Physics Module 2

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IRCRAFT

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AINTENANCE

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NGINEERING

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2008

EASA Part‐66 Module 2

Shahzad Khalil

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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]

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PREFACE

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PHYSICS

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

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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

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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.

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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

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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

square kilometer km2 1,000,000 0.3861 square miles

hectare ha 10,000 2.47 acres

acre a 100 119.60 square yards

square

centimeter cm

2 _0.0001 _{0.155 square inch}

Capacity

Unit Abbreviation Number of _Liters Approximate U.S. Equivalent

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

cubic decimeter dm3 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

centiliter cl 0.01 0.61 cubic inch 0.338 fluid _ounce

Mass and weight

Unit Abbreviation Number of _Grams Approximate U.S. Equivalent

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

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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 1,852 metres

¾ 1.150779 mile (statute) ¾ 2,025.372 yards ¾ 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 Multiplication _Factor Name Symbol Multiplication _Factor

Yotta Y 1024 deci d 10-1 Zetta Z 1021 _centi _c ₁₀-2 Exa E 1018 milli m 10-3 Peta P 1015 _micro _µ ₁₀-6 Tera T 1012 nano n 10-9 Giga G 109 _pico _p ₁₀-12 Mega M 106 femto f 10-15 Kilo k 103 atto a 10-18 Hecto H 102 zepto z 10-21 Deca D 10 yocto y 10-24

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2.1-MATTER

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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.

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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.

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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

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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 COVALENT BOND

Complete Transfer of Electron Sharing of Electron

High boiling and Melting Point 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.

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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.

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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.

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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 Fx= 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.

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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.

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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.

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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 GaugePressure. 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

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2.2.2-KINETICS

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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.

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Velocity-time graphshows 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 Inertiastates 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 Accelerationstates 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 Interactionstates 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).

Weightis 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

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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}

unit is radian /sec2.

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 = α r

Where Ө, ω and α are angular distance, angular velocity and angular acceleration respectively.

Angular Equation of motion Linear Equation of motion

Ө = (ω1+ ω2)t/2 Ө = ω1t+1/2 αt2 ω22 = ω12 +2αӨ α = (ω2 – ω1 )/t S = ( v+ u) t/2 S= ut +1/2 at2 v2 _{= u}2_{+ 2 aS} 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

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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”.

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2.2.3-DYNAMICS

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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 = T

R

+ 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’.

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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.

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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.

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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 15000-18000 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.

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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.

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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.

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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.

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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

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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.

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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

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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

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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.

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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 fluidspeed 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.

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Thermodynamics

Thescience of heat and its relation to work is thermodynamics.

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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).

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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.

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Physics Module 2

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A

IRCRAFT

M

AINTENANCE

E

NGINEERING

S

ERIES

2008

EASA Part‐66 Module 2

Shahzad Khalil

PHYSICS

Shahzad Khalil

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CONTENTS

PHYSICS

2.1-MATTER

2.2-MECHANICS

2.2.1-STATICS

Intentionally hidden

2.2.2-KINETICS

2.2.3-DYNAMICS

During take‐off

Thrust = D + ma

At landing ma = T

+ D + B

2.2.4-Fluid Dynamics

Thermodynamics