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Physics in Focus (Year 12 Student Book), 2nd Edition
(a d1v1s10n of Pearson Austraha Group Pty Ltd) 707 Collins Street, Melbourne. Victona 3008 PO Box 23360, Melbourne, Victor.a 8012 www.pearson.com.au
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PEARSON PHYSICS
NEW SOUTH WALES
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We a r e grateful to the follow i ng peop le for thei r time an d expertise i n contr ibuting t o t he Pearson Physics 12 New Sou th Wales project.
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Doug Bail
Education Consultant
Contributing Au t hor and Skills and Assessment Author
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Norbert Dommel Lecturer
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Brianna Hore
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Module 5 Advanced mechanics
- CHAPT
Projectil e moti
How can models that are used t o explain projecti le motion be used to anal yse and make
Module 6 Electromagnetism
What happens to stationary and moving charged particles when t h ey interact with an electric o r magnetic f ield?
Un der what circumstances is a force produced on a current-carrying con ductor in a magn etic field?
1 Force on a conducto r 6 2 Forces between conductors
Chapter 6 Review
• CHAPTER 7 Electromagnetic induction
How are electric an d magnetic fields related?
7. 1 Magnetic flux
7 2 Faraday' s and Lenz' s laws
7.3 Transformers
Chapter 7 Review
• CHAPTER 8 Applications of t he motor effect
How has the knowledge about t he motor effec t been appl ied to technological advances?
Module 7 The nature of light
• CHAPTER 9 Electr omagn etic sp ectrum Wha t is
supports the classical wave model of
and what predictions can be made using this model?
What evidence supports the particle model of light and what are the implications of this evidence for the development of the quantum model of l ight? 11 1 Black- body radiation
11.2 The photoelectric effect
does the behaviour of light affect concepts of
is it known that atoms are made up of protons, neutrons and electrons?
Module 8 From the universe to the atom
is it known that classical physics cannot explain the properties of the atom?
is it known that human understanding of matter
still incomplete?
The Standard Model
Evidence for the Standard Model
17 Review
8
How to use this book
Pearson Physics 12 New South Wales
Pearson Physics 12 New South Wales has been written to be fully a ligned w ith the new Stage 6 syllabus fo r New South Wales Physics. The book
Revision box Revi sion boxes are used to remind students of vital concepts previously covered that a re requ i red for current learning.
Physics Inquiry
Physics Inquiry features are i nquirybased ac t ivities that assist students to discover concepts before learning about them. They encourage stud ents to t h i nk about what happens in the world and how science can provide explanations.
Sec tion
Each chapter is clearly divided into manageable sections of wo rk. Best-practice l iteracy and i n structional design a re combined with h igh -qual ity, relevant photos and illust rations to hel p students better understand the idea or concept being developed.
PhysicsFile
PhysicsFile boxes i nclude a range of interesting and real-world examples to engage students
Physics in Action
Physics in Actio n boxes place physics in an appli ed situation or a r e levant context They r efer to the nature and practice of physics, its applications and associated issues, and the histor ica l development of its concepts and ideas.
Worked examples are set out in steps that show thinking an d working. Th is format greatly enhances student understanding by cl early linking underlying logic to the relevant ca lcu lation s. Each Worked example is followed by a Try yourself activi ty. This mirror problem allows students to immediately test their understanding.
Additional c ontent
Additiona l content includes material that goes beyond the core content of the syllabus They are intended for students who wish to expand the ir depth of understanding in a particular area.
summary to hel p students consolidate t he key points and concepts.
How to use this book
Chapter review
Each chapter finishes with a list of key terms covered in the chapter and a set of questions to test students' ability to apply the knowledge gained from the chapter.
Icon s
The NSW Stage 6 syllabus ' Learning across the curriculum' and ' General capabilities' content are addressed throughout the series and are identified using the following icons.
'Go to' icons are used to make important links to relevant content within the same Student Book.
This icon indicates when it is the best time to engage with a worksheet (!NS), a ts practical activity (PA), a depth study (OS) or module review (MR) questions in Pearson Physics 12 New Soulh Wales Skills and Assessment book.
This icon indicates the best t ime to engage with a practica l activity on Pearson Physics 12 New Soulh Wales Reader+.
Module review
Each module finishes with a set of questions, incl ud ing multiple c hoice and short answer. These assist students in drawing together their knowledge and understa nd ing, and applying it to these types of quest io n s.
Glossary
Key terms are shown in b old in sections and listed at t he end of each chapter. A compre hensive glossary a t t he end of the book includes and defines all the key terms.
Answers
Numerical answers and key short response answers are included at the back of the book. Comprehen sive answers and f ully worked solutions for all section review questions, Worked example: Try yourse lf fea tu res, chapter review q u estions and module review q uestions are provided on Pearson Physics 12 New South Wales Reader+.
Pearson Physics 12
New South Wales
Student Book
Pearson Physics 12 New South Wales has been written to fully align wi th the new Stage 6 syllabus for New South Wales. The Student Book includes the very latest developments i n and applications of physics and incorporates best-practice literacy and instructional design to ensure the content and concepts are fully accessible to all students.
Skills and Assessment Book
Pearson Physics 12 New South Wales Skiffs and A ssessm ent book gives students the edge in preparing for all forms of assessment. Key features include a toolkit, key knowledge summaries, worksheets, practical activities, suggested depth studies and module review questions. It provides guidance, assessment practice and opportunities for developing key skills.
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Online teacher support for the series i ncludes syllabus grids, a scope and sequence plan, and three practice exams per year level. Fully worked sol utions to all Student Book questions are provided, as well as teacher notes for the chapter inquiry tasks. Skills and Assessment book resources include solu tion s to all work sheet s, practical activities, depth studies and module review questions; teacher notes, safety notes, risk assessments and lab technician ' s checklists and recipes for all practical activit ies; and assessment rubr ics and exemplar answers for the depth studies.
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' ~orking scientifically
This chapter covers the skills needed to successfully plan and conduct primary and secondary·sourced investigations.
1.1 Questioning and predicting describes how to develop, propose and evaluate inquiry 4u~lio11::i. c:tmJ llyµuU,~ When 1,;rei:.1li11g c:1 hypuU1~i::, c:1 wn::i.ithmiliuu or the variables must be included.
1.2 Planning investigations w i ll help you learn to identify risks in your investigation and to make sure all ethical ooncems are considered. It is important to choose appropriate materials and technology to carry out your investigation. You will a lso need to confirm that your choice of variables allows for a reliable collection of data.
1.3 Conducting investigations is a guide to conducting scientific investigations. It describes methods for accurately collecting and recording data to reduce errors. Appropriate procedures need to be carried out when disposing of waste.
1.4 Processing data and information describes how to process your data appropriately. From an array of visual representations, you will learn how best to represent your informattOn and how to identify trends and patterns in your data.
1.5 Analysing data and information explains how to analyse your results. It explains error and uncertainty and how to construct mathematical models to better understand the sci entific principles of your research.
1.6 Problem solving will help you use critical thinking to demonstrate an understanding of the scientific principles underlying the ~ution to your inquiry question.
1.7 Communicating explains how to communicate an investigation clearty and accurately using appropriate scientific language, nomenclature and scientific notation.
Outcomes
By the end of this chapter you will be able to:
• develop and eval uate questions and hypotheses for scientific investigation PH l 2·l
• desi gn and eval uate investigations in order to obtain primary and secondary data and information PH12•2
• conduct investigations to collect valid and reliable primary and secondary data and information PH12-3
• select and process appropriate qualitative and quantitative data and information using a range of appropriate media PH 12-4
• analyse and evaluate primary and secondary data and information PH 12•5
• solve scientific problems using primary and secondary data, critical thinking skills and scientific processes PH12·6
• communicate scientifte understanding using suitable language and term inology for a specific audience or purpose PH12•7.
Content
By the end of this chapter you w ill be able to:
• develop and evaluate inquiry questions and hypotheses to identify a concept that can be investigated scientif ical ty, involvi ng primary and secondary data (ACSPHOO I , ACS PH061 , ACSPH096)
• modify questions and hypotheses to reflect new evidence
• assess risks, consider et hical issues and select appropriate materials a nd technologies w hen designing and p lanning an investigation (ACSPH03 1, ACSPH097)
• justify and evaluate t he use o f va riables and experimental control s to ensu r e tha t a valid p r ocedu r e is developed that a llows fo r the reliable collection of data (ACSPH 002)
• evaluate and modify an investigation in r esponse to new evidence
• employ and evaluat e safe work practices and manage risks (ACSPH0 3 l)
• use appropriate technologies to ensur e and evaluate ac curacy
• select and extract information from a wide range of rel iable secondary sources a nd acknowledge them using an accepted referencing styfe
• select q ua litative and quantitatrve data and information and represe nt them using a range of formats, digital technologies and appropriate media ( ACSPH004, ACSPH007, ACSPH064, ACSPHIOI)
• apply quan titative processes where appropriate
• evaluate and i mprove the quality of data
• derive trends. patterns and relationships in data and info rmation
• assess error, u ncertainty and limi tations i n data (ACSPH004, ACSPHOOS, ACSPH033, ACSPH 099)
• assess the relevance, accuracy, valid ity and reliabi lity o f primary and secondary data and suggest improvements to in vest igations (ACSPHOOS)
• use modelling (including mathematical examples) to explain phenomena , make prediction s and solve problem s using evidence from primary and secondary sour ces (ACSPH006, ACS PHO IO)
• use scientific evidence and c ritical thi n king s ki lls to solve p roblems
• select and use sui table for m s of d igita l, visual, w ri tte n a nd/or oral com m unication
• select and apply appropria te scient i f ic notations, nomenc latu re and scientific language to communicat e in a va r iety of con t exts (ACSPH008, ACSPH036, ACSPH067, ACSPH 102)
• co nstruct evidence-based arguments and engage in peer feedbac k to evaluate an a rgument or conclusion (ACSPH034, ACSPH036).
Ph)'s,a5taee 6 S)'labuS O NSW EducabonStlndan:bAu~ to, 11nd on behlllf of the Crown., nct,t of the Sate~ NSW. 2017
li!MMl·i:1
In Year 11 yo u learnt th at scientific investigation s are broken down into primary investigations ( suc h as expe rim en ts in a lab, field wor k or designing a model) a nd secon dary-sourced investigations ( such as a literature review)
1.1 Questioning and predicting
Before starting your investigatio n, you n eed to understand the working scie ntificall y skills essential to co mple ting a m eaningful scientific im-estiga tio n \Vo rking scie ntificall y itwo lves man y dynamic an d inte rrelated p rocesses.
11,ese are:
Questio n ing and Predic ting
Planning lm·estigario n s
Co nduc ting l n ves tig atio ns
Pr ocessing Dara and In formatio n
Anal ysing Data a nd info rmatio n
Pr o blem Solving
Co mm unic ating.
During this c ourse you will c h oose and im plem ent the processes appro priate to your inves tig atio n and u se yo u r knowledge and u n der s ta nding o f p h ysics to draw and communicate conclus ion s and su ggest areas for futu re r esearch . T his section is a guide to som e o f the key st eps tha t should be take n when first d eve lo ping your inqu ir y q uestion s and hypotheses.
WHAT INITIATES AN INVESTIGATION?
There are many sta rtin g points for an investigatio n. C u riosity can be tri ggered thro ug h o b ser vati o n and adva nces in techno logy.
Observation
Obse r vatio n includes u s ing all your se n ses a nd the ins truments a vailable to allow cl oser in s pec ti on o f things tha t the human eye c anno t see T hrou g h careful obse r vatio n, you can learn a lo t a bout the forces acting o n a n o b ject, inclu ding support forces and resistive forc es su ch as frictio n a nd a ir resistance
The idea for a primary inves tig atio n of a c o mpl ex p r oble m arises fro m prio r learnin g and ob se r vatio ns that raise fur the r questi o n s
H ow obse r vations are interpreted d epends o n pas t ex pe r ie n ces and knowledge But to enquiring minds, o b se rvatio n s will u suall y p rovoke fur the r questio n s, such as th ose g ive n below.
\Vhat velocity mu st a sate ll ite be m oving at to travel in a geosyn chrono us orbit ?
H ow d oes the motio n o f c harged particles in a n e lectric field co mpare to th e m ovem e nt of an object with mass in a grav itational fie ld ?
\ Vha t cau ses in te rferen ce in sig na ls tra velling th rough a wi re?
\Vhat modificati o n s could be m ad e to im prove th e e fficien cy o f a tra n sform er ?
\Vhat a pplication s are ther e fo r s pecial r ela tivity?
\Vhat infor m ation d oes the spectrum from a star reveal?
M :m y o f the:~e q 11 ~ r io n ~ ca n n o t he :m ~w e rect h y oh~er v:uion a l o n e , h ut they c:m be a n swered throu g h scie n tific in vestig atio ns. Lots o f great discoveries ha ve been m ade when a scie ntist ha s been b usy investigating an othe r p roblem Good scie n tists ha\'e ac u te p owe r s o f o b ser vatio n and e n q u ir ing mi n d s, a nd they m ake the m ost o f these ch a n ce o p po rtuni ties
ADVANCES IN TECHNOLOGY
Technology plays an important role in science. Atoms do not have sharply defined boundaries and so it is n ot possible to measure their radii directly. Developments in technology have allowed for th e accumulatio n of evi dence for scientific theories, laws and m odels, such as technology to measure the di stance betwee n nuclei of atoms in m olecules. For exam ple, in a hydrogen molecule ( H i) the two nucl ei are 64 p m ( picometres) ap art. The radius of eac h hydrogen ato m is a ss umed to be ha lf of that distance, i.e. 32 pm.
The opposite is also true, wi th the de,·elopment of new scientific theories, laws and m odels driving a need fo r n ew, improved techn ologies, such as the de,·elopme n t of neutri n o detectors , UV- vi sible s pectrosco py, infrared s pectroscopy a n d n uclea r magnetic resonance spectro scopy
Inquiry question, hypothesis and purpose
The inquiry question, purpose (aim) and hypothesi s are linked. Each o f these can be refi ned during the p l anning of the i nvestigation
An in quiry question defines what is bei ng investigated. It is important that you can i nterpret what an inquiry question is asking you to do. Compile a l ist of top ic ideas and start a literature review to for mulate your inquiry question. Evaluate and ref i ne your i nquiry questi o n once you have deci ded on a topic. Remember to consider the resources availabl e to you when deci d ing on your inqui ry question
A hypothesis i s a p r edi ction that i s based on evi dence and prior knowledge. A hypothesis often takes the form of a proposed relationsh ip between two or more variables i n a cause-and-effect rel ationship ; in o t her words, ' If x is true and th is i s tested, the n y will occur.'
A good hypothesi s shoul d be a statement that contains the i ndependent and dependent variables, be measurabl e
PEER REVIEW
and be falsifi able. You may need to adjust your hypothesis as you conduct further research into your chose n topic
A purpose is a statement describing in detail what will be i nvestigated. It is also known as the aim of your investigati on The purpose includes the key steps requ ired to test the hypothesi s. Each purpose should directly relate to the vari abl es in the hypothesis , a nd describe how each will be measured An exper i ment or investigation determ i nes the relationshi p between variab les and measures the resul ts.
There are three categori es of variables: independent, dependent a nd contro lled Variables ar e e ither qualitative ( includes nominal and ordinal vari ables) or quantitative ( includes discrete and co ntinu ous vari ables).
Reliable primary and secon dary sources should be used when research ing your topic and during your i nvestigation
Scientists often publish their findings in peer-rev iewed journal s Examples o f peer-reviewed p hysics jo urnal s include :
N ew Journal of Physics
R evietl.l of Modern Physics
J o urnal of H i'gh fi1 ergy Physics
Jnsi'ghts i n J\4edical Physi cs
J ournal of Pu re and Applied Phy sics
Journal of A st rophysics a 11d A erospace cedmology
Peer- reviewed journals ha\"e a n ed it o rial boa rd , co mprising experts in a partic ular field , who read a draft article a n d ask questions of the author before agreein g to publish the article
Your teacher ma y suggest that you pa r tner with a student in yo ur class, to pro vide each o ther with co n structive feedback regarding your in qu iry qu estion and/ or hypothesis. There are many benefits r esulting from collaborating with others, including building o n ideas and considering alternatfre perspecth·es. Fo r example, the current understanding o f l ight is the result o f research conducted b y s everal scien ti sts in the 19th an d 20th centuries.
PHYSICSFILE
Detecting gravitational waves
In the early part of the twentieth century Einstein formulated the theory of general re lativity. This theory µretJicled gravitational Wdves. Although hyJ)Ulhesisetl, scientists of the day were unsure how to detect them Two American scientists, Kip Thorne from California Institute of Technology (Caltech) and Rainer Weiss from Massachusetts Institute of Technology (Mil], started to collaborate on detecting these waves.
Weiss was an experimental physicist, and had already started designs on a detector, and researched possible sources of disturbance that would interfere with the readings. Thorne was a theoretical physicist, and came to the collaboration with an understanding of the implications of gravitational waves, and the theoretical events that would cause them. In 1984 Caltech and MIT set up a joint pr()fect called UGO (Laser Interferometer Gravitational-Wave Observatory).
UGO has over 1000 scientists worlting in the team, led by Barry Barish, modifying and improving the detection equipment and the hypothesis, and interpreting the readings from the equipment. UGO is so complicated and sensitive that the project was broken into different stages; it took three decades to set up the project and turn it on with the required sensitivity. The UGO detector {Figure 1.1.1) uses long detector arms that are perpendicular, and a laser light that is sent down both arms, bounci ng off mirrors at the end, and returning to the detector. Any change in length of the arms results in a changing interference pattern on the detector.
The consequences of detecting gravitational waves are wide reaching for science, and open up new areas of investigation as well as providing more evidence that supports the general theory of relativity. This was recognised when Weiss, Thorne and Barish were awarded the Nobel Prize in Physics in 2017.
\Vhen collaborating with o the r s, con side r the following:
Is the inquiry questio n clea r ?
Can the inq uiry q uestio n be answered in the time available?
Is the aim clear?
Is a h ypothes is written so that it can be disproved ?
Are the indep endent, dependent and c ontrolled variables cle arl y d efined ?
\Vhat are the s tren gth s of the in quiry questio n ?
\Vhat q uestions do you have about the inquir y qu estio n ?
FIGURE 1 1 1 UGO CS used in the search for gravitational waves
1.1 Review
f1'l:t:t\ii
Before you begin your resea rch, it is important to conduct a literature review. By utilisi ng data from primary and/or secondary sources, you will better understand the context of your investigation to create an informed inquiry question. The purpose (aim) is a statement describing in detail what w ill be investi gated.
A hypothesis is a tentative explanation for an observation that is based on evidence and prior knowledge. A hypothesis must be testable and falsifi able and defi ne a proposed relationship between two va r iables.
Distingu ish between the terms inquiry q uestion, hypothesis and purpose of an investigation
2 Which of the followi ng describes an inquiry question?
A How does the diffraction pattern of light depend on t he wavelength?
B The d i ffracti on of light increases wit h an increase in wavelength.
C Diffraction and refraction have opposite trends wi th respect to wavelength.
D Diffraction is the bending of waves at a corner.
3 For each of the followi ng hypotheses, select the independent and dependent variables.
a If water at 9Q<>C is allowed to cool to room temperature in d i fferent shaped conta iners, the conta iner w i th the l argest surface area will reach room temperature in a shorter period o f time
b If the launch angle of a proj ecti le i s 45°, then the horizontal d i stance travelled will be a m aximum.
c If you increase the thickness of foam bumpers attached to the front of a cart travelli ng at 1 ms- 1 , then the force experienced during a head-on collision will be r educed.
d If t h e emf applied to a c ircuit consi sting of ohmic res i stors is inc r eased, then the total curre nt in the circu i t will incr ease proportionally.
Once an inquiry question has been chosen, stop to evaluate the question before progressing. The question may need further refinement or even further investigation before i t is suitable as a basis for an achievable and worthwhile investigation. A major planning point is to not attempt something that i s not possible to complete in the time available or w i th the resources on hand.
There are three categories of variables: independent, dependent and controlled.
4 In an experiment about friction a student records the surface materi al t hat a ball is rolled over What type of variable is the surface material?
5 Which of the following is the most speci fic inquiry questi on?
A Do helmets make r i d i ng a bike safer ?
B Does the use of a foam helmet reduce the i mpact force when falling from a bike?
6 Which of the following inquiry questi ons is obj ective and specific ?
A How does the angle of release affect the peri od of motion of a pendulum?
B Does the moti on of a pendulum change when it is released from h ig her up?
C Pendulums make good metronomes
7 Select the best hypothesis from the three options below. Give reasons for your cho ice
A Hypothesi s 1: If the mass on a spring i s i ncreased, then the length the spri ng is extended will increase proportional ly.
B Hypothesi s 2: Springs have a sti ffness that is t he force required to extended them 1 m
C Hypothesi s 3: Spring extension is measured in millimetres.
1.2 Planning investigations
After you have formulated you r hypothesis, d efined the purpose o f your investigation and determined your variabl es, you w ill need to plan and design your im·estigation. Taking the time to carefully plan and d esign a practical in n~tigation before beginning will help you to maintai n a dear and concise focus throughou t. Preparation is essential. This section is a guide to so m e o f the key s teps tha t sh ould be taken w h en planning a nd design in g a practical in vestigatio n .
CHOOSING AN APPROPRIATE TYPE OF INVESTIGATION
After you have drafted your inquir y ques tio n , purpose, hypothes is and va riables, you wil l need to c ons id er an appropriate type o f investigatio n. Examples of various investigations are l is ted in Table 1.2.1. \Vh en s electing the type of investigation you will use, remem ber to cons ider how much time yo u have available, and whe the r )'OU will need to work in a gro up or in dividually.
Wi&Mttiitt
Primary data Design and conduct experiments
Test a claim
Test a device
Secondary data
Creating Field work
Data analysis
Measure and reliably compare the specific heat capacity for a range of metals.
Heavier obJects will go down a slide faster than hght objects.
Test the effi ciency of a solar panel.
Make a documentary or Investigate the use of nuclear radiatton in media report Australia.
Conduct a literature review
Develop an evktencebased argument
Write a journal article
Write an essayhistorical or theoretical
Develop a n environmental management plan
Analyse a work of fiction or film for scienti fic relevance
Crec1te c1 vi5uc1I presentation
Investigate emerging technologies
Desi gn and invent
Research applications of special relativi ty in everyday life.
Create an argument to counter the claim that t he Earth is flat
look at t he styfe of a peer-reviewed }oumal and wri te a literature review in that particular style.
Write about a Nobel Prize winner for Physics or the history of the development of the atomic model.
Create an envi ron mental management p lan for the safe handling of u nstable nuclei based on your understanding of nuclear decay.
Book: The Martian, Andy Weir (2011) and/or Film: The Martian, director Ridley Scott (2015)
Create c1 5eientific po5ter
Investigate perovskite solar cells.
Build your own hydro-generator.
Create a working model Create a working model of a door bell.
Create a portfolio
Compile various resources to answer an inqu iry question.
May be a starting point This could be initiated by the following stimuli: for an investigaUon - an excursion - engagement with community experts.
Pri mary and secondary-
Use original data to construct and analyse sourced investigations graphs or ta bles.
Analyse data from a variety of sources.
TABLE 1 2.1 Examples of different types of investigations
Organising information
It is importanl to be able to organ ise the in formation that you collect in your investigation. This is particularly important if your inves tigation is an in-depth literature review.Table 1.2.2 sh ows h ow you might be able to summari se informatio n from primary and seco ndary sources.
TABL E 1.2.2 Example of categories that help you to keep track of in formation as you conduct a literature review.
~ The effective temperatures of O-type stars from UV spectroscopy Advances in Space Research Journal Vo l 53, Issue 6 , 15 March 2014, pp. 973-81
Author
Luciana Bianchi, Miriam Garcia
Sample size
Use of UV spectroscopy to determine t he parameters of the photosphere (surface) and stel lar wind (ejected gases). Data fills in a gap when comparing effective temperature and spectral type. The downward trend was confirmed.
spectra, temperature, element formation
WRITING THE PROCEDURE
The procedure (also known as the m e thod) o f your in\'estigation is a step-by- s tep description of h ow the hypothes is w ill be tested. Conside r using a diagram of your FIGURE 1.2.1 An equipment set-u p for equipment set-up s uch as the o n e sh own in Figure 1.2 . 1. determining spri ng stiffness
\Vhe n detailing the p r ocedure, make s ure it has the following elements so that it is a vali d , rel iable and accura te investigation.
Methodology elements
Va li dity refers to whether an experiment or investigation i s in fact testing the set hypothesi s and purpose A valid i nvestigation is designed so that only one va r iable is being changed at a time. To ensure validity, carefully d etermine t h e i nde pendent variable and how it will change, the dependent variable, and the controlled variables and how they will be maintained.
Reliab i l ity refers to the notion t hat the experi ment can be repeated many times and the average of the results from all the repeated expe r iments w ill be con sistent
This can be mai ntained by defining the cont rol and ensuring there i s sufficient replication of the experiment. A ccuracy is the ability to obtai n the correct measurement. To obtain accurate results, you must minimise systematic errors.
Preci s i o n is the abi lity to consi stently obtai n the same measurement. To obtain precise results, you must minimise random e rror s.
Build some testing into your investigation to confirm the accuracy and reli ability of the equipment and your abi lity to read the information obtained. Reasonable steps to ensure the accuracy of the i nvestigation inc lude c onsidering the unit in which the independe nt and dependent variables will be measured and the Instruments that will be used to measure the variables.
Select and use appropr iate equ ipment, materials and procedures For exa mple, select equipment that measures to smaller degrees to reduce unce rtainty a nd r epeat the measuremen ts to confirm them
Describe th e material s and procedure in appropria te detai l. Th i s should ensure that every measur ement can be repeated and the same r esul t obtai ned with in reasonable margins of experime ntal error (less than 5% is r easonable). Pe r ce ntage uncertainty, som eti mes referred to as percentage error, is a way to quantify how a ccurate a measuremen t is Thi s will be discussed in Section 1.4-.
Section 1.4 page 17
Recording numerical data
\Vhen using measur ing instruments, the number of s ignificant figures (or d igi ts) a nd decimal pl aces you use is determined b y how precise your measurements are. You will lear n more about how t o iden tify and use an appropria te number of significan t figures and decimal places in Section 1.4.
Data analysis
Data analysi s is pan of the procedure. Co n sider how the data w ill be presented a nd analysed, for example in tables, so that p anerns c.an be seen Graphs can show relationships and enable comparisons. Preparing an empty table showing the data that needs m be obtained will help in the p lanning of the investigation.
The n ature of the data being collected, s uch as whether the variables are qualitative or quanti tati,·e, influences the type of method or tool that you can u se to analyse the data. T he aims and the hypothesis will also influence the choice of analysis tool.
It is a good idea to draft a table of results before you commence an experiment A sample results tab le is shown in Table 1.2.3. Table 1.2.4 shows how you m igh t analyse the different types of rnriables in an in,·estigation.
1 2.4 Types of var~bles and the W<f'/S in which they could be measured and used within an investigation.
State the mqu1ry quest ion
Ust the independent va riable Is t he variable q ua ntitative or qualitative?
list the dependent variable(s). What equipment will you use to measure these ?
List the variables that you will control What will you do to control t hese variables?
What ,s the specific heat capacity of copper'
The independent vari able is the electrical energy being suppl ied t o the calorimeter (quantitative).
The dependent variable is the time taken to increase the temperature of the calori meter contents by a given amount
All mineral waters will be stored at room te m perature u nt il analysed The tem perature of each will be measu red with a n ethanolfilled glass thermometer. The uncertainty of the t hermometer tS ±0. l °C
Sourcing appropriate materials and technology
\Vhen d es igning your inves tigation, you ,,~II need to decide on the mate rial s, technology and instrumentation tha t ,,~ II be used to carry ou t your resear ch. It is important to find the right bala nce between items that are easily accessible a nd those which will give you accurate results. You will also need to conside r any costs or risks associated with usi ng the techn o logy, how familiar you are with usi ng it, and a ny limitations the tec h nology has that w ill impact you r investigation. As you mo,,e on to co nduc ting your investigation, it wil l be important to t ake note of the p rec ision of your chosen instrumentation and how thi s affects the accuracy and validi ty of your results. This will be discussed in greater detail in Section 1.3.
TABLE 1.2.3 Results table for investigating the specific heat capacity of copper using a calorimetEJ.
TABLE
Data logging
Ask your teacher whe ther data-loggi ng equipment might be available. Some schools have access to equipment such a s mo tio n sensors (Figure 1.2.2), temperature sensors and force sen sors.
rlGURE 1.2.2 Determining the veloaty of an obtect can be done with different ~els of accuracy and precision (a) Ticker tape can have an effect on the motion, changing the accuracy of the measurement as well as the J)(ea51on (b) A motion sensor can measure the velocity wrth greater accuracy and preaseon.
Modifying the procedure
The procedure may need modifying as the investigation is carr ied out. Th e following actio ns will he lp to determine any issues in the procedure and h ow to modify them
Record everything.
Be prepared to make changes to the approach.
N o te any difficulties encountered and the ways they were m·ercome. \Vhat were the failures and s uccesses? Ever y test carried out can contribute to th e under s tanding o f the investigation a s a whole, no matter how much o f a disaster it may first appear
D o n o t panic G o over the theory again, a nd talk to the teacher and other studen ts. A different perspective can lead to a solu tio n ff the expected data is no t o b tained _, do n ' t worry As long as it can be c ritica ll y nnrl nhjrct iw ly rvnlun terl, t hr limimtinm. nf the im0estigntinn ~ n hf- i rlenf'ilirrl nn rl further investigatio n s proposed , the work is worthwh il e.
COMPLYING WITH ETHICAL AND SAFETY GUIDELINES
Ethical considerations
S om e im·cstigatio ns require an ethics apprO\-al; consult ,,;th the t eacher. \Xfhen you arc planning an im·estigation, identify all parts of the procedure that migh t invoh·e ethical cons ideratio n s, and evaluate their necessity. You may be able t o change the methodology to reduce o r eliminate any possible ethical issues.
Risk assessments
Risk assessments are performed to identity, assess and control hazards A risk assessment shoul d be performed for any situation. i n the laboratory or outside in the field Always ident ify the risks and control them to keep everyone as safe as ix>ssible
Ways to reduce r i sk are, in order from most effective to l east effective, elimination, substi tution, engineering (modifying equipment), administrative control and personal p rotective equi pment. Special care. such as weari ng sunscreen, i nsect repellent, appropriate clothing and gloves as necessary, must be taken to m i nimise the risks t hat come with working outdoors. Someone with first-aid training should al ways be present. and any injuries or accidents must be immed iatel y reported to you r teacher or lab technician.
IGO TO IYear 11 Section 1 2
PHYSICSFILE
Ethics and radiation
There are many different types of radiation, including waves from the electromagnetic spectrum and alpha and beta particles released during the decay of radioactive nuclei. Some radiation occurs naturally, including cosmic radiation and the decay of unstable radioisotopes. Alpha particles are the nuclei of helium atoms, He, beta particles are electrons, and gamma rWfS are very-hig~energy electromagnetic waves. Figure 1.2.3 shows that skin can stop the penetration of alpha particles However, alpha partides are damaging to living tis.sues if ingested or inhaled, or if they enter a wound.
The decay of radioisotopes to produce different types of radiation can be represented by equations of balanced nuclear reactions. For example, the decay of naturally occurring uranium-238 produces thorium-234, an alpha particle and gamma radiation. This decay is represented by the following equation: ~ u 2 ~ Th +~He+ y
The Greek letter y is used to represent gamma radiation. Notice that when the decay produces alpha or beta particles, a new element is also formed. Carbon--14 is a radioisotope that decays to produce beta particles, represented by the following equation:
The following applications of radiation can be useful to society:
• the use of nuclear magnetic resonance, infrared, atomic absorption and UV-visible spectroscopy in chemical analysis
• radiotherapy as a cancer treatment use of X- rays to diagnose broken bones and dental decay the production of energy from nuclear fission reactions in power plants.
However, radiation can also be harmful to society:
• if nuclear weapons are used in war
• if nuclear waste contaminates water and food
• if medical practitioners and dentists are exposed to X-rays when imaging patients for medical purposes.
aluminium lead
nGURE 1.2.3 Skin can stop the penetration of alpha particles
PEER REVIEW
Your teacher ma y suggest that you p artner with a student in your class, to provide each o lher with constructi\"e feedback regarding your planning.
Consider the following:
Is the type of im estigation appropriate and relevant to the inquiry question ?
Is the procedure written in easy- to-understand logical ste ps?
Is the p rocedure valid and reliable?
Has a thorough and complete risk assessment been undertaken before s ta rting the investigation?
\ Vhat are the strengths of the type of in,·estigation and procedure?
\ '(/hat q u estion s do you have a bom the type o f in\"estiga tion and p rocedure?
1.2 Review
fi 11:t:t\ii
The procedure of your investigation is a step plan. When detaili ng the procedure, ensure it complies as a valid, reliable and accurate investigation.
It is also important to determine how many times the experiment needs to be repllcated. Many scientific investigations lack sufficient repetition to ensure that the results can be considered reliable.
1 Gi ve the correct term (accurate, reliable or valid} that describes an experi ment w i th each of the following c onditions
a The experiment addresses the hypothesis and a ims
b The experiment is repeated and cons i stent results are obtai ned.
c Appropriate equipment is chosen for the desired measurements.
2 A student wants to measure the range of a proj ectile on the school oval. They intend to be there for an hour in summer Which of the following PPE should be included in the r i sk assessment for the activity on the oval? More than one response may be correct.
A use of a fume cupboard
B sunhat and sunscreen
C gloves
D eye goggles
Ri sk assessments must be carried out before conducting an investigation to make sure that when you carry out your procedure, you and others are kept safe. If you have elements of your investigation whi ch are too high- risk you will need to re-evaluate your design.
It is important to choose appropriate equipment for your experiment- not just personal protective equipment (PPE) that will help keep you safe, but atso instrumentation that will give you accurate results.
3 A journal article reported the materials and procedure used to conduct an experiment The experiment was repeated three times and all values were reported in the resu l ts section of the article.
Repeating an experiment and rei:x>rting results supports:
A precision
B re liability
C accuracy
D systematic errors
4 You are conducting an experi ment to determine the effect of bumper foam density on the impact force during a collisi on.
Identify:
a the independent vari able
b the dependent variable
c at least one controlled vari able.
5 A student i ncl uded a diagram of the experimental setup in her procedure. Use the d i agram to wri te clear instructions for the procedure.
Collecting and recording data
For an investigation to be scientifi c, i t must be objective and systematic. Always record all quantitative and qualitati ve data collected and the methods used to collect the data in your l ogbook. Also record any incident. feature or unexpected event that m ight have affected the quality or val idity o f the data The recorded data i s known as raw data Usually thi s data needs to be processed i n some manner before it can be p r esented.
Safe work practices
Remember to always employ safe work practices whi le conducting your experiment. See Section 1.2 for how to conduct r isk assessments
You wi ll al so need to keep in m ind sa fe procedures to follow when disposing of waste-consult your teacher or education and government websites for i nformation
IGO IYear 11 Section 1.2
1.3 Conducting investigations
Once the planning and design of a practical investigation is complete, the next step is to undertake the investigation and record the results. As with the plann ing stages, there arc key steps and s kills to keep in mind t o maintain high standards a nd minimise potenti a1 errors throughout the investigation (Figure 1.3.1 )
This section wi ll focu s o n the best methods of conducting a p ra ctical in vestigati o n, a nd of syste m atically genera ting , recording and processi ng data.
FIGURE 1.3.1 When reading analog devices, it is important to observe the meter or ruler straight on to avoid parallax errors.
l·ie'iHl·UI
Identifyi ng errors
Er rors can occur for a va r iety of reasons. Bei ng aware of potential errors hel ps you to avoid or minimise them. As shown in Figure 1.3.2, ther e are three types o f errors that can occur i n an experi ment.
Mistakes are avoi dable errors. A measurement that invol ves a mistake must be rejected and not included i n any ca lculations, or averaged with other measurements of the same quanti ty IGO IYear 11 Sectio n 1.3
A sy stema tic e r r o r i s an error that is consistent and will occur again if the investigati on i s repeated in the same way. Systemati c errors are usually a result of instruments that are not calibrated correctly or methods that are fl awed. Whatever the cause, resulting errors are in the same d i rection for every measurement and the average will be e i ther too high o r too low as a result. The~ l e~c1 to h i~~- h~mplP.~ of h i ~!. are shown i n Figure 1.3.3.
Errors
Mistakes (avoidable errors)
Systematic errors {including b ias) Random e rro rs
n Gu RE 1 3 2 Types of errors that can be made in an experi ment.
Poor definitions of concepts and variables, e.g. classifying qualitative light intensity of d iodes without defining ' bright' or 'd im'
Incorrect assumptions, e.g. assuming ohmic conditions for non-ohmic devices
Frrnr<; in i nvP<;tie;:itinn riP'-ien ;:inci procedure, e.g. using a voltmeter when a multimeter should have been used
FIGURE 1.3.3 Types and examples or bias in an electric circuit analysis.
Random errors occur in an unpredictable manner and therefore follow no regular pattern. The measurement is sometimes too large and sometimes too small. The effects of random errors can be reduced by taking mu ltiple measurements of the same quanti ty, then calculating an average.
Techniques to reduce error
Use appropriate equipment
Use the equipment that is best suited to the data that needs to be collected to validate the hypothesis. Determining the uni ts of the data being collected and at what scale will help to select the correct equipment. Using the r ight uni ts and scale w i ll ensure that measurements are more accurate and precise (with smaller systematic errors).
To m in imise errors, check the precision of the equipment that you intend to use Voltmeters and ammeters often have different scales that can be used depending on the expected reading (Figure 13.4). It is always best to start with the largest scale, and adjust it until the measurement is in the smallest range that co ntains it.
Use calibrated equi pment
Before carrying out the investigation, make sure the instruments or measuring devices are properly cal ibrated and are, in general, functioning cor rectly.
Use equi pment correctly
Use the equ ipment properly. Ensure any necessary train ing has been done to use the equipment and that you have had an opportunity to practise using the equipment before beginning the i nvestigation Improper use of equip ment c a n resu lt in inaccurate, imprecise data w ith large errors, and the val id ity of the data can be comprom ised.
Incorrect reading of measurements is a common mistake Make sure all of the equipment needed in the investigalion can be used correctly and record the instructions in detail so they can be referred back to if the data doesn't appear correct
Increase sampling size
In general, the larger the sample taken for anal ysis, the more precise the measured values will be However, there are practical limi ts to this. For example, you wi ll be l im ited by the size of the contai ner and number of conta iners you can transport back to school, if collecting samples in the field.
Repeat the investigation
As d iscussed in Section 1.2, reliability is ensured by repeating your experiment. Modi fications to your procedure may be needed before repeating the investigation to ensure all variables are being tested under the same conditions
Reference secondary-sourced information
As you conduct your investigation, it is important to make note of any secondary-sourced information that you use. This will then be included in your written report. This is discussed in further detai l in Section 1.7.
FIGURE
PEER REVIEW
Your teach er m ay suggest that you parmer with a srudem in your class, to provide each other with constructive feedback regardi n g your data collection.
Consider the following:
Is the data presented clearly in tables and/or graphs? Are all entries in the logbook dated?
Are appropriate headings and units included?
If anything unexpected occurred during data collection, was this recorded?
\Xlhat are the strengths of the data collected?
\Xlhat questions do you have a bout the data collected?
1.3 Review
l11i:l#\N
It is essential that during the investigation you record the following in your logbook: all quantitative and qualitative data collected the methods used to collect the data any incident. feature or unexpected event that might have affected the quality or validity of the data.
Mistakes are avoidable errors, and measurements affected by mistakes should be d iscarded
ltli·i'iiiii·i:ti
1 Where should observations and measurements be recorded?
2 Identify the type of error that is described in each scenario below, and how it could be avoided.
a the electronic scale was not zeroed/tared before samples were weighed
b 50 g masses were used rather than 5 g masses
c one result is significantly lower than all the rest d one student judged a water sample as ' cloudy', while another student recorded it a s 'very cloudy'
3 The velocity of a cart after rolling down a ramp is being measured by timing the cart as it travels between two markers known to be 20c m apart. A student doing this investigation recorded the following times with the same initial conditions: 0.25s, 0.28s, 0.02s, 0.20s, 0.22s, 0.72s. Identify the measurements that were a mistake Find the average time.
A systematic error is an error that is consistent and will occur again if the investigation is repeated in the same way. Systematic errors are usually a result of instruments that are not calibrated correctly or methods that are flawed. Random errors occur in an unpredictable manner and are generally small. A random error could be, for example, the result of a researcher reading the same result correctly one time and incorrectly another time.
4 Identify whether each error is a mistake, a systematic error or a random error.
a A weigh scale that should have measured a mass of 25.00 ± 0.03g actually measured 24.92 ± 0.03g.
b A student misread the value on the slotted mass for a Hooke's law investigation.
c A ball was weighed three times with the follow ing results: 147.93g. 147.94g and 147.92 g
1.4 Processing data and information
Once you have cond ucted your investigation and collected data, you will need to find the best way of collating this. This section is a guide to the different fo rms of rep re se nta tio n that will help you to better understand your data .
RECORDING AND PRESENTING QUANTITATIVE DATA
Raw da ta is unlikely to be used direc tly to test the hypothesis. H owe\·er, raw data is essential to the investigation and plans for collecting the raw data sh ould be made carefully. Con si d er the formulae or graphs that will be used to a n alyse the data at the end o f the investigatio n Th is will help to determin e the type o f raw data that needs to be c o llected in o rder t o test the hypothesis
Once you have determined the data that needs to be collected, prepare a table in which to record the data.
l;J@Ht·i:1
Significant figures
Signif icant f igu res are the numbers that convey meaning and precis ion. The number of significant f igures used depends on the scal e of the i nstrument A signi fi cant figure is an i nteger or a zero that follows an integer. A zero that comes before any integers is not s ignificant.
When you record raw data and report processed data, use the number of si gnificant figur es availabl e from your equipment or observati on. Using either a greater or smaller number of significant figures can be misleadi ng For example, Table 1.4.1 shows measurements of five samples taken using an electron ic bal ance accurate to two decimal places. The data was entered into a spreadsheet to calcu l ate the mean, wh ich was displayed wi th four decimal p l aces.
You wou l d record the mean as 5.69g, not 5.6940 g. because two decimal places is the precision limit of the instrument. Record ing 5.6940g would be an example of false precision.
TABLE 1 4.1 All example of false precision in a data ca lculation.
Multiplying or dividing
When multiplying or d ividing measurements, r eport the final value to the least number of signi ficant figures used with in that calculation. For example, to cal culate the resistance, in ohms. of a component using the potential difference and current. the formula is V = IR. If V = 5.62V (three significant figures), and the current (f) is 1.465A (four signif icant figures), the resistance, in ohms, shoul d be reported to the least number of significant figures, i.e. to three significant figures (V= IR; 5.62 = 1.465 x R; R= 31l4n to three significant figures)
Although d igital scales can measure to many more than two figures and calculators can give 12 fi gures, be sensi bl e and follow the signi ficant figure r ules
Adding or subtracting
When addi ng or subtracti ng measurements, report the ca l cu lated value to the least number of decimal p l aces. For example, when calcula t ing the net force o n an obj ect, the follow ing measur ements were r ecorded.
Weigh t of tenni s ball : 0 5733N
Air res istance (frictiona l force): 0 93 N
Net force = 0.93 - 0.5733 = 0.3567 = 036 N. The origina l answer of 0 3567 N is an example o f fa lse preci si on as one value in the data was not m easured to f ive decimal places. The final answer must be stated to the smallest number of decimal p laces seen in the data, i e. 0.36 N
Decimal places
As with signifi cant figures. you must be careful to record your measurements to the precision of the equipment used. If a wei gh ing bal ance can r eport a mass measurement to two decimal places, you should record your va lue to two decimal p l aces.
When adding or subtracting measurements, report the ca l cu lated value to the least number of decimal p l aces used i n the calcu lation. For example, in an investigation t he following measurements were recorded :
Sampl e A 4.93
Sampl e B 5.54
Sampl e C 4.82
The average of these resu l ts is 493 + 5f + 4.82 - 5.0966666667
As the sampl e results are all to two decimal places, this average also needs to be rounded to two decimal places, i.e. 5.10. It woul d be misleading to report the average to a greater number of d ecima l pl aces
ANALYSING AND PRESENTING DATA
The raw data that has been obt a in ed n eeds to be presented in a way that is clear, concise a nd accurate.
There are a number of ways of presenting data, including tables, graphs, flowcharts and diagrams. l'be best way of ,isualising the data depends on its narure Try several fo rmats before making a final decision, to create the best possible presentation.
Presenting raw and processed data in tables
Tables organi se data into rows and columns and can vary in complexity according to the nature of the data. Tables can be used to organise raw data and p r ocessed data or to summa r ise results.
The simplest form of a table is a two-column forma t. In a two-column table, the f irst column should contain the independent variable and the secon d co lumn should contain the dependent variable
Tables should have a descriptive title, column headings (including the unit) and numbers aligned to the decimal point
A tab~ of processed data usually presents the average values of data, the mean However, the mean on i ts own does not provi de an ac curate picture of the results.
To report processed data more accurately, the uncertainty s hould be presented as well.
Uncertainty
When there i s a range of measurements of a parti cular value, the mean must be accompani ed by the uncertai nty for you r results to be presented as a mean in an accurate way.
Uncertainty is calculated as: uncertainty•± maximum variance from the mean
Graphs
Percentage uncertainty
Percentage uncertainty (also known as percen tage error) is a way to quantify how accurate a measurement i s. To calculate the per centage uncertainty of your data you take the uncertainty and divide it by the measurement. then mu ltip ly by 100.
Other descriptive statistical measures
Other statistical measures that can be used, dependi ng on the data obtained are:
mode: the mode is the value that appears most often in a data sel Th is measure is useful to describe qualitative or d iscrete data.
medi an: the median i s the ' mkidle' value of an ordered l ist of va lues. The medi an is used whe n the data range i s spread, for example, due to the presence of unusual results. making the mean unrel iable
Table 1.4.2 is a gui de to choosi ng the most appropriate m easure of central tenden cy for a data s el
TABLE 1..4.2 The most appropnate measure of central tendency to use in descnplJ,e slallslJcs depends on the type ol data.
Ty pe o f d ata Mode Me d i.an Me.an
nominal (quahtat1ve) ordinal (qualltahve)
discrete or continuous (quantitative) , , maybe
h is imponant lhat you choose an approp riate g r aph type lo suit lhe data lhat rou ha,·e collected. Table 1.4.3 summar ises suita ble graph s fo r discrete or continuous quantitati, e data
TABLE
1 4.3
Type of
d iscrete
graph
con ti nuous bar graph, h istogram or pie diagram
line graph or scatter plot, including a trend l i ne 1f ap propriate
nitrogen (N), -78%
oxygen (0). - 21 9li
minute tra ces o f neo n (Ne), helium (He), metha ne (CH, ), krypton ( Kr), hy drogen (H), xenon (Xe) and ozon e (OJ carbon dioxi de (CO2) , 0.0496 wate r vapou r (H2O), 0 4% argon (Ar), - 1%
FIGU RE 1.4.1 Pie chart showing distribution of e~ments from a sample analysis
600 X 500 \400 ;,:
X X X X X X X X
0 5 10 15 20 25 30 35 Thi ckness (mm )
rlGUR E 1.4.2 Sc.alter plot of the radiation in tensity through different thickness material
4 6 8 JO 12
Potential difference across primary co i l (V)
FIGURE 14 3 Graph, including trend line, showing resu lts of an investigation into two different transformers t o see which is better lo use with a m<Kfel motor
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Outliers
Sometimes when the data is collected, there may be one point that does not fit with the trend and i s clearl y an error. Th i s is called an o utlier An outlier is often caused by a mistake made in measuring or recordi ng data, or from a random error in the measuring equi pment. If th ere is an outlier, include i t on the graph, but ignore i t w hen addi ng a trend line
In ge neral, tables provide more d etailed data than graph s, but it is e as ie r t o obsen·e trends and patte rn s in data in graphical fo rm than in tabular fo rm.
Graphs are u sed when two variables are being considered and o n e variable is d epen de nt on the other. The graph shows the r elati onship betwee n the ,miables.
~Jnere are several types of graphs that ca n be used, including line graphs, bar grap hs and p ie diagrams. The best one t o use will depend o n the nature of the data.
General rules to follow when maki n g a graph ( Figure 1.4.4) include the follo,,~ng: Keep the graph sim ple and u n cluttered. Use a descriptive title.
Represent the independent variable o n the x-axis and the dependent var iabl e on tht":y--axi~
1\<l ake axes proportionate to the data.
Clearly label axes with both the n1riable a nd the unit in which it is m easu red.
Graph 1: 'Graph of velocity of glider with time as it travels down an inclined air track'
AJwa'fS give a descriptive title to the graph or diagram.
Nways mark where axis value is.
Always write values clearly
Draw line of best fiL Use a ruler for straight lines and a practised sweep for curves.
If you have an outlier go back to your workings and check it again to see if you can explain why
Origi n does not have to be (0, 0).
Different scales may be used.
Give the quantity name in full with units in brackets
FIGURE 1 4.4 A graph is a better way to observe trends and patterns i n data compared to a tabl e
Distorting th e truth
Poorly constructed graphs can alter your perception of the d a ta For example, in F igu re 1.4.5 you can see two graphs that s how the same data- the meas u rement of the per iod of o scill ation o f a pendulum with d ifferen t mas ses.
