 kg = 5 kg. But if a 2 N force acts on an object and then a 3 N force is also applied, the resultant force could have any value between 1 N and 5 N, depending on the directions of the forces. There are two ways of adding two vector quantities together to find the resultant. Parallelogram Method: From the same point, draw two arrows (A and B in the diagram) to represent the vector quantities in size and direction. The resultant (A+B) is represented in size and direction by the arrow that is the diagonal of the parallelogram. Let

R= A+B

Then magnitude of resultant | R | = (A2 + B2 )1/2 and the angle between R and the horizontal is found by TanӨ = A / B Triangle Method (Head to Tail rule): Draw one arrow to represent vector ‘A’ acting from a point. Starting at the arrowhead end of vector A, draw a second arrow to represent vector B. The resultant, A+B is represented by the vector that completes the triangle, starting where A starts and ending where B finishes. Force: Force is an agent which changes or tends to change the state of rest or motion of a body. Unit of force is the Newton. Resolution of Forces: A vector quantity such as a force can have effects in more than one direction. An example of this is an object on a slope. The weight force acting on the object has two effects. One effect is to pull the object down the slope and the other is to provide the contact force between the object and the surface.


Couples: A Couple is a set of two equal and opposite forces whose lines of action do not coincide. The forces have a turning effect or moment called a torque about an axis which is normal to the plane of the forces. The SI unit for the torque of the couple is Newton meter.

If the two forces are F and -F, then the magnitude of the torque is calculated by: where τ is the torque, F is the magnitude of one of the forces, d is the perpendicular distance between the forces The magnitude of this torque is not dependent on the distance of the axis from either of the lines of action. Suppose that the two forces are distance, d, apart and that the axis is distant, x, from one of the lines of action, then the torque τ is given by:

Examples of couple are turning of a water tap, rotation of an electric motor and lift-weight forces on aircraft etc. Equilibrium When different forces are acting on a body and the net force on a body is zero, and it is not moving, the body is said to be in a state of static equilibrium. In physics, the subject of statics deals with the calculation of forces acting on bodies those are in static equilibrium. First Condition for Static Equilibrium: For a body to be in static equilibrium, the vector sum of all the forces on it must be zero. Σ F= 0 The sum of the components of F must also be zero. For forces acting in three dimensions. Σ F x= 0 ,

Σ Fy= 0,

Σ Fz= 0

The sum of all forces on right direction equal the sum of all forces in the left direction. The sum of all forces on up direction equal the sum of all forces in the down direction. The sum of all forces on front direction the sum of all forces in the rear direction.

Strength of Materials Whenever a force is applied to a body a deformation takes place temporary or permanent. The response of material to the application of force depends upon the size and direction of force and the time for which the force is applied, the type of material and the area on which the force acts. The material attempts to neutralize the applied force by exerting an opposing force or reaction. If the applied force exceeds the reaction, the material breaks. With most materials if the applied force is small the material behaves elastically. If the force is greater than a certain amount then the material will change shape permanently. Stress: Force per unit area is called stress. i.e. Stress = Force / Area. It is represented by Sigma ‘σ’ σ = F /A Its unit is N/m2. Strain: A stress can produce change in shape, volume or length in an object. This change in the shape of the object is called strain. It is represented by epsilon ‘ε’. Strain = Change in length / Original length Elasticity: The phenomenon of returning to its original shape and size after the force is removed is called elasticity. There is a limit of applied force, otherwise the object will not return to its original shape, this limit is called elastic limit. Tension: Tension is the stress which tends to pull things apart. When you try to break a length of rope, you exert a type of stress which is called tension. Compression: Compression is the opposite of tension. It is the stress which tends to push materials together. When you grasp a football at both ends and push, the ball is subject to compression. The landing gear struts of an aircraft are also subject to compression. Shear: Shear stress is caused by forces tending to slip or slide one part of a material in respect to another part. This is the stress that is placed on a piece of wood clamped in a vise and you Chip away at it with a hammer and chisel. This type of stress is also exerted when two pieces of metal, bolted together, are pulled apart by sliding one over the other or when you sharpen a pencil with a knife. The rivets in an aircraft are intended to carry only shear. Bolts, as a rule, carry only shear, but sometimes they carry both shear and tension. Torsion: Torsion is the stress which tends to distort by twisting. You produce a torsional force when you tighten a nut on a bolt. The aircraft engine exerts a torsional force on the crankshaft or turbine axis. All the members (or major portions) of an aircraft are subjected to one or more of these stresses. Sometimes a member has alternate stresses, such as compression one instant and tension the next. Some members can carry only one type of stress.


Wire and cables, for example, normally carry only tension. Hooke’s Law: Within the elastic limit of a material the change in shape is directly proportional to the applied force. A good example is spring balance.

The extension produced is directly proportional to the load:

where: is the distance that the spring has been stretched or compressed away from the equilibrium position, which is the position where the spring would naturally come to rest (usually in meters), is the restoring force exerted by the material (usually in Newtons), and is the force constant (or spring constant). The constant has units of force per unit length (usually in Newton per meter).

Modulus of Elasticity (E): Stress is directly proportional to strain in the elastic. Stress = Strain * a constant Stress/ Strain = a constant (E) Modulus of Rigidity (G):= Shear stress/ Shear strain; Measured in GN/m2 Bulk Modulus (k):= Bulk Stress/ Bulk strain The change in volume per unit original volume without a change in shape. Note: solids have all three modulli, liquids and gases only k.


In an open-tube manometer, one end of the tube is open to the atmosphere, and is thus at atmospheric pressure. The other end is connected to a region where the pressure is to be measured. Again, if there is a difference in pressure between the two ends of the tube, a column of fluid can be supported in the tube, with the height of the column being proportional to the pressure difference.

The actual pressure, P2, is known as the absolute pressure; the pressure difference between the absolute pressure and atmospheric pressure is called the Gauge Pressure. Many pressure gauges give only the gauge pressure. To convert to absolute pressure add 14.7 to the value in psi or 1.03 to the value in kg/cm2 Absolute Pressure = Atmospheric Pressure + Hydrostatic Pressure Its units of measurement are pounds per square inch absolute (psia) or kilograms per square centimeter absolute (kg/cm2 absolute). Buoyancy A body immersed in a liquid, either wholly or partially, is buoyed up by a force equal to the weight of the liquid displaced by the body. The following mathematical equation can be derived from Archimedes' Principle: the buoyancy of a submerged body = weight of displaced liquid – weight of the body. Therefore, we may conclude that: ¾ The body will float if the buoyancy is positive (body weight < weight of displaced liquid). ¾ The body will be suspended if the buoyancy is neutral (body weight = weight of displaced liquid). ¾ The body will sink if the buoyancy is negative (body weight > weight of displaced liquid).



Exospheere: from 5000 – 1000 km m (300 – 6000 mi) up to 10,000 km (66,000 mi), freee-moving paarticles that may m migratee into and ouut of the magneto osphere or thhe solar windd.

Atm mospheric layyers

e exobase bouundary y solar radiaation. Ionosphhere: the partt of the atmoosphere that is ionized by It plays an importannt part in atm mospheric eleectricity andd forms the innner osphere. It has practical importance because, b am mong edge of the magneto nt places on the other fuunctions, it innfluences raddio propagattion to distan Earth. Itt is located in the thermoosphere and is responsibble for auroraas. thhermopause bboundary m 80 – 85 km m (265,000 – 285,000 ft)) to 640+ km m Thermoosphere: from (400+ mi), m temperatture increasiing with heigght. meesopause boundary Mesosphere: The mesosphere m ex xtends from m about 50 km m (160,000 ft) f to the rangge of 80 to 85 km (265,0000 – 285,0000 ft), temperrature decreaasing with heiight. This is also where most m meteorrs burn up when w enteringg the atmosphhere. straatopause bouundary phere: The sttratosphere extends e from m the tropospphere's 7 to 17 1 km Stratosp (23,000 – 60,000 ft)) range to ab bout 50 km (160,000 ft). Temperaturre increasees with heighht. The stratoosphere conttains the ozoone layer. troppopause bouundary Tropospphere: The trroposphere is the lowest layer of the atmospheree; it begins at a the surfacee and extendds to betweenn 7 km (23,0000 ft) at thee poles and 17 km k (60,000 ft) at the equuator, with some variatioon due to weeather factors. The troposp phere has a great g deal of vertical mixxing becausee of m solar heeating at the surface. This heating waarms air massses, which makes them lesss dense so they t rise. Whhen an air m mass rises, thee pressure uppon it decreasees so it expaands, doing work w againstt the opposin ng pressure of o the surrounding air. To do work is to t expend ennergy, so thee temperaturee of m decreasses. As the teemperature ddecreases, water w vapor inn the the air mass air masss may condeense or solidiify, releasingg latent heat that further uplifts the t air mass.


2.2.2-KINETICS Deals with the bodies in motion without reference of force and mass


Linear Motion Linear displacement and distance: The linear displacement is the length moved in a given direction - it is a vector quantity. The magnitude of the displacement is the distance - a scalar quantity.

Linear velocity and speed: The linear velocity is the rate of change of displacement with time. As displacement is a vector so velocity is a vector. The magnitude of the velocity is speed. It is the rate of change of distance with time - hence it is a scalar. If a body moves with uniform velocity then it must move in a fixed direction with constant speed. The average speed of a body is the total distance moved divide by the total time taken. The instantaneous velocity shows the velocity of an object at one point. For example, when you are driving a car and its speedometer swings to 90 km/h, then the instantaneous velocity of the car is 90 km/h. Position-time Graph (s/t curve) A position-time graph simply shows the relationship between time and position. From the following data, for example, time (s) 0 1 2 3 4 5 position (s) 0 20 50 130 150 200 You can draw the following graph: As speed is rate of change of distance with time, the slope, gradient, of the s/t curve is the speed.


Velocity-time graph shows the relationship between velocity and time. For example, if a car moves at constant velocity of 5 m/s for 10 seconds, you can draw a velocity-time graph that looks like this:

The area below the line represents the displacement the object traveled since it can be calculated by (time * velocity) which equals to displacement. As acceleration is rate of change of speed (v) with time (t), the slope, gradient, of the v/t curve is the acceleration. The average acceleration is the ratio between the change in velocity and the time interval

Relative Motion : When the car A is at 50 km/h and the car B is at 30 km/h at opposite direction, the velocity of the car A relative to the car B is 80 km/h. NEWTON'S LAWS OF MOTION: ¾ The Law of Inertia states that an object will either remain at rest or continue to move at constant velocity in a straight line unless acted upon by an external force. ¾ The Law of Acceleration states that the acceleration of a body is directly proportional to the applied force and inversely proportional to its mass. a = F/m or F = ma. ¾ The Law of Interaction states that To every action there is always an equal and opposite reaction. The Unit of Force is the "Newton", "n". One Newton of force will accelerate one kilogram mass at the rate of one meter/second/second. F = ma, so 1N = (1Kg) x (1m/s/s). Weight is the force of gravity, since F = ma, then weight = mg so a body whose mass is 80kg, will weigh 784Newton (wt) = 80kg x 9.8m/s2


Angular Velocity: refers to a body moving in circular path and may be defined as. ω = Angular distance moved / time taken Or

ω= Ө / t rad./sec

Angular Acceleration: Angular acceleration is defined as the rate of change of angular velocity with respect to time. i.e. α = Ө/ s2 so its 2 unit is radian /sec . The linear equations of motion can be transformed to represent angular motion using a set of equations which we will call them transformation equations. Transformation equations S= Ө r V= ωr a =αr Where Ө, ω and α are angular distance, angular velocity and angular acceleration respectively. Angular Equation of motion Ө = (ω1+ ω2)t/2

Linear Equation of motion S = ( v+ u) t/2

Ө = ω1t+1/2 αt2

S= ut +1/2 at2

ω22 = ω12 +2αӨ

v2 = u2 + 2 aS

α = (ω2 – ω1 )/t

a= (v-u) /t

Centripetal Force: Whenever an object moves in a circular path we know the object is accelerating because the velocity is constantly changing direction. All accelerations are caused by net force acting on an object. In the case of an object moving in a circular path, the net force is a special force called the Centripetal force. Centripetal is Latin word for "center seeking". So a centripetal force is a center seeking force which means that the force is always directed toward the center of the circle. Without this force, an object will simply continue


Vibration may be classified as either free or forced. Free vibration refers to an elastic system where having starred to vibrate, due to an initial disturbance, it is allowed to continue unhindered. The simply supported spring-mass system when subject to initial push or pull away from its equilibrium position and then allowed to vibrate is a classic example of free vibration system. Forced vibration refers to a vibration that is excited by an external force applied at regular intervals. The system will no longer vibrate at its natural frequency but will oscillate at the frequency of the external exciting force. Thus e.g. a motor with an out of balance rotor will setup a forced vibration on the supporting structure, on which it rests. Aircraft structures having elastic properties are capable of relative motion in response to dynamic inputs from rotating masses such as power plants and aerodynamic loads. If this motion repeats itself after a given interval of time then vibration is present in the system Sources of vibration on Aircraft are: Aerodynamic Forces: The airframe and flight controls are buffeted by the air as it passes over. These vibrations are called as fluttering which may destroy the aircraft in its severe case. Improved aircraft design and static balancing of flight controls can minimize it. Wheels: wheels are balanced before fitting as they can cause structural damage. Nose L/G and tail wheels are very much susceptible to it and when occurs is called as Shimmy. On helicopters rotor blades and head are also source of vibration. The Engines are also monitored for vibration and indication provided to flight crew in the flight deck and the vibration is minimized by dynamic balancing of blades or propellers of the engine. Anti vibration mountings are provided to instruments and panels in the cockpit and to the LRU’s in the Avionic equipment bay. Vibration is generally considered as lost energy and should be avoided as irregular vibrations may cause components to be damaged or fail. The term ‘Frequency’ is usually associated with the vibration which is the number of vibrations that occur in one second and is measured in Hertz. Rotating parts of aircraft are both statically and dynamically balanced to reduce vibrations. For non rotating parts damping is provided by some form of friction or inertia loading. Some parts of structure are damped by the use of mass-balance weights. Freely vibrating systems (without friction) vibrate with their “natural frequency” which depends upon their mass only. When friction is present then their frequency of vibration is considered as “damped natural frequency”.


Wedge: It can be usedd to separate two t objects, oor portions off objects, lift an a object, or hold h an objecct in place. It I operates byy converting a force appliedd to the wide end into forces perpendicuular to the inclined surfaces. Mechaniccal advantage of a wedge = the ratio of iits length to itts thickness. Where a short s wedge with w a wide anngle does the job faster, it requires moree force than a long wedge with a sm maller angle.

The mech hanical advaantage of a wedge w is the length of thee sloping sidde of the wed dge divided by the wiidth of the th hick end of the t wedge. T Therefore thee formula forr a wedge is:

In other words, w divid de the length of the wedgge by its widdth at the thicckest edge. The moree acute the angle a of the wedge, w the m more mechannical advantaage it will haave. Wheel an nd Axle: Thhe most wideely recognizeed applicatioon, i.e. liftingg water from m a well. Thee form con nsists of a whheel that turnns an axle annd in turn a rope r convertts the rotational motion tto linear mo otion for the purpose of lifting. l This macchine is a torrque multipliier, i.e. the output o is a toorque. The most m widely recognized r applicatioon, i.e. Liftiing water fro om a well. The T form con nsists of a whheel that turnns an axle and in turrn a rope con nverts the rootational mottion to linearr motion forr the purposee of lifting. This macchine is conssidered as a torque t multiiplier, i.e. thee output is a torque, item ms such as gears and d screwdriveers also fall within w this category. Let R and r be the radii of the wheel and the axxle respectiv vely.Then Velocity raatio= distancce moved byy effort/distannce moved by b load = 2πR/2πr = R/r



2.2.3-DYNAMICS The branch of mechanics concerned with the motion of bodies under the action of force

Force: A force is that which can cause an object with mass to accelerate. Force has both magnitude and direction, making it a vector quantity. According to Newton's second law, an object with constant mass will accelerate in proportion to the net force acting upon it and in inverse proportion to its mass. An equivalent formulation is that the net force on an object is equal to the rate of change of momentum it experiences. Forces acting on three-dimensional objects may also cause them to rotate or deform, or result in a change in pressure.

Newton's second law of motion relates the concept of force with the time-derivative of momentum: F = dp / dt Inertia: Inertia is the tendency of all objects to resist a change in motion. It is directly proportional to an object’s mass. The heavier the object is, the more inertia it has and it would keep going forever if it was in a frictionless environment. Another way to put it is inertia is how much an object will resist a change of velocity. It is experienced during the take-off and landing of an aircraft, being respectively, pushed back into your seat when taking-off or thrown forward when aircraft applies brakes on landing.

During take‐off

Thrust = D + ma

At landing ma = TR + D + B The inertia force will always act to balance the resultant force on the body i.e. in a direction opposite to that of the acceleration ‘a’.


Transformation of Kinetic and Potential Energy: A moving pendulum changes potential energy into kinetic energy and back again. When the bob (weight on the end of string) is first released, it has potential energy due to its height, but no kinetic energy since it is not yet moving. As the bob accelerates downward, potential energy is traded for kinetic. At the bottom of its swing, the bob has no potential energy since it cannot fall any further. The bob is moving quickly at this point since all of its former potential energy has been transformed into kinetic energy.

A roller coaster ride is a thrilling experience which involves this transformation. The ride often begins as a chain and motor (or other mechanical device) exerts a force on the train of cars to lift the train to the top of a very tall hill. Once the cars are lifted to the top of the hill, gravity takes over and the remainder of the ride is an experience in energy transformation.

Momentum: Momentum is defined as quantity of motion possessed by a body. Momentum is a vector quantity. It comprises the product of mass and velocity of a body. p = mv its units are Kg-m/Sec or Newton-Sec. It is therefore interesting to note that a large body having a small velocity may have same momentum as that of a small body with a relatively high velocity.


A simple rule of thumb (Sperry’s rule of precession) to determine the direction of precession is: “Take one of the forces producing the torque move it in the direction it is pointing onto the spinning rotor. Move it round in the direction of the spinning rotor by 90 degrees and the rotating mass will move in a direction as if acted on by a force at this point”. Gyros are used in aircraft instrumentation for attitude and heading indications. Modern Aircrafts have replaced them with laser gyros.

One degree of freedom Gyro The rotor has freedom to rotate about just one axis at right angles to the spin axis so the gyro is said to have one degree of freedom. In the fig, below he rotor is suspended in two gimbals, an inner gimbal and an outer gimbal. The rotor is now free to turn relative to the frame about two axis BB and CC. the gyro is now said to have two degrees of freedom.

Two degrees of freedom Gyro


The property of rigidity is used extensively in Aircraft gyros. This means that if the frame is moved (as in pitch or roll movement) the gyro rotor axis will continue to point to a fixed point in space.

Precession in a two degree of freedom Gyro: Lets see how sperry rule is applied to gyro ¾ As a theoretical model continue the movement of force in the same direction onto the rotor (point A) ¾ Allow the force to move 90o in the direction of rotor rotation to point B. ¾ Imagine the force pushing at this position on the rotor and this is how the gyro would move

Methods of spinning Gyro Rotor: Early gyros and some standby instruments are driven by Air. Air is drawn by an engine driven vaccuum pump at a controlled pressure of 4-4.5in of Hg. The air impimges on cut buckets cut into the rim of the rotor so causing it to rotate at high speed (typically 1500018000 rpm for two degree of freeedom gyro and 42000rpm for one degree of freedom gyros). Air enters the sealed instrument case via a filter. The air comes from aircraft cabin.


Free or Space Gyro: Free or space gyros such as spinning top have their axes of spin always pointing to a fixed point infinitely far away in space. For example, if the gyro axis of an aircraft instrument gyro is vertical at the north pole then as the aircraft flies around the world to the equator then at the equator the axis would be horizontal.If fitted to an artificial horizon instrument then indication at the pole would be level flight, but the indication at the equator would show the aircraft is in a vertical dive although the aircraft is actually flying straight and level. All attitude references would be with respect to earth to give the pilot accurate information about the attitude of the aircraft in relation to the earth. This means that the gyro must be tied to earth and is called as tied gyro. Since it is tied to earth hence called as Earth Gyro. The term earth Gyro does not mean that it is electrically earthed. Wander Any movement of spin axis from its reference is called as wander. ¾ Apparent wander ¾ Real wander ¾ Transport wander Transport wander: Transport wander can occur when a gyroscope is transported from one point on the Earth to another. Any wander observed will be in addition to that caused by the rotation of the Earth. This wander is only apparent when the gyroscope crosses a meridian that is converging with another. So, at any latitude other than the Equator, any East-West movement will cause transport wander. As North-South movement involves tracking along a meridian (and not crossing) then no transport wander occurs. Although East-West movement along the Equator does involve crossing meridians, because all meridians are parallel at the Equator then once again no transport wander occurs.


Frriction When ann object with some mass is placed onn a surface (nnon smooth), and when it i is pushed or pulledd, it usually experiences e a resistive foorce which acts a in a direction opposiite to the push or pull p (or stricttly speaking, it makes ann angle of 1880 degrees w with the horizzontal componeent of the appplied force).This resistivve force is caalled as frictiion. “It is a force that teends to oppoose relative motion”. m When ann object is staationary on a horizontal surface, duee to friction, it offers a reesistance whenever some horizzontal force is applied too it. This fricction is up too a certain lim mit, proportio onal to the hoorizontal forrce applied, aand is knownn as static frriction, and during this time the body b remainns stationaryy (does not m move). The maximum m poossible static friction between a particular body and a particular p suurface is giveen by F max sttat. = k stat .N Where F max. stat is thhe maximum m possible staatic friction for f that bodyy and that paarticular surface, k stat. is a connstant of proportionality called co-effficient of sttatic friction n and N is thhe normal reeaction forcee experienceed by the boddy. The frictiional force depends d onlyy on: ¾ ¾

The type of su T urfaces H hard thee surfaces aree pressed toggether. How

NOTE: Notice N that neither the suurface area of o contact noor the horizoontal force on the body affects th he maximum static frictioon. When thee horizontal force applieed exceeds a certain limit, the body ssort of "breaaks away" annd begins to o move. The frictional foorce drops shharply, and from fr this poiint onwards, it remains approxim mately constaant. This fricttion is now known k as kin netic frictioon (also calleed as slidingg or dynamiic friction) and for a particular body b on a parrticular surfaace is given by F kin. = k kin .N Where Fkin. is the kin netic friction, kkin. is a connstant of prooportionalityy; called co-eefficient of kinetic friction fr and N is the norm mal reactionn force on thee body.


Laws of Friction Law 1 When two bodies are in contact, the direction of the forces of Friction on one of them at its point of contact is opposite to the direction in which the point of contact tends to move relative to the other. Law 2 If the bodies are in equilibrium, the force of Friction is just sufficient to prevent friction and may therefore be determined by applying the conditions of equilibrium of all the forces acting on the body. The amount of Friction that can be exerted between two surfaces is limited and if the forces acting on the body are made sufficiently great, motion will occur. Hence, we define limiting friction as the friction which is exerted when equilibrium is on the point of being broken by one body sliding on another. The magnitude of limiting friction is given by the following three laws. Law 3 The ratio of the limiting friction to the Normal reaction between two surfaces depends on the substances of which the surfaces are composed and not on the magnitude of the Normal reaction. This ratio is usually denoted by µ. Thus if the Normal reaction is R, the limiting friction is µR. For given materials polished to the same standard µ is found to be constant and independent of R. µ is called The Coefficient of friction. Law 4 The amount of limiting friction is independent of the area of contact between the two surfaces and of the shape of the surfaces, provided that the Normal reaction is unaltered. Law 5 When motion takes place the direction of friction is opposite to the direction of relative motion and independent of velocity. The magnitude of the force of friction is in a constant ratio to the Normal reaction but this ratio may be slightly less than when the body is just on the point of moving.


φ tan s

Angle of Friction: It is sometimes found convenient to replace the normal force N and friction force F by their resultant R.

The angle fs is known as the angle of static friction. The four cases are

a) No horizontal forces are applied to the block and R reduces to the normal force, N.

b) P is applied to the block and the horizontal force Px does not have enough force to overcome frictional resistance.

c) The horizontal force, Fmax is sufficient to start the block in motion.

d) The block is in motion.

Another example that will show how the angle of friction may be used to advantage in the analysis of certain types of problems. For block on an incline.


2.2.4-Fluid Dynamics Fluid dynamics is the sub‐discipline of fluid mechanics dealing with fluid flow: fluids in motion. It has several sub disciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion). The use of fluid to do work is called hydraulics.


Viscosity of liquids is higher than that of gasses which have very low viscosities resulting from their greater moleculer freedom. The flow of fluids is generally considered to be of two forms: The first is a flow in which the fluid travels in parallel layers called Laminar Flow, much like the pages of a book with no interchange between layers occuring. However each layer has a drag effect over the adjacent layers both sides so that a velocity gradient is produced across the flow. The slowest moving layer being next to the solid surface with which it is in contact.

The second form is a Turbulent Flow where the fluid flow is swirling and there is complete interchange between the layers with the flow even moving back on itself. It is a complete random chaotic motion, in which particla motions are continuously in an unpredictable manner.

Obviously laminar flow is much more efficient than the turbulent flow and the former is usually preferred in hydrodynamics and Aerodynamics. For example when air flows over the Aircraft in flight, drag is reduced by laminar flow and lift is improved with laminar flow over the wing surface.


But the quantity L/t is simply the rate at which distance is covered by the fluid, that is, the fluid’s velocity.

So we have an expression for the rate at which mass flows in terms of the velocity of fluid flow, density of the fluid and area of the pipe in which the fluid is flowing. This result is very reasonable.

We now complicate our analysis of fluid flow by examining what happens to the fluid if the size of the tubing through which it flows changes. We will allow the change to be gradual and continuous so that laminas flow is maintained. Consider the following diagram which shows the pipe slowly constricting from area A1 to area A2. From practical experience we know that the velocity of fluid through the small area is larger than the velocity of the fluid through the large area.

Many of us have heard the expression “still water runs deep.” This phenomenon can be explained and quantified by examining the flow rate of mass through the tubing. Because no fluid can leave through the walls and there are no “sources” or “sinks” wherein the fluid can be created or destroyed, the mass crossing each section of the tube per unit time must be the same. This is simply the principle of conservation of mass. This principle is embodied in the equation of continuity.

or

This equation expresses the law of conservation of mass in fluid dynamics.


If fluid is incompressible, as will be the case with all examples considered here, then the density is constant (d1 = d2), and Eq. takes on simpler form

or

Example: Water flows through a 1 inch diameter hose with a speed of 2 ft/sec. Find the speed of water through the nozzle of the diameter is reduced to 1/8 inch. We use the principle of conservation of mass to solve this problem. Av = constant Reducing the diameter of the hose will reduce the area. Consequently the velocity must be increases by the same factor that the area is decreased. We must find by what amount the area is decreased. For a circle Area = π r2 Where r is the radius. In this problem the diameter is reduced by a factor of eight. Subsequently, the radius is also reduced by a factor of eight. But the area is reduced by a factor of 64. This results in an increase in velocity by a factor of 64.

Bernoulli’s Equation – Conservation of Energy Let us continue to observe what happens to a fluid as it flows through a pipe of varying area. We have already determined that if the flow is laminar and the fluid is incompressible then the product Av is constant. Now use Newton’s second law of motion and consider the pressure acting on a flowing fluid. Let us begin by considering the following question. Question: In which region, A B, or C, in the figure below would you expect the pressure on the walls of the pipe to be the greatest? (Region A > region C > region B)

The stagnation pressure exists at a stagnation point, where a fluid streamline abruptly terminates at the surface of the stationary body, here, the velocity of the body must be zero. The total pressure (PT) is the sum of the static, dynamic and hydrostatic pressure. Examples: 1. Water (density = 1000 kg/m3) flows through a hose with a velocity of 1 m/sec. As it leaves the nozzle the constricted area increases the velocity to 20 m/sec. The pressure on the water as it leaves is atmospheric pressure (1 Atm. = 100,000 N/m2). What is the pressure on the water in the hose? Express the answer in N/m2 and Atm. Inside: v1= 1m/sec P1 =? Outside: v2 = 20 m/sec P2 = 100,000 N/m2 Density of water = d = 1000 kg/m3 Notice that care has been taken to put all values in SI units.

Express the result in atmospheres.

2. Bernoulli’s equation can also be used to show how the design of an airplane wing results in an upward lift. The flow of air around an airplane wing is illustrated below. In this case you will notice that the air is traveling faster on the upper side of the wing than on the lower.


Compressibility: Compressibility occurs in all fluids but only under very high pressures are liquids noticeably compressed. For most hydraulics systems liquids are usually considered incompressible with their density only being affected by changes in temperature. However gases are easily compressed as well as being affected by temperature changes. Air is a gas and will compress as in a pump or when a body (such as an airplane) moves through it. However when a body moves through air at low speeds, including low speed flight, the amount of compression is so small that for most calculations the air is considered to act as if it is incompressible. But as the speed of sound (760 miles per hour 1226 km per hour at sea level), is approached the effect of compressibility (and expansions) in calculations gains more importance and must be considered. The Venturi Tube: The venture tube is a practical application of Bernoulli’s theorem. Originally used as a meter for measuring the quantity of flow of liquid in a pipeline, it provided for the basis of the theory of lift on an airfoil (the wing on an aircraft). The venture has a reduction in cross sectional area from the mouth of the tube to the throat, with a gradual increase in cross section from the throat to the outlet designed to avoid turbulence. When used to measure pressure manometer tubes are positioned at the throat and mouth. (With gases the manometer tubes are replaced by U tubes often containing mercury).

Venturi Tube: The pressure at "1" is higher than at "2" because the fluid speed at "1" is lower than at "2".

As the fluid flows through the venture, the reading on the manometer tube position on the throat is seen to be less than the pressure reading on the manometer positioned on the mouth, in accordance with Bernoulli’s theorem. Figure shows a diagram of the Venturi meter, by considering the outline shape in following fig. it can be seen to form the shape of an aerofoil where the greater velocity across the upper surface produces a decrease in pressure and subsequent lift.


Thermodynamics The science of heat and its relation to work is thermodynamics.

Sadi Carnot (1796-1832): the father of thermodynamics


Temperature: “The average K.E. of all the molecules of a body is termed as temperature” All kinds of matter is composed of molecules which are in constant motion and they possess kinetic energy. It is observed that greater the K.E., higher is the temperature. If it were possible to measure K.E. then a direct measurement of temperature could be made. However, this is not possible but the effect of increased molecular energy or vibration is expansion and this can be measured. The thermometer is an instrument that measures an increase in molecular K.E. in terms of the expansion of either mercury or alcohol.

A thermometer has two important elements: the temperature sensor (e.g. the bulb on a mercury thermometer) in which some physical change occurs with temperature, plus some means of converting this physical change into a value (e.g. the scale on a mercury thermometer). The height of liquid column is an indication of temperature. Calibration: Thermometers can be calibrated either by comparing them with other certified thermometers or by checking them against known fixed points on the temperature scale. The best known of these fixed points are the melting and boiling points of pure water. (Note that the boiling point of water varies with pressure, so this must be controlled.) The traditional method of putting a scale on a liquid-in glass or liquid-in-metal thermometer was in three stages: 1. Immerse the sensing portion in a stirred mixture of pure ice and water and mark the point indicated when it had come to thermal equilibrium. 2. Immerse the sensing portion in a steam bath at 1 standard atmosphere (101.3 kPa/760.0 mmHg) and again mark the point indicated. 3. Divide the distance between these marks into equal portions according to the temperature scale being used. For Celsius scale these two fixed points are 0 and 100 respectively and for Fahrenheit theses are 32 and 212 respectively. Other fixed points used in the past are the body temperature of a healthy adult male which was originally used by Fahrenheit as his upper fixed point (96 °F ) to be a number divisible by 12 and the lowest temperature given by a mixture of salt and ice, which was originally the definition of 0 °F (−18 °C).


Resistance thermometers are based on the principle that current flow becomes increasing more difficult with increase in temperature. They are used where a larger range of temperature is being measured approximately -200 to 1200oC. Thermister thermometers work along similar lines, except in this case they offer less and less resistance to the flow of electric current as temperature increases.

Thermocouple thermometers are based on the principle that when two different metal wires are jointed at two junctions and each junction is subjected to a different temperature, a small current will flow. This current is amplified and used to power an analog or digital temperature display. These sensors are used to measure aircraft engine and jet pipe temperatures; they can operate from about -200 to 1600oC.

Thermocouples

Heat: Heat is a form of energy and is defined as “The total kinetic energy of all the molecules contained in a body”. A modern idea of heat is that it is energy in transition and cannot be stored by matter. Heat may be defined as: transient energy brought about by the interaction of bodies by virtue of their temperature difference when they communicate. Matter possesses stored energy but not transient energy, such as heat or work. Heat can only travel or transfer from a hot body to a cold body, it cannot travel uphill.


A red-hot iron rod from which heat transfers to the surrounding environment.

Within matter the amount of molecular vibration determines the amount of K.E. of a substance possesses. For incompressible fluids the amount of molecular vibration is relatively small and can be neglected. For compressible fluids and gases the degree of vibration is so large that it has to be accounted for in thermodynamics. This K.E. is classified as internal energy and is a form of stored energy. Heat Energy Transfer Transfer of thermal energy can occur by conduction, convection, radiation or any combination of these. Conduction: Conduction is the transfer of thermal energy from a region of higher temperature to a region of lower temperature through direct molecular communication within a medium or between mediums in direct physical contact without a flow of the material medium. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from atom to atom. Conduction is greater in solids, where atoms are in constant contact. In liquids (except liquid metals) and gases, the molecules are usually further apart, giving a lower chance of molecules colliding and passing on thermal energy. Metals (e.g. copper) are usually the best conductors of thermal energy. This is due to the way that metals are chemically bonded: metallic bonds (as opposed to covalent or ionic bonds) have free-moving electrons and form a crystalline structure, greatly aiding in the transfer of thermal energy.

As density decreases so does conduction. Therefore, fluids (and especially gases) are less conductive. This is due to the large distance between atoms in a gas: fewer collisions between atoms means less conduction. Conductivity of gases increases with temperature but only slightly with pressure near and above atmospheric. Convection: Convection is a combination of conduction and the transfer of thermal energy by fluid circulation or movement of the hot particles in bulk to cooler areas in a material medium. Unlike the case of pure conduction, now currents in fluids are additionally involved in convection. This movement occurs into a fluid or within a fluid, and cannot happen in


The change of momentum produced in this case is called the impulse of the force i.e. Impulse = impulsive force x time = change in momentum Conservation of linear momentum: The law of conservation of linear momentum is a fundamental law of nature, and it states that the total momentum of a closed system of objects (which has no interactions with external agents) is constant. Considering two bodies of mass mA and mB moving in the same straight line, with mass A, moving at a greater speed uA than mass B which is at uB, eventually mA catches up with mB and collision occurs. At collision each delivers the same impulsive force ‘F’ to the other present for a very small period time t. After impact the respective velocities are vA and vB with the bodies continuing in the same direction as before.

Total momentum before impact = total momentum after impact mAuA + mBuB = vAuA + vBuB There are two basic kinds of collisions, both of which conserve momentum: ¾ Elastic collision conserves kinetic energy as well as total momentum before and after collision. ¾ Inelastic collisions don't conserve kinetic energy, but total momentum before and after collision is conserved. A collision between two pool balls is a good example of an almost totally elastic collision. A common example of a perfectly inelastic collision is when two snowballs collide and then stick together afterwards.


Specific Heat Capacity Table Specific Heat Capacity at 25oC in J/go /K H2 gas 14.267 H2 O 4.184 o ice @ 0 C 2.010 o steam @ 100 C 2.010 Air 1.020 Iron 0.444 Zinc 0.39 copper 0.385 Sand 0.290 silver 0.240 mercury 0.14 Gold 0.129 Substance

The thermal energy needed to produce a temperature rise depends on the mass of the material, type of material (the molecular size and number of molecules per Kg.) and the temperature rise to which the material is subjected. Thermal Energy

Q= m c ∆t

For Gases there are two types of specific heats and they both have different values and it is better to distinguish them. Specific Heat at constant Volume (CV): If one Kg of gas is supplied with an amount of heat energy sufficient to raise the temperature by 1K while the volume of the gas is kept constant, then the amount of heat energy supplied is known as the specific heat capacity at constant volume and is denoted by CV. Under these circumstances no work is done, but the gas has received an increase in internal energy U. The specific heat at constant volume for air is 718J/Kg/K. Specific Heat at constant Pressure (CP): If one Kg of gas is supplied with an amount of heat energy sufficient to raise the temperature by 1K while the pressure is held constant, then the amount of heat energy supplied is known as the specific heat capacity at constant volume and is denoted by CP. This implies that when the gas has been heated it will expand a distance b, so work has been done. Thus for the same amount of heat energy there has been an increase in internal energy U, plus work done. The value of CP is therefore greater than CV. The specific heat at constant pressure for air is 1005/Kg/K.


Expansion of Hydrogen gas at constant pressure. Volume Temp. Temp. V /T (K) (mL) (oC) (K) 25 -23 250 0.1 30 27 300 0.1 35 77 350 0.1 40 127.5 400.5 0.1 45

177

450

Graph

0.1

In other more thermodynamics-based definitions, the relationship between the fixed mass of a gas at constant pressure is inversely proportional to the temperature applied to the system, which can be further used by stipulating a system where α represents cubic expansivity of a gas, with θ representing the temperature measured of the system in Kelvin: Vα T V = Vo (1 + α θ) To maintain the constant, k, during heating of a gas at fixed pressure, the volume must increase. Conversely, cooling the gas decreases the volume. The exact value of the constant need not be known to make use of the law in comparison between two volumes of gas at equal pressure:

. Therefore, as temperature increases, the volume of the gas increases. Theoretically as a temperature reaches absolute zero the volume will also reach a point of zero. Standard Conditions of Temperature and Pressure: The current version of IUPAC's standard is a temperature of 0 °C (273.15 K, 32 °F) and an absolute pressure of 100 kPa (14.504 psi), while NIST's (National Institute of Standards and Technology) version is a temperature of 20 °C (293.15 K, 68 °F) and an absolute pressure of 101.325 kPa (14.696 psi). The characteristic Gas equation: The ideal gas law is the equation of state of a hypothetical ideal gas, The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation: PV=nRT


The equation for latent heat is: Q=mL

where: Q is the amount of energy released or absorbed during the change of phase of the substance (in joules), m is the mass of the substance, L is the specific latent heat for a particular substance (J kg-1). In other words, specific latent heat is found when energy is divided by mass. Latent heats and change of phase temps of common fluids and gases Substance

Latent Heat Fusion J/g

Melting Point °C

Latent Heat Vaporization J/g

Boiling Point °C

Alcohol, ethyl

108

-114

855

78.3

Ammonia

339

-75

1369

-33.34

Carbon dioxide

184

-57

574

-78

21

-268.93

Helium Hydrogen

58

-259

455

-253

Lead

24.5

372.3

871

1750

Nitrogen

25.7

-210

200

-196

Oxygen

13.9

-219

213

-183

Water

333

0

2260 (at 100oC)

100

Thermal Expansion of Solids and Liquids Most solids and liquids expand when heated and contract when cooled. The thermal expansion is usually small and unnoticeable. Nevertheless these expansions and contractions are important because the forces they exert are very great and must be compensated for in many structures such as railway lines, concrete roads and steel bridges. When an iron rod is heated, the vibration of the molecules increases and their displacement or amplitude also increases. As the amplitude of vibration increases, the average distance between the molecules of the rod becomes larger and this accounts for its expansion in length. Linear thermal expansion: The linear thermal expansion is the one-dimensional length change with temperature.

Application of thermal expansion: • •

•

A glass jar will break if you fill it half-full of very hot water. The top and bottom of the jar want to be different sizes. Concrete roads and sidewalks are built in sections, with space left between the panels. Otherwise, they would crack on very cold days and heave and buckle on very hot days. If the ocean becomes 1 degree (oF) warmer, its volume will increase by 0.01%. Since the ocean is several miles deep, this implies that the surface will rise about a foot, giving a change in the sea level. In the process, the beach line moves landwards 20 feet. People owning beach houses (or even living close to the ocean) find this alarming. Anomalous Expansion of Water:

When water has become solid ice (below 0oC), its volume is considerably larger, and its density smaller. Hence ice floats in water. Ice has a crystalline structure. Normally the substances in the solid state occupy a smaller volume than in the liquid state. Due to the angular shape of the water molecules, ice has open-structured crystals. The forces binding water molecules together are strongest at certain angles. Ice in this open structure occupies a greater volume than it does in the liquid state. Consequently, ice is less dense than water. This behavior of water is of great importance in nature. The anomalous expansion of water has a favorable effect for animals living in water. Since the density of water is maximum at 40C, water at the bottom of lakes remains at 40C in winter even if the surface freezes. Water at the freezing point 0oC is less dense and so "floats". It means ice forms at the surface while the lake remains liquid below the ice. This allows marine animals to remain alive and move near the bottom.


When a working fluid is a subject to a process, then the fluid will have started with one set of properties and ended with another, irrespective of how the process took place. For example, if a fluid within a system has an initial pressure (p1) and temperature (T1) and is then compressed producing an increase in pressure (p2) and temperature (T2), then we say that the fluid has undergone a process from state one to state two. We say that work is transferred in a thermodynamic system, if there is a movement of the system boundaries.

Three types of thermodynamic systems are distinguished depending on the kinds of interaction and energy exchange taking place between the system and its surrounding environment: •

Isolated systems are completely isolated in every way from their environment. They do not exchange heat, work or matter with their environment. An example of an isolated system would be an insulated rigid container, such as an insulated gas cylinder.

•

Closed systems are able to exchange energy (heat and work) but not matter with their environment. A greenhouse is an example of a closed system exchanging heat but not work with its environment. Whether a system exchanges heat, work or both is usually thought of as a property of its boundary. Example is cylinder and piston assembly of the internal combustion engine.

•

Open systems: exchanging energy (heat and work) and matter with their environment. A boundary allowing matter exchange is called permeable. The ocean would be an example of an open system. Example is gas turbine.

In reality, a system can never be absolutely isolated from its environment, because there is always at least some slight coupling, even if only via minimal gravitational attraction. In analyzing a system in steady-state, the energy into the system is equal to the energy leaving the system. First law of thermodynamics: In thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the conservation of energy. “The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings.”


That is, it is impossible to extract energy by heat from a high-temperature energy source and then convert all of the energy into work. At least some of the energy must be passed on to heat a low-temperature energy sink. Thus, a heat engine with 100% efficiency is thermodynamically impossible. Thermodynamic processes: There are one or two processes which will help us to discuss the thermodynamic cycles of internal combustion engine and the gas turbine engine. Reversible and irreversible processes: A system is said to be reversible, when it changes from one state to another and at any instant during this process, an intermediate state point can be identified from any two properties that change as a result of the process. For reversibility, the fluid undergoing the process passes through a series of equilibrium states.

Irreversible Process Reversible Process In practice, because of energy transfers, the fluid undergoing a process cannot be kept in equilibrium in its intermediate states and a continuous path cannot be traced on a diagram of its properties. Such real processes are called Irreversible and they are usually represented by a dashed line joining the end states. The seven most common thermodynamic processes are shown below: 1. 2. 3. 4. 5. 6. 7.

An isobaric process occurs at constant pressure. An isochoric process, or isometric/isovolumetric process, occurs at constant volume. An isothermal process occurs at a constant temperature. An adiabatic process occurs without loss or gain of heat. An isentropic process (reversible adiabatic process) occurs at constant entropy. An isenthalpic process occurs at a constant enthalpy. A steady state process occurs without a change in the internal energy of a system.

Isochoric process: It is a process during which volume remains constant. The name is derived from the Greek isos, "equal", and khora, "place."


but since pressure is constant, this means that

Applying the ideal gas law, this becomes Assuming that the quantity of gas stays constant (e.g. no phase change during a chemical reaction). Since it is generally true that

then substituting the last two equations into the first equation produces:

.

The quantity in parentheses is equivalent to the molar specific heat for constant pressure:

cp = cV + R and if the gas involved in the isobaric process is monatomic then

and

An isobaric process is shown on a P-V diagram as a straight horizontal line, connecting the initial and final thermostatic states. If the process moves towards the right, then it is an expansion. If the process moves towards the left, then it is a compression. Enthalpy: An isochoric process is described by the equation Q = ∆U. It would be convenient to have a similar equation for isobaric processes. Substituting the second equation into the first yields

The quantity U + p V is a state function so that it can be given a name. It is called enthalpy, and is denoted as H. Therefore an isobaric process can be more succinctly described as .

Isothermal Process: An isothermal process is a change in which the temperature of the system stays constant: ∆T = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. An alternative special case in which a system exchanges no heat with its surroundings (Q = 0) is called an adiabatic process. In other words, in an isothermal process, the value ∆T = 0 but Q ≠ 0, while in an adiabatic process, ∆T ≠ 0 but Q = 0.

.


Work done by expanding a gas: Consider a piston and cylinder arrangement as shown in fig below, in which one Kg of a gas is contained at temperature TK. The piston has a cross sectional area of 1m2 is free to slide and rests on the gas, exerting a constant pressure by virtue of its weight. Now let the temperature of the gas increase by 1K. This will produce an increase in volume and the piston will move to a new position. Let l (as lima) meters be the movement of the piston.

Expanding Gas.

Now work done = Force x Distance moved = F x l joules =Pxaxl But a x l = change in volume Work done = P (V2-V1), where V2= final volume V1=initial volume If now, we consider incorporating the characteristic gas equation, PV= m RT, this becomes PV=RT for m=1Kg. For the initial volume PV1= RT And for the final volume PV2= R (T+1) Since

work done = P (V2-V1) = PV2-PV1

Then by substitution, work done = R (T+1) – RT Work done = R (the characteristic Gas constant)


ot cycle actingg as a heat Fig1: A Carno engine, illustrated on a temperature‐ entropy diagram. The cyclle takes placee between a ho ot reservoir aat temperaturre TH and a cold d reservoir at temperature TC. The verticcal axis is tem mperature, thee horizontal axxis is entropy.

FFig2: A Carnott cycle acting as a heat e engine, illustra ated on a preessure‐volume d diagram to illu ustrate the work done.

Two Stro oke Engine: The two stroke enginne employs the t crankcasee as well hieve all the elements off the Otto as the cylinder to ach o two stro okes of the piston. p cycle in only


From first law of therm modynamics W Q1 = Q2 +W And from second law oof thermodyn namics W>0 i is esseential if heat is to be i.e. a work input transferred from a cold to a hot boddy.

A Typicaal Example: One commoon type of heeat pump woorks by explooiting the ph hysical propertiees of an evap porating and condensing fluid knownn as a refrigeerant. mple diagram m of a heat pu ump's vapor‐ Fig. A sim compresssion refrigerration cycle: 1) Condeenser, 2) expansion valve, 3) evapo orator, 4) com mpressor.

The workking fluid, inn its gaseouss state, is preessurized andd circulated tthrough the system by a compresssor. On the discharge d sidde of the com mpressor, thee now hot annd highly preessurized gas is cooledd in a heat ex xchanger, callled a condennser, until itt condenses iinto a high pressure, p moderatee temperaturre liquid. Thee condensedd refrigerant then t passes tthrough a prressurelowering device like an expansioon valve, cappillary tube, or o possibly a work-extraacting devicee such as a turbine. This device theen passes thee low pressu ure, (almost) liquid refriggerant to another heat h exchang ger, the evapporator wheree the refrigerant evaporaates into a gaas via heat absorptio on. The refrig gerant then returns r to the compressoor and the cyycle is repeatted. In such a system it iss essential th hat the refrigeerant reaches a sufficienntly high tem mperature when com mpressed, since the secoond law of thhermodynam mics preventss heat from flowing f from m a cold fluuid to a hot heat h sink. Sim milarly, the fluid must reeach a sufficciently low temperature when alloowed to expand, or heat cannot flow w from the coold region innto the fluid. In particulaar, the pressuure differencce must be great g enoughh for the fluid d to condensse at the hot side and stilll evaporatee in the loweer pressure region r at the cold side. The T greater thhe temperatuure differencce, the greateer the requireed pressure ddifference annd consequeently more ennergy is needed too compress the t fluid. Thhus as with all heat pump ps, the energgy efficiency (amount off heat movved per unit of o input worrk required) decreases with w increasinng temperatuure differencce.


Due to the variations required in temperatures and pressures, many different refrigerants are available. Refrigerators, air conditioners, and some heating systems are common applications that use this technology. Refrigerants: Until the 1990s, the refrigerants were often chlorofluorocarbons such as R-12 (dichlorodifluoromethane), one in a class of several refrigerants using the brand name Freon, a trademark of DuPont. Its manufacture was discontinued in 1995 because of the damage that CFCs cause to the ozone layer if released into the atmosphere. One widely-adopted replacement refrigerant is the hydrofluorocarbon (HFC) known as R-134a (1,1,1, 2tetrafluoroethane). R-134a is not as efficient as the R-12 it replaced (in automotive applications) and therefore, more energy is required to operate systems utilizing R-134a than those using R-12. Other substances such as liquid ammonia, or occasionally the less corrosive but flammable propane or butane, can also be used. Since 2001, carbon dioxide, R-744, has increasingly been used, utilizing the transcritical cycle. In residential and commercial applications, the hydrochlorofluorocarbon (HCFC) R-22 is still widely used; however, HFC R-410a does not deplete the ozone layer and is being used more frequently. Hydrogen, helium, nitrogen, or plain air is used in the Stirling cycle, providing the maximum number of options in environmentally friendly gases. More new refrigerators are now exploiting the R600A which is iso-butane, and does not deplete the ozone and is friendly to the environment. Ideal properties of Refrigerant include: ¾ ¾ ¾ ¾ ¾

Be in-expansive and readily available Be non toxic, non corrosive, and present a low fire and explosion risk Working pressures should be above atmospheric temperatures but not too high Specific enthalpy of vaporization at the low temperature should be as high as possible Specific volume at compressor inlet should be as small as possible to keep the overall system mass down ¾ The refrigerant should not react with oil if the compressor is lubricated with oil in the refrigerant The aircraft uses a heat pump/Refrigeration system (Air cycle Machine) which automatically cools or heats depending on the temperature requirement. Heat of Combustion: During a chemical reaction chemicals may be formed or broken down into simpler units or elements. Such processes may be accompanied by heat being either received or expelled, during the reaction. This is known as the heat of reaction. If the reaction takes place quickly and the element combines with oxygen, heat will be generated, known as the heat of combustion. To determine, satisfactorily, the heat of combustion of a fuel an experimental method is often used, using an apparatus known as the bomb calorimeter. This measures the heat output of a known mass of the fuel, burnt in an adequate supply of oxygen i.e. Air. Hence the units of ‘heat of combustion’ are joules/Kg.

OPT O TICS S (L Light) Optics is the sciencee that describbes the behaavior and pro operties of light and the interaction i o of light w with matter

Ibn al-Haytham a is regarded as a the "fatheer of modern n optics" for his influentiial Book of Optics (written ( whiile he was unnder house aarrest), whichh correctly explained e andd proved thee modeern intromisssion theory of vision.


Nature of Light: Light consists of electromagnetic waves. Electromsgnetic waves consists in turn of oscillating Electric and Magnetic fields. These fields travel through space vibrating at right angles to each other and to the direction of motion.

Light waves are part of whole group of electromagnetic waves or radiation, that includes Xrays, UV rays, Infra red rays and radio waves. Light waves can be produced by the change of orbit of electrons inside atoms, and although each type of radiation has a different source they all have certain properties in common.

¾ They travle through space at 300,000Km/Sec i.e. the speed of light. ¾ They follow the realation v=fλ ¾ They carry energy from one space to another and an absorption cause an increase in temperature.

← Frequency Decrease Frequency increase →


A convexx mirror, fissh eye mirror or divergging mirror is a curved mirror in whhich the reflectivee surface bullges toward the t light souurce. Convex mirrors m refleect light outw wards; thereffore they aree not used to focus lighht. Such mirrrors always form a virtu ual image, siince the focu us F and the centre of cuurvature 2F are a both imaginary pointts "inside" th he mirror, whhich cannot be reached. Therefore im mages formeed by these m mirror cannoot be taken on screen. (A As they are inside the m mirror) A collimated (paralleel) beam of light l divergees (spreads out) o after refleection from a convex miirror, since thhe normal too A conveex mirror diaggram showingg the surfacce differs wiith each spott on the mirrror. the focu us, focal Lenggth, centre off curvatu ure, principal axis, etc

The imag ge is always virtual (rayss haven't acttually passedd though th he image), diminished d (ssmaller), andd upright. These feaatures make convex mirrrors very useeful: everythinng appears sm maller in thee mirror, so tthey cover a wider fieeld of view th han a normaal plane mirroor does as th he image is "compressed d". Convexx mirror image e formation

Focal lenngth of a sph herical mirror: f = R / 2 Concavee mirrors: A concavve mirror, or o convergin ng mirror, hhas a reflectiing surface thhat bulges in nward (awayy from the incident lighht. Concave mirrors refllect light inw ward to one ffocal point; thereforee they are useed to focus light. l Unlikee convex mirrors, concave c mirrrors show diifferent typees of image dependinng on the distance between the objecct and the mirror itsself. These miirrors are callled "converrging" becauuse they tendd to collect lig ght that fallss on them, reefocusing paarallel incom ming rays towaard a focus. This is becaause the lightt is reflected d at different angles, sincce the normaal to the surfaace differs with w each spott on the mirrror.


For concave (converging) mirrors, as long as the object is placed greater than one focal length in front of the mirror, a real image is produced. When the object is placed exactly one focal length in front of the mirror, no image is formed since the rays reflected from the mirror are parallel and can never intersect either in front of or behind the mirror. When the image is placed within one focal length of the mirror, a virtual, enlarged image is formed when the reflected, diverging rays, are "dotted back" behind the mirror. Concave spherical mirrors are considered to be positive mirrors since their mirrored surface faces "towards the center of the sphere". For convex (diverging) mirrors, no matter when the object is placed in front of the mirror, a virtual, upright, reduced image is formed "behind the mirror" between F and V. Convex spherical mirrors are considered to be negative mirrors since their mirrored surface faces "away from the center of the sphere". Always remember, virtual images are formed by diverging rays; while real images are always formed by converging rays. It is also important to be aware that mirrors can be classified according to the characteristics of the virtual images they form: ¾ Plane mirrors: virtual images are the same size as their objects ¾ Concave spherical mirrors: virtual images are larger that their objects ¾ Convex spherical mirrors: virtual images are smaller than their objects Variation in the speed of light: the speed of light varies as it travels from medium to medium. The refractive index gives the ratio of this speed change. Thus: Refractive index = Speed of light in vacuum / Speed of light in medium The above relationship implies that the greater the refractive index of the medium or the more the light is bent through the medium then the lower the speed of light. Refraction of Light: when a ray of light is incident on the boundary separating the two mediums having different densities. A part of the light gets reflected and rest of the light changes its direction as it enters the second medium.


Critical angle is that angle of incidence for which a ray of light while moving from a denser to a rarer medium just grazes over the surface of separation of the two media (that is, angle of refraction = 90o).

The conditions to be satisfied for total internal reflection to take place are ¾ The ray of light must travel from a denser medium to a rarer medium ¾ The angle of incidence must be greater than the critical angle for those two mediums Mirage and Looming:


Principle of reversibility: The principle of reversibility states that light will follow exactly the same path if its direction of travel is reversed. Lenses: A lens is a portion of a transparent refracting medium bounded by two surfaces which are generally spherical or cylindrical or one curved and one plane surface. Basically, the lenses are classified as 1. Convex or Converging Lens 2. Concave or Diverging Lens Convex Lens: A lens which is thicker in the middle and thinner at the edges is called a convex lens. In a convex lens at least one of its surfaces is bulging out at the middle. According to their shapes the convex lenses are classified as

Concave Lens: A lens which is thinner at the middle and thicker at the edges is called a concave lens. Like convex lenses these lenses are also classified as

Terminology Used in Optics: Optical Center: It is the center of a lens. It is denoted by the letter O. A ray of light passing through the optical center of a lens does not suffer any deviation. It is also referred to as optic center

Principal Axis: Is the straight line joining the centers of curvatures of the two curved surfaces of a lens


The nature of images formed by a convex lens depends upon the distance of the object from the optical center of the lens. Let us now see how the image is formed by a convex lens for various positions of the object. When the object is placed between F1 and O. The image is: ¾ Formed on the same side of the lens ¾ Virtual ¾ Erect ¾ Magnified When the Object is Placed at F1 . The image is: ¾ ¾ ¾ ¾

Formed at infinity Real Inverted Magnified

When the Object is Placed Between F1 and F2. . The image is ¾ ¾ ¾ ¾

Formed beyond 2F2 Real Inverted Magnified

When the Object is placed at 2F1. The image is: ¾ Formed at 2F2 ¾ Real ¾ Inverted ¾ Same size as the object


A concave lens always gives a virtual, erect and diminished image whatever may be the position of the object. Let us now draw ray diagrams to show the position of the images when the object is placed at infinity, between O and F1 and any position between infinity and O.

When the Object is at Infinity The image is: ¾ ¾ ¾ ¾

Formed at F1 Erect Virtual diminished

When the Object is Placed between O and F1 The image is – ¾ ¾ ¾ ¾

formed between O and F1 Erect Virtual diminished

When the Object is placed at any Position between O and infinity The image is – ¾ ¾ ¾ ¾

formed between O and F1 Erect Virtual diminished


Basic elements of a Fiber Optic cable: ¾ Core material for data transmission ¾ Cladding- allows for light reflection back into the core ¾ Outer covering-for weather/wear protection and to give mechanical strength The core material is either plastic or glass (glass on Aircraft systems). The cladding is a material whose refractive index is less than that of core. Total internal reflection at the core cladding interface confines the light to travel within the core. This means that light once launched into the fiber cable; remains trapped in the core and emerges with a little loss at the end. A fiber with plastic core has plastic cladding outside. Such fibers exhibit high losses but are widely used in communication systems for short distance transmission. Multi component glasses containing a number of oxides are used for all but the lowest loss fibers which are usually made from pure silica. In low and medium loss fibers a glass or plastic cladding surrounds the glass core. The highest performance cables have glass core and glass cladding which makes them more expansive than the others but have a higher performance with less loss. The outer coating is an abrasion-resistant water proof plastic material which increases mechanical strength of the fiber. This together with any additional strengthening fibers allows for any geometrical irregularities, distortion or roughness of adjacent surfaces which could otherwise cause scattering losses. (Cables cannot be bent through too tight a radius as this will cause high signal loss).

Optical Fiber light Transmission: the structure of a glass fiber is shown in fig. above. The core with index n2, is surrounded by a cladding with index n1, where n1

Single mode m fibers have small diispersion beccause light can c propagate at small anngles to the axis. This means therre is less sprread as it passses down thhe fiber and rrelatively litttle distortionn p of short pulses. Such fibeers can be ussed in system ms with largee bandwidth hs. They requuire greater precision p in fabricatioon and it is more m difficullt to couple llight unto thhem efficienttly. They aree used for thee systems with w high daata rates and long distancce transmissiion. The corre diameter is of the sam me order as the t waveleng gth of light source s (LAS SER diode). Fibres wiith a graded index of reffraction offerr a comprom mise. A parabbolic radial variation v of the indexx of refractio on acts like a continuous focusing eleement. The largeer core radiu us multi modde fibers are either step in ndex or gradded index fibbers. In the step indeex fibers therre is a step ch hange in thee refractive inndex at the core c claddingg interface.

o the fiber. Multimode The refraactive index of the gradeed index fibeer varies acrooss the core of fibers hav ve a small coore radius, which w permitts the light to o travel alonng only one path p in the fiber. velling at an angle to thee axis are bennt back towaard to the axiis by the graadient in the Rays trav refractivee index. A raay travellingg at an angle to the axis travels t fartheer than one along a the axiis but it speends more tim me in regionn with low inndex of refraaction. Thus it has higherr average velocity than t the axiaal ray. The choice of the parrabolic profiile tends to kkeep the diffe ferent rays inn phase and thus t keeps t in multtimode fiberss dispersioon small. Thee short pulsees of light aree lengthenedd much less than with step p index profiles. The largeer core diam meter of multiimode fiber makes it eassier to send llight into fibber and makees the fiber connection easy. e Light may m be sent via LED’s; where as sinngle mode fibers require d LASER diode.


For low photon energy (long wavelength) transmission the loss rises from the tail of the infra red absorption caused by photon scatter. Be remembering that photon is a basic unit of light like electron which is basic unit of electricity. Radiation losses: These lossses occur at any bend in the optical fiber. The light will radiate out of the fiber at any bend. For example, with a single mode fiber with a 1% difference of index of refraction, the radiation loss is negligible for bend radii greater than 1mm, but for a bend radius of 0.5mm the losses would be substantial.

Optical Wavelength Losses: Attenuation is also a function of optical wavelength. Figure above shows the typical attenuation versus wavelength characteristics of a plastic and a monomode glass fiber. At 0.8 µm the attenuation of the plastic fiber is 350db/km and that of the glass fiber is approximately 1db/km. the minimum attenuation of glass fiber is 0.2db/km at 1.55µm. Non confinement loss: occurs when the light enters the fiber but at a large angle to the fiber centre line. The maximum acceptance angle αm taken from the center line of the fiber at the end of the fiber is: Sinαm = √n22 – n12 = Numerical Aperture Provided the acceptance angle is less than αm then the incident light will be confined within the fiber. Microbend Losses: Scattering caused by microbends between cladding and the core.


Wave Motion and Sound A disturbance or variation that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure, electric or magnetic intensity, electric potential, or temperature

Wave motion: A stone thrown into a quiet pool of water causes waves to spread out in ever widening circles whose center is the point where the water was first disturbed. Small objects floating on the pool move up and when wave passes through their positions; they do not move outwards as the waves do. This shows that disturbance caused in the water is an up and down movement of the water. Although the waves on the water travel outwards from the centre of disturbance, the water itself does not move outwards. Such up and down movement or vibration of the water which causes waves is an example of wave motion. “A disturbance or variation that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure, electric or magnetic intensity, electric potential, or temperature”. All waves have similar characteristics, and since all forms of wave motion follow the same laws and principles, knowing the fundamentals of wave motion is important in understanding sound, light, and other types of waves.

There are two categories of waves: ¾ Mechanical ¾ Non-mechanical Mechanical waves Mechanical waves require a medium for the transfer of energy to occur. For example, water waves are mechanical. Tsunami waves released after an earthquake transfer the energy of the quake to distant shorelines. Sound waves are another type of mechanical wave. They are compression waves that have a frequency between 20-20000 hertz and travel at a speed of approximately 340 m/sec at room temperature. Different substances carry compression waves at various speeds; metals carry it faster than water which transfers it faster than air. As a mechanical wave travels through a medium, it loses energy to the medium. The molecules in the medium are forced to vibrate back and forth, generating heat. Consequently, the wave can only propagate through a limited distance. When this event happens, we say that the wave has been damped. Damping can be observed by the fact that the wave's amplitude has decreased.


hese two largge categoriess, there are ttwo principlee types of waaves: Within th ¾ Transverrse - waves in i which the particles vib brate at rightt angles to th he direction of the wavve's velocityy (ex: waves along a strinng). Transveerse waves can be polarized since these vibrations caan be constrrained to movve in only on ne plane. Exampless are waves produced p in a Rope or sttring, Light waves, w water waves

¾ Longitud dinal - wavess in which thhe particles vibrate v paralllel to the dirrection of thhe wave's veelocity (ex: sound) Sound waaves: A louddspeaker conne moves back-andd-forth to creeate a sound, which is a compresssion wave. Slinky: You Y can strettch out a Slin nky along thee floor andd give one en nd a back-annd-forth shove. Thhe compresssion will movve along the Slinky to its other end. AC electrricity: Electrrons move back-and-fortth in a wire, sending a w wave of electtric power through the t wire. Thee electrons stay s in their ggeneral regioon in AC eleectricity, whhile the flow through and a out the wire w in DC electricity. e Characteristics of waves w The characteristics of a waveform m are waveleength, ampllitude, veloccity, and freequency. Alll periodic waveforms w h have these common c charracteristics. There aree special casses, where onnly one crestt of the wavee is seen, likke the the waave at a ballgamee or the sounnd caused by y an impact oor explosion.. In those casses, there is still a wavelenggth, but theree is no frequ uency, since the waveforrm is not periodic. Wavelen ngth: Wavelength is defi fined as the ddistance from m one crest ((or maximum m of the wave) to the next creest or maxim mum and is denoted by syymbol ‘λ’.


An indication of amount of energy a wave possesses is given by the amplitude of the wave. The greater the amplitude, the greater the energy carried, but measurements of wave energy, that is ‘wave intensity’ are calculated from both frequency and amplitude and is the energy deposited on a unit area every second. Interference is the addition (superposition) of two or more waves that result in a new wave pattern. The principle of superposition of waves states that the resultant displacement at a point is equal to the vector sum of the displacements of different waves at that point. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant wave amplitude is greater. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased.

Combined waveform Wave 1 Wave 2

Constructive Interference

Destructive Interference

Standing waves Standing waves are produced whenever two waves of identical frequency interfere with one another while travelling opposite directions along the same medium. Standing wave patterns are characterized by certain fixed points along the medium which undergo no displacement. These points of no displacement are called nodes (nodes can be remembered as points of no displacement). The nodal positions are labeled by an N in the animation above. The nodes are always located at the same location along the medium, giving the entire pattern an appearance of standing still (thus the name "standing waves"). Nodes are the result of the destructive interference of the two interfering waves.


Sound Waves Sound is a series of compression waves that moves through air or other materials. These sound waves are created by the vibration of some object, like a radio loudspeaker. The waves are detected when they cause a detector to vibrate. Your eardrum vibrates from sound waves to allow you to sense them. Sound has the standard characteristics of any waveform. Sound is a waveform that travels through matter. Although it is commonly associated in air, sound will readily travel through many materials such as water and steel. Some insulating materials (Sound proofing) absorb much of the sound waves, preventing the waves from penetrating the material. Because sound is the vibration of matter, it does not travel through a vacuum or in outer space. Also note that light and radio waves are electromagnetic waves. They are completely different than sound, which is vibration of matter. Electromagnetic waves are related to electrical and magnetic fields and readily travel through space. The back-and-forth vibration of an object creates the compression and rarefaction of sound. The motions of a loudspeaker cone, drumhead and guitar string are good examples of vibration that cause compression waves.

Transverse Wave (water wave)

Characteristics of sound: A sound wave has characteristics just like any other type of wave, including amplitude, velocity, wavelength and frequency. 1). Amplitude: The amplitude of a sound wave is the same thing as its loudness. Since sound is a compression wave, its loudness or amplitude would correspond to how much the wave is compressed. It is sometimes called pressure amplitude.


A sound intensity of 0 dB represents the threshold of human hearing. This corresponds to an intensity of 10-12 W/m2(Io) . (The threshold of pain is somewhere between 120 dB and 130 dB, depending on an individual's sensitivity to pain.)

Minimum sound intensity perception in humans varies with frequency. A frequency of about 4 000 Hz yields the lowest threshold for people with acute hearing ability. The human ear is most sensitive to frequencies between 1 000 Hz and 5 000 Hz. ich is being measured.

Sound intensity decreases as distance increases from the source. An inverse square law relationship is observed. I α 1/d2 Extremely loud sounds, as from a sudden explosion, may cause the eardrum to rupture. It is recommended (or required in certain circumstances) that ear protectors be used when one is exposed to noisy environments. Hearing protectors cannot protect adequately against intense sounds which travel through the skeleton into the bones in the middle ear. (i.e., with vibrating power tools, some heavy machinery, etc.) 5). Frequency: Since sound is a compression waveform, its frequency is the rate that the maximum compressions pass a given point in a second. The unit of frequency is the hertz (Hz), which means cycles per second. Infrasound consists of very low frequency sound, beyond the range of hearing of humans. Audio frequencies are those that can be heard. Ultrasound consists of very high frequencies, again beyond the human range of hearing. Knowing the speed of sound in air, you can convert frequencies into wavelength. It is also the rate at which a guitar string or a loud speaker vibrates. Frequency is also called the pitch of a sound. It is called the note in musical sounds. The pitch of a sound that we experience is determined by its wavelength or its frequency. The shorter the wavelength, the higher the frequency becomes, and the higher the pitch that we hear. Since the speed of sound in air at room temperature is about 344 meters/second, the following chart shows the wavelengths for typical infrasonic frequencies. Frequency (f)

Wavelength (λ)

10 Hz

34.4 meters

0.1 Hz

3400 m

0.001 Hz

344 kilometers


Examples If TC = 0° C, then v = 331.4 + 0 = 331.4 m/s If TC = 20° C, then v = 331.4 + 0.6*20 = 331.4 + 12 = 343.4 m/s This also shows that as the temperature of air goes up, the speed of sound goes up. Doppler Effect for Sound The pitch of the sound an observer listens from a moving source will be either higher or lower than the emitted frequency, depending on the direction the source is moving. This is called the Doppler effect. When the source of sound is moving toward listener, the pitch observer hear is higher than what was emitted from the source and the wavelength is shorter than emitted. Note that the speed of the source must be less than the speed of sound. An aircraft flying at the speed of sound or greater creates a sonic boom, which is a different effect. Frequency: The equation for the observed frequency of sound when the source is traveling toward observer is fo = fv/(v − vt) where • • • • •

fo is the observed frequency f is the emitted frequency v is the velocity of sound vt is the velocity of the source toward you v > vt (vt less than v)

Note that if the speed of the source is equal to the speed of sound, then dividing by 0 is impossible. Wavelength: Also, since the velocity of the wave equals the frequency times the wavelength (v = fλ or f = v/λ), the equation for the observed wavelength when the source is traveling toward observer is: λo = λ(1 − vt/v) where • • •

λo is the observed wavelength λ is the emitted wavelength (Greek symbol lambda) v > vt (vt less than v)



Physics Module 2

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