Mod 2 - Physics

2.1: The Nature of Matter

DEFINITION - matter is anything that occupies space and has mass, it also has weight or is attracted by earths gravity

Matter cannot be created or destroyed, but is able to change its form with the release of energy.

2.2: The Structure of Atoms

Electrons negatively charged, Relative mass 1

Protons positively charged, Relative mass 1

Neutrons no charge, mass 1/1847

An atom has a nucleus, consisting of protons and neutrons, and layers of orbiting electrons, Shells - 2:8:8

Most of the mass in an atom is concentrated in the protons and neutrons in the nucleus.

A complete atom is electrically neutral, electrons = protons 

Electrons orbit the nucleus in distinct shells. Electrons in shells close to the nucleus are held very tightly to it, while those in the outer shell are much less attracted

a current of 1 ampere flow, 6.24 x 1018 electrons will have passed every second.

2.3: Chemical Elements and Compounds

DEFINITION - A chemical element consists of one or more atoms of the same type

There are 92 naturally occurring elements, information on elements is contained in the periodic table

A Molecule consists of 2 or more atoms.

A Compound is if 2 or more different atoms are combined, a chemically different substance is formed i.e. H2O - Water 

Compounds usually have very different properties to their constituent elements

In a covalent compound, bonds are formed when atoms share electrons i.e. water

In an ionic compound, electrons move from the outer shell of one atom to the outer shell of another. This leaves charged particles called ions. 

positive Ion - Lost electron 

negative ion - Gained electron

2.4: States of Matter

3 states determined by motion of Molecules

• Solid state

- A solid has a definitive volume and shape

• Liquid state

-A liquid has a definite volume but an indefinite shape

• Gaseous state.

- neither a definite shape nor volume.

2.5: Changes between States

- heat energy may be used to change its state.

Solid to Liquid – Fusion (Melting)

- When a solid is heated, the molecular speed of movement is increased until it becomes great enough to overcome the cohesive force that held the solid in its rigid shape

- takes place at melting point

Liquid to Gas – Vaporisation (Boiling)

-When a liquid is heated, the speed of the molecules again is increased until it becomes great enough to break the intermolecular bonds and a gas is formed.

- volume of gas is 1000x greater than liquid

- boiling temp is determined by the pressure above liquid, greater pressure = higher temp

CHAPTER 3 - STATICS

3.1: Forces

- A force is a push or a pull which one object exerts on another

- The effects of the applied force are called its components.

- Usually we make one horizontal in direction and the other vertical. They are called the horizontal and vertical components of a force

- Applying basic trigonometry gives us
Horizontal Component: Fx = F cos θ
Vertical Component: Fy = F sin θ

Measuring Forces

g=Weight
      Mass

- The SI unit of force is called the Newton (N) and is the force that produces an acceleration of 1 ms-2 when it acts on a mass of 1 kg.

-  The FPS unit of force is the Poundal (pdl), and is the force that produces an acceleration of 1 ft/s-2 when it acts on a mass of 1lb.

3.2: Vectors and Scalars

Quantities that only have a size or magnitude are called Scalars.
Quantities that have a direction as well as a size or magnitude are called Vectors.

Scalars                  Vectors

Mass                      Force

Time                       Velocity

Temperature           Acceleration

Distance                 Momentum

Speed                     Electrical Current

Energy                    Electrical Voltage

Work

Power

Pressure

3.2: Vectors and Scalars 

Force, may be represented by a straight line in which the length of the line is the magnitude and arrow represents the sense of direction

Concurrent means acting upon or through the same point.
Coplanar means contained in the same plane surface.

A single “total” force called the resultant replaces the original forces

Adding Vectors

- Tringle Law - If 2 sides of a triangle represent 2 vectors in sequence, then the third closing side of the triangle, in the opposite direction of the sequence, represents the resultant
- Parallelogram Law - If 2 adjacent sides of a parallelogram represent 2 vectors, then the diagonal of parallelogram through the common point represents the resultant
- Polygon Law - The polygon law is an extension of earlier 2 laws of vector addition. It is, in fact, successive application of the triangle law to more than 2 vectors.

3.3: Turning Forces

Torque or Moment is the turning effect of a force. It depends on the magnitude of the force and a distance called the lever arm. This is the perpendicular distance from the force to the axis of rotation.
                                                 Torque (T) = Fd or Moment (M) = Fd
 

Static objects can still be subject to torque i.e. wing root

  Term                                                                  Definition
Fulcrum               The fulcrum is the point or axis about which the rotation takes place.

Leverage /           Perpendicular distance from the line of action of the force to the fulcrum.
Moment arm

Resulting             The resulting moment is the difference in magnitude between the total 
Moment               clockwise moments and the total anti-clockwise moments about the fulcrum.

clockwise shown with (+) counter clockwise (-)

The principle or law of moments states that:
"When a body is in equilibrium under the action of a number of forces, the sum of the clockwise moments about any point is equal to the sum of the anti-clockwise moments about that point."

Lever 

A small force at larger distance can overcome larger force over smaller disance  

3.4 Couples

DEFINITION - A couple consists of 2 parallel forces that are equal in magnitude, opposite in sense and do not share a line of action

Produces only rotation

resultant force = zero

example - steering wheel : When they apply a force that is equal in magnitude yet opposite in direction the wheel rotates

 A pure couple always consists of 2 forces equal in magnitude.

3.5: Centre of Gravity and Centre of Mass

Although the mass of a body is spread throughout all the space it occupies, there is a single point though which it may be balanced, This point is called the centre of mass

In a uniform gravitational field the centre of mass is the same point as the centre of gravity

The centre of gravity, G, of a body is defined as the point through which the whole weight acts for any orientation of the body.

A lamina is the name given to a thin plate or sheet of material of uniform thickness and density.

The centre of gravity of an irregular lamina can be found by: Suspend the lamina so that it swings freely about a point of suspension P1. From P1 a plumb line to hang freely above the surface of the lamina and mark the line on the surface. Suspend the lamina from another point P2 (could be 90 degrees), and repeat the procedure.

static equilibrium There are 2 conditions for this: sum of the external forces is zero; and the sum of the moments of the external forces, taken about any point, is zero. I.e Lorry over a bridge, Weight = Support 

3.6: Stress

External forces - they act on the structure and produce internal forces inside the components that make up the structure.

stress σ = force
                  area
The units of stress are Pa (pascal). 1 Pa = 1 Nm-2 (newtons per square metre)

Tensile Stress - The load is stretching the component so that it becomes longer and thinner. The area under tensile stress is perpendicular to the line of action of the forces
Compressive Stress - The load is squeezing the component so that it becomes shorter and thicker - direct and perpendicular too

Shear Stress -In shear, the load tends to cause layers in the component to slide over one another. The forces and area under stress are in the same direction.

Torsion - Torsion is a rotational stress, I.e. shafts are under a torsional stress 

3.6: Strain 

One characteristic of matter is that it tends to be elastic, meaning it can be forced out of shape when a force is applied and then return to its original shape when the force is removed.

When an object becomes distorted by an applied force, the object is said to be strained

Return = elastic / distorted = strained 

strain ε = change in length   (L2-L1)
                   original length         (L1)     

expressed as a %

Aircraft wings in strain would bend upwards - upper surface would be under compression and lower in tension 

3.6: Elasticity

Plastically - A component loaded beyond its elastic limit, there is a permanent deformation 

The greater the load the more a component deforms, and very often the strain is directly proportional to the stress. The property of a material that is used to quantify this behaviour is the modulus of elasticity (also called Young’s modulus)

modulus of elasticity E = stress
                                         strain 

The modulus of elasticity is a measure of the “stiffness” of a material

3.7: Pressure and Buoyancy in Liquids

Density 

Density = Mass
                Volume

Relative density

relative density = density of substance
                        1000

An old-fashioned name for relative density is “specific gravity”

Hydrostatic Pressure

Hydrostatic pressure p = liquid density x depth x gravity 

Basic Hydraulics

- use liquid pressure to transfer energy

• Liquids are incompressible
• Liquid pressure acts equally in all directions
• Changes in pressure are transmitted instantly throughout the liquid.

At the pump piston, P = Effort ÷ Piston Area (A1).
At the motor piston, P = Load ÷ Piston Area (A2).
So Effort ÷ A1 = Load ÷ A2. Therefore Effort ÷ Load = A1 ÷ A2.

If A1 is smaller than A2 then a small effort can raise a large load. This ratio gives the Mechanical Advantage (MA) of the system. 

- Master and Slave pistons 

Measuring Pressure

Devices that measure pressure are called manometers

A liquid column manometer is a U-shaped tube filled with a liquid that is used to measure the pressure difference of gases on either side of it.

pressure difference = ρgh.

If atmospheric pressure is greater than pressure from a test fluid then the fluid will sit lower in the 'U' tube, vice versa for if test fluid exerts greater pressure 

Measuring Pressure

Measuring Atmospheric Pressure

The instrument used to measure atmospheric pressure is called a barometer.

A dish is filled with mercury, as is a long, narrow, closed tube. The tube is turned upside down without letting any air in and then placed in the dish. Air molecules in the atmosphere push down on the surface of the mercury and support a column of it in the tube. The greater the atmospheric pressure, the higher the column of mercury.

On a normal day at sea level atmospheric pressure supports 760 millimetres of mercury (760 mmHg). 1 atmosphere = 1000 hPa = 1 bar = 1000 millibar = 760 mmHg.

altitude ^ = pressure v 

Measuring Pressure

DEFINITIONS

Absolute Pressure
Pressure may be measured from zero pressure i.e. from a vacuum. This is called absolute pressure.

Gauge Pressure
Pressure may be measured from atmospheric pressure, i.e. is measured as a value above atmospheric pressure. This is called gauge pressure. Gauge pressure is used to measure engine oil pressure, hydraulic pressure and other operational pressures built up by pumps. 

Differential Pressure
This is an extension to the idea of gauge pressure. Only the difference between 2 pressures is required. 

Absolute pressure = gauge pressure + atmospheric pressure

Buoyancy

Archimedes’ principle
“When a body is completely or partially immersed in a fluid it experiences an up thrust, or apparent loss in weight, which is equal to the weight of fluid displaced.”

This upwards force is called buoyancy.

When a block is put in the tank it becomes buoyant and some of the water is displaced. Hydrostatic pressure acts on the bottom of the block, providing an up thrust on it. 

Pressure on the top surface of block:
Ptop= ρg htop.

Pressure on the bottom surface:
Pbot = ρg hbot.

Chapter 4: Kinetics

4.1: Linear Motion

A SCALAR quantity is completely defined by stating its magnitude. A VECTOR quantity is completely defined by stating its magnitude and direction.

Speed = Distance / Time 
Velocity = Displacement / Time

acceleration = change in velocity
                       Time

Velocity-time graphs 
Velocity-time graphs can tell us a lot about the motion of an object:
- The gradient of a velocity-time graph gives the acceleration of the object at that time.
- All the velocity-time graphs will have straight lines, with no curves. - uniform acceleration
- The area under a velocity-time graph gives the displacement in that time

4.2: Equations of Motion

u = initial velocity (ms-1 )
v = final velocity (ms-1 )
t = time interval (s)
a = acceleration (ms-2 )
s = displacement (m)

a = v-u
      t

v = u + at

v^2 = u^2 + 2as 

s= ut + 0.5at^2

s=(v+u)t
    2

4.3 Projectile Motion

- A projectile has a combination of horizontal and vertical velocity components

- A projectile is an object upon which the only force acting is gravity

A projectile is any object that once projected continues in motion by its own inertia and is influenced only by the downward force of gravity.

Vertical Projection
In this type of motion, velocity is either vertically upwards or downwards.

Horizontal Projection
In these situations, the horizontal motion is constant velocity, whereas the vertical motion is constant acceleration.

4.4: Newton’s Laws

1 st Law: “If no unbalanced force acts on a mass it will either remain stationary, or move at constant speed in a straight line.” An object at rest will stay at rest, an object in motion will remain in motion

2 nd Law: “If an unbalanced forces acts on a mass it will accelerate in the direction of the unbalanced force. The acceleration is proportional to the unbalanced force and inversely proportional to the mass.” F=MA

3 rd Law: “Every action has an equal and opposite reaction.” or ‘‘whenever one body exerts a force on another, the second body exerts on the first a force of equal magnitude in the opposite direction’’

“Unbalanced force” is another name for a resultant

4.5: Velocity Ratio, Mechanical Advantage and Efficiency

Machines
A machine is a device which allows us to do work in a more convenient way. In a machine we apply a force (called the effort) to make something move (called the load).
A machine is a “force magnifier”. The ratio of the load to the effort is called the mechanical advantage of a machine:

mechanical advantage MA = load
                                                effort

The velocity ratio tells us how far the effort has to move in relation to the load:
velocity ratio VR = distance moved by effort
                              distance moved by load

No real machine is perfect, and in general we say that efficiency is given by:
efficiency = MA / VR 

4.6: Rotational Motion

(Angular) Velocity = angle travelled / time (Rads-1 )
=
Angle travelled = 2πN (Rads) / time

(2π = 360 degrees) + (Where N is the number of revolutions completed)

The Relationship between Angular and Linear Velocity
At any instant in time an object travelling in a circle has a linear velocity (v) that points in a direction that is at a tangent to the circle and perpendicular to the radius.

Linear Velocity (v) = angular velocity (ω) x radius of circle (r)

Centripetal Acceleration and Centripetal Force

A centrifugal force is the apparent outward force on a mass when it is rotated
- When an object moves in a circle at a constant speed its velocity is constantly changing. Its velocity is changing because its direction constantly is.

A centripetal force is the force that makes a mass follow a curved path
A centrifugal force is the reaction to a centripetal force. if there will be no centripetal force on a mass on a string being moved in a circle, the mass will fly off at a tangent to the circle

Moment of Inertia
The moment of inertia I of an object depends on the distribution of mass of the object. For example, a skater spinning with arms and legs out has a higher moment of inertia than with arms and legs close to the body
The moment of inertia of a body about an axis is a measure of the resistance of that body to rotation about the specified axis

I = ½mr^2

4.7: Periodic Motion

An oscillation (“vibration”) is a regular to-and-fro movement.

Frequency - The number of vibrations per second, and is measured in hertz (Hz).
Period - The time for one complete oscillation
Amplitude - The maximum displacement from the undisturbed position

The period, t, and the frequency, f, are linked by the equation:
t = 1/f

Pendulums
A pendulum is an example of a simple mechanical oscillation. The heavy mass at the end of the string (called the “bob”) is displaced through a small angle, theta. 

Vibration, Harmonics and Resonance

Natural frequency - If left to swing freely, the swing will always make the same number of oscillations in a certain time, and it depends on its geometry and the material it is made from. The natural frequency of an oscillator is the frequency at which it will vibrate freely after a single displacement

Forced System - The energy is added at the same frequency as the natural oscillations, A forced vibration is one in which an object is made to vibrate at the frequency of another oscillator or forcing agent

Resonance - All types of matter, regardless of whether it is a solid, liquid, or gas, have a natural frequency. If two pieces of matter have the same natural frequency, and one of them starts to vibrate, it can transfer its wave energy to the other one and cause it to vibrate. Resonance of an oscillator occurs when the forcing frequency equals the natural frequency. 

Vibration, Harmonics and Resonance

Mechanical resonance
Resonance in mechanical systems is very common, but engineers avoid it as best they can, as this can lead to stresses and damage.

Electrical Resonance
Resonance in electrical systems occurs in several systems including radio systems. A capacitor / inductor circuit is tuned to a particular station. When the circuit natural frequency matches that of the radio signal, resonance occurs and a strong signal is received.

Harmonics

- Objects don’t usually vibrate at one single frequency
- When a guitar string is plucked it vibrates at what is called its fundamental frequency - pitch
- Harmonics all have frequencies that are multiples of the fundamental frequency

- greater the frequency the smaller its amplitude

Chapter 5: Dynamics

5.1: Mass Force

There are 3 types of mass:
- Inertial mass is a measure of an object's resistance to changing its state of motion when a force is applied.

- Passive gravitational mass is a measure of the strength of an object's interaction with the gravitational field. Within the same gravitational field, an object with a smaller passive gravitational mass experiences a smaller force than an object with a larger passive gravitational mass.

- Active gravitational mass is a measure of the strength of the gravitational field due to a particular object. Gravitational field can be measured by allowing a small ‘test object’ to freely fall and measuring its free-fall acceleration.

5.2: Inertia, Work, Power and Energy

Work
- Work is done when a force moves an object through a displacement. Work done W = Fs
                                                (W - Work, F= Force, s = Displacement)

Potential Energy
- When an object is raised vertically, work is done against gravity and the object gains gravitational potential energy                (potential energy, EP = mgh)

Kinetic Energy
- A moving mass has kinetic energy:               kinetic energy, EK = ½mv^2
      kinetic energy is proportional to mass and the square of the velocity

The principle of conservation of energy
- “Energy can be neither created nor destroyed, but may be changed from one form into another.”

Power
- P = Work done / time taken       P=W/t

5.3: Momentum

The momentum before = the momentum after
momentum p = mv

- A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision

- An inelastic collision is one in where part of the kinetic energy is changed to some other form of energy in the collision. For example, in a head on collision between vehicles, typically quite large amount of kinetic energy are converted into heat, sound and work done to deform the shape of the vehicles

In both cases, momentum is conserved

5.4: Impulse

impulse = change in momentum = Force x time (Ns)
  Ft = m(v - u)

5.5: Gyroscopes

Gyroscopes consist of a symmetrical rotor spinning rapidly about its axis and free to rotate about one or more perpendicular axes

The two principal properties of a gyro are:
- Rigidity in inertial space (inertial space being a fixed spatial reference)
- Precession.

Rate Gyroscope - Used in Aircraft instruments

Definition of Terms The following fundamental mechanical definitions provide the basis of the laws of gyrodynamics:
- Momentum - Momentum is the product of mass and velocity (mv).
- Angular Velocity - Angular velocity is the rate of motion through an angle in degrees, radians, or revolutions per unit time.
- Angular Momentum - This is the product of moment of inertia and angular velocity.
- Moment of Inertia - The moment of inertia I, of a body about any axis is the sum of the products of the mass, m, of each element of the body and the square of r, its distance from the axis I = mr^2 .

5.5: Gyroscopes

Laws of Gyroscopes

1st Law - If a rotating body is so mounted as to be completely free to move about any axis through the centre of mass, then its spin axis remains fixed in inertial space however much the frame may be displaced.

2nd Law - If a constant torque is applied about an axis perpendicular to the spin axis of an unconstrained, symmetrical spinning body, then the spin axis will precess steadily about an axis mutually perpendicular to the spin axis and the torque axis. Precession ceases as soon as the torque is withdrawn, but if the torque application is continued, precession will continue until the direction of spin is the same as the direction of the applied torque

Direction of Precession
Direction of Precession can be be shown through the simple 'Rule of thumb" - If you curl the fingers of your right hand in the direction of that expected rotation, then your thumb will point perpendicular to the spin axis in the direction of the torque produced by gravity, precession is the force trying to turn the spin axis.

5.5: Gyroscopes

Precession

In addition to the apparent wander of the gyroscope, bearing friction and rotor unbalance will cause precession of the spin axis away from its correct position

Precession = F          = 1
                     SI             R

where:
R = rigidity
S = speed of the rotor
I = moment of inertia
F = external force

Gyroscopic Resistance
Created by internal couples in a precessing gyroscope.

5.5: Gyroscopes

Rigidity
Rigidity is the reluctance of the gyroscope to change the direction of its spin axis. The magnitude of rigidity is directly proportional to the speed of the rotor. The faster it spins the greater the rigidity it acquires. 

R= SI
      F

R = rigidity S = speed of the rotor I = moment of inertia F = external force

5.6: Friction

Friction is a force that occurs when two surfaces rub together. It resists the relative motion of the surfaces, and occurs because of their “rough” nature.

A graph of force versus time might look like an increase in static friction (No movement), it reaches limiting friction (where a mass reaches the point to move), the friction will decrease and level off horizontally into kinetic friction (friction during movement

Coefficient of static friction
The friction force is at a maximum.

Coefficient of static friction =  Friction Force
                                                  Normal reaction

5.6: Friction

Types of Friction

Static friction - occurs between two surfaces that are not moving past each other. The maximum size of friction force is called the limiting frictional force and occurs when one object is just about to move relative to the other - symbol u

Kinetic Friction - The coefficient of friction between moving surfaces - symbol u'

Rolling Friction - The name for friction between surfaces which are rolling past each other without slipping. i.e wheels down a slope - symbol u''

Coefficients of Friction
u’’<u ie rolling friction < kinetic friction < static friction. Also,u’ is approximately (0.75xu) for most surfaces.

Chapter 6: Fluid Dynamics

6.1: Properties of Fluids

A fluid is either a liquid or a gas; they have the ability to flow. 

6.2: Specific Gravity and Density

The mass density ρ of a substance is its mass per unit volume. We previously discussed density (and relative density)
                                                        Density = Mass / Volume

Specific weight w is the weight per unit volume.
                     Specific Weight = Weight / Volume       Specific Weight w = density x g

Specific gravity or Relative density s is the ratio of the weight of a substance to the weight of an equal volume of water at 4ºC.

SG = w for substance             density of subtance
             w for water                    density of water 

6.2: Hydrometers

Hydrometers

Hydrometers are floating instruments used to measure the density of liquids. A hydrometer has a long neck or stem with a density scale reading. A large bulb filled with air displaces the liquid and provides an up thrust to make the hydrometer float (Archimedes principle)

In a liquid of low density the hydrometer sinks further down the liquid, displacing a greater volume of liquid until the weight of liquid displaced equals its own. In a liquid of higher density the hydrometer floats higher up.

This means the density scale reads from top to bottom for increasing liquid density.

To increase the sensitivity of the hydrometer i.e. increase the gaps between the scale markings, a longer narrower stem may be used.

6.3: Viscosity and Fluid Resistance

The viscosity of a fluid is its resistance to flow.

When a fluid is flowing different layers in it have different velocities and shearing forces are set up between the layers, Water has a low viscosity, whereas oil generally has a much higher viscosity.

Liquid viscosity decreases with an increase in temperature.
Gases also have viscosity. It is much less than that of liquids and increases with an increase in temperature.

An ideal fluid is one that has zero viscosity i.e. zero resistance to flow; real fluids do have viscosity.

Co-efficient of Dynamic Viscosity μ is defined as the shear force per unit area required to drag one layer of fluid with unit velocity past another layer unit distance away.

Co-efficient of Kinematic viscosity ν is defined as the dynamic viscosity divided by the density of the fluid.                        v=μ/p            p=density of fluid 

6.4: Fluid Compressibility
Compressibility is the ability of a fluid to be compressed. Gases are compressible whereas liquids are not.
Laminar and Turbulent Flow
Laminar - Air molecules will be moving in the same direction as the general flow, flowing slowly over a flat or smoothly curved solid surface
Turbulent - The flow is no longer in smooth, stable layers. The air molecules follow complicated, irregular paths and there are many swirls and vortices. At any particular instant, an air molecule may be moving in any direction relative to the general flow
Air Resistance
Any object moving through a fluid experiences forces that resist its motion. The air resistance (or drag) on an aircraft arises because of two sets of forces: friction forces along the aircraft’s skin; and pressure forces that are perpendicular to the skin.
Air resistance is much greater in turbulent flow than it is in laminar flow, Three features of a body determine its air resistance, Shape, Frontal area and Smoothness.
Boundary layer
A boundary layer is a layer of air close to the surface of a moving object that is moving at less than the free-stream velocity, Further away from the surface the effects of skin friction are less, until at the edge of the boundary layer the velocity is the same as that of the undisturbed air.

6.5: Bernoulli’s Theorem

The theorem states, in effect, that as speed increases so pressure decreases and vice versa

It is on the principle of Bernoulli’s law that lift is produced on an aircraft wing. The wing aerofoil is designed to increase the velocity of airflow across the top surface thus decreasing the pressure on the top of the aerofoil. At the same time the velocity of air below the aerofoil is less, therefore the pressure is greater and lift is generated

A Venturi tube consists of a tube which narrows to a throat (reduced diameter). The airflow at the throat is increased while the pressure is decreased.
A venturi is a convergent-divergent duct. Its cross-sectional area falls from A to B (convergent) and then increases from B to C (divergent).

A venturi can be used to measure the flow rate of a fluid. The flow rate depends on the pressure differential between A and B, and so if manometers (or other pressure measuring instruments) are connected there the flow rate can be determined

Chapter 7: Thermodynamics

7.1: Heat and Temperature

Heat is a form of energy.
Temperature is the degree of “hotness” or “coldness”.

Absolute Zero = -273.15C

Kelvin - which uses absolute zero as its base point. Absolute zero = - 273.15C = 0 K.

The Celsius scale of temperature uses the freezing point of water (0C) and the boiling point of water at standard pressure (100C)
The Fahrenheit scale depicts the freezing point of water as 32F and the boiling point as 212F 

Approximate Calculations

Celsius to Fahrenheit = 2C+30                           Fahrenheit to Celsius = (F-32)
                                                                                                                    2
    

7.2: Measuring Temperature

Heat energy always flows from a hot object to a cold object - "2nd law of thermodynamics"

Thermometers are devices that measure temperature, There are various types of thermometer used for measuring temperature:
Gas Pressure Thermometer - The pressure of a fixed mass of gas in a fixed volume depends on its temperature. A pressure gauge could be calibrated to read temperature
Thermocouple - A temperature difference across a "hot" and "cold" junctions results in a small voltage which is measured on the voltmeter, 20 microvolts per degree Celsius.
Thermistor - The electrical conductivity of materials varies with temperature. higher T = lower R
Mercury-in-Glass Thermometer - The commonest type of thermometer is the mercury in a glass thermometer. Since the freezing point of mercury is about -39C, and the boiling point +357C, this thermometer is not used for temperatures much above 300C or below -30C
For temperatures below -39C, thermometers containing alcohol may be used

Thermocouple used in aircraft systems

7.3: Heat transfer

There are three modes of heat transfer:

Conduction - Heat is transferred through a material by the vibrations of its particles. Some materials are very good thermal conductors (for example silver and copper), while others are poor thermal conductors (asbestos, wood, ceramic). A material which is used to inhibit the flow of heat is called an insulator.

Convection - Convection currents arise in fluids. If a region in a fluid becomes warmer it expands. This makes it less dense than the neighbouring fluid so it rises through the body of the fluid. 
“Free” convection occurs when a fluid moves only because of the heating effect itself. “Forced” convection occurs when a fluid is driven by separate means such as a pump or fan

Radiation - Warm objects radiate infra-red radiation. Infra-red radiation is invisible and it is the only way for heat to travel through a vacuum. Thermal imaging cameras detect different wavelengths of radiation to make a visible image.

7.4: Heat Capacity, Specific Heat Capacity and Latent Heat
When a body is supplied with heat energy one of two things may happen:
1. The temperature of the body increases.
2. The state of the body changes from solid to liquid (“melting”) or from liquid to gas (“vaporisation”).

A graph to shows what happens to the temperature of a solid substance when it is heated at a constant rate
A to B: The temperature of the solid substance increases as heat energy is supplied to it. Eventually the melting point of the substance is reached.
B to C: Once the substance starts to melt the heat energy supplied to it changes it from a solid to a liquid. The bonds between the particles change. While this is happening the temperature of the substance doesn’t change.
C to D: When the substance is all in the liquid state, any more energy supplied to it again causes its temperature to rise. Eventually the liquid reaches its boiling point.
D to E: At the boiling point energy supplied to the liquid causes it to change state into a gas. Bonds between the liquid particles are broken. This happens at constant temperature.
E to F: Energy supplied to gas causes its temperature to rise

7.4:  Specific Heat Capacity

The property of a material that determines the rise in temperature is called the specific heat capacity. It is the amount of heat energy that is required to raise the temperature through 1 degree Celsius (or Kelvin).

Heat energy EH = mcΔT

where: EH = heat energy measured in joules (J)
m = mass measured in (kg)
c = specific heat capacity measured in (Jkg-1K-1 )
ΔT = change in temperature (T2-T1) measured in (oC or K)

The heat capacity of a body is the product of its mass and the specific heat capacity of its material. 

specific heat capacity of Water = 4200Jkg-1K-1

7.4:  Latent Heat

Latent Heat If a substance is at its melting point or boiling point, any further heat supplied to it will cause it to change state. This is called “latent heat” because in a sense it is hidden.

The specific latent heat of fusion of a substance is the amount of heat energy required to change 1 kg of the solid substance at its melting point into a liquid. The specific latent heat of vaporisation of a substance is the amount of heat energy required to change 1 kg of the liquid substance at its boiling point into a gas.

When a solid melts the bonds between its particles loosen but the particles stay close together. When a liquid vaporises the bonds are completely broken and the particles are (on average) much further apart.
This tells us that more energy is needed to change a liquid into a gas than change a solid into a liquid. The specific latent heat of vaporisation is much greater than the specific latent heat of fusion.

For water, the specific latent heat of: fusion = 333 kJkg-1 vaporisation = 2260 kJkg-1

7.5: Volumetric expansion

In general, solids liquids and gases expand when heated. The property of a material that quantifies this is called its coefficient of linear expansion

L2-L1=aL1(T2-T1)                                               A2-A1=BA1(T2-T1)                V2-V1=yV1(T2-T1)

L2 - final lenth                                                    A2 - Final Area                        V2 - Final volume
L1 - initial length                                                 A1 - Initial Area                       V1 - Initial Volume
a - coefficient of linear expansion                      B = 2a                                       y = 3a
T1 - inital Temp
T2 - Final Temp

Heat of Combustion
When a fuel is burned thermal energy is released. The amount of heat energy released when 1 kg of a fuel is burnt is given by its heat of combustion (or energy of combustion). 

7.6 Gas Laws

The first law of thermodynamics states that energy is conserved. In other words, energy cannot be created or destroyed, only changed from one form into another. 

A reversible process is an idealised process in which a system can be returned to its original state without leaving any trace within the system or its surroundings that the process has taken place. All real processes are irreversible.

The kinetic theory of gases relates the macroscopic properties of a gas (pressure, density, temperature etc.) to the microscopic behaviour of its particles (speed, mass, kinetic energy etc.).

Perfect gas
A “perfect” gas is one that behaves in an idealised way. For example, if a perfect gas is cooled at constant pressure, its volume is proportional to its absolute temperature.
For a fixed mass of perfect gas: pV=mRT 
p - Pressure, V - Volume, m - mass, R - Gas Constant (287 Jkg-1K-1 for air), T - Temperature

The General Gas Equation
The pressure, volume and temperature in a fixed mass of gas are related by the general gas equation:                                                    P1V1 = P2V2
                                                                     T1          T2

Constant Volume Process
The p-v diagram for a constant volume heating process is shown by a directly vertical line down `the y axis intersecting the Volume axis, this simplifies the equation to P1/T1=P2/T2 
Pressure Law 
Pressure law states "No work is done in a constant volume process"

Constant Pressure Process
The p-v diagram below is for a constant pressure process. This is also known as an isobaric process. The p-v diagram shows a horizontal line intesecting the pressure axis.
(Think Hyperbaric chamber to remember Isobaric = pressure)
Charles' Law 
“Work may be done in a constant pressure process”

Constant Temperature
If we pump up a bicycle’s tyre fairly vigorously we often feel the pump getting warm. However, if we do this very slowly the temperature stays more or less constant. Such a process is called an isothermal process.
The p-v graph shows a curve from higher up pressure on the Y axis curving down to a high volume on the X axis.

Boyle's Law
States that when the temperature of a given mass of confined gas is constant, the product of its pressure and volume is also constant

Adiabatic
In an adiabatic process, no heat is transferred between the working fluid and its surroundings.
The p-v graph of an adiabatic process is the reversal of isothermal which shows a curve from higher up volume on the X axis curving up to a high volume on the Y axis.

7.7: Heat Cycles

Engines, heat pumps and other thermodynamic machines invariably work in thermodynamic cycles. This means that the working fluid undergoes a series of property changes before returning to its original conditions, This is the Joule cycle, also known as the Brayton cycle.

7.8: Laws of Thermodynamics

Zeroth Law: If two systems are each in thermal equilibrium i.e. at the same temperature, with a third systems then they are in thermal equilibrium with each other. In other words there is no heat energy flow.

First Law: The first law is often called the Law of Conservation of Energy. This law suggests that energy can be transferred from one system to another; however it cannot be created nor destroyed. Therefore the total amount of energy available in the universe is constant.

Second Law: Heat can never pass spontaneously from a colder to a hotter body. As a result of this fact, natural processes that involve energy transfer must have one direction, and all natural processes are irreversible.

Third Law: This law states that if all thermal motion of molecules (kinetic energy) could be removed, a state called absolute zero would occur. Absolute zero results in temperature of 0 K or -273.15ºC.

Chapter 8: Optics

8.1: Nature of Light

Light is a transverse wave - It is a form of energy - electromagnetic radiation

speed of light is approximately 3 x 108 ms-1 or 186,000 miles/second

From the wave speed equation v = fh  = v-velocity f-frequency h-wavelength 

The Electromagnetic Spectrum
White light consists of a range of wavelengths. At one end of the spectrum is red light, which has a wavelength of about 700 nanometres (7 x 10-7 m), while at the other is violet light which has a wavelength of about 400 nanometres (4 x 10-7 m).

8.1 Real and Virtual Images

An image is said to be real if the rays entering the eye come from the image itself; an image is said to be virtual if the rays entering the eye only appear to come from the image.

Ray tracing - gives the position of the images by drawing one ray perpendicular to the lens, which must pass through the focal point, and a second ray that passes through the centre of the lens, which is not bent by the lens.

Virtual images are formed by diverging lenses or by placing an object inside the focal length of a converging lens. The ray-tracing exercise is repeated for the case of a virtual image.

Reflection - the energy in a wave is sent back from the barrier in a new direction. Light is reflected from a mirror; sound “bounces” off a wall to make an echo; an aircraft reflects a radar signal.

The law of reflection - tells us that the angle of incidence equals the angle of reflection.
The angles of incidence and reflection are measured from a line perpendicular to the mirror called the “normal”.

Refraction

A change in medium causes the properties of a wave to change, in particular its speed, it can also change the angle. waves travel slower in shallow water, waves will slow down from deep water to shallow. If the incident wave does not meet the boundary at a right angle, its direction will change.

Refractive index
Air                         1.0003
Water                        1.33
Glass                          1.5
Diamond                     2.5

Diffraction - When a wave meets a barrier it may be absorbed. If the barrier is not continuous, the waves will move past it, like water waves moving past a harbour wall, It turns out that the waves are able to move into part of the region that we would expect to be calm. This is called diffraction.
It turns out that waves of long wavelength diffract more than waves of short wavelength. A typical FM radio signal has a wavelength of a few metres, whereas a microwave signal (radar or mobile phone) has a wavelength of a few centimetres. The radio signal will diffract much more than the microwave signal and will be easier to receive in a hilly region.

Interference
Interference occurs when waves from two coherent sources act together. (Coherent sources have the same frequency and are in phase).
Constructive - amplify wave
Destructive - flatens amplitude 

8.3: Mirrors and Lenses

When we look in a mirror we see an image of our face. This image is: Virtual

Size
Images formed by spherical mirrors may be magnified (enlarged) or diminished (smaller)

Curved Mirrors
There are 3 types of curved mirror:
1. Cylindrical – part of the curved surface of a cylinder. Produces distorted images (too tall, too short etc.).
2. Spherical – part of a sphere. Used to produce a magnified image (dentist’s mirror), or a wide field of view (car rear view mirror).
3. Parabolic – a section through a cone, rotated. Used to focus rays coming from a distant object at a point (satellite dish) or produce a parallel beam from a point source of light (car headlamp).

8.3: Mirrors and Lenses

Lenses

Lenses refract light to produce images. Most optical instruments use at least one lens to form an image. There are 2 basic types of lens:
Convex Lens - A convex lens converges light rays: A convex lens brings light rays from a distant object to a focus (“focal point”), F. The distance from the lens to the focus is called the focal length, f. There is a focal point on either side of the lens. If the lens is symmetrical, the lens will have the same focal length on both sides.
Concave Lens - A concave lens diverges light rays: A concave lens spreads out light rays from a distant object. To someone looking through the lens, the rays appear to be coming from point F, the virtual focus. The focal length of the lens is shown as f on the diagram

Dispersion of Light
The speed of light is slower in various materials than it is in a vacuum or outer space, When the light passes into a material at an angle, the light beam is bent or refracted according to Snell's Law and the index of refraction of the material.  This spreading out of the beam of light is called dispersion.

Total Internal Reflection

Total internal reflection is an optical phenomenon that occurs when light is refracted (bent) at a medium boundary enough to send it backwards, effectively reflecting all of the light. The critical angle is the angle of incidence above which the total internal reflection occurs.

The angle of incidence needs to be shallower (closer to the boundary) than the critical angle, then the light will stop crossing the boundary altogether and instead totally reflect back internally. 

This can only occur where light travels from a medium with a higher refractive index to one with a lower refractive index.

The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when total internal reflection occurs. (The colour of the rays is to help distinguish the rays, and is not meant to indicate any colour dependence)

Snells law = Sin i 
                    Sin r

Optical Fibre

An optical fibre is essentially a very long and narrow strand of extremely transparent material, usually glass.
- sends on/off signal to transfer data
- several signals of which may be carried in the same fibre at the same time
- makes use of internal reflection

Single mode 
- They have a very narrow core (about 0.01 mm) and provide only one path for a light signal. Signals have very low attenuation in single-mode fibres, making them suitable for long distance communications.

multimode
- They are relatively wide (about 0.060 mm in diameter) and provide a number a number of different paths for a light signal to travel. Signal attenuation is much greater than in single-mode fibres and they are used over relatively short distances.

9.1: Wave Motion

A wave is a regular disturbance that carries energy outward from a source. Sound, light, radio signals and water waves are all examples of wave motion.

2 types of wave:

Transverse Wave
- In a transverse wave the disturbance is perpendicular to the motion of the wave.
- The period is the time taken for one complete wave to pass the point. The amplitude is the maximum displacement from the undisturbed position
- The wavelength is the distance between two successive peaks (or troughs)

Longitudinal Wave
- In a longitudinal wave the disturbance is in the same direction as the motion of the wave. In air, with no sound, the molecules are moving around randomly at high speed
- regions where the molecules are likely to be either close together (“compressions”) or far apart (“rarefactions”)

Velocity, Wavelength and Frequency

v = fh
Where: v = velocity (ms-1 ) f = frequency (Hz) h = wavelength (m)

The velocity of a wave depends on the medium it is passing through. For instance, water waves move faster in deep water than they do in shallow water, and light travels faster in air than it does in glass.

The frequency of a wave is the number of waves passing a point in one second.

Wave interference is the phenomenon which occurs when two waves meet while travelling along the same medium.

- Constructive interference - displacement which is greater than the displacement of the two interfering pulses
- Destructive interference - is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction

9.3 Production

Sound waves are generated by vibrating objects. They travel as longitudinal waves and require a medium to travel in (i.e. a solid, liquid or gas). The longitudinal sound waves are pressure waves with successive regions of high and low pressure. Our ears are sensitive to the fluctuations in pressure that occur as a sound wave passes

9.4 Intensity

The amount of energy which is transported past a given area of the medium per unit of time is known as the intensity of the sound wave: Intensity = Power        =    Energy   
                                                                                        Area             time x area

Reverberation
When many echoes merge into one prolonged sound the effect is called reverberation.

This can be a problem – too much reverberation causes sounds to become confused and indistinct. Too little reverberation means that the sound energy is absorbed very quickly. A good concert hall has just the right amount of reverberation. The sound reflecting and absorbing properties of a room are called its acoustics.

9.5 Pitch and Quality of Sound
Our perception of pitch (high or low notes) allows us to distinguish between different frequencies

People with good hearing can hear sounds in a range of 20 Hz to about 20 kHz. Elephants use infrasound (very low frequencies or subsonic) to communicate, and bats and dogs can hear sounds well beyond the human hearing range (ultrasound).

When an object vibrates it does so mainly at its fundamental frequency. However, other vibrations at harmonic frequencies also occur. These harmonics (at 2, 3, 4, 5 … times the fundamental frequency)

9.6: Doppler Effect
The speed of sound in a gas:
• Increases with an increase in density.
• Decreases with a reduction in temperature (in Kelvin)

Doppler Effect works on both light and sound objects. For instance, when a sound object moves towards you, the frequency of the sound waves increases, leading to a higher pitch. Conversely, if it moves away from you, the frequency of the sound waves decreases and the pitch comes down.