Neville Warren MSc, DipEd, MACE
PASCAL PRESS
Copyright © 2002 Neville Warren ISBN 1 877085 12 X Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www.pascalpress.com.au Publisher: Vivienne Petris Joannou Editor: May McCool Typeset by Precision Typesetting Services, Sydney Cover by DiZign Printed in Singapore by Green Giant Press
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The total time allocated is approximately 22 hours. This includes 13 hours for the three core topics, approximately 5 hours for the option topic (depending on the topic), three hours for the exam and an hour to go through the answers. To revise in a month you will need to keep to a schedule.
Generators For example, you The Motor Effect might choose to follow the following Electromag netic Induction timetable. Space Gravity Space Launch and Return Future Space Travel Special Relativity Motors and
Electric Generators Transformers Electric Motors From Ideas to Implementation
Cathode Rays Quantum Theory Solid State Devices Su percond uctivity
the following: Medical Physics Astrophysics Quanta to Quarks
Do ONE option from
Sample Examination (3 hours) Check answers (1 hour)
Check that you know the key points in each topic that you are studying. This quick test should take only 10 minutes to complete. Check your answers by referring to the bottom of the page. This is important feedback for you.
If you got any of the test questions wrong, you can quickly find an explanation and more information on this question by going to the same number in this section. You should also read the other key points for this topic to help you revise thoroughly.
These are exam-style questions that you should be able to answer in order to prepare for the exam. In this section you apply your knowledge. Make sure you have fully revised your work in the Key Points section. Complete answers are found at the back of the book. Hints to some questions are provided in case you need extra help with them. They are found at the bottom of the page. Marks are allocated for each question. Always check the marks and use them as a guide for how much to write in your answer.
When you have completed all sections you are ready to complete the exam paper. Set aside the required time and try to do it under exam style conditions - this way you will benefit most from it.
Complete answers are provided for each question. Mark your paper to see how well you have done. Tips for the HSC exam can be found on the inside back cover. A suggested time is given for each section. Try to follow it. A week-by-week time plan for the month is given on the contents page to help you plan your study timetable.
A force F acts between two masses separated by a distance d. If the masses are both doubled and their separation is halved, the new force is now: F
2F
4F
16F
Surrounding any object with mass is a _ _ _ _ field. The gravitational field strength of a mass m placed a distance r from the mass is g. If the distance from the mass is halved, the new gravitational field strength is: g/4
g/2
2g
4g
The acceleration due to gravity near the Earth's surface is approximately equal to _ _ _ _ m.s-2. _ _ _ _ is the force on an object due to a gravitational field. The acceleration due to gravity on Mars is 3.8 m.s-2. The weight of a 10 kg mass on Mars is: 38 m.s- 2 38 N 0.38 N 10 N The mass of an object on Earth is 5 kg. Its mass on Mars (where the acceleration due to gravity is 3.8 m.s-2) is: 5 kg 5N 19 kg 19 N When a force is applied to a mass and the mass moves through a distance, we have done on the mass. If this force is used to move the mass vertically, we have increased the mass's _ _ __ The gravitational potential energy has its zero value at _ _ __ The gravitational potential energy Ep of an object of mass m placed a distance r from the Earth (mass ME) is given by: Ep =_G
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Michael Faraday is credited with the discovery of the generation of an electric current in a conductor by a moving magnet. Coil
Faraday found that when a magnet is pushed into a coil of many turns connected to a sensitive current-measuring device (a galvanometer) a current is produced as long as the magnet is moving relative to the coil. If there is no movement between the coil and magnet, no current is produced. When the magnet is withdrawn from the coil, current is again produced but it flows in the opposite direction to that when the magnet is inserted.
Magnet
Galvanometer
Magnet moving towards a conducting coil
Electromagnetic induction involves the conversion of mechanical energy into electrical energy.
Magnetic flux is a measure of the number of lines of force emerging from a given area as shown in the diagram on the right.
Magnetic flux density is synonymous with magnetic induction. The greater the density of flux lines (also called 'lines of force'), the greater the magnetic field.
Magnetic flux
Faraday's law states that the induced emf is proportional to the rate of change of magnetic flux. That is, the faster the magnetic flux through the circuit changes, the greater will be the emf induced. This can be made to happen by moving the magnet (or coil) faster, and/or increasing the magnetic induction and/or by having more coils.
Lenz's law states that the induced emfis in such a direction that the current it produces opposes its production. This is a consequence of the law of conservation of energy. If the emf (and its associated current) aided the production instead of opposing it we could create an infinite amount of energy from a finite amount of work - we would effectively get 'something for nothing'. This would violate energy conservation.
The direction of the induced current can be found by the right-hand palm rule. When a motor is operating it involves relative motion between a conductor and magnetic field and so it produces a back emf. This opposes the supply emf and limits the current flowing in the motor. This in turn limits the speed of the motor - the motor is self-regulating.
Thumb points in direction of induced current
Fingers point in direction .*-;~=±==7 of magnetic field
l -? _
Palm points in When an electric motor is starting, the back emf direction of will be small and so the current in the coil from opposing force the supply will be large. (Remember that the back emf opposes the supply voltage.) To keep the Right-hand palm rule current within manageable limits to prevent it burning out the motor, a starting resistance is placed in series with the coil. As the coil speeds up (and hence the back emf increases) the starting resistance can be decreased and eventually removed.
Circular eddy currents are induced in bulk conductors in the presence of changing magnetic flux. These eddy currents obey Lenz's law. They also represent a waste of energy as they cause heating of the conductor. Eddy currents are put to good use in induction cookers and in electromagnetic braking. AC flowing in coils placed below a glass-ceramic cook top induces eddy currents in the metal pans placed on top, heating the pan and its contents. In certain modern trains, electromagnets are brought near to the moving metal wheels inducing eddy currents in the wheels. These currents flow in a direction to oppose their cause in agreement with Lenz's law. This provides a retarding force on the wheels that stops the wheels (and hence the train). Braking is very smooth since the force is greatest when the wheels are turning fastest and gets less as the speed of the wheels gets less.
CHECKLIST - Can you: 1. Describe Faraday's discovery of electromagnetic induction? 2. Define magnetic flux, magnetic flux density and magnetic induction? 3. Qualitatively and quantitatively describe Faraday's law? 4. Explain the cause of Lenz's law and relate this to back emf, eddy currents and electromagnetic braking?
Below is a schematic diagram of a simple experiment to illustrate electromagnetic induction, similar to one that you could do at school. Explain what is required for a current to be induced and give three ways in which the induced current can be made larger (assuming you had access to additional equipment). Explain your reasoning. Coil
Magnet
Galvanometer
A physics teacher was overheard telling a class that 'Lenz's law is simply a consequence of energy conservation'. What is Lenz's law? How does this law relate to energy conservation. Many electric motors, especially large ones, have a starting resistance. Clearly explain why this is needed. A student set up an experiment similar to that in the diagram below. Explain the student's observations.
Aluminium disk spins freely on its axle Solid disk stops spinning when magnetic field brought close to disk
A disk with slits continues to spin for much longer than a solid disk in the presence of a magnetic field
Generators use the principle of _____ induction to convert _____ energy into energy. AC generators have four essential features. These are: ______________ and ______________ DC generators also have the four essential features of AC generators but they also have a . This is used to convert into _____ Generators work by moving a conducting coil to a magnetic field. As the coil rotates, the magnetic through the coil varies and so a/an is induced between the ends of the coil. Maximum emf is produced when the coil passes through the horizontal plane. True or false? _ _ __ In what direction is the emf induced in the generator (Lenz's law)? _ _ _ __ Real generators differ from the simplified idealised models discussed in class. Three ways in which they differ are: ___________________________________ and
The biggest loss of energy from where it is generated in the 'power station' to the consumer occurs in the where some of the electrical energy is converted into _ _ _ __ Electricity has impacted on society in a number of ways including: _________________________________ and
High voltage power lines are said to be associated with increased risk of certain _ _ _ _ . There is currently evidence about these alleged health risks.
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Electric generators use the principle of electromagnetic induction to convert mechanical energy into electrical energy (the reverse of electric motors). The mechanical energy can be supplied by steam derived from water heated by the combustion of fossil fuels or the heat from nuclear reactors, by the kinetic energy of falling water (hydroelectricity) or wind generators. Generators consist of an armature, field structure, slip rings and brushes as in
Field magnets
the diagram. In addition to the structures in 2 above, DC generators also have a commutator whose role is to convert AC into DC. Generators work by moving a coil relative to a magnetic field. Consider the simplified diagram of an AC generator. As the coil is made to rotate, the magnetic Carbon brushes flux through the coil varies, from a held in place by springs minimum when the coil is parallel to the AC generator field, to a maximum when the coil is perpendicular to the field. As a result, an emf is induced between the ends of the coil and current can flow in an external circuit. Faraday's law says that the emf is proportional to the rate of change of magnetic flux through the circuit. Hence the emf varies from a maximum as it passes through the horizontal plane (the rate of change is greatest here) to a minimum as it passes through the vertical plane. In agreement with Lenz's law, the emf is induced in such a direction that its associated current flows in a direction so that its magnetic field opposes the cause of the induced emf.
Time
2
3
4
5
AC generator output
Real generators differ from the simplified model used above. In general, real generators use electromagnets to produce the magnetic field rather than permanent
magnets; have hundreds of coils wound around a soft iron core; have the armature as the stator (the non-moving part) in AC generators - it is the rotor in DC generators; have three pairs of electromagnets place at 1200 to each other (producing three-phase power). Some energy is lost in transmission from the power station to where it is used. This can occur because of friction in the rotor bearings; heat generated by currents in the transmission cables and energy losses in the generator's iron core.
Electricity has profoundly affected society. The discovery of how to generate large amounts of electricity and transport it to distant sites led to electricity becoming the primary source of industrial and domestic energy. This exacerbated some of the problems of the industrial revolution - the shift of the population from the country to city slums, longer working hours ... as well as the associated current environmental issues of global warming and acid rain. Controversy exists about the alleged harmful affects of living close to power lines. A number of scientific investigations have been done on the relationship between the occurrence of certain cancers and the proximity of living near high voltage power lines. The results are conflicting or inconclusive: some investigations show a statistically valid association; others do not. The jury is still out.
CHECKLIST - Can you: 1. Identify the main components of a generator? 2. Compare a generator with a motor? 3. Describe the principle of operation of AC and DC generators? 4. Compare the advantages and disadvantages of AC and DC generators? 5. Explain how energy is lost as it is transmitted from the generator to the consumer? 6. Describe the effect of electricity on society and the environment?
The device that changes the direction of the current in a DC generator is the: armature brush commutator slip rings In a simple AC generator, a coil of wire is placed between the poles of two magnets and is rotated in an anticlockwise direction as shown. Sketch the expected output on the axes provided at the positions indicated by the numbers 1-5. Repeat on the second set of axes for a DC generator.
~
0 5;:> 2
~ 3
0 5;:> 4
~ 5 OJ OJ
OJ OJ
.l!l
.l!l
~
~
Time
Time
The first continuous current-generating device was invented by Michael Faraday and was called Faraday's disk dynamo. It consisted of a copper disk that could be rotated between the poles of a strong magnet. Copper brushes carried current away. Briefly explain how this works. Copper brushes
Clearly describe the effects of the development of AC and DC generators on society and the environment.
Transformers are used to electrical energy from one circuit to another. They can also be used to change the AC _ _ __ Transformers consist of three essential features, a _____ coil, a _____ coil and a soft core. _____ voltages in the coil induce changing voltages in the _ _ _ __ coil by the process of mutual induction. Transformers operate on
only.
In a step-down transformer: the current in the secondary is less than the current in the primary the voltage in the secondary is greater than the voltage in the primary the voltage in the secondary is less than the voltage in the primary. In a step-up transformer there are more coils in the primary than in the secondary. True or false? _ _ _ __ In an ideal transformer, the power in the secondary is same/different from the power in the secondary?_ _ _ __ In a step-up transformer, compared to the secondary, the voltage and current in the primary are respectively: bigger and bigger bigger and smaller smaller and bigger A transformer has a primary of 1000 turns and is used to step-up the voltage from 12 V to 240 V. How many turns are needed in the secondary? (Assume 100% efficiency.) What current flows in the primary if the secondary is operating at 12 W? To minimise energy losses in transmission, electricity is transmitted at voltages as high as V. Transformers in electricity _____ are used to reduce the voltages to suitable amounts for homes and industry. Many household appliances contain _ _ __ Energy losses due to eddy currents are minimised in transformers by having the soft iron core _ _ __ Transformers and generators have had a _ _ _ _ impact on our lives. :j.ue)!:I-!UO!S pa:j.eu!wel SJaWJ0:l-sueJ:j. SUO!:j.e:j.s qns OOO'OOS \;j L 'OOOIOC ) awes aSle:l- ) )\;j AJepUmas 'AJewpd 'OU!oue4) UOJ! 'AJepumas 'AJewpd aoe:j.lol\ 'Ja:l-sueJ:j. :SJaMSutf
Transformers are devices for transferring electrical energy from one circuit to another. They also allow AC voltages to be easily changed in magnitude. Transformers consist of two coils the primary and the secondary both of which are wrapped around the same soft iron core. The primary coil has alternating voltages supplied to it. The secondary has alternating voltages induced in it.
Changing AC voltages in the primary sets up a changing magnetic flux in the soft iron core. This sets up a changing magnetic field in the secondary coil and so an emfis induced in it. The process is called mutual induction. Transformers operate on AC only and not DC. This is because a changing magnetic field is required for electromagnetic induction to occur. A step-up transformer increases the voltage in the secondary coil compared to the primary coil. Conversely, in a step-down transformer the secondary voltage is less than the primary voltage. A step-up transformer has more coils in the secondary than in the primary. In a step-down transformer, the secondary has fewer coils than the primary. The conservation of energy necessitates that in an ideal transformer, the power in the primary circuit is equal to the power in the secondary circuit. Since P = VI it follows that as voltage increases, the current decreases. It follows that in a step-up transformer, the voltage in the secondary is larger than the voltage in the primary but the current in the secondary is less than the current in the primary. In an ideal transformer (100% efficient) the voltage, current and number of turns (coils) are related by
VP
n
I
v = L = -IS 5
ns
P
Power is transmitted at extremely high voltages, as high as 500 kV (500 000 V). This is done to reduce the current and so lessen the energy losses in the transmission lines where the heating effect in the wires is proportional to the square of the current. Transformers in sub-stations are used to change the voltage (and current) to values suitable for use in industry and households by stepping the voltage down. This is generally to 240 V for household use and 415 V for industriallcommercial use.
Many home electrical appliances such as TVs and computers require voltages other than the 240 V supplied to homes. Transformers are able to change the voltage to the required amount. Transformers limit eddy currents in their core by having the core made of individual sheets (laminates) electrically insulated from each other. This lessens energy losses due to heating of the iron core. The invention of transformers (along with generators) meant that electricity could be easily distributed around the country and so electricity became the energy source of the industrialised world. This has had significant impact on the way we live. No longer are we restricted to daylight hours for work. We can now communicate almost instantaneously via radio, TV, mobile phones (the batteries of which require charging), etc. Greenhouse gas emission from fossil-burning fuels is a significant environmental issue. Imagine your life without electricity.
CHECKLIST - Can you: 1. Explain the use and principle of operation of transformers? 2. Compare step-up and step-down transformers? 3. Solve problems using Vp Vs
=:2.e.. =~ ns
Ip
4. Relate voltage and current changes to energy conservation? 5. Explain the role of transformers in electricity sub-stations and in the home? 6. Describe how transformers have impacted on society?
A transformer can be used: to increase voltage to decrease current both a and b to increase power.
A schematic diagram of an electric transformer is shown.
Output voltage
Primary coil
Secondary coil
What is the purpose of transformers? Clearly explain how a transformer works, describing the role of each of the labelled components. If the primary has 1000 turns and the secondary has 250 turns, what is the secondary voltage if the primary voltage is 240 V? (Assume 100% efficiency.)
Eddy currents can be a problem in power generation. Discuss how these eddy currents arise and how they can be minimised to lessen their impact.
The transfer of electrical energy from electric power stations to the consumer is not 100% efficient. Briefly discuss the energy losses involved and how they are kept as low as possible.
AC electric motors have a _____ and a _ _ _ __
AC motors, unlike DC motors do not require a _ _ _ __
The most common type of AC motor is the _____ motor.
These motors work on the principle that a _____ magnetic field will exert a _____ on a stationary coil.
A rotating magnetic field can be relatively easily produced by using _ _ __
A field like that above will _____ a current in the coil. Interaction of the two fields results in the coil being around.
AC induction motors are widely used because of their ________ design, relatively cost and their _ _ _ _ _ __
The electric motor used in small appliances such as food processors and electric power saws is most likely to be: a single-phase AC induction motor a three-phase AC induction motor a DC motor an AC synchronous motor.
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AC electric motors have two essential features - a rotor (the moving part) and the stator (the stationary part). Some also have slip rings to bring electricity to and from the motor. AC electric motors have the advantage over DC motors in that they do not require a commutator (the AC automatically reverses 50 times per second). Commutators have problems associated with sparking, ozone production from the sparking and energy loss in the brushes. In addition there are problems with the wearing of the brushes. The most common type of AC motor is the induction motor. AC induction motors work on the principle that a rotating magnetic field will exert a torque on a stationary coil.
AC can relatively easily produce a rotating magnetic field. AC induction motors work by having the stator produce a rotating magnetic field. This induces (hence induction motor) an electric current in the rotor by the process of electromagnetic induction. This current produces a second magnetic field. The two magnetic fields interact with the rotating field dragging the rotor around. AC induction motors are cheap, efficient and simple to manufacture which accounts for their wide use. In particular they are used for low power « 1 kW) applications in homes.
95% of all electric motors are single-phase induction motors. These represent the majority of motors in the home. Industry tends to use three-phase induction motors since they can have larger power ratings.
CHECKLIST - Can you: 1. Describe the main features of an AC electric motor? 2. Describe the principle of operation of AC induction motors? 3. Relate the power rating of AC motors to their uses? 4. Explain the advantages of AC induction motors?
In an AC induction motor: current is induced in the rotor current is induced the stator current is supplied to the rotor from an external source a commutator converts AC to DC.
AC induction motors have the advantage over DC motors that: they don't require a commutator they are simple to design they are relatively cheap all of the above.
Many power tools and appliances used in the home have relatively low power -0.5-1 kW. Explain why these are most likely AC induction motors.
Briefly describe the principle of operation of an AC induction motor.
The German Geissler invented a pump efficient enough to reduce the pressure in a glass tube to a small fraction of normal air pressure. By placing metal _ _ _ _ in these tubes it was possible to get to flow through the tubes. As the pressure is reduced in these tubes, different were produced that depended on the gas pressure.
patterns
At a low pressure of -0.01 kPa a green glow appears in the end of the glass tube opposite the negative electrode, the _ _ __ This glow was found by Crookes to be caused by from the negative electrode. Charged particles can be affected by: electric fields magnetic fields
emanating
both electric and magnetic fields.
Various cathode ray tubes and certain properties of cathode rays are shown. Draw a line that correctly links the tube with the property. Cathode ray tube Property Maltese cross rays carry energy and momentum magnet brought near rays travel in straight lines fluorescent screen i rays are deflected by magnetic fields paddle wheel The nature of cathode rays, _ _ _ _ or
, was long debated.
A parallel plate capacitor is a useful device because it provides a _ _ _ _ electric field, the intensity of which is calculated from the equation _ _ __ A charge of 3.2 x 10-19 C moves at right angles to a magnetic field of 0.1 T at a speed of 2.0 x 107 m.s-1. What is the magnitude of the force acting on the charge? J.J. Thomson successfully measured the _ _ _ _ to -,-_ _ _ ratio for cathode rays.
A cathode ray tube has three main components _ _ _ _ __ Cathode ray tubes are found in _ _ __
_ _ _--,-__ and
_ _ _ _ and _ _ __
The cathode ray _ _ _ _ is a useful experimental measuring device. The _ _ _ _ nature of electrons is used in electron _ _ __ sadmSOD!W 'aAeM admsoliPso SAL 'sadmsoliPso 'sadmSOD!W ssew 'afiJelp UOJpaia uaaDS lua)saJonlJ. 'walsAs fiu!palJ.ap 'unfi UOJpaia N n-O L x 17'9 PIli =:1 'wJ0J.!un ap!+J ed 'aAeM ! ?8 ) 'I!! ?8 q '!! ?8 e ) SUOJpala aA!lefiau apOLjle) UO!leplS 'afiJeLj)s!p AlPppala 'sapoJpala 'wnmeA :SJ~r_ " /i'~ 'POOil{ l'~'~rtime is proportional to the fourth ,.. 200 400 600 800 1000 A(nm) power of its absolute temperature, that is £ = (J'P. But assuming the star to be Black body radiation curves a sphere, the luminosity is given by L = 4nW(J'T4 where R is the radius of the star's photosphere. All quantities other than R can be measured thereby allowing R to be calculated. -"~"-".
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CHECKLIST - Can you: 1. Explain the production of emission and absorption spectra and compare them with a black body spectrum? 2. Explain the operation of a spectroscope? 3. Describe the different types of spectra from stars, emission nebulae, galaxies and quasars? 4. Explain how stellar spectra can be used to classify stars? 5. Describe the information that can be deduced from spectra? 6. Explain the use of the Stefan-Boltzmann law to determine stellar radii? 7. Determine the temperature of a star from its black body radiation curves?
All we know about celestial objects comes to us in the form of the object's spectrum. What is meant by the term 'spectrum'? What are the two basic spectral types? State three pieces of information that astronomers can deduce from a stellar object's spectrum. The diagram is a representation of the formation of a particular type of spectrum. Collimating slit
Glass
Spectra composed of dark lines on a bright background
What type of spectrum is it? Clearly explain how this spectrum forms. Explain clearly how this of type of spectrum helps us discover information about stellar objects? The spectral class of some stars is shown in the table. Star
Spectral class
Aldebaran
K5
Betelgeuse
M2
Deneb
A2
Hadar
B1
Which star is the hottest? Justify your answer. What is the likely colour of Betelgeuse? Justify your answer. Clearly explain how the Stefan-Boltzmann law can be used to calculate the radius of a star. Equations may be useful in your explanation.
The measurement of the brightness of stars is: spectroscopy astrometry photometry. The luminosity of a star depends on the _____ and the surface _____ of the star. In addition to the factors in 2 above, the brightness of a star also depends on its _____ from us. A star alpha has a magnitude of -1 and another star beta has a magnitude of +1. How much brighter is alpha than beta? A star's brightness is determined by its _____ and _____ magnitudes. The absolute magnitude is the brightness a star would have if it were placed _ __ pa rsecs from us. Two identical stars alpha and beta exist with alpha twice as far away as beta. What is the ratio of the apparent magnitudes of alpha to beta? The star Arcturus has an apparent magnitude of 0.00 and an absolute magnitude of -0.3. How far away is Arcturus? Spectroscopic parallax: uses parallax to determine distances to stars does not use parallax to determine distances to stars. The of a star is a measure of its magnitude measured separately through blue and yellow filters. This value is for blue stars and _ _ __ for stars. _____ tubes are used to measure low light intensities more effectively than _____ plates in photometry.
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Photometry is the measurement of the brightness of stars and other celestial objects. These measurements allow information about a star's temperature, composition, age, etc. to be determined. Luminosity (L) is a measure of the rate at which a star emits radiant energy, that is, it
is a measure of the total power emitted by a star. This depends upon the size of the star and its surface temperature. The brightness (I) of a star is a measure of the intensity of radiation arriving at the Earth from that star. This is determined by three factors, the star's size (radius), surface temperature, and distance from us. Brightness is given in terms of magnitude where a first-magnitude star is defined to be 100 times brighter than a sixth-magnitude star. It follows from this definition that the brighter the star, the smaller the magnitude and a difference of one magnitude always corresponds to the same brightness ratio, that is, ~hoo = 2.512. The brightness of a star determines its absolute and apparent magnitude. The absolute magnitude (M) is defined as the brightness the star would have if it were a standard distance from us - this distance is 10 parsecs. This allows astronomers to compare stars in terms of characteristics such as their size and temperature. For two stars with absolute magnitudes MA and MB and apparent brightness IA and 18 respectively,
MB-MA)
we have IA = 100(- s IB
The apparent magnitude (m) of a celestial body is its magnitude as measured by an observer (usually on the Earth). For two stars with apparent magnitudes m A and m8 respectively and intensities IA and 18 we have: m B -mA
=2.5log1O~' This is equivalent to IB
IA =2.S(mB -m A ) IB
The magnitude of a star can be used to deduce the distance to the star. For a star with an apparent magnitude m at a distance d and absolute magnitude M at a distance of 10 parsecs it is found that m - M
= 510g 10 -
d
10
m - M is called the distance modulus.
Spectroscopic parallax uses stellar spectra to determine distances (it does not actually use parallax). Astronomers determine its spectral class and luminosity from its observed spectrum and place it on the Hertzsprung-Russell diagram to determine its absolute magnitude. By comparing this with its apparent magnitude, the distance can be calculated. The colour index of a star is the difference between the magnitude measured using a blue filter and the magnitude using a yellow filter that is, CI = B - V. Blue stars have a negative colour index, red stars a positive colour index. Photometry relies on photomultiplier tubes and photographic plates. Photomultiplier tubes convert weak light into easily measurable electric currents. They provide faster measurements of magnitude than photographic plates which rely on visual comparisons of the star images.
CHECKLIST - Can you: 1. Define absolute and apparent magnitude and how these can be used to determine the distance to celestial objects? 2. Solve problems using the formulae m - M
= 510910 ~
and
~ = 2.5(ma- mA)?
'8
10 3. Describe the principles behind spectroscopic parallax? 4. Define colour index and explain how it is used? 5. Compare the use of photomultiplier tubes and photographic plates in photometry?
The apparent magnitudes of some celestial objects are shown in the table. Object
Apparent magnitude
Moon
-12.6
Sirius (brightest star)
-1.4
Vega
0
Venus (max)
-4.4
What is meant by the term 'apparent magnitude'? Which celestial object in the table appears brightest to us? Explain your answer. Compare the brightness of Venus with that of Sirius. Show your working. The absolute and apparent magnitudes of various stars are shown in the table. Star
Apparent magnitude
Absolute magnitude
Spica
+1.00
-2.4
Castor
+1.59
+1.0
Pollux
+1.16
+1.0
What is the significance of the fact that Castor and Pollux have the same absolute magnitudes but different apparent magnitudes? Explain your reasoning. Which star has the greatest luminosity? Explain your answer. How far away is Castor? The spectral class of some stars is shown in the table. Which star has the most positive colour index? Explain your reasoning. Spectroscopic parallax is a method used to determine the distance to certain stars. Clearly explain how this is done.
Star
Spectral class
Aldebaran
K5
Betelgeuse
M2
Deneb
A2
Hadar
B1
Binary or multiple stars make up a significant proportion of all stars known. True or false? _ _ __ Binary (or multiple) stars can be eithervisual, _ _ _ _ , spectroscopic or _____ binaries. In a visual binary, _____ stars are visible through a telescope orbiting in ellipses around a common of mass. In an binary, the motion of one star leads to variations in the _____ of the light from the star. Spectroscopic binary stars are recognised by their periodic doubling of the _____ lines as the stars periodically and from the Earth. In binaries only one of the pair is visible. The presence of the other is deduced from its on the orbit of the visible component. Two stars in a binary pair orbit their common centre of mass with a period of 3 years. They have an average separation of 3 astronomical units. What is their mass in units of solar mass? Stars whose brightness changes either regularly or irregularly are called _ _ __ stars. Cepheids are _____ yellow stars whose brightness varies with a regular pattern. The first Cepheid to be investigated and to have its _ _ _ _ curve plotted was
0-_ _ __
For Cepheids, as the period of the light variations increases: the brightness increases the brightness decreases the brightness is unaffected.
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Binary stars consist of two stars orbiting about their common centre of mass and obeying the law of universal gravitation. About half of all known stars are binary or multiple stars. Binary stars can be visual, eclipsing, spectroscopic or astrometric binaries. Visual binary stars have orbits around a common centre of mass which can be directly observed as ellipses traced out against the background stars. Both stars are visible. In eclipsing binary stars one of the pair eclipses (moves in front of) the other at regular intervals leading to variations in the brightness of the light from the eclipsed star as in the diagram. Duller star
A
U~~ I~
1\I i
I
I ~ I
i -
I
I
I
I
Brighter star eclipses \ duller star , (secondary \, eclipse) DUII::tar
Duller star eclipses brighter star (primary eclipse)
eclipses brighter star (primary eCIiPse~ Time
Eclipsing binary stars
Time
Light curve for total eclipse (flat bottom)
Light curve for partial eclipse (V shape)
In spectroscopic binaries the Doppler shift in their spectral lines is used to determine their presence. This is characterised by a periodic doubling of lines as the stars recede and approach the observer at regular intervals as in the diagram. Red
Violet
I
t
Red shift
