Physics Year 11

8/11/2019 Physics Year 11

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THE WORLD COMMUNICATES

INTRODUCTION

In transmitting information from source to receiver, energy is transformed from oneform into another.

When we use an ordinary fixed telephone, energy has been transformed fromsoundmechanicalelectrical then backelectricalmechanicalsound.

When we use a mobile phone, sound energy is converted to electromagneticenergy (microwaveshigh frequency radio waves) and is transferred from sourceto receiver via radio transmitters. The electromagnetic energy is then transformedback into sound energy by the receiver.

WAVE TYPES

A wave transports energy from one point in space to another. Waves do notmove matter.

Mechanical wavesare those that require a physical medium through which totravel eg sound waves, water waves, earthquake waves etc. Electromagneticwavesrequire no medium through which to travel and thus can travel through avacuum eg light, radio waves, gamma rays etc. In this topic we will study bothcategories of waves.

MECHANICAL WAVES

There are three types of mechanical waves: Transverse, Longitudinal (or Compression)and Torsional.

TRANSVERSE WAVES:

Transverse wavesare waves in which the particles of the medium through which the

waves are traveling vibrate at right angles to the direction of travel of the wave motion.

Eg a wave travelling on a rope, water waves on the surface of a lake, S-waves of anearthquake.


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LONGITUDINAL WAVES:

Longitudinal wavesare waves in which the particles of the medium vibrate

parallel to and anti-parallel to the direction of motion of the waves. Eg sound wavesand P-waves of an earthquake.

WAVE TERMINOLOGY

The y-axis = displacement, the distance of a

particle from its equilibrium position

The x-axis can represent either time or

distance from a specified point within the

medium. A displacement-time graph shows the

displacement of one particle of the medium astime goes by. A displacement-distance graph

shows the displacement of all particles of the

medium at one instant in time.

A= amplitude, the maximum displacement from equilibrium of any

particle

Crestand troughare the points of maximum displacement from equilibrium above

and below equilibrium position respectively.


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= wavelength, the distance between two consecutive identical points on the

wave eg between two crests or two troughs.

v= velocity, the speed with which the energy is being transferred in the direction of

motion.

period, T, which is the time in seconds for one complete wave to pass a given

point, or the time for any particle to make one complete vibration.

Frequency, f, which is the number of complete waves that pass a given point in

one second or the number of complete vibrations in one second undergone by

any particle due to the passing wave. Frequency has units of s-1or hertz.

Clearly, T and f are reciprocals of one another and so: T = 1 / f

Since a wave will advance a distance of one wavelength in a time of one period and

since velocity is defined as the displacement of a particle per unit time, we have:

Velocity, v = displacement/time = f . , since T = 1 / f.

So we have that: v = f . Units of v are m/s or

ms-1.

Consider the following representation of a continuous longitudinal wave:

Note that the term compression is used to denote any area where particles of the

medium have moved closer together than when they are at equilibrium. The termrarefactionrefers to any area where particles of the medium have moved further

apart.

Note that by definition the amplitude, A,of the longitudinal wave is the maximum

displacement from equilibrium of any of the particles. Likewise, the wavelengthis

the distance between any two consecutive, identical points on the wave, in this case

the centre to centre distance between two consecutive compressions. Clearly then,

the centres of compressions and rarefactions are equally spaced along the wave.


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SOUND WAVES

All sound waves are produced by the vibrationsof particles in a medium. For

instance, in order to speak we must exhale air over vibrating vocal cords in our

larynx. The vocal cords force the air particles to vibrate in the form of a longitudinal

wave and this wave moves from our throat, out through our mouth and strikes the

ear drum of the person to whom we are speaking. The eardrum is forced to vibrate

with the same frequency as the longitudinal wave and these vibrations are

interpreted by the brain as speech. The human ear can perceive vibrations with

frequencies between about 20 Hz and 20000 Hz.

All sound waves are longitudinal waves. As such, all sound waves require a medium

through which to travel. Whatever the medium, sound waves progress as a series of

compressions (high pressure regions) and rarefactions (low pressure regions)

produced by the original vibrating source. When a tuning fork is struck with a rubber

hammer, the prongs of the tuning fork initially move towards each other. This

produces a compression of the air molecules between the prongs and a

corresponding rarefaction outside the prongs. As the prongs move apart, a

rarefaction is produced between them and a compression outside them. As this

motion continues, the air molecules vibrate with the same frequency as the tuning

fork and transfer sound energy from the tuning fork to the listener via a series of

collisions. The air molecules themselves do not undergo any net movement but

vibrate about their equilibrium positions.

SOME SOUND TERMS:

The pitchof a sound (how high or low it is) depends on its frequency. The higher the

frequency, the higher the pitch. For a sound or note of specific frequency, like that

produced by a tuning fork, the pitch is the same as the frequency. However, for a

complex sound such as a chord played on a piano, the pitch is not so easily defined.


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It can no longer be taken as identical to the frequency of the sound, since the sound

contains several nearly equal amplitude waves of various frequencies.

The loudnessof a sound depends upon the amplitude of the wave that produces it.

The greater the amplitude, the louder the note, because more energy is used to

produce a larger amplitude.The term volumeis sometimes used instead of

loudness.

DRAWING LONGITUDINAL WAVES:

It is usually more difficult to draw a longitudinal wave than a transverse one. This is

because for a longitudinal wave, the particle displacements lie in the same direction

as the wave travels. So, it is often convenient to represent such a wave as a

transverse wave equivalent. This is accomplished by simply using a vertical axis to

represent the longitudinal displacements of the particles from equilibrium.Longitudinal displacements to the right are represented as vertical displacements

upwards. Longitudinal displacements to the left are represented as vertical

displacements downwards.

In the diagram that follows, a longitudinal wave and its transverse wave equivalent

are shown together. The numbers at the top indicate the longitudinal displacements

(in cm) of the particles from their indicated rest positions at an instant in time. Minus

means to the left, plus to the right. The numbers at the bottom indicate the

corresponding vertical displacements (in cm) used to produce the transverse wave

equivalent. Minus means down, plus means up. Note that the compressions and

rarefactions in a longitudinal wave are NOT analogous to the crests and

troughs in a transverse wave (inspite of the Syllabus stating otherwise).The

compression and rarefaction centres of the longitudinal wave occur at positions of

zero displacement of the particles and therefore correspond to the zero displacement

points of the transverse wave. The points on the longitudinal wave where the particle

displacement from equilibrium is maximum, correspond to the crests and troughs of

the transverse wave equivalent.


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REFLECTION OF SOUND:

When any wave strikes the boundary between the medium in which it is travelling

and a different medium, three phenomena occur. Wave is:

Transmittedacross the boundary into the new medium.

Reflectedinto the medium through which it has just come.

Absorbedby the boundary

The extent to which any of these happen depends on the nature of the wave, the

media and the boundary.

Reflectionoccurs when a wave incident on a boundary is forced to return into the

medium in which it was originally travelling. In the diagram below an incident sound

wave strikes the boundary surface at X and is reflected along the line shown. Note

the use of rays, lines with arrows, to show the direction of travel of the waves.

Laws of Reflectionand apply to both longitudinal and transverse waves. Note that a

wave incident on the boundary surface with an angle of incidence of zero degrees (i= 0o) will be reflected back along the same line.


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1.The incident ray, normal and reflected ray are in the same plane; and

2.The angle of incidence, i, is equal to the angle of reflection, r.

When a sound wave is reflected back to its source, it is known as an echo.

Echoes are used in a wide variety of applications. Sonar (SOund Navigation And

Ranging) is a method of finding the depth of water or the size and shape of objects

under the water by sending out ultrasonic(> 20000Hz) pulses and measuring the

time of travel and angle of return of the echoes. Ultrasound is used in medicine to

produce images of internal body organs and babies in the womb and in industry to

detect flaws in metal.

THE PRINCIPLE OF SUPERPOSITION FOR SOUND WAVES

When two or more sound waves travel through the same medium at the same timethey produce effects on each other. This is called interference.

The Principle of Superpositionstates that when waves interfere, the totaldisplacement of the medium at any point is the algebraic sum of the individualdisplacements at that point. Note that in all the graphs that follow in this section,the horizontal axis represents timeand the vertical axis represents displacementof particles of the medium from their equilibrium positions.


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The two interfering waves travelling in the same direction have been drawn to a

different scale than the resultant wave, shown below. This complex waveform

represents a beata periodic fluctuation in sound intensity or loudness. The graph

clearly shows a gradual increase in loudness up to a maximum followed by a gradual

decrease to zero. The pattern then repeats. The audible beat frequency is thedifference between the frequencies of the interfering waves.

Fb= f2f1

THE ELECTROMAGNETIC SPECTRUM

You will recall that the two basic categories of waves are mechanical andelectromagnetic. Let us say a little about the latter. Electromagnetic radiationconsists of waves of energy that are caused by the acceleration of chargedparticles. Electromagnetic waves(or radiation)consist of electric and magneticfields vibrating transversely and sinusoidally at right angles to each other and to thedirection of travel of the waves.

EM waves require no medium through which to travel and thus can travelthrough a vacuum. In free space all EM waves move with the same speed 3 x108ms-1.

The wide range of wavelengths (and corresponding frequencies) over

which EM waves exist in nature is called the electromagnetic spectrum.This spectrum is as follows:


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The cut-off wavelengths or frequencies for each of the different types of EM radiation are

not precise. There is some overlap. Some types of EM radiation can be further broken

down into sub-types. The radio wave band of the spectrum contains the AM radiocommunications band at its higher wavelength end, followed by the TV band and thenthe radar and microwave bands at the lower wavelength end. The very narrow visiblelight band contains all the visible colours: red, orange, yellow, green, blue, indigo andviolet, in order from higher to lower wavelength. The visible light band occupies theposition between about 780nm and 380nm wavelength.

USES OF EM RADIATION AND METHODS OF DETECTION

EM radiation has many effects and uses in everyday life. As mentioned above, the

radio band is used extensively for communications of all kinds. The Ultra-High

Frequency (UHF) band, ranging from 300 megahertz (MHz) to 3,000 MHz is used

mainly for communication with guided missiles, in aircraft navigation, radar, and in

the transmission of television. FM radio stations use the Very High Frequency (VHF)

band from 30 MHz to 300 MHz. Short wave radiouses the High Frequency (HF)

band from 3 MHz to 30 MHz because waves in this band are easilyreflected by

the Kennelly-Heaviside layer (the E-layer) of the ionosphere, allowing very long

distance communication by short wave radio.AM radio broadcasts use the

Medium, Low and Very Low Frequency (MF, LF, VLF) bands from 3000 kHz down to

3 kHz. The ionosphere also reflects these waves. Note that the exact allocation of

frequency bands varies from country to country and is usually controlled bygovernment authorities.

Radio waves can be detected by the combination of (i) an aerial for receiving theelectromagnetic waves and converting them into electrical oscillations and (ii) diodes inappropriately tuned electronic circuits in the receiver that produce an audio-frequencysignal.

Microwaves, which occupy the very top of the radio wave band from 3GHz up to300 GHz, can pass through the ionosphere and are used in radar, spacecommunication such as with satellites, radio and television, meteorology,

microwave landing system (MLS) for aircraft, distance measuring, materialsresearch and even ordinary old cooking.Microwaves can be detected using a


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waveguide. This is a hollow conducting tube containing a dielectric (insulator) andis used to guide UHF EM waves along its length by reflection off the internal walls.A cavity resonator may be added to collect the energy.

Infrared radiation is heat radiation and is used in guidance systems of missiles, for

linking computers in networks, as a diagnostic tool in medicine (thermography), inremote sensing aerial and satellite IR photography to search for minerals ormonitor crops, in night-vision goggles, in cooking, heating, drying and so on. IR can

be detected by a thermopile or a photo transistor.

Visible light is the means by which we view the world, mainly by reflection. It is also

used in communication to transport huge volumes of information over very largedistances by internal reflection of light in optical fibres. Light waves have highfrequencies and the information-carrying capacity of a signal increases with frequency,making light perfect for the job. Light is detected by our eyes, by photo cells, camerasand light sensitive diodes.

Ultraviolet radiation is largely responsible for damage to skin and eyes exposed tosunlight for too long. It is used in the treatment of skin complaints, for killingbacteria, for fluorescent lighting, in burglar alarms, automatic door openers andcounters and a host of other applications. UV radiation can be detected byphotographic film, photovoltaic cells and by the fluorescence it causes in ZnS andother salts.

X rays are used in medicine both to supply images of internal body structures andto destroy tumours, in industry for detecting cracks in metal and in researchlaboratories for determining crystal structure by diffraction. X rays can be detectedby photographic plates and film, ionization of gases and by the photoelectric effect,

where the X rays knock electrons out of a metal surface.

Gamma rays (-rays) can be used to destroy cancerous tumours, to detect flaws in

metals and to sterilize equipment. -rays can be detected by Geiger-Muller tubesand photographic plates and film.

ENERGY CONSIDERATIONS

The energy carried by an EM wave is related to its frequency. An EM wave offrequency f, has an energy E, given by Plancks Law: E = hf, where h = Plancksconstant (6.63 x 10-34Js). (As an aside, this law forms the basis of Quantum

Theory.) A quick look at the EM spectrum diagram shows that -rays (high

frequency) are the most energetic EM radiation and that radio waves (lowfrequency) are the least energetic.

Another frequency related characteristic of EM radiation is its penetration powerthrough the Earths atmosphere. EM radiation of different frequencies isscattered, reflected and absorbed by different amounts in the atmosphere.Ofthe EM radiation that falls on Earth from space, only the visible and radio bandsmake it all the way to the ground without much attenuation taking place onthe way down.Some low frequency ultraviolet radiation and some regions in theinfrared are able to traverse the atmosphere but other frequencies of EM radiationare completely blocked. For all intents and purposes most of the UV and all of

the X-ray and gamma-ray wavebands of the EM spectrum are effectivelyfiltered out by the atmosphere well before they reach the ground.


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It is useful to know how the intensity of EM radiation varies with distance from thesource. Intensityis defined as the rate of energy transfer per unit area normal tothe direction of travel of the wave at any given point. It can be shownexperimentally, that the intensity I, of light falling on a surface varies inversely withthe square of the distance d, between the source and the surface. That is, if the

distance between the source and the surface doubles, the illuminance (the intensityof illumination on the surface) decreases by a factor of 4. This relationship is calledthe inverse square lawand applies only where the distance is large comparedwith the size of the source.

For example, if a surface receives 1 lux of light at a distance of 2 metres from a source

and the surface is then moved to be 4 metres from the source, that surface will thenreceive (1/2)-squared, or 1/4, lux of light.

It can be further shown that this inverse square law applies to all EM radiation, notjust to light. Therefore, in general, for EM radiation:

I

1/d2

WAVE MODULATION

Modulation is the process of impressing one wave system upon another of higher

frequency. Audio-frequency (AF) waves such as speech and music from a tape ormicrophone must be combined with radio-frequency (RF) carrier wavesin order to betransmitted over the radio. Either the frequency(rate of oscillation) or the amplitude(height) of the carrier waves may be modified in a process called modulation. The AF

waves enter the modulator and interact with the carrier to determine either the

amplitude of the carrier wave (amplitude modulation AM) or the frequency of thecarrier wave (frequency modulation FM). The modulated carrier wave can then be

transmitted to its destination. Once it is received, the modulated carrier wave is fed intoa decoding device or de-modulator that extracts the original AF wave from it.

Let us examine frequency modulation as an example. In this type of modulation thefrequencyof the carrier waveis varied above and below its unmodulated value by anamount that is proportional to the amplitude of the modulating signal and at a frequency

equal to that of the modulating signal. The amplitude of the carrier wave remainsconstant.

where Em= amplitude of the carrier wave, F = frequency of the unmodulated carrier

wave, F = the peak variation of the carrier wave frequency away from the frequency F,caused by the modulation, f = frequency of the modulating signal. Note that thisexample is simply meant to emphasize that there is a clearly defined mathematical

process behind signal modulation. You do not have to remember or even be able to usesuch equations in this course. An example of frequency modulation is shown below. Thewaveforms are not drawn to scale.


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Compared with amplitude modulation, frequency modulation has several advantages.The FM signal is not susceptible to electrical interference, unlike that for AM, and aproperly tuned receiving-set can take advantage of its larger frequency range anddynamic range to reproduce high-fidelity sound. Also, FM signals are broadcast in theVHF short wave band and such waves are not reflected by the Earths ionosphere. This

means that FM signals can only travel as far as the horizon, which has the advantage ofreducing interference, and coverage is therefore more stable than with AM.

The same modulation processes outlined above are used with microwaves and visiblelight to transmit information from one place to another. Narrow-band frequencymodulation is the most common mode of transmission for the microwave signals used

with mobile phones. Each call is assigned a carrier wave unique to the transmitter fromwhich it is sent. Frequency-modulated radar can determine the distance to a moving orstationary object.

Optical glass fibres are rapidly becoming common features of communications systemsaround the world. Visible light is used as the carrier of information in optical fibres. Light

can be amplitude or frequency modulated and then transmitted over huge distances withlittle loss in intensity. It should be noted however, that analoguesystems such as AM orFM, where the signal consists of a continuously changing pattern, are notthe primary

transmission modes in fibre optics systems. Despite the huge bandwidth available, it isalmost impossible to handle large numbers of channels (conversations) with acceptably


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low levels of distortion. A digital system, in which information is transmitted as a seriesof on-off pulses (pulse modulation), is used for high volume transmission of informationthrough optical fibers.

Just as an aside, it is interesting to ask why we need carrier waves at all? In radiotransmission, you could theoretically transmit radio signals at audio frequencies.However, because the wavelength of electromagnetic waves at audio-like frequencies ishuge and the frequency of a radio transmitter dictates the size of the antenna and the

power requirement, you would need a very big antenna and a very big power supply todo this. So, we've learned to transmit at higher "carrier" frequencies, modulating eitherthe amplitude or frequency of the carrier signal with our audio and subtracting thecarrier at the receiver end. (Basically, for an antenna, the lower the frequency to be

transmitted or received, the larger the physical size of the antenna. For example, a VHFhalf-wave dipole will be about three times the size of a UHF dipole.)

BANDWIDTH LIMITATIONS IN THE EM SPECTRUM

As we have seen, a large portion of the EM spectrum is used for communicationpurposes. However, since each particular type of communication medium, AM radio, FMradio, TV and so on, requires a certain minimum range of frequencies to ensuresuccessful transmission, an obvious problemarises. The EM spectrum used forcommunication purposes has a finite range.

The technical name for the range of frequencies that an EM signal occupies on a giventransmission medium is bandwidth. So, for example, a typical VHF-FM radio broadcastsignal has a bandwidth of about 200 kHz (0.2 MHz), while a typical analogue television

broadcast video signal has a bandwidth of 6 MHz. In Australia VHF-FM radio stations areallocated a 200 kHz bandwidth between 88 and 108 MHz. So the available radio channelfrequencies are 88.1 MHz, 88.3 MHz and so on up to 107.9 MHz. Obviously there is a

limit to the number of channels available and therefore to the number of FMradio stations that can broadcast a signal.

The same problem exists for all forms of communication that make use of EM radiationtransmitted through the atmosphere or free space. A government authority strictlycontrols access to the available bandwidths in each particular band of the spectrum (AM,FM, TV, mobile phones, microwave, etc) and competition for bandwidth allocation is

intense. From time to time people or organizations that can no longer demonstrateefficient & effective use of their allocated bandwidth are not re-allocated that bandwidthwhen their license comes up for renewal.

Research scientists are constantly trying to expand the range of the EM spectrum that

can be used for communication purposes. For instance much work is being done atpresent on carrier frequencies in the millimetre wave region (near-infrared).

Just in passing, it should be stated that this bandwidth limitation does not apply to hard-wired systems such as digital cableand fibre opticsystems. Available bandwidth insuch systems can be expanded without limit by installing more cable.

REFLECTION AND REFRACTION OF EM WAVES

The laws of reflectionas stated in the section on reflection of sound, apply to EM

waves as well. They will not be re-stated here. The only further comment required


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is to stress that when EM waves reflect from a plane surface, they may suffer a phase change. Sound waves do not.

Two particles that move in step with each other on a wave, that is have the samedisplacement and move in the same direction at the same time, are said to be in

phase. If two particles A and B are simultaneously located at the top of crests onthe same wave, they are in phase. As A moves back down to equilibrium and thendown to a trough, so too does B.

On reflection from a plane surface EM waves undergo a 180oor phase

change,if they strike the plane surface from the side of lower optical density (eg

light travelling in air & reflecting off glass). That is, a crest striking the surface is

reflected as a trough. Likewise a trough becomes a crest. This does not happen with

sound waves. For instance, a compression striking a plane surface is reflected as a

compression.

Examples of the use of reflection of EM waves inthe transfer of informationare many. Reflection of short wave radio waves by the ionosphere and the internalreflection of light through optical fibres have already been mentioned. Anotherexample is that of Radar(RAdio Direction And Ranging) for locating distant objectsby the reflection of microwaves. Pulses or continuous waves of microwaves arebroadcast, reflect off a distant object and the reflections are picked up by areceiving aerial. The distance and direction to the object are given by the directionof the receiving aerial and the time between the transmission of the wave and thereception of its reflection. The transmitting and receiving aerials can be made torotate to scan an area. The reflected pulses are recorded by a cathode ray tubecircularly scanned in synchronization to produce an echo map of the scanned area.

Other examples of the application of reflectioninclude:

A plane mirrorusually consists of a coating of metallic silver at the back of aflat sheet of glass. Reflections from this surface produce images of objects infront of the mirror. These images are called virtual images, since the rays oflight reaching our eyes do not actually come from the point where we see theimage. See Diagram (a) below.

Parabolic reflectorsare parabolic concave mirrors that focus parallelbeams of light at a single point. They are used in solar furnaces, reflectingtelescopes, car headlights and many other applications. See Diagram (b)below.

Diverging mirrorsthese are convex mirrorsand cause parallel beams oflight to spread apart. The image is always upright and smaller than the object,which allows the observer to see a wide-angle view. They are used to helppeople see around corners in driveways and shops andas rear view mirrorson trucks and buses. See Diagram (c) below.


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Doubtless we have all seen examples of the light bendingproperties of water.

Recall the experiment where a ruler is placed in a beaker of water and appears tobend upwards. The end of the ruler in the water appears to be higher in the waterthan it actually is. The reason for this is that the light reflecting from the end of theruler bends down towards the water surface as it passes from water to air. When itenters our eyes, the light appears to have come from a position in the water abovethe actual position of the end of the ruler. This bending of light raysas they passfrom one medium to another is called refraction.

For the rest of this section we will use lightas an example of EM waves. Thevelocity of light in a medium depends on the optical densityof the medium. Thehigher the optical density, the lower the velocity of light. Water is more optically

dense than air and so the velocity of light in water is lower than its value in air. It isthis difference in the velocityof light in different media that causes the light tobend as it passes across the boundary between two media.

In the following diagram several wavefronts(lines of crests) of light are showntravelling towards the boundary between two media of different optical density.Their direction is shown by the ray(arrowed line) at right angles to the wavefront.The waves have a velocity v1in medium 1 and a velocity v2in medium 2. Note thatwe will assume that the density of medium 1 is less than that of medium 2 andtherefore that v1> v2. The waves strike the boundary at an angle of incidence i,measured as always from the normal to the boundary around to the incident

ray. As the waves move across into medium 2, they slow down and thereforetheir direction changes. As indicated by the ray, the waves bend towards the


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normaland are transmitted into medium 2 with an angle of refraction r, measured

from the normal to the refracted ray.

Notice also that because the velocity has decreased as the waves pass frommedium 1 to medium 2, so too has the wavelength. This happens because the

frequency of a wave remains the same as it passes across the boundarybetween two media. Therefore, from v = f , since vdecreases and fremains

constant, must decrease.

The relationship between the velocities of light in the two media and the angles ofincidence and refraction is given by Snells Law:

It can be shown that the ratio of the velocity of the wave in medium 1 to thevelocity of the wave in medium 2 is a constant. This constant is called the relativerefractive indexfor waves travelling from medium 1 into medium 2 and is ameasure of the amount of bending of the waves that occurs as the waves move

from medium 1 into medium 2.

Every material has a specific refractive index () value. This is called the absoluterefractive index of the materialand is defined as the index of refraction of lightgoing from a vacuum into the medium in question. A more complete statement ofSnells Lawcan then be written as:


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Where = the relative refractive index for waves moving from medium 1 into

medium 2, 1= the absolute refractive index of medium 1 and 2= the absoluterefractive index of medium 2.

VELOCITY CHANGES CAUSE WAVEFRONTS TO BEND

Let us outline how the change in velocity that a wavefront experiences as it passes

across the boundary between two media of different optical densities causes the

wavefront to change its direction of travel and therefore bend. Consider the following

diagram that shows a single plane wavefront striking the boundary between two

media at point W.

Wavefront WY strikes the boundary and moves into a medium in which its velocity is

reduced. From W, the wavefront travels to X in the same time as Y takes to reach

the boundary. Since WX < YZ, clearly WY cannot be parallel to XZ. The change in

velocity of the wavefront has caused the wavefront to bend.

TOTAL INTERNAL REFLECTION AND CRITICAL ANGLE

Clearly, if a ray of light travels from a slower (more dense) to a faster (less dense)

medium, as in the example used earlier of the ruler in the beaker of water, the rayof light bends away from the normal towards the boundary surface. As the angle ofincidence increases from zero, there comes a case where the angle of refraction is90o, ie the ray travels along the boundary between the two media. This angle ofincidence is called the critical angle. Any ray having an angle of incidence greaterthan the critical angle, is totally reflected back into medium 1. This phenomenon iscalled total internal reflectionand plays an important role in several areas ofphysics and particularly in communication technology such as the transmission oflight through optical fibres.

From Snells Law we can write:


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and therefore that:

Where ic= the critical angle and medium 2, the faster medium, is a vacuum or air.Note that for a vacuum is defined as 1, while for air is close enough to 1 formost purposes.

Total internal reflection can only occur for light passing from a more optically densemedium to a less optically dense one. Typical critical angles include 49ofor water,42ofor crown glass and 24ofor diamond.

One application of total internal reflectionis found in fibre optics. Good qualityglass of high refractive index is coated with a thin layer of glass of lower refractiveindex. Light is passed into the end of the thin fibre. Any ray of light striking the

boundary between the two glass media at an angle greater than the critical angle,will be totally internally reflected along the whole length of the fibre. Light cantherefore travel from one end of the fibre to the other without loss. See below.

DEVELOPMENTS IN COMMUNICATION TECHNOLOGY

Many types of communication data are stored or transmitted in digitalform:

Fibre optics communication dataphone calls, computer data

Mobile telephone calls

Sound and picture recordings on magnetic tape, Compact Discs (CDs) and

Digital Versatile Discs (DVDs)

Computer data itselfthe huge volume of data available on the internet,computerized records kept by businesses, banks, governments, local councils,the police and military and so on.

Digital TV signals & Digital Audio Broadcasting (DAB) signals - DAB combinestwo technologiesdigital sound recording & data compression.

Communications satellites utilise very small aperture terminals (VSATs) whichrelay digital data for a multitude of business services.

Holographic data - holograms can store large quantities of data by varying therecording angle relative to the photographic plate. To retrieve the data the

hologram must be illuminated with a laser beam at different angles.


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Smart weapons eg tomahawk missiles can be launched over 1000 km fromthe target and follow precise directional instructions to reach its target.

ELECTRICAL ENERGY IN THE HOME

INTRODUCTION:

Although electrical effects have been known since the time of the ancient Greeks at

least, the development of electricity as a source of usable power has reallyhappened only in the last 200 years or so.Luigi Galvani(1737-1798)was an Italian

anatomist who discovered animal electricity(about 1786). Galvani was

investigating the effects of electrostatic stimuli on muscle fibre in frogs, when he

discovered that he could make the muscle twitch by touching the nerve with various

metals without a source of electrostatic charge. He found that the best reaction was

obtained when two dissimilar metals were used. He attributed the effect to 'animal

electricity'. In other words, he believed that the electricity was produced by the

animal.

Alessandro Volta(1745-1827)was a French physicist who invented the voltaic pile(the first battery) and thus provided science with its earliest continuous electric

current source. Voltas invention (about 1800) demonstrated that animal electricity

could be produced using inanimate materials alone, thus ending a long dispute with

Galvani, who insisted that it was a special property of animal matter. Volta had

always suspected that the source of the electricity produced in Galvanis experiment

was the interaction of the two dissimilar metals, rather than the animal.

Over the last 200 years, society has become increasingly dependent on

electricity as a source of power.Consider for a moment the difference thatelectricity has made to the quality of life of people today compared to 200 years ago.

Think of how electricity is used today in lighting, heating or cooling, refrigeration,

food preparation, transport, communication, manufacture of goods and materials,

entertainment, data storage and manipulation, household cleaning tasks, medical

applications and building & construction industries to mention just a few areas.

Electricity is employed wherever possible as a medium of energy transfer and use

for several reasons: (1) It can be efficiently transported from generators to the point

of use through a network of wires. (2) It can be very efficiently converted into other

usable energy forms, such as heat, light, mechanical, and chemical energy. (3) It is
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easily controllable at the point of use, requiring a simple flick of a switch to turn an

electrical device on or off.

Indeed, the availability of large, inexpensive supplies of electricity is important to themaintenance and development of all modern countries. Without electricity, industry

would grind to a halt, communications would cease, and our food supply would beseriously affected. The easy availability of electricity allows us to enjoy our presentstandard of living.

ELECTROSTATICS

As early as the 7thCentury BC, the ancient Greeks were aware that amber, when

rubbed vigorously, could attract dust and cloth from a distance. Today, we say that

such objects are charged. For example, a plastic ruler when rubbed has the ability

to pick up tiny pieces of paper. Electrostatics is the study of stationary charge.

CHARGE

Experiments by William Gilbert (1544-1603), Benjamin Franklin (1706-1790) and

others suggested the following rules regarding charge:

There are only two kinds of chargecalled positive and negative. These were

originally called vitreous and resinous respectively, because of the materials

which produced each type of charge.

Like charges repel.

Unlike charges attract.

Charles Coulomb (1736-1806) discovered the following law governing the behaviour

of charges:

For two charges q1and q2, distant r apart, the force between them varies directly as

the product of the two charges and inversely as the square of the distance between

them.

Mathematically,

The SI unit of charge is the coulomb (C). One coulomb of charge is equal to the

charge on 6.25 x 1018electrons.

2

21.r

qqkF


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ELECTRIC FIELDS

A field in physics is a region of influence of some kind. If a stationary charge

experiences a force in a particular region of space we say that there is anelectric field present in that region.

The magnitude of the electric field strength at a particular point in space is defined asthe force per unit charge at that point.

E = F/q

where E = electric field strength, q= size of the charge and F = force experienced by

qat the point in question. Both E and F are vector quantities and thus, must be

specified in terms of size and direction.

The SI units of electric field strengthare NC-1.

The direction of the electric field at any point is defined as the direction in which a

positive test chargewould move if placed in the field at that point.

The relative strengths and directions of different electric fields may be represented

diagrammatically by using lines of force. The spacing of the lines of force indicates

the strength of the field. The closer the lines are together, the stronger the field. The

direction of the field at a given point is indicated by the direction of the tangent to the

lines of force at the point in question. Lines of force, also called field lines, are

always drawn as emanating from positive charges and as terminating at negative

charges.

The following are examples of the electric field around various objects.


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A dipoleconsists of a positive and negative charge separated by a short distance.

Note that in (c) the field is uniform between the plates but non-uniform towards the

edges.


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As shown in (d) above, the electric field inside a conductor under electrostatic

conditions is zero. Also note that charge tends to accumulate at narrow or sharpends of objects. You may like to think about why this would be expected and any

consequences that may follow from such a phenomenon.

Once you think you have an explanation have a look atExplanation of E-Field

Around A Pear-Shaped Conductor.

POTENTIAL DIFFERENCE

Consider a charge of + qcoulombs in a uniform electric field as shown below:

To move charge +qfrom A to B back against the field direction, we must do work.The amount of work, W, that we must do is found from:

where F = the forceapplied to move the charge & d = displacement moved by the

charge in the direction of the applied force. The SI unit of workis thejoule (J).

In the E field, the force, F, on the charge is given by

dFW .
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Therefore we have:

as the work done.

Since we have done work on qto move it from A to B, we can say that we have

increased its potential energy(ie its ability to do work for us).

Further, we can say that there is a difference in potentialbetween points A and B,

in the E field. In general, we can say that there is a potential differencebetween

any two points in an electric field, whenever we have to do work to move a charge

from one point to the other. By definition:

That is, the potential difference between A and B, VAB, equals the work done in

moving the charge from A to B, WAB, divided by the size of that charge, q. Since thework done is the change in potential energy of the charge, we can say that the

potential difference between two points is the change in potential energy per

unit charge moving from one point to the other.

Note that another term often used for potential difference is voltage. The SI unit of

potential difference is the volt (V). 1V = 1JC-1.

ELECTRODYNAMICS

Electrodynamics is the study of moving charges. A currentis defined to be a flow of

charge. By definition, the direction of a current is taken to be the direction in which

the positive charge flows. This is called a conventional current.

This direction was chosen because the early researchers in this field did not know

whether the moving charges in a current were positive or negative. Today we know

that it is the electronsthat actually carry the charge in a current, but for convenience

we still use conventional current direction as the direction of flow of a given current.

Mathematically, we define current as the rate at which charge flows(ie the amountof charge flowing per unit time):

qEF

qEdW

q

WV ABAB


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The SI unit of current is the ampere (A). 1A = 1Cs-1.

When current flows continually in one direction it is called a direct current (DC).

When a current consists of charges that periodically change direction, backwards

and forwards, it is called an alternating current (AC).

CONDUCTORS AND INSULATORS

Substances containing large numbers of electrons that can move from one atom to

another (free electrons) are called conductors, since they can be used to conduct astream of electrons from one point to another. At ordinary temperatures, silver is the

best conductor but it is too expensive for most uses. Copper is nearly as good a

conductor as silver and far less expensive.

No material used at ordinary temperatures is a perfect conductor. There is always

some opposition to the flow of electrons. This opposition results in the loss of

energyfrom the moving steam of electrons. This lost energy appears in the form of

heat, which warms the conductor. If too much energy is lost the rise in temperature

may melt or vaporize the conductor.

In many substances, including glass, most plastics, rubber and wood, the outer or

valence electrons are linked by chemical bonds to the corresponding electrons of

adjacent atoms. In these substances the electrons are not free to move. Since

electrons cannot move from atom to atom within these materials, they cannot

conduct a flow of electrons. These substances are called non-conductors or

insulators.

RESISTANCE OF CONDUCTORS

The opposition that conductors offer to the movement of electrons across them is

called the resistance of the conductor. Resistance is a property of a body due to the

arrangements of the atoms of the body. Every material has a certain ability to resist

the passage of an electric current through it. Thus, every material has a certain

resistance value.

The resistance of a conductor is found experimentally to depend on four

physical factors:

t

qI


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Type of materialdifferent materials can have different atomic arrangements

(different geometrical arrangements, different spacing between the atoms,

different sized atoms etc). Silver, copper and aluminiumare all metallic

conductors used to conduct electricity in various applications. If all other factors

are equal the three metals still have different resistance values because of theirslightly different structures on an atomic scale.

Length of conductorthe longer a conductor, the higher the resistance

(resistance length).

Cross-sectional area of conductorthe larger the cross-sectional area, A, of a

conductor, the smaller the resistance (R 1/A)

TemperatureTemperature effects on conductors are quite complex. In general,

the metals used as conductors suffer an increase in resistance as their

temperature increases. A formula exists which allows the resistance values of

conductors to be determined for temperatures other than the reference

temperature of 20oC. This formula is beyond the scope of the current syllabus.

OHMS LAW

Consider a current, I, flowing through a metal conductor, the potential difference

across its ends being V.

In 1826 George Ohmfound that for a given conductor at constant temperature, the

ratio of the potential difference across its ends to the steady current flowingthrough it was a constant.This constant is called the resistance of the conductor.

This relationship is now called Ohms Law.

I

VR


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The SI unit of resistanceis the ohm (). A conductor is said to have a resistance of

one ohm if when the potential difference across its ends is one volt, the current

flowing through it is one ampere. It is worth noting that Ohms Law does not apply to

all conductors. Those conductors obeying Ohms Law are called ohmic conductors.

A conductor may obey Ohms Law over a particular temperature range and be non-ohmic outside that range.

ELECTRIC CIRCUIT DIAGRAMS


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COMBINATIONS OF RESISTORS

(i) RESISTORS IN SERIES:

Resistors joined end to end, so that the current only has one path along which it may

travel, are said to be connected in series. For the circuit segment shown below the

potential difference between points A and B is V.

Clearly, the current through each resistor is the same. Also, the total potential differenceacross the segment is equal to the sum of the potential differences across each resistor

(Kirchhoffs Voltage Law). Therefore, the total resistance, R, of the segment is foundfrom:

IR = IR1+ IR2+ IR3

IR = I.(R1+ R2+ R3)

R = R1+ R2+ R3

Thus, the effective resistance of a number of resistors in series is equal to thesum of the resistances of the individual resistors.

(ii) RESISTORS IN PARALLEL:

Resistors in parallelprovide two or more different paths by which the current can

travel through the circuit. In the following diagram the total current, I, splits into three

components I1, I2and I3, such that I = I1+ I2+ I3(Kirchhoffs Current Law).


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The ends of each resistor are connected to the same points, A and B, in the circuit. It

follows that the potential difference across each resistor is the same and in each case isequal to V.

Since I = I1+ I2+ I3, we can write (from Ohms Law):

Thus, the reciprocal of the effective resistance of a number of resistors inparallel is equal to the sum of the reciprocals of each individual resistance.

MEASURING CURRENT & VOLTAGE IN CIRCUITS

An ammeteris used to measure the currentflowing in an electrical circuit or in part ofa circuit. The ammeter is placed in seriesin a circuit to enable it to sample thecurrent that it is to measure. The ammeteris designed so that it has a very lowresistance, so that it does not alter the current flowing in the circuit.

A voltmeteris used to measure the potential differenceacross an electrical circuit

or across elements in a circuit. The voltmeter is placed in parallelwith an element

to enable it to measure the difference in potential between one end of the element

and the other. The voltmeteris designed with a very high resistanceto ensure that

it does not change the current in the element across which it is connected. If it

321 R

V

R

V

R

V

R

V

321

1111

RRRR


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changed the current in the element, it would have changed the voltage across the

element, which is what it was trying to measure.

THE WORK DONE BY A CURRENT

In crossing a conductor, work must be done by the electrons to overcome the

resistance of the conductor. The energy expended by the electrons is transformed

into heat. Thus, a conductor gets hot when current passes through it.

Consider a current of I ampere flowing through a conductor of resistance R ohm,

with a potential difference of V volt across its ends. Remember that the work done in

taking qcoulombs of charge between two points differing in potential by V volts is

given by:W = qV.

So, the energy expended, W = qV

= VIt, since I = q/t

= RI2t, since V = IR

= V2t/R, since I = V/R

Clearly, the total amount of energy used by an electrical component or circuitdepends on the length of time the current is flowing.

POWER IN ELECTRICAL CIRCUITS

Power is the rate at which energy is transformed from one form into another. Bydefinition, power is equal to the rate at which energy is expended.

Therefore

So clearly, the power dissipated by an electrical component is determined by multiplyingthe current through the component by the voltage across the component. The SI unit forpoweris the watt (W).

Or using Ohms Law to re-arrange the equation,

P = I

2

R or P = V

2

/R.

t

WP

VIP


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UNITS FOR ELECTRICITY CONSUMPTION

If you take a look at your parents electric power billyou will notice that the amount

of electrical energy consumedby your household is quoted in units of kWh

kilowatt-hours. This seems strange considering that the correct SI unit for energy isthejoule (J). Lets see why the kWh is used in place of the joule in this instance.

Consider an electric radiator. The amount of electrical energy used by a radiator can

be calculated as follows: Say the radiator has a power rating of 2000 watts. Using

the definition of power, that means the radiator will use 2000 joules of energy every

second. Thus, the total energy used in a time of tseconds will be 2000 tjoules,

since W = P t.

Lets assume we use the radiator for 90 days at an average of 4 hours use per day.

The amount of energy used will be:

Energy = 2000 x 4 x 60 x 60 x 90 = 2 592 000 000 joules.

Rather large isnt it? And remember this is just the energy used by one radiator for a

few hours each day for a quarter of the year. Imagine how large the total energy

usage for a whole household would be! Here we have the main reason as to why

the kilowatt-hour is used to measure electricity consumption rather than the

joule. The joule is a very small unit of energy, while the kilowatt-hour is a much

larger unit. Electrical energy authorities in Australia use the kWh as the unitfor energy simply because it produces more friendly, easily understood energy

consumption figures.

The kilowatt-hour is defined as the amount of energy used in one hour by an appliancerated at 1 kW (1000 W). The equivalent energy in joules is:

1 kWh = (1 x 103watts x 60 x 60 seconds) = 3.6 x 106J

Clearly, the kilowatt-hour is a much larger unit than the joule.

So, for our example of the radiator, the amount of energy used in kWh is:

Energy = 2 kilowatts x 360 hours = 720 kWh

I think most people would agree that this is a much more manageable figure than theroughly 2.6 billion joules calculated above.

MAGNETIC FIELDS

Electric currents produce magnetic fields.In fact, any moving charge has a

magnetic field associated with it. These magnetic fields are the same as those producedby ordinary bar magnets.


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We know that if we bring the north poles of two bar magnets close together, they repelone another. The same thing happens if we bring two south poles close together. If webring a north pole and a south pole close together, they attract one another. Insummary, like poles repel and unlike poles attract.

Just as we did in the case of electric fields, we can use lines of force to represent amagnetic field. The direction of the field is indicated by arrows on the lines. The strengthof the field is indicated by the separation of the lines.

By definition, a magnetic field is said to exist at a point if a compass needle (small bar

magnet) placed there experiences a force. The direction of the field is the directionof the force on the north pole of a compass needle placed at the point inquestion.

The shape of the magnetic field around a bar magnet is as shown below. Note that thefield lines emerge from the north pole and re-enter the magnet at the south pole. Themagnetic field lines themselves are continuous. They travel through the magnet. Notealso that no example of a single magnetic pole (monopole) existing on its own has everbeen found. (Some experimental physicists are still looking for magnetic monopoles certain theories on the nature of matter in the universe suggest that they could exist.)

GENERATION OF NATURAL MAGNETIC FIELDS

Bar magnets and other so-called permanent magnets are made out of a material called

ferromagnetic material. Iron, cobalt and nickel and the many alloys made from theseare all ferromagnetic. This implies that these substances are all attracted strongly by amagnet.

Ferromagnetic materials derive their magnetic properties from the spin motion of

electrons in atoms. The spinning of an electron makes it behave like a little currentloop, which has a magnetic field like that of a bar magnet, but on a much smaller scale.In most materials, the field from one electron cancels that from another, the net effectbeing no magnetic field. Ferromagnetic materials, however, consist of small regions (10-12

to 10-8

m3

volume) called magnetic domainsin which the spins of electrons line upwith each other to produce north and south poles. In the absence of an external


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magnetic field, these domainspoint in random directions. Inthe presence of a weakmagnetic field, the domainsline up in a particular directionand produce a net magnetic

effect.

If a magnetic field is requiredto keep the domains aligned,the magnet is called a

temporary magnet (eg soft iron). If the domains remain aligned, the magnet is called

a permanent magnet (eg hard steel). Note that even in permanent magnets, thedomains will eventually relax into a random orientation, once out of the influence of theweak external magnetic field. This relaxation may take many, many years.

MAGNETIC FIELDS CAUSED BY CURRENTS

Since every moving charge has a magnetic field associated with it, a current must also

have a magnetic field associated with it. In fact, for a current moving through a straightconductor, the magnetic fields of the component charges add together to producecircular magnetic field lines concentric about the conductor. See below.

The direction of the field is given by the Right Hand Grip Rule, which states: Hold thethumb of the right hand in the direction of the conventional current flow through the

conductor. The direction in which the fingers of the right hand naturally curl around theconductor, is the direction of the magnetic field. In the example below, the X in the

middle of the conductorindicates that the current is flowing down into the page,perpendicular to the page. The field is then clockwise, looking from above the page, bythe RH Grip Rule.

SOLENOIDS

A solenoidis simply a coil of insulated wire. If we pass a current through a solenoid, wefind that the solenoid has a magnetic field similar to that of a bar magnet. This

field can be intensified greatly by adding a soft iron coreinside the solenoid. Such an

arrangement is called an electromagnet.


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Another way of representing a solenoid is to draw it in cross section, as shown below.


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In the diagram above, the solenoid has been cut through vertically. The current is

coming upout of the page through the bottom row of conductors (indicated by the

dot in the middle of each conductor) and down into the page through the top row

of conductors. Using the RH Grip rule, the magnetic field direction is as shown.

We can understand why a solenoid has such a magnetic field by realizing that the

fields due to each turn of wire in the coil, simply add together to produce the typical

bar magnet field. Note that at points inside the solenoid and reasonably far from

the wires, the magnetic field is fairly uniform and parallel to the solenoid axis.

In the limiting case of adjacent, square, tightly packed wires, the solenoid becomes

essentially a cylindrical current sheet and the requirements of symmetry then make

the previous statement necessarily true.

APPLICATIONS OF MAGNETIC FIELDS IN HOUSEHOLD APPLIANCES

In the home various appliances make use of magnetic fields.The electric motors

that drive many labour saving items of electrical equipment rely on magnetic fields

for their operation. Entertainment devices, such as the TV and stereo require

magnetic fields for the operation of their speakers and various other components.

Cassette and video tapes use magnetic tape to store music only and pictures &

music respectively. Computers are now common household appliances used for

entertainment or work. They use magnetic means of storing and manipulating data

(eg hard disk drives). Some people use magnetic devices for controlling household

pests, such as cockroaches. The effectiveness of such devices is still a matter ofsome controversy. Some people use magnetic bracelets and amulets as a treatment

for all sorts of medical conditions eg arthritis. In the home, applications of magnetic

fields have resulted in improvements in the standard of living. They save time and

human energy; they provide entertainment and relaxation; and they may have other

uses in keeping houses free from insect pests and in treating various medical

conditions.

EXERCISE:Explain ONE application of magnetic fields in household

appliances.

HOUSEHOLD CIRCUITS

In Australian homes electrical energy is available from the mains supply at a voltage

of 240V AC*and a frequency of 50Hz. This electricity is supplied by the nearest

substation. Two wires carry the electricity into each house. One wire is called the

activeand carries one of the available three phasesof electricity supplied by the

substation. The other wire is called the neutral and is connected to the groundat

the substation. At the house there is a third wire, called the earth wire, which is also

connected to the ground, via a copper rod literally driven into the ground.


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The active wire is connected to the Main Switchat the Meter Box. The neutral wire andthe earth wire are connected to the neutral barin the Meter Box. From the MeterBox, a number of circuits branch out through the house for different purposes.The Meter Box contains switches to electrically isolate the whole house or parts of it, anelectricity meterthat measures the amount of electrical energy taken from the PowerStation, a mains fuse and a fuse (or circuit breaker) for each of the separate circuits in

the house. For houses with off-peak electric hot water systems, there is also a separateelectricity meter and timer to turn the water heater off and on.

The number of separate circuits branching out from the Meter Box depends on the

size and design of the home, including the number of electrical appliances to be

used. There is a limit to the amount of electrical energy that can be safely

carried by household circuits.If there are too many power points to wire into one

circuit, one or more other circuits will be used. There will always be at least two

different circuitsthe lighting and power circuits (to power points and fixed

appliances). These are kept separate since the lighting circuit usually requires a

smaller fuse than the power circuit.

* Notethat the 240V value of the mains supply is really an average value. It is really

the RMS (root mean square) voltage, which is the DC equivalent potential difference,

which would be required for a direct current to deliver the same energy to a circuit as

the changing AC supply. The actual voltage varies from 339 V to339V during each

AC cycle.

CONDUCTORS USED TO SUPPLY HOUSEHOLD ELECTRICITY

Copperis the most common conductor used to provide household electricity. It is

relatively cheap and a better conductor than all metals other than silver.

Consequently, copper is used in most household wiring. Silver is occasionally used

in some high quality electronic equipment due to its higher conductivity but it is not

used widely due to its high price. Gold is also used sometimes for electrical contacts

not because it is the best electrical conductor but because it is perhaps the least

chemically reactive of metals. Aluminiumis not as good a conductor as silver or

copper but it is used in the wires for overhead power line distribution because of its

light weight. The light weight allows the supporting structures to be placed further

apart and this reduces the overall cost.

ELECTRICAL SAFETY

As mentioned above, fuses and circuit breakersare common devices found in

household electrical circuits. Both devices are designed to protect the house wiring fromoverload and thereby prevent fires. For each separate household circuit, a fuse or circuitbreaker is placed in the meter box, in series between the external power supply and the

internal house wiring. In the case of a fuse, if too much current is drawn for too long atime, the fuse simply melts, thus breaking the circuit and protecting the wiring. In the

case of a circuit breaker, if too much current is drawn for too long, the circuit breaker


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opens, breaking the circuit and protecting the wiring. Circuit breakers are rapidlybecoming more common than fuses, as they can simply be reset after use.

All household electrical appliances are either earthedor double insulated(explainedbelow). Many appliances are earthed by connecting a conducting wire from the metalbody of the appliance to the earth wireof the household. As mentioned previously, thisearth wire is connected to the ground. If a fault within the appliance results in currentfrom the active wire leaking to the metal body of the appliance, two things will happen

almost simultaneously. Firstly, the current will flow safely to the ground via the earthwire. Secondly, due to the large increase in current flowing in this household circuit viathe short-circuit to ground, the fuse in this household circuit will blow or the circuitbreaker in this household circuit will open, as the case maybe.

Insulators play an important part in making household electrical appliances safe to use.

Individual electrical conducting wires are covered with insulating material such as PVC(polyvinyl chloride) to prevent leakage of current. Power cables that enclose sets ofinsulated wires connected to appliances are also made from PVC or similar material.Light switches and power point plates are made from hard plastics. Fuse wires are held

in place in household circuits using porcelain plugs. The internal insulation of electricalequipment may be made of mica or glass fibres with a plastic binder.

Many small electrical appliances are double insulatedwhich means that not only arethe wires inside insulated but also the body itself, being made of plastic, is an insulator.

Desk lamps, battery rechargers, electric drills, hair driers, electric mixers and electricrazors are just a few examples. Such appliances have only two wires connected to themand a plug with two pins, one for the active and one for the neutral. Any metal screws orpins used to hold parts together are totally enclosed in plastic tubes. There are no

electrically conductive parts that give a path for a current to the outside, even if a faultinside puts the body in direct contact with the active wire.

Having mentioned some of the safety features present in household electrical circuits

and appliances, it is appropriate to consider the dangers of electricity. Electricity

can kill a person in two ways:

It can cause the muscles of the heart and lungs (or other vital organs) to

malfunction; or

It can cause fatal burns.

Even a small electric current can seriously disrupt body cell functions. When the electriccurrent is 0.001A or higher, a person can feel the sensation of shock. At currents tentimes larger, 0.01A, a person is unable to release the electric wire held in his/her handbecause the current causes his/her muscles to contract violently. Currents larger than

0.02A paralyze the respiratory muscles and stop breathing. Unless EAR is startedimmediately the victim will suffocate. A current of 0.1A passing through the region of theheart, will shock the heart muscles into rapid, erratic contractions (ventricular

fibrillation) so the heart can no longer function. Death would usually follow in a matter ofa few minutes. Currents of 1A and higher through body tissue cause serious burns.

Typically, the 240V AC mains supply causes a 25mA (milliampere) current inthe body, which can easily cause death.This is the reason why some countries use110V AC as their mains supply voltage it is safer in the event of an electric shock. With

AC, the frequency of the supply also affects the damage that the current causes. Sinceheart muscle is most sensitive to electricity of frequency 30-100Hz, the Australian mains


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frequency of 50Hz is ideal for inducing fibrillation. Higher frequencies, DC electricalcurrent, and AC which does not pass through the heart do not cause fibrillation butrather heat up and burn the muscle they flow through, sparing skin and fat.

Overall, the most important quantity to control in preventing injury is theelectric current. Voltage is important only in that it can cause current to flow.Even though your body can be charged to a potential thousands of volts higher than themetal frame of your car, simply by sliding across the car seat, you feel only a harmless

shock as you touch the door handle. Your body cannot hold much charge on itself, andso the current flowing through your hand to the door handle is short-lived and the effecton your body cells is negligible.

MOVING ABOUT

MECHANICS:

The branch of Physics that is concerned with the motion and equilibrium of bodies ina particular frame of reference is called mechanics. Mechanics can be divided

into three branches: (i) Staticswhich deals with bodies at rest relative to some

given frame of reference, with the forces between them and with the equilibrium of

the system; (ii) Kinematics- the description of the motion of bodies without

reference to mass or force; and (iii) Dynamicswhich deals with forces that change

or produce the motions of bodies.

Some common terms used in the study of mechanics (and indeed many other

branches of Physics) are: scalars, vectors and SI Units.

1.ScalarsA scalar is a physical quantity defined in terms of magnitude (size)only

- eg temperature, mass, volume, density, distance.

2.VectorsA vector is a physical quantity defined in terms of both magnitude and

direction - eg force, velocity, acceleration, electric field strength.

Diagramatically we can represent a vector by a straight line with an arrow

on one end. The length of the line represents the magnitude of the vector

quantity and the direction in which the arrow is pointing represents the

direction of the vector quantity. We will say much more about vectors later inthis topic.

3.System International (SI) UnitsThe internationally agreed system of units.

There are seven fundamental units. The three that we will use in this topic are the

metre (length), the kilogram (mass) and the second (time). Various prefixes

are used to help express the size of quantities eg a nanometre (1 nm) = 10-9of a

metre, a gigametre (1 Gm) = 109metres.


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MOTION:

The following terms are commonly used to describe motion.

1.Displacementis the distance of a body from a given point in a given direction. It

is a vector quantity. The SI unit of displacement is the metre (m).

2.SpeedThe speed of a body is the rate at which it is covering distance. It is a

scalar quantity. The SI units are m/s, which can also be written as ms-1.

where vav= average speed, d= total distance travelled and t= total time taken to

travel distance d.

3.VelocityThe velocity of a body is its speed in a given direction. In other words,

velocity is the rate of change of displacement with time. It is a vector quantity with

the same SI units as speed.

where vav= average velocity, r= change in displacement and t= change in

time taken to achieve that change in displacement.

Another way to express average velocity is as the average of the initial and finalvelocities.

where vav= average velocity, u= initial velocity of the body and v= final velocity

of the body. Note that this equation applies ONLY when the velocity of the

body is increasing or decreasing at a constant rate.


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4.AccelerationThe acceleration of a body is the rate of change of the velocity of

the body with time. It is a vector quantity, with units of (metres/second)/second,

written as ms-2.

OR

where aav= average acceleration, v= change in velocity of the body and t=

change in time over which the change in velocity took place.

where aav= average acceleration, v= final velocity, u= initial velocity, and t=

time over which the change in velocity took place.

Note that a body accelerates when:

a.It speeds up;

b.It slows down;

c.It changes direction.

MOTION GRAPHS:

Note that in this section the variable swill be used to represent displacement

instead of r. You will find in Physics that these two variables are both in common

use to denote displacement.


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Displacement-Time Graphs.

Clearly, the gradient (slope) of a displacement-time graph gives the velocity.

Gradient =S/t

= velocity

Note that a positive gradient implies a positive velocity and a negative gradient

implies a negative velocity.

For a curved displacement-time graph, the gradient of the tangent to the curve at a

particular point equals the gradient of the curve at that point, which in turn equals the

velocity of the object at that particular time. Such a velocity, that is, the velocity at a

particular instant in

time, is called the

instantaneous velocity.

An example of an

instrument that

measures instantaneous

velocity is the

speedometer in a car. In

older cars the

speedometer was linked

mechanically to the

transmission. These

days, however, a device located in the transmission produces a series of electrical


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pulses whose frequency varies in proportion to the vehicle's speed. The electrical

pulses are sent to a calibrated device that translates the pulses into the speed of the

car. This information is sent to a device that displays the vehicle's speed to the driver

in the form of a deflected speedometer needle or a digital readout.

Note that a straight line displacement-time graph implies that velocity is constant. A

curved line displacement-time graph implies that velocity is changing with time (ie

the object is accelerating).

Velocity-Time Graphs

These may be used to gain information about the displacement, velocity and

acceleration of an object at various times.

The gradient is clearly the acceleration of the object.

Gradient =v/t

= acceleration

Note that a positive gradient implies a positive acceleration and a negative gradient

implies a negative acceleration.

Also, the area under the graph,


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in the case above, has units of: seconds x metres per second = metres. Thus, the

area under a velocity-time graph is equal to the displacement travelled by the

object in the time t.

Note that a horizontal straight line velocity-time graph implies that acceleration iszeroie velocity remains constant.

A non-horizontal, straight line velocity-time graph implies that acceleration is

constant and non-zero.

A curved line velocity-time graph implies that acceleration is varying.

Acceleration-Time Graphs

These may be used to gain information about the velocity and acceleration of anobject at various times.

The area under an acceleration-time graph gives the change in velocity of an

object during the time interval t.Check the units of the area: (ms-2x s = ms-1).

A horizontal straight line acceleration-time graph implies that velocity is varying at a

constant rate (ie velocity is increasing or decreasing by the same amount each

second). That is, acceleration is constant.

RELATIVE VELOCITY:

Often it is necessary to compare the velocity of one object to that of another. For

instance, two racing car drivers, A and B, may be travelling north at 150 km/h and

160 km/h respectively. We could say that the velocity of car B relative to car A is 10


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km/h north. In other words, driver A would see driver B pull away from her with a

velocity of 10 km/h north.

Likewise, two jet aircraft, C and D, flying directly at each other in opposite directions

(hopefully as part of an aerobatics display) may have velocities of 900 km/h north

and 1000 km/h south respectively. We could say that the velocity of D relative to C is

1900 km/h south. In other words, jet C will observe jet D flying towards it at a speed

of 1900 km/h.

Clearly, when the objects are travelling in the same direction, the velocity of one

relative to the other is the difference between their speeds, taking due care to state

the appropriate direction. When the objects are travelling in opposite directions the

velocity of one relative to the other is the sum of their speeds, again taking due care

to state the correct direction. There is a vector equationwhich can be used to

calculate the relative velocities of objects, even when the objects travel at variousangles to one another but this equation is outside the scope of the present syllabus

(for some unfathomable reason).

FORCE:

What is Force?

A force can be defined as a push or a pull that can cause a change in the state of

motion of an object or a change in the shape of an object. In fact, all accelerations(and decelerations) are caused by forces.

Does every force cause acceleration?

Again, from our everyday experience, we know the answer to this question is no. If

a person pushes on the brick wall of a house, the house does not accelerate.

Sometimes when we want to push or pull an object from one place to another we

find that no matter how hard we push or pull, we just cannot move (accelerate) the

object.

What is the relationship between force and acceleration?

We could perform an experiment to determine the relationship between the size of a

force applied to an object at rest on a laboratory bench and the change in velocity

experienced by the object over a set period of time (ie the acceleration). Such an

experiment would produce results as shown below.


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This graph clearly shows that:

The acceleration produced by a given force is inversely proportional to the

mass of the object.

From experiments such as those above, we can say that:

and

NEWTONS LAWS OF MOTION

Newtons First and Second Laws:

By combining the results above and defining the units of force appropriately, we canwrite that:

.

This can be taken as a statement of Newtons Second Law. The SI Unit of forceis the newton (N), defined so that 1N = 1kgms-2.

Note that in the above equation, Fis the vector sum of all the forces acting on the

object, mis the mass of the object and ais its vector acceleration. To remind us of thatfact we will write:

.

Note that if the resultant force on the object is zero, there is no acceleration. Therefore,in the absence of a resultant force, an objects velocity will remain unchanged. In otherwords, an object at rest will remain at rest, and an object in motion will remainin motion with uniform velocity, unless acted upon by a net external force. This


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is a statement of Newtons First Law, which in fact is contained in the SecondLaw as a special case (for F = 0).

[Top]

Newtons Third Law:

Forces acting on a body originate in other bodies that make up its environment. Any

single force is only one aspect of a mutual interaction between two bodies. We find byexperiment that when one body exerts a force on a second body, the second bodyalways exerts a force on the first. Furthermore, we find that these forces are equal insize but opposite in direction. A single, isolated force is therefore an impossibility.

If one of the two forces involved in the interaction between two bodies is called anaction force, the other is called the reaction force. Either force may be called theaction and the other the reaction. Cause and effect is not implied here, but a mutualsimultaneous interaction is implied.

This property of forces was first stated by Newton in his Third Law: To every actionthere is always opposed an equal reaction; or, the mutual actions of two bodiesupon each other are always equal, and directed to contrary parts.

In other words, if body A exerts a force on body B, body B exerts an equal but oppositelydirected force on body A; and furthermore the forces lie along the line joining the bodies.Notice that the action and reaction forces, which always occur in pairs, act ondifferent bodies. If they were to act on the same body, we could never haveaccelerated motion because the resultant force on every body would be zero.

Consider the following examples:

1.Imagine a boy kicking open a door. The force exerted by the boy B on the door Daccelerates the door (it flies open); at the same time, the door D exerts an equal but

opposite force on the boy, which decelerates the boy (his foot loses forward velocity).The force of the boy on the door and the force of the door on the boy is an action-reaction pair of forces.

2.When you walk, you apply a force backwards on the earth. Likewise, the earth appliesa force to you of equal magnitude but in the opposite direction. So, you moveforwards.

The force of the person on the earth and the force of the earth on the person is an
http://webs.mn.catholic.edu.au/physics/emery/prelim_moving_about.htm#Tophttp://webs.mn.catholic.edu.au/physics/emery/prelim_moving_about.htm#Tophttp://webs.mn.catholic.edu.au/physics/emery/prelim_moving_about.htm#Top


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action-reaction pair of forces.

3.Consider a body at rest on a horizontal table:

Each of the pairs of forces above is an action-reaction pair of forces.

Definitions of Mass and Weight:

The mass of an object is a measure of the amount of matter contained in theobject. Mass is a scalar quantity.

The weight of an object is the force due to gravity acting on the object. Weightis a vector quantity.

The weight, W, of an object is given by Newtons 2ndLaw as:

where mis the mass of the object and gis the acceleration due to gravity (9.8 ms-2close to the earths surface).

USEFULNESS OF VECTOR DIAGRAMS:

Many of the quantities with which we deal in Physics are vectors. Sometimes weneed to add a number of vectors together. For instance, we may be trying to calculatethe total or resultant force acting on a car when several forces act on the carsimultaneously the wind, friction, gravity and the force supplied by the engine.

Sometimes we need to subtract two vectors. For instance, we may be trying to calculatethe change in velocity of a car as it goes around a bend in the road. The change invelocity of the car equals the final velocity of the car minus initial velocity of the car.

When the need arises to add or subtract vector quantities, this proves to beeasy only when the vector quantities act along the same straight line. If the


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vectors act at an angle to each other we really need to draw a vector diagramto assist in solving the problem.

Vector analysis is an extremely important aspect of Physics and there are

several different methods available to add, subtract and even multiply vectors.

Unfortunately, the current Syllabus requires that you have only a very basicunderstanding of vector analysis. So, we will examine a single, simple but very

useful method of adding and subtracting vectors.

VECTOR ADDITION:

The method we will use is called the Vector Polygon method. To find the sum of

a number of vectors draw each vector in the sum, one at a time, in the appropriate

direction, placing the tail of the second vector so that it just touches the head of the

first. Continue in this fashion until all of the vectors in the sum have been included in

the diagram. Note that it does not matter which vector you start with.

The vector that closes the vector polygon in the same sense as the component

vectors is called the equilibrant. It is the vector which when drawn into the diagram

gets you back to where you started. The vector that closes the vector polygon in

the opposite sense to the component vectors is called the resultant. The

resultant is the answer to the sum of all the vectors. Its size can be calculated

mathematically or measured using a ruler if the vector polygon has been

drawn to scale. The direction of the resultant can be calculated mathematically

or can be measured using a protractor if the vector polygon has been drawn toscale. Either way, the direction of the resultant must be stated in an

unambiguous way.

Sometimes in Physics our vector additions only involve two vectors at a time. In this

case, the polygon formed is a triangle, making the mathematical calculation of the

magnitude and direction of the resultant quite straight forward.

EXAMPLE 1:A fighter pilot flies her F-14D Tomcat jet with a true airspeed of 400

km/h North. A crosswind from the East blows at 300 km/h relative to the ground.

Calculate the jets resultant velocity relative to the ground.

Note: For aircraft, the true airspeed

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Physics Year 11