IB Physics IA Guide

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International Baccalaureate

Physics Internal Assessment Guide

© Kari Eloranta 2013

C ONTENTS

Contents

ii

Preface

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Introduction 1.1 General Information . . . . . . . . . . . . . . . . . . . . . .

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Design 2.1 Design Criterion . . . . . . . . Summary of Design Aspect 1 . Summary of Design Aspect 2 . Summary of Design Aspect 3 .

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Guidelines for Data Collection and Processing 3.1 Data Collection and Processing (DCP) . . Summary of DCP Aspect 1 . . . . . . . . . DCP Aspect 1 Explained . . . . . . . . . . Instrumental Uncertainty . . . . . . . . . Summary of DCP Aspect 2 . . . . . . . . . DCP Aspect 2 Explained . . . . . . . . . . Summary of DCP Aspect 3 . . . . . . . . .

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Guidelines for Conclusion and Evaluation Conclusion and Evaluation . . . . . . . . . . . . . . . . . . . . . Summary of CE Aspect 1: “Concluding” . . . . . . . . . . CE Aspect 1 “Concluding" Explained . . . . . . . . . . . . Summary of CE Aspect 2: “Evaluating procedure(s)” . . . CE Aspect 3: “Improving the investigation" . . . . . . . . Summary of CE Aspect 3: “Improving the investigation" CE Aspect 3: “Improving the investigation" Explained . .

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P REFACE This is the first draft of my new "Physics Internal Assessment Guide". You should use it alongside with the IBO’s Physics Guide whenever you are engaged in practical work. As this is only the first draft, there will probably be quite many errors, inconsistencies and omissions in the material. I hope that there are not too many, so that you find the material useful. I appreciate any feedback and corrections you can offer. “Develop a passion for learning. If you do, you will never cease to grow.” Anthony J. D’Angelo In Jyväskylä, 1 January 2013 Kari Eloranta Teacher of Physics Jyväskylän Lyseon lukio International Baccalaureate

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CHAPTER

1

I NTRODUCTION This little guide explains the process of internal assessment in physics in some detail. It serves as your secondary source of information, as you work on your practicals.

Figure 1.1: Your teacher will be monitoring your performance during the two year course in physics, and give you a mark on your manipulative skills (© Dacopeland). The internal assessment is assessed according to the sets of assessment criteria, and achievement level descriptors. For each criterion, there are three descriptors that describe your level of achievement. Internal assessment comprises 24% of your final assessment.

1

2

Introduction

Officially assessed work reports are divided into two groups. The first is a design practical, where you design a physical experiment at school during a double lesson, and finalise the work at home. The second is a combined Data Collection and Processing, and Conclusion and Evaluation practical, where you make the measurements at school, and write the work report at home. Note! The work report must be printed and returned in a week from the day of a practical. During the week, your teacher can comment on your work once. When you return your work report, you should take two copies of your work: one for yourself, and one for the school archives. No electronic, or late returns will be accepted.

1.1 General Information about Internal Assessment Criteria and Aspects Internal Assessment is criterion-related. It means that you will be assessed in relation to identified assessment criteria, and not in relation to the work of other students. Your practical work is assessed according to sets of assessment criteria, and achievement level descriptors in the “Physics Guide, First Exams 2009”. For each assessment criterion, there are three descriptors that describe your level of achievement. The same internal assessment criteria are used for both Higher and Standard Level. Your teacher aims to find, for each criterion, the descriptor that matches your achievement level most accurately. Each aspect is assessed as c (complete, 2 marks), p (partial, 1 mark) and n (none at all, 0 marks). To earn complete in any aspect, your work does not necessarily have to be perfect. It is enough to reach the level described. There are five assessment criteria that are used to assess your practical work in physics: • Design (D), • Data Collection and Processing (DCP), • Conclusion and Evaluation (CE), • Manipulative Skills (MS), and • Personal Skills (PS)

1.1. General Information

Note! Design, Data Collection and Processing, and Conclusion and Evaluation are each assessed twice. Manipulative Skills is assessed summatively over your two year course in physics. Personal skills is assessed once only during the group 4 project.

There are three aspects in each of the assessment criteria. The maximum mark for each criterion is 3 × 2 = 6 marks representing three completes. Since the first three criteria are assessed twice, and last two once, the maximum marks are 2 × 6 × 3 + 2 × 6 = 48. Your teacher assesses your work, and adds your marks together to to determine the final mark out of 48 for the IA component. The result is then scaled at IBCA to give a total out of 24% of your total marks in physics.

3

CHAPTER

2

D ESIGN

2.1 Design Criterion In design, you have to plan a physical measurement and following analysis from scratch. Design prompts are open-ended tasks, where teacher gives you very little information. It is a challenging creative process, in which you have to understand the nature of physical measurement in detail.

Figure 2.1: Which kind of experiment would you design relating to the formation of soap bubbles (© Brocken Inaglory)?

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6

Design

There are three aspects in the Design criterion.

Figure 2.2: The Design criteria from the “Physics, first exams in 2009” guide (© IBO). In design, your teacher gives you an open-ended investigation. Based on the teacher prompt, your first task is to devise a proper quantitative research question. In the question, you have to have an independent variable that affects the value of the dependent variable. Independent and Dependent Variable A variable that is manipulated in the experiment is called an independent variable. The result of the manipulation leads to the measurement of the dependent variable.

You have to choose from several independent variables that provide a suitable basis for the experiment. Your teacher is not allowed to tell you how to select the relevant independent variable, and how to collect and analyse the data. Note! If you need to carry out the designed practical in practise, you should design an experiment that lends itself to a proper graphical analysis, where you can draw a line of best fit, and calculate the associated uncertainties.

2.1. Design Criterion

As we study how the changing value of the independent variable affects the measured value of the dependent variable, we try to keep other variables constant during the measurement. Controlled Variable A controlled variable is one that should be held constant so as not to obscure the effect of the independent variable on the dependent variable.

Summary of Design Aspect 1: Defining the Problem and Selecting Variables Design Aspect 1 is about stating a research question and recording variables. In Design Aspect 1: “Recording raw data” you should” • choose an independent variable. • choose a dependent variable, if it is not included in the teacher prompt. • list all relevant controlled variables. • state a quantitative research question.

In your work report you need to clearly identify your variables as the dependent (measured), independent (manipulated or free to roam (time)), and controlled (constants). A relevant controlled variable is the one that can reasonably be expected to affect the outcome.

Summary of Design Aspect 2: “Controlling Variables” Design Aspect 2 is about designing a method for the effective control of the variables. In Design Aspect 2: “Controlling Variables” you should • explain, how the value of independent variable is manipulated. • explain, how the value of dependent variable is measured. • explain carefully the control of variables.

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8

Design

You should pay special attention to explaining how the control of variables is achieved. For example, it is not enough to state that the length of a thread was measured, but also to explain how it was measured. If the control of relevant variables is not practically possible, you should try to monitor the values. For example, if ambient temperature is relevant to your measurement, but you cannot control the class room temperature, you should record the temperature in each measurement.

Summary of Design Aspect 3: “Developing a Method for Collection of Data” Design Aspect 3 is about designing a method by which you can have enough relevant data for graphical analysis. In Design Aspect 3: “Developing a Method for Collection of Data” you should • make repeated measurements, if just possible. • explain, how many measurement points you intend to have. • decide the suitable range of data. • consider boundary conditions. • explain, how the data is manipulated. • explain, how data analysis is carried out including propagation of error.

What “sufficient relevant data” constitutes depends on the context. If you record discrete values, you should have at least five measurement points. If you measure the dependent variable as a function of time, the duration of the experiment should be long enough. If realistic, you should make repeated measurements. For example, to measure the period of a simple pendulum, it is not enough the measure the period of one oscillation. Instead, you should measure the time for a number of oscillations (for example ten), and from that value calculate the time for one oscillation with the associated uncertainty. The range of data is important. For example, in a pendulum experiment, the thread length could range from 20.0 cm to 170.0 cm in steps of 30.0 cm. This way the range is large enough, and you collect enough measurement points (in this case six). The laws of physics have a limited range in which they can be applied. That is why you have to often consider the boundary conditions

2.1. Design Criterion

of the experiment. For example, for a simple pendulum, the oscillatory motion is harmonic only when the release angle is under 10°. So, we measure the period for the constant 10° release angle. Note! In design, you should consider the time constraints and other resources as well: the designed investigation should be doable in a double lesson with the equipment the school has.

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CHAPTER

3

G UIDELINES FOR D ATA C OLLECTION AND P ROCESSING

3.1 Data Collection and Processing (DCP) In Data Collection and Processing (DCP) you have to record and process raw data, and present processed data with uncertainties in graphical form.

Figure 3.1: When position of a cart is measured by the position sensor, the position is a dependent, and time an independent variable.

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Guidelines for Data Collection and Processing

There are three aspects in Data Collection and Processing.

Figure 3.2: The Data collection and processing criteria from the "Physics, first exams in 2009” guide (© IBO).

Summary of DCP Aspect 1: “Recording Raw Data” Data Collection and Processing Aspect 1 is about recording appropriate quantitative raw data with associated uncertainties.

In DCP Aspect 1: “Record raw data” you should • record raw data with units and uncertainties in a table. • record enough data in an appropriate range. • round uncertainties to one significant figure. • explain the reasoning behind the uncertainties. • represent measured values and uncertainties with the same precision.

DCP Aspect 1 Explained Raw data is the actual data measured. Table 3.1 is an example of how raw data with uncertainties should be recorded.

3.1. Data Collection and Processing (DCP)

13

Table 3.1: Raw data in a simple pendulum experiment. l is the length of thread, and t i time for ten oscillations in trial i . l /cm ± 0.5 cm 20.1 49.8 80.7 110.1 142.2 169.8

t 1 /s ± 0.4 s 9.1 13.6 17.6 21.1 23.8 26.2

t 2 /s ± 0.4 s 9.0 13.9 18.3 20.8 24.0 25.9

t 3 /s ± 0.4 s 9.3 14.0 18.1 21.3 23.5 26.4

Note! The symbols of quantities, units and uncertainties are recorded in the first row of the table.

Table 3.2: All data is recorded with units and uncertainties. l /cm ± 0.5 cm

t 1 /s ± 0.4 s

t 2 /s ± 0.4 s

t 3 /s ± 0.4 s

l /cm means that all values of length l are divided by the unit cm. As a result, you do not repeat the unit in numerical values of a column. All uncertainties must be rounded to one significant figure.

Note! You should always record uncertainties, explain the reasoning behind them, and explain, if an uncertainty may be neglected.

For example, it is not enough to say, “there is uncertainty in manual timing due to reaction time”, but also to estimate the magnitude of uncertainty (for example, 0.2 s). Occasionally, an uncertainty is so small that it may be neglected. As an example, consider a position sensor. Since the device records position as function of time, and the instrumental uncertainty in time is 0.01 s, the uncertainty in time may be neglected.

14

Guidelines for Data Collection and Processing

Instrumental Uncertainty

Instrumental uncertainty The accuracy of a digital device is called the instrumental uncertainty.

You will find the instrumental uncertainty of digital measurement devices from the manual of a device. If a manual is missing, you may assume that the uncertainty is the precision of the digital device. For example, if mass is measured by a digital scale as 76.3 g, you may estimate the uncertainty as 0.1 g. Note! In a physics extended essay the instrumental uncertainty of digital devices should always be checked from the manual.

Usually, the instrumental uncertainty of analogue devices must be estimated. If you are using a graduated scale, the instrumental uncertainty may be estimated as the smallest division in the scale. For example, if you measure the height of a box as 7.3 cm by a ruler divided into millimetres, the instrumental uncertainty is 0.1 cm (the precision of the instrument). From the accuracy of a measurement device, the uncertainty in the measurement can be estimated. Note! The uncertainties in data are recorded on the first row of a table.

Note! A common mistake is to record values with greater precision than uncertainty.

For example, time is wrongly recorded as 5.12 s, when uncertainty in manual timing is ±0.2 s. Instead, the time should be rounded to tenths of a second to match the precision of the uncertainty ((5.1 ± 0.2) s).

3.1. Data Collection and Processing (DCP)

15

Table 3.3: In each column, the precision of data is constant, and matches the precision of uncertainty.

l /cm ± 0.5 cm 20.1 49.8 80.7 110.1 142.2 169.8

t 1 /s ± 0.4 s 9.1 13.6 17.6 21.1 23.8 26.2

Summary of DCP Aspect 2: “Processing Raw Data”

In DCP Aspect 2: “Processing raw data” you should • represent processed data and propagated uncertainties with units in a table. • round propagated uncertainties to one significant figure. • represent processed values and propagated uncertainties with the same precision. • draw the best fit line • calculate the slope of the best fit line • represent the equation of the best fit line

To meet the criteria in Data Collection and Processing Aspect 2, you need to process the raw data correctly. This includes all arithmetic operations, transforming data into a form suitable for graphical representation, constructing the coordinate axes, plotting the data, and determining the best fit line and its slope. If the dependent variable should be directly proportional to the independent variable, you have to plot the data on a proper coordinate system, draw the line of best fit, and calculate the slope of the line. Then, the raw data has been processed.

16

Guidelines for Data Collection and Processing

Note! Processing the raw data without a graph line does not earn complete in Aspect 2.

In many cases, especially at Higher Level, the raw data is not linear. In such a case the processing of raw data includes also the linearisation of data. Then, you plot the processed data, draw the line of best fit, and calculate the slope of the line for the linearised data.

DCP Aspect 2 Explained In a repeated experiment we have to calculate the average of measurement values. In Internal Assessment, you are allowed to use a simple method of finding the uncertainty in the average. Uncertainty in the Average The uncertainty in the average is ∆x =

x max − x min 2

(3.1)

where x max is the maximum and x min the minimum value in the sample.

This method of calculating the uncertainty in the average exaggerates the uncertainty a little. If you want to use a more scientific method, you can use the standard error of the mean. Standard Error of the Mean The standard error of the mean is defined as s σ= p N

(3.2)

where s is the standard deviation of the sample and N is the number of measurements. You should calculate the standard deviation with a calculator, or using a spreadsheet. Refer to the User’s Manual for detailed instructions of how to do it. Note! Use of Standard Error of the Mean is compulsory in Physics Extended Essays.

3.1. Data Collection and Processing (DCP)

17

Linearisation of Data Typically, we want to have a linear relationship between the variables to be able to draw a line of best fit. Note! If data is not linear, we need to linearise it for graphical analysis, and propagate uncertainties.

As an example, consider the equation of the period T of simple pendulum. Period T of Simple Pendulum The period of simple pendulum is T = 2π

s

l g

(3.3)

where l is the length of the cord, and g is the acceleration due to gravity.

As you can see, period T is proportional to the square root of length l . Since period T is not directly proportional to length l of the pendulum, we have to linearise Equation 3.3 by a variable interchange. Squaring both sides of Equation 3.3 gives T2 =

4π2 l g

(3.4)

which is an equation of a straight line in a (l , T 2 ) coordinate system 2 whose slope is m = 4π . So, for linearisation, we have to calculate the g

square of the period T 2 , mark the measurement points to a (l , T 2 ) coordinate system, and draw a line of best fit for the processed data.

Because we calculated the square of the period, we need to propagate uncertainties. Because in multiplication fractional uncertainties . add, the fractional uncertainty in the period squared T 2 is 2 × ∆T T Graphing After having processed the raw data, you have to use a regression tool, such as Logger Pro, for graphical analysis. In the simple pendulum experiment the uncertainty in the measurement of length is negligible. As a result, only vertical error bars are drawn.

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Guidelines for Data Collection and Processing

Table 3.4: Processed data in a simple pendulum experiment. l is the length of the thread, t av average of times of ten oscillations, T period, ∆T uncertainty in the period, T 2 period squared, and ∆T 2 the uncertainty in the period squared. l /cm ± 0.5 cm 20.1 49.8 80.7 110.1 142.2 169.8

s2

t av /s

∆t av /s

T /s

∆T /s

T 2 /s2

∆T 2 /s2

9.1 13.8 18.0 21.1 23.8 26.2

0.2 0.2 0.3 0.3 0.4 0.3

0.91 1.38 1.80 2.11 2.38 2.62

0.02 0.02 0.03 0.03 0.04 0.03

0.83 1.90 3.2 4.5 5.7 6.9

0.04 0.06 0.1 0.1 0.2 0.2

T2

7 b

6 b

5 b

4 b

3 2 1

b

b

l

0 20

40

60

80

100

120

140

160

180

cm

Figure 3.3: The period squared T 2 as a function of lenght l . The points fall on a line.

Next, we draw the line of best fit. The line has to go through the error bars.

3.1. Data Collection and Processing (DCP)

19

T2

s2 7

b

6 b

5 b

4 b

3 2 1

T 2 = 0.041l − 0.055

b

b

l 0 20

40

60

80

100

120

140

160

180 cm

Figure 3.4: The period squared T 2 as a function of lenght l .

Note! You have to state the equation of the best line. If the dependent variable should be directly proportional to the independent variable, the y-intercept is a measure of a systematic error in the experiment.

The equation of the best fit line is T 2 = 0.041l − 0.055, where the yintercept is b = −0.055 s2 . The value is so small that it might be a result of the mathematical algorithm of the spreadsheet program used, rather than an indication of a systematic error in the experiment.

20

Guidelines for Data Collection and Processing

Outliers Occasionally, a point with error bars may not fall on a line even if it should. Such a point is called an outlier. In your work report, you have to consider all outliers, and act accordingly.

Typical reasons for outliers include • You have underestimated uncertainties. In this case you have to correct the uncertainties, and repeat the process with longer error bars. • Real physical behaviour. For example, you have exceeded the range in which linear model is valid. Such points should not be included in the linear fit. • An error in measurement has occurred. For example, a value is not recorded correctly, or a malfunction of a device has occurred. Such a point may be left out of the process. • You have mistyped a data point. If the correct value is known, retype the point, or leave it out.

In all cases, you have to clearly explain your reasoning in the treatment of the outlier. If you decide to leave a point out, you have to make sure you have enough data left. In the graph above, the best fit line goes through the error bars, and no further action is needed.

3.1. Data Collection and Processing (DCP)

Summary of DCP Aspect 3: “Presenting Processed Data” Aspect 3 is about presenting the processed data appropriately including units and uncertainties. To achieve complete in DCP Aspect 3, you need to

In DCP Aspect 3: “Presenting processed data” you should • determine appropriate scales for the graphs. • mark the measurement points with error bars when the error bars are not negligible. • explain where uncertainties are not significant. • draw the minimum fit line and maximum fit line. • represent the equation of the minimum and maximum fit line clearly in context with the lines. • label the axes with units appropriately. • label the tables, diagrams and graphs and add captions to them. • represent processed values and (propagated) uncertainties with the same precision.

Minimum and Maximum Fit Lines To find the uncertainties in the slope, you have to draw a minimum and maximum fit line. The process should be carried out manually in the data processing software used. Note! To draw a minimum and maximum fit line, you may use only the first and last measurement points. • The minimum fit line gives the minimum value of the slope. It goes through the highest error bar point of the first value, and through the lowest error bar point of the last value. • The maximum fit line gives the maximum value of the slope. It goes through the lowest error bar point of the first value, and through the highest error bar point of the last value.

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Guidelines for Data Collection and Processing

Here are the minimum and maximum fit lines for our example data. s2

T2

7 b

6 5

2

a M

4

T t: fi x

in M

2

=

b

=

2

b

3

l− 42 0 0.

: fit

T

0 06 0. b

− 9l 3 0 0.

08 0.

b

1 b

l 0 20

40

60

80

100

120

140

160

180 cm

Figure 3.5: The minimum (green) and maximum (red) fit lines in the simple pendulum experiment. s2

T2 b

7 6 5

2

a M

4

T t: fi x

in M

2 1

=

b

2

b

3

l− 42 0 0.

fit

:T

=

0 06 0.

b

b b

− 9l 3 0 0.

08 0.

b

b

b b

l 0 20

40

60

80

100

120

140

160

180 cm

b

Figure 3.6: First and last points with error bars magnified. Red line is the maximum fit, and green the minimum fit line.

3.1. Data Collection and Processing (DCP)

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Uncertainty in the Final Result Once you have drawn the lines, you calculate the uncertainty in the slope of the best fit line. Uncertainty in the slope of the best fit line The uncertainty in the slope of the best fit line is ∆m best =

m max − m min 2

(3.5)

where m max is the slope of the maximum fit line, and m min the slope of the minimum fit line. The uncertainty in the best fit line of the simple pendulum experiment becomes m max − m min 2 0.0422 s2 cm−1 − 0.0390 s2 cm−1 = 2 2 −1 ≈ 0.002 s cm

∆m best =

If the slope is used in the calculation of the final result, we have to propagate the uncertainty to the final result as well. The slope of the best fit line in the simple pendulum experiment is m best =

4π2 g

(3.6)

from where it follows that the acceleration due to gravity is g=

4π2 4π2 = ≈ 9.6 m s−2 . m best 0.041 s2 cm−1

(3.7)

The uncertainty in the acceleration due to gravity is ∆g =

∆m best 0.002 s2 cm−1 g= × 9.629 m s−2 ≈ 0.5 m s−2 . m best 0.041 s2 cm−1

(3.8)

Thus, according to the data acquired in the simple pendulum experiment, the acceleration due to gravity is g = (9.6 ± 0.5) m s−2 Data collection and processing is a relatively straightforward process, and you should have little difficulty in learning the skills needed to achieve high marks in it.

CHAPTER

4

G UIDELINES FOR C ONCLUSION AND E VALUATION

Conclusion and Evaluation In Conclusion and evaluation you have to state a conclusion, evaluate weaknesses and limitations in the experiment, and suggest improvements.

Figure 4.1: Students in Ouagadougou, Burkina Faso, discussing physics.

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Guidelines for Conclusion and Evaluation

In writing Conclusion and evaluation, you should divide your text into clear paragraphs for fluent communication. In order to be able to write good conclusion and evaluation, you need to understand the physics of the experiment, and the main principles of experimental research. There is no single way of writing proper conclusion and evaluation. In these instructions we propose a way of dividing your text into clearly organised paragraphs. This way, conclusions and evaluations are easier to read. It is also easier for you to make sure that you have considered all necessary factors. There are three aspects in Conclusion and evaluation.

Figure 4.2: The Conclusion and evaluation criteria from the "Physics, first exams in 2009” guide (© IBO).

Conclusion and Evaluation

Summary of CE Aspect 1: “Concluding” Conclusion and evaluation criteria Aspect 1 is about stating a justified conclusion with uncertainties, and analysing the reliability of data.

In CE Aspect 1: “Concluding” you should • Restate the final result with the associated uncertainty. • State the fractional uncertainty from the processed data. • Comment on the accuracy of the result. • Compare the result with the text book or literature value (if applicable). • Fully reference the literature consulted (if applicable). • Discuss the linearity of data (if applicable). • State the systematic error with units and its direction (if applicable). • Discuss the random errors encountered. • Discuss observations, trends and patterns revealed by the data.

CE Aspect 1 “Concluding" Explained Step 1: Stating the result In the first paragraph of conclusion and evaluation you restate the experimental result with the associated uncertainty, and compare it with a fully referenced literature value. In my experiment, the value for the acceleration due to gravity was found to be g = (9.6 ± 0.5) m s−2 (4.1) The accepted value in Jyväskylä1 being g = 9.82 m s−2 . The fractional uncertainty is 5%.

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Guidelines for Conclusion and Evaluation

In comparing your result with the reference value you should: • state the absolute or fractional difference between the values. • consider the uncertainty in the reference value (if applicable). • check, does the probable range of the experimental value overlap include the reference value. • check, if the reference value has an associated uncertainty, does the probable range of the experimental value overlap the probable range of the reference value.

According to the IBO, a percentage error should be compared with the total estimated random error as derived from the propagation of uncertainties. In the absence of a reference value, you should comment on the reliability of the result, based on how accurate the measurements were, and how reliable the process was in the experiment. Step 2: Analysing the graphs In analysing the graphs, your first task is to comment on the observed trends, such as linearity of the data. You should check from the graph: • do the measurement points fall on a line? • does the line go through all error bars? • is there any indication of a systematic error? • are there any outliers? • is there anything else worth noting?

If the measurement points fall very nearly on a line, the associated random errors are small. If the points deviate from the line clearly, but the line nevertheless goes through the error bars, the data is consistent with the line. Note! If the graph is a straight line where the line goes through all the error bars, you should state that the data is linear.

Conclusion and Evaluation

If the data does not follow the expected trend, reasons for it need to be considered. The most common case is the one, where the data is expected to be linear, but it is not. Typical reasons for non-linear data include • The data should not be linear in the first place. For example, in uniformly accelerated motion, the distance travelled h is proportional to the time t squared (h = 12 at 2 where a is the acceleration). • The changes in ambient or internal physical conditions has affected the results. For example, the electric current I in a conductor is not directly proportional to the potential difference V across the component, because of the increasing temperature of the component (non-ohmic behaviour). • The range of the linear model has been exceeded. For example, the spring force F is not directly proportional to the displacement x from the equilibrium position, because the string has been stretched beyond its linear range (Hooke’s law F = −k x). Or air resistance opposes motion so much that the falling object is not in a free fall anymore. • The physics of the experiment has been misunderstood. For example, in a falling ball experiment the falling height should be directly proportional to the final speed squared, not just final speed.

If your data is not linear, you should go back to DCP and check, if it is possible to linearise the data, and does it make sense to do so. If not, you should try to find and analyse the reasons for the non-linear behaviour. If there are any outliers, you need to ponder upon the reasons for them. The instructions for the treatment of outliers are in Section 3.1. Systematic error in a linear graph If the dependent variable should be directly proportional to the independent variable, the best fit line should go through the origin. Usually, however, the line does not go through the origin exactly, indicating a systematic error in the data. Note! You should state the systematic error in the data with units, and try to find out the reason for it.

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Guidelines for Conclusion and Evaluation

Systematic errors are most often caused by: • by the software algorithm in a linear fit. • systematic misuse of a measurement device. For example, a zero-offset error in a scale. • systematic misreading of a scale. For example, reading a thermometer at an angle, measuring volumes in a graduated cylinder at an angle, and misreading a scale in a multimeter. • Forgetting to add or subtract a fixed value from measurement results. For example, forget to add atmospheric pressure to overpressure values in using gas laws, and not to subtract background radiation in studying the activity of a radioactive sample.

A small deviation from the origin is most often caused by the algorithm the measurement software uses. In this case you should clearly state that the systematic error is most probably caused by the algorithm of the measurement software. If the systematic error cannot be accounted for by software, you must try to find a reason for it. Systematic errors are sometimes hard to detect. Note! Remember that a repeated experiment does not reduce the effect of a systematic error unless the source of the error is removed.

Random errors In the conclusion you should also comment on the random errors encountered. You should pay special attention to unexpected random errors in the data, such as random errors caused by fluctuating reading in a multimeter. A more detailed analysis of random errors goes to the Aspect 2: ”Evaluating procedure(s)". According to physics syllabus, conclusions that are supported by the data can be acceptable even if they appear to contradict accepted theories. In such a case, however, you have to be extremely careful, and double check you work to verify that you have not just missed something obvious.

Conclusion and Evaluation

Summary of CE Aspect 2: “Evaluating procedure(s)” Conclusion and Evaluation criteria Aspect 2 is about evaluating the strengths and weaknesses of the experiment.

In CE Aspect 2: “Evaluating procedure(s)” you should • Comment on the overall quality of the process. • Identify weaknesses and limitations in the process. • Go through the sources of uncertainty in the decreasing order of importance. • Discuss all sources of uncertainty that affect the accuracy of the measurement. • Discuss the method of measurement in detail, and identify all relevant weaknesses. • Appreciate whether the limitations cause a systematic or random uncertainty.

First, you should comment on overall quality of the experimental procedure, and data collected.

• Was the experiment suitable for its intended purpose? • What were the major limitations in the experiment.

You should go through the significant weaknesses, limitations, and sources of uncertainty in the process in decreasing order of importance. In the first paragraph in evaluating the procedures, you analyse the major weakness in the experiment. In the second paragraph the second most important weakness and so on. In analysing weaknesses you should consider the equipment and time management well, such as instrumental uncertainty, and did the equipment fit well with the experiment. If time management affected your measurements, you should comment on that as well. It is important that you show some appreciation of the significance of each weakness and source of uncertainty. You must also have some appreciation of whether each factor would cause a systematic or a random uncertainty.

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Guidelines for Conclusion and Evaluation

CE Aspect 3: “Improving the investigation" In Conclusion and evaluation Aspect 3 you have to suggest realistic improvements in respect of identified weaknesses and limitations. This includes the description of how the experimental procedure could be improved for better accuracy of the experimental result.

Summary of CE Aspect 3: “Improving the investigation"

In CE Aspect 3: “Improving the investigation" you should • Address the weaknesses and limitations identified in CE Aspect 2. • Suggest realistic improvements. • Suggest exactly what should be done to reduce random uncertainties. • Suggest exactly what should be done to reduce systematic uncertainties

CE Aspect 3: “Improving the investigation" Explained

The ways of improving the weaknesses and limitations identified in Aspect 2 include • Improving the accuracy of the measurement by using more accurate instruments. For example, using a more accurate multimeter or scale. • Improving the external and internal physical factors relating to the accuracy of the experiment. For example, in measuring the thermal capacity of an object, insulating the system better from its surroundings to reduce thermal energy losses to the surroundings. • Improving the measurement process. For example, change the measurement location from outdoors to indoors to eliminate the effect of wind.

An easy way of improving the accuracy of a measurement is to use more accurate instruments. Ideally, you should suggests instruments

Conclusion and Evaluation

that are available at your school. As an example, consider a case, where the position of a rolling ball on the floor was measured as a function of time by using manual timing and 5 metres long tape measure. Using a position sensor instead would improve both the accuracy of the measurement of time, and the accuracy of the measurement of position. It is always best the state exactly which instrument you would use, and how much it would improve the accuracy of the measured quantity. To improve the accuracy of the measurement of time and position, I would use Vernier Motion Detector 2 http://www.vernier.com/files/manuals/md-btd.pdf. As a result, the instrumental uncertainty in time would be reduced to ∆t = ±0.01 s, and that of position to ∆s = ±0.001 m. You may use the Internet in finding information about the instruments. For example, you find information about Vernier accessories at http://www.vernier.com/support/manuals/. Improving the external and internal physical factors relating to the accuracy of the experiment is not always easy. For example, many physics experiments are carried out in ordinary classroom conditions. When many people work at the same time in the class, the class room temperature tends to rise. As a result, it is difficult to control the class room temperature. Or, to eliminate the effect of air resistance, it would be nice to perform an experiment in a vacuum. But that would be impossible in most practical cases. Improving the measurement process is most often relevant, when as a result of the measurement process, uncertainties are exceptionally high. For example, the uncertainty is away too high, if you measure the falling time manually. Once again, using a position sensor reduces the uncertainty to the minimum. Or if you want to measure the resistivity of the material a twisted wire is made of, you can improve the uncertainty in measuring the length by using a straighter wire.

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