The WHY and HOW of Student Practical Investigations

1. The WHY and HOW of Student Practical Investigations Brian McKittrick & Dan O’Keeffe

2. General comments • Addressing mostly experienced PI handlers • Impossible to cover thoroughly • Much very familiar to many of you • Consulted a number of physics teachers • Include personal impressions and tips • Focus - Area of study 3 in Unit 4 rather than Unit 2, though most will still apply • More like ‘HOW and WHY’ rather than ‘WHY and HOW’ • Some diagrams from a prac book I wrote in 1990s • PP slides & additional notes available post-conference on VicPhys site

3. WHY ASK AN OLD CODGER TO TALK ON PIs? • 1956-58 Science at Uni of Melb: STAV STS • 1959-71 Teaching - Hobart, Perth & Melb: Students entering Experimental section of STS • 1972-73 Teaching in UK: ‘Long Investigations’ an assessed part of A level Nuffield Physics • 1974-…: Students entering Vic STS especially Experimental section • Early 1980s: As member of VISE Physics Subject Committee, with Dan O’Keefe & Andrew Tait – ‘Extended Experimental Investigations’ accepted as Option in Vic Yr 12 Physics • Varying emphasis since then under VBOS, VCAB and VCAA • New SD with increased importance • Other states: Checked most states, only QLD has it

4. WHAT WILL I TRY TO COVER? • Preparing students for PI • Students selecting topic – and your approval • Students’ detailed research plan • Equipment • Collecting & processing data • Using tables • Uncertainty and error in measurements • Total uncertainty when combining measurements • Using graphs • Uncertainty on graphs • Line of best fit • Interpretation of graphs • Log-log analysis • Graphs of the valuable relationship y = axn • Deductions and conclusions • Poster report • Assessment

5. PREPARING YOUR STUDENTS • Introduce PI ~ 3 weeks before experimental period • Outline task and time (SD: 7-10 h class time) • Study design formal statement: A student-designed practical investigation … waves, fields or motion … the student to develop a question … hypothesis … course of action to answer the question … primary quantitative data, analyse & evaluate the data … a conclusion … twocontinuous independent variables ... Results in scientific poster format … logbook must be maintained • Real research unlike typical prac work • Log book – constant companion

6. DECIDING WHAT TO INVESTIGATE & ORAL APPROVAL • Waves,fields &/or motion • Hobby, sport • An area of physics of interest to them • Brainstorming • Students asked to “come tomorrow with 3 ideas” • STS handbooks • Internet searches with selected keywords • Teacher’s prompt list (if all else fails) – last resort • Teacher’s prompt restricted list • Task mandated e.g. ‘Vol of A4 sheet’

7. DECIDING WHAT TO INVESTIGATE & ORAL APPROVAL • Equipment provided - task & design from student • Limitations: • Completion feasible in time available? Often underestimated • Equipment available? • Location limitations? • Safety & ethical considerations? • Sources of ideas for students:Several lists on VicPhys site: http://www.vicphysics.org/practicalactivities.html • Tentative oral approval after short discussion with teacher

8. DETAILED RESEARCH PLAN • Two specific research questions, identifying variables • Hypotheses • Experimental design (incl data collection) • Special requirements • Labelled diagram of experimental setup • List of materials required • Example of a template

9. DETAILED RESEARCH PLAN – page 1

10. DETAILED RESEARCH PLAN – page 2

11. EQUIPMENT CONSIDERATIONS • Diagram of equipment helps to clarify their ideas • OK to modify or change equipment (Grrr!) • Sophisticated equipment does not mean better research • Construction of unavailable equipment must be completed before experimental period • Unavailable equipment • Locating unusual items through internet • Students specificity on their equipment list, eg size and number

12. EQUIPMENT CONSIDERATIONS • Assembled by • Lab tech • Students • Teacher or • Some combination of above • Storage prior to and during experimental period: • Specified cupboards • Boxes (name or number-labelled) • In lab or prep room • Some equipment left in situ if possible

13. COLLECTING DATA • Log book • Dry or dummy run • Some quick readings to • clarify if equipment OK • clarify if technique OK • provide desirable range of readings • recognise & eliminate effect of other variables

14. COLLECTING DATA • As real research work and not typical structured experiments, which usually ‘work’: • Teething problems • Necessary modifications to equipment or procedure should be seen as OK • OK to seek reasonable help from teacher • Give reasonable time on wrong track before intervention • OK to restrict or extend original aims - discuss with teacher • Avoid ‘data stockpiling’ - Processing data periodically important • Estimate and record uncertainties while taking readings • Where necessary repeat readings appropriate number of times to reduce effect of random errors

15. PROCESSING DATA • Tabulating • Uncertainty & errors • Graphing • Spreadsheeting & using calculators • Deducing relationships from tables & graphs

16. USING TABLES - Accepted conventions • Title & headings Door opening force F required and distance d from hinge

17. USING TABLES - Accepted conventions • Large & small nos

18. USING TABLES - Accepted conventions • Leave space on right of table for possible future columns • Recording data on prepared Excel sheet • Other useful systems for recording and processing data e.g. • Logger Pro • CAS calculators • ‘Box & whisker’ plots

19. USING TABLES - Accepted conventions • Testing possible relationships using tabulated readings F decreasing while d increasing. So F may  1/d ?If so, Fd is constant. So check it. It is.If Fd is not constant, could test F/d2, i.e. is Fd2 constant? Door opening force F required and distance d from hinge

20. UNCERTAINTY IN MEASUREMENTS • There is an uncertainty in every measurement made.E.g. mass of a hockey ball = (161 ± 2) g • With every uncertainly there is a probability. It is usually qualitative.In above example, highly probable that the actual mass is between 159 and 163 g • Normally retain one uncertain figure in a measurement.

21. UNCERTAINTY IN A MEASUREMENT – DEPENDS ON? • Limit of reading an instrument • Instrument with a scaleleast count (smallest subdivision on scale) = 1 mm resolution (smallest change we can detect) ≈ usually 1/5 or 1/10 divSo uncertainty here probably 1/5 of least count ≈ 0.2 mmSo length = (42.7 ± 0.2) mm • Digital readout Normally one unit in extreme right hand digit on the scale • Accuracy of instrument • Usually supplied by manufacturer, not available to student • Usually teacher’s assistance needed • If 5% on a voltmeter, reading = 6.4 V. Justifiable record = (6.4 ± 0.3) V

22. UNCERTAINTY IN A MEASUREMENT – DEPENDS ON? • Limit of setting an instrument • How accurately the quantity to be measured can be ‘set’ or identified, e.g. distance to where shot put landed. • Usually larger than how accurately you can read the measuring instrument • Allowing for any systematic errors • E.g. An ammeter may have a zero reading +0.2 A • So apply a zero correction of -0.2 A to all readings, or adjust zero reading • Most systematic errors, if recognised, can be eliminated • Allowing for any random errors • Slight variations in repeated readings • Causes: e.g. limitations of observer’s eye, minor changes in temperature, variations in human reaction time • Important to take repeated readings in these situations

23. UNCERTAINTY IN A MEASUREMENT – DEPENDS ON? • Response time of measuring equipmentIf time dependent, e.g. a thermometer, may need to wait a little • Allowing for multiple sources of uncertainty in a measurementRandom errors may give (17.2 ± 0.3)oC.Manufacturer’s accuracy might be ±0.2oC. These uncertainties should be added, giving (17.2 ± 0.5)oC. • Estimating uncertainties takes experience and time to develop • Better to be pessimistic than optimistic – students often underestimate them. • Consultation with teacher and other students often helpful.

24. TOTAL UNCERTAINTY WHEN COMBINING MEASUREMENTS – Basic approach • Adding or subtracting quantities E.g. Predicting the final length of a heated rod Initial length = 94.3 mmincrease in length = 1.87 mm Predicted final length = 96.17 mm Retain 1st uncertain figure & use second one to round off firstSo retain the ‘1’ in 96.17 & use the ‘7’ to round off the ‘1’ Justified final length = 96.2 mm • Multiplying or dividing quantities E.g. Deducing the distance covered from multiplying speed by timeRound off the product or quotient with the same number of sig figs as in the quantity with the least number. • Probably more advanced method expected at this level

25. UNCERTAINTY AND ERROR TERMS • Often term ‘error’ is used incorrectly when ‘uncertainty’ is meant. • Absoluteuncertainty (AU): - the largest likely uncertainty in the measurement, e.g. (15.6 ± 0.2)oC, where it is highly probable that the temperature ϴ is between 15.4 and 15.8oC. AU(ϴ) = 0.2oC Unfortunate term as ‘absolute’ is too definite a description! • Percentage uncertainty (PU): the percentage the absolute uncertainty if of the measurement, i.e. PU(ϴ) = 0.2/15.6  100 = 1.28 ≈ 1.3%Normally PU stated to 1 sig fig, unless first number is small, say, 1 or 2, then 2 sig figs

26. UNCERTAINTY AND ERROR TERMS • Percentage error (PE): percentage by which experimental value deviates from a ‘true’ or accepted value. If an experiment gave speed of light c as(3.2 ± 0.9)  108 m s-1 & accepted value 3.0  108 m s-1, then PE(c) = 0.2/3.0  100 ≈ 7%. Note that the PU from the experiment, PU(c) = 0.9/3.2  100 ≈ 28%. Accuracy of the experiment is indicated by PU not PE. • Human (or personal) errors are‘mistakes’and not inevitable and can be avoided with careful technique.E.g. misreading a scale, a calculating mistake, being prejudiced in favour of earlier over later readings.Claiming that these limited your accuracy in a report is admitting incompetence. • Systematic errors and random errors are accepted terms.

27. CONVENTIONS WHEN STATING UNCERTAINTY • Round brackets placed around a measurement and its uncertainty, e.g. (25 ± 1) s, not 25 s ± 1 s • Absolute uncertainty is usually given rather than percentage uncertainty, e.g. (25 ± 1) s, not (25 ± 4%) s • With large or small numbers using standard form, power of ten and unit are both placed outside the brackets, e.g. (6.3 ± 0.2)  10-8 m, not (6.3  10-8 ± 0.2  10-8) m • Similarly for prefixes to units,e.g. (63 ± 2) nm, not 63 nm ± 2 nm • Absolute and percentage uncertainties normally stated to one sig fig, or perhaps to 2 if first sig fig is ‘I’ or ‘2’ • A measurement should be quoted to the same decimal place as its absolute uncertainty, • e.g. (2.60 ± 0.02) s, and not (2.604 ± 0.02) s or (2.6 ± 0.02) s

28. TOTAL UNCERTAINTY WHEN COMBINING MEASUREMENTS – ‘Advanced’ approach • Adding or subtracting quantitiesE.g. adding two length measurementsAbsolute uncertainty in sum or difference of two quantities is the sum of their absolute uncertainties(Detailed developments of this and the following rule will be given in the post-conference notes on VicPhys site) • Multiplying or dividing quantitiesE.g. deducing the distance covered from multiplying speed by timePercentage uncertainty of a product or quotient of two quantities is the sum of their two percentage uncertainties

29. TOTAL UNCERTAINTY WHEN COMBINING MEASUREMENTS – ‘Advanced’ approach • Tidying up after using these two rules • Adding or subtractingAddition of two lengths could give rise toTotal length L = 91.379 cm and AE(L) = 0.058 cmSo L = (91.379 ± 0.058) cm,But we normally retain only one sig fig in the AU, using the second to round off the first.So L = (91.379 ± 0.06) cm,But we retain only one uncertain figure in the measurement, using the second to round off the first.So L = (91.38 ± 0.06) cm, in the conventional form.

30. TOTAL UNCERTAINTY WHEN COMBINING MEASUREMENTS – ‘Advanced’ approach • Tidying up after using these two rules • Multiplying or dividingMultiplying a velocity by a time to provide a distance s could give rise to s = 51.41 m and PU(s) = 6% and from these two, AU(s) = 3.0846 mSo s = (51.41 ± 3.0846) m,But we normally retain only one sig fig in the AU.So s = (51.41 ± 3) m,But we only retain one uncertain figure in the measurement.So s = (51 ± 3) m, in the conventional form.

31. TOTAL UNCERTAINTY WHEN COMBINING MEASUREMENTS – ‘Advanced’ approach • Unnecessary accuracyOccasionally in an experiment measuring two quantities, one - a very accurate method, the other not very precise. If combined, final uncertainty will be decided by uncertainty of the less accurate measurement and the additional effort on the more accurate measurement may have been wasted.

32. USING GRAPHS Items done automatically using Excel shown in GREEN. CAS (Computer Algebraic System) calculators also provide shortcuts. • Title • Axes selection: Independent variable - horizontal axis. Dependent variable - vertical axis • Choosing scales: Rough sketch to plan ranges of scales and portrait or landscape Maximise range on graph, otherwise a curve may appear asa straight line.

33. USING GRAPHS

34. USING GRAPHS • Axes labelling: • Variable with full words or abbreviation if defined elsewhere & unit in brackets • Choose convenient scale to assist interpolation when plotting or reading points – awkward horizontal scale here

35. USING GRAPHS • Axes labelling: • Avoid very large & very small numbers. Use standard form or prefixes and place with unit in brackets • Plotting points: If on graph paper, use sharp pencil & surround (e.g. circle or square) • Tabulating & immediately plotting points identifies • gaps in range • doubtful readings

36. UNCERTAINTY ON GRAPHS • Absolute uncertainty of each point for dependent variable - vertical uncertainty bars (error bars) • Uncertainty bars can be added to Excel graphs: (Internet site given on post-conference notes on VicPhys site) • If uncertainty of independent variable for plotted points is significant (mostly not), use • horizontal uncertainty bars or • rectangular ‘uncertainty boxes’ (not a universal convention! but helpful when drawing line of best fit)

37. LINE OF BEST FIT In most cases can assume the change is smooth and so draw a smooth or straight line Draw smooth line through the vertical uncertainty bars (or boxes if horizontal uncertainties significant) Avoid forcing line to go through a maximum number of points It enables giving different pairs of reading different rather than identical weightings

38. LINE OF BEST FIT In most cases can assume the change is smooth and so draw a smooth or straight line Draw smooth line through the vertical uncertainty bars (or boxes if horizontal uncertainties significant) Avoid forcing line to go through a maximum number of points It enables giving different pairs of reading different rather than identical weightings

39. LINE OF BEST FIT • When working on graph paper • using a transparent ruler helps drawing a justifiable line • using a pencil facilitates erasing it to improve the line • ‘Outliers’ • should be checked for incorrect plotting or • incorrect readings from the equipment (and check if apparatus still available) • should not be erased – rather, have an explanation on the graph [Fig. 21.7]

40. LINE OF BEST FIT • Using a pencil facilitates erasing it to improve the line • The point (0, 0) sometimes justifiably added to experimental points, e.g. distance travelled by a cyclist from a stationary start against time elapsed • If line of best fit appears to be curved, easier to draw it with hand on inside rather than outside of the curve • Computer and calculator spreadsheeting enabling graphing saves time, though some omit some graphical conventions

41. INTERPRETATION OF GRAPHS • Pictorial representation – conclusions easier • Hunch or hypothesis checking • Possibility of determining mathematical relationship between 2 variables • Interpolation possible • Discontinuities & possible mistakes obvious • Possible useful information from • maximum & minimum points • intercepts on axes • gradient • area under graph

42. GRAPHS OF THE VALUABLE RELATIONSHIP y = axn • Covers many shapes & helpful in testing possible relationships between 2 variables • A less valuable introductory process for this exercise, even though more rapid, method is the use of linear regression.

43. LOG-LOG ANALYSIS • A one-stop, more direct analysis than checking possible forms of y = axn • Rationale: If y = axnlog y = log axn = log xn + log a = nlog x + log aA graph of log y against log x should give • a straight line • with gradient n and • intercept on the log y axis of log a • So a graph of log y against log x should enable us to deduce the value of the two constants n and a in y = axn

44. LOG-LOG ANALYSIS • Example: effect of pressure on an enclosed gas against its volume • Possibly some sort of inverse relationship between V and P

45. A one-stop approach: plot log Vagainst log P Gradient = n ≈ -1 So V = aP-1i.e. V = a/P or V is inversely proportional to P LOG-LOG ANALYSIS

46. Simpler method: Using log-log paper, plotting values of P & V, without calculating their logs. Gradient n obviously -1. The determination of the constant a may not be important, as we’re more interested in the proportionality between P and V. LOG-LOG ANALYSIS

47. If a needs to be determined, with a displaced origin on the both graphs, it is easier to determine a using values of P and Vfrom the table that are also on the straight line, i.e. second top set of values, with P = 1.5  105 Pa and V = 4.0  10-5 m3 With V = a/P 4.0  10-5 = a/1.5  105a = 6.0 So V = 6.0/P LOG-LOG ANALYSIS

48. DEDUCTIONS & CONCLUSIONS Elements worth considering when drawing conclusions from the data & its analysis: • Answering original research questions in word & mathematical form, stating evidence • Hypotheses borne out? • Identifying the variables or ranges of readings that were major limit to the accuracy of the result • Limitations in both the data collected and method used • For a deduced algebraic equation between 2 variables, record the units for the variables and any constants • For a deduced proportionality between two variables, no units are required

49. POSTER REPORT • Whether investigation carried out in a pair or group, poster generation must be done individually • Forms of poster presentation: • PowerPoint presentation • A word document for hard copy version form • Hard copy as a collection of sheets in a folder • Hard copy or digital copy on a single poster. Plan placement of components. Content to an essential minimum. For hard copy version have font able to be read from 1 to 2 m away. • Helpful templates on VicPhys website: http://www.vicphysics.org/practicalactivities.html

50. POSTER REPORT • Students aware of statement from Study design, p. 13:‘The production quality of the poster will not form part of the assessment’Should reduce excessive time on prettying it up & emphasises content of investigation • Should not exceed 1,000 words