IB Physics IA Guide

7/23/2019 IB Physics IA Guide

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Forfirst

exams2009

International Baccalaureate

PhysicsInternal Assessment

Guide

Kari Eloranta

2013


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CONTENTS

Contents ii

Preface iii

1 Introduction 1

1.1 General Information . . . . . . . . . . . . . . . . . . . . . . 2

2 Design 5

2.1 Design Criterion . . . . . . . . . . . . . . . . . . . . . . . . . 5

Summary of Design Aspect 1 . . . . . . . . . . . . . . . . . . 7



3 Guidelines for Data Collection and Processing 11

3.1 Data Collection and Processing (DCP) . . . . . . . . . . . . 11

Summary of DCP Aspect 1 . . . . . . . . . . . . . . . . . . . 12

DCP Aspect 1 Explained . . . . . . . . . . . . . . . . . . . . 12Instrumental Uncertainty . . . . . . . . . . . . . . . . . . . 14


DCP Aspect 2 Explained . . . . . . . . . . . . . . . . . . . . 16


4 Guidelines for Conclusion and Evaluation 25

Conclusion and Evaluation . . . . . . . . . . . . . . . . . . . . . . 25

Summary of CE Aspect 1: Concluding . . . . . . . . . . . 27

CE Aspect 1 Concluding" Explained . . . . . . . . . . . . . 27

Summary of CE Aspect 2: Evaluating procedure(s) . . . . 31

CE Aspect 3: Improving the investigation" . . . . . . . . . 32Summary of CE Aspect 3: Improving the investigation" . 32

CE Aspect 3: Improving the investigation" Explained . . . 32

ii


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PREFACE

This is the first draft of my new "Physics Internal Assessment Guide".

You should use it alongside with the IBOs 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. DAngelo

In Jyvskyl, 1 January 2013

Kari Eloranta

Teacher of Physics

Jyvskyln Lyseon lukio International Baccalaureate

iii


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1INTRODUCTION

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 assess-

ment criteria, and achievement level descriptors. For each criterion,

there are three descriptors that describe your level of achievement. In-

ternal assessment comprises 24% of your final assessment.

1


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2 Introduction

Officially assessed work reports are divided into two groups. Thefirst

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 Evalua-

tion practical, where you make the measurements at school, and writethe 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 As-

sessment Criteria and Aspects

Internal Assessment is criterion-related. It means that you will be as-

sessed 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 crite-

ria, and achievement level descriptors in the Physics Guide, First Exams

2009. For each assessment criterion, there are three descriptors that de-scribe 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 prac-

tical work in physics:

Design (D),

Data Collection and Processing (DCP),

Conclusion and Evaluation (CE),

Manipulative Skills (MS), and

Personal Skills (PS)


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1.1. General Information 3

Note!

Design, Data Collection and Processing, and Conclusion and Evalu-

ation are each assessed twice. Manipulative Skills is assessed sum-

mativelyover your two year course in physics. Personal skills is as-sessed once only during the group 4 project.

There are three aspects in each of the assessment criteria. The max-

imum mark for each criterion is 32= 6 marks representing three com-pletes. Since the first three criteria are assessed twice, and last two once,

the maximum marks are 263+26= 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.


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2DESIGN

2.1 Design Criterion

In design, you have to plan a physical measurement and following anal-

ysis 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-endedinvestigation. 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 ofthe dependent variable.

Independent and Dependent Variable

A variable that is manipulated in the experiment is called an inde-

pendent variable. The result of the manipulation leads to the mea-

surement 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 tellyou 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 graphi-

cal analysis, where you can draw a line of best fit, and calculate the

associated uncertainties.


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2.1. Design Criterion 7

As we study how the changing value of the independent variable af-

fects 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 vari-

ables.

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 manipu-

lated.

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 mea-

sured.

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 Collec-

tion 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 propaga-

tion 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 mea-

sure the period of one oscillation. Instead, you should measure the time

for a number of oscillations (for example ten), and from that value cal-

culate the time for one oscillation with the associated uncertainty.

The range of data is important. For example, in a pendulum exper-

iment, 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 ap-

plied. That is why you have to often consider the boundary conditions


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2.1. Design Criterion 9

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 re-

sources as well: the designed investigation should be doable in a

double lesson with the equipment the school has.


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3GUIDELINES FOR DATA COLLECTION

AND PROCESSING

3.1 Data Collection and Processing (DCP)

In Data Collection and Processing (DCP) you have to record and pro-

cess raw data, and present processed data with uncertainties in graphi-

cal 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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12 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.


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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 ti time for ten oscillations in trial i.

l/cm

0.5cm t1/s

0.4s t2/s

0.4s t3/s

0.4s

20.1 9.1 9.0 9.3

49.8 13.6 13.9 14.0

80.7 17.6 18.3 18.1

110.1 21.1 20.8 21.3

142.2 23.8 24.0 23.5

169.8 26.2 25.9 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/cm0.5cm t1/s0.4s t2/s0.4s t3/s0.4s

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 be-

hind them, and explain, if an uncertainty may be neglected.

For example, it is not enough to say, there is uncertainty in man-

ual timing due to reaction time, but also to estimate the magnitude ofuncertainty (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 po-

sition as function of time, and the instrumental uncertainty in time is

0.01 s, the uncertainty in time may be neglected.


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Instrumental Uncertainty

Instrumental uncertainty

The accuracy of a digital device is called the instrumental uncer-tainty.

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 ex-

ample, 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 digitaldevices 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 uncer-

tainty may be estimated as the smallest division in the scale. For exam-

ple, 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 0.2s. Instead, the time should be rounded to tenthsof a second to match the precision of the uncertainty ((5.10.2) s).


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

the precision of uncertainty.

l/cm0.5cm20.1

49.8

80.7

110.1

142.2

169.8

l/cm0.5cm20.1

49.8

80.7

110.1

142.2

169.8

t1/s0.4s9.1

13.6

17.6

21.1

23.8

26.2

t1/s0.4s9.1

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 oper-

ations, transforming data into a form suitable for graphical representa-

tion, constructing the coordinate axes, plotting the data, and determin-

ing the best fit line and its slope.

If the dependent variable should be directly proportional to the in-

dependent 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.


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Note!

Processing the raw data without a graph line does not earn com-

plete 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 measure-

ment 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= xmax xmin2

(3.1)

where xmax is the maximum and xmin the minimum value in the

sample.

This method of calculating the uncertainty in the average exagger-

ates 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

= sN

(3.2)

where sisthe standard deviation of the sample and N is the number

of measurements.

You should calculate the standard deviation with a calculator, or us-

ing a spreadsheet. Refer to the Users Manual for detailed instructions of

how to do it.

Note!

Use of Standard Error of the Mean is compulsory in Physics Ex-

tended Essays.


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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 pen-

dulum.

Period T of Simple Pendulum

The period of simple pendulum is

T= 2

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 pendu-

lum, we have to linearise Equation 3.3 by a variable interchange.

Squaring both sides of Equation 3.3 gives

T2 = 42

gl (3.4)

which is an equation of a straight line in a (l, T2) coordinate system

whose slope is m= 42g

. So, for linearisation, we have to calculate the

square of the period T2, mark the measurement points to a (l, T2) coor-

dinate system, and draw a line of best fit for the processed data.

Because we calculated the square of the period, we need to prop-

agate uncertainties. Because in multiplication fractional uncertaintiesadd, the fractional uncertainty in the period squared T2 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 ex-

periment the uncertainty in the measurement of length is negligible. As

a result, only vertical error bars are drawn.


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0

1

2

3

4

5

6

7

20 40 60 80 100 120 140 160 180

l

cm

T2s2

T2 = 0.041l0.055

Figure 3.4: The period squared T2 as a function of lenght l.

Note!

You have to state the equation of the best line. If the dependent vari-

able 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 T2 = 0.041l0.055, where the y-intercept is b=0.055s2. The value is so small that it might be a resultof the mathematical algorithm of the spreadsheet program used, rather

than an indication of a systematic error in the experiment.


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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 valueis not recorded correctly, or a malfunction of a device has oc-

curred. 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 treat-

ment 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.


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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 andmaximum 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 themaximum value of theslope.

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

0

1

2

3

4

5

6

7

20 40 60 80 100 120 140 160 180

l

cm

T2s2

Max

fit: T

2 =0.0

42l

0.060

Min

fit: T

2 =0.0

39l

0.08

Figure 3.5: The minimum (green) and maximum (red) fit lines in the

simple pendulum experiment.

0

1

2

3

4

5

6

7

20 40 60 80 100 120 140 160 180

l

cm

T2s2

Max

fit: T

2 =0.0

42l

0.060

Min

fit: T

2 =0.0

39l

0.08

Figure 3.6: First and last points with error bars magnified. Red line is the

maximum fit, and green the minimum fit line.


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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

mbest =mmaxmmin

2(3.5)

where mmaxis the slope of the maximum fit line, and mmin the slope

of the minimum fit line.

The uncertainty in the best fit line of the simple pendulum experi-

ment becomes

mbest=mmaxmmin

2

= 0.0422s2 cm10.0390s2 cm1

2

0.002s2 cm1

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

mbest = 4

2

g (3.6)

from where it follows that the acceleration due to gravity is

g= 42

mbest= 4

2

0.041s2 cm1 9.6ms2. (3.7)

The uncertainty in the acceleration due to gravity is

g= mbestmbest

g= 0.002s2 cm1

0.041s2 cm19.629ms2 0.5ms2. (3.8)

Thus, according to the data acquired in the simple pendulum exper-iment, the acceleration due to gravity is

g= (9.60.5)ms2

Data collection and processing is a relatively straightforward pro-

cess, and you should have little difficulty in learning the skills needed

to achieve high marks in it.


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4GUIDELINES FOR CONCLUSION AND

EVALUATION

Conclusion and Evaluation

In Conclusion and evaluation you have to state a conclusion, evaluate

weaknesses and limitations in the experiment, and suggest improve-

ments.

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

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26 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 re-

search.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).


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Conclusion and Evaluation 27

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 ap-

plicable).

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 ex-

perimental 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= (9.60.5)ms2 (4.1)The accepted value in Jyvskyl1 being g = 9.82ms2. The frac-tional uncertainty is 5%.
http://-/?-http://-/?-


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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 un-certainties.

In the absence of a reference value, you should comment on the reli-

ability 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.


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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

at2 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 differ-

ence V across the component, because of the increasing tem-

perature of the component (non-ohmic behaviour).

The range of the linear model has been exceeded. For ex-

ample, 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 (Hookes law

F=k x). Or air resistance opposes motion so much that thefalling 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 goback 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 inde-

pendent 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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Systematic errors are most often caused by:

by the software algorithm in a linear fit.

systematic misuse of a measurement device. For example, azero-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 measure-

ment results. For example, forget to add atmospheric pres-

sure to overpressure values in using gas laws, and not to sub-

tract background radiation in studying the activity of a ra-

dioactive sample.

A small deviation from the origin is most often caused by the algo-

rithm 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 bysoftware, 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 ofa systematic error unless the source of the error is removed.

Random errors

In the conclusion you should also comment on the random errors en-

countered. You should pay special attention to unexpected random er-

rors 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 theo-

ries. In such a case, however, you have to be extremely careful, and dou-

ble check you work to verify that you have not just missed something

obvious.


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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 ran-

dom 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 ma-

jor 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 ran-

dom uncertainty.


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CE Aspect 3: Improving the investigation"

In Conclusion and evaluation Aspect 3 you have to suggest realistic im-

provements in respect of identified weaknesses and limitations. This

includes the description of how the experimental procedure could beimproved 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 As-

pect 2.

Suggest realistic improvements.

Suggest exactly what should be done to reduce random un-

certainties.

Suggest exactlywhat should be done to reduce systematic un-

certainties

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 relat-

ing to the accuracy of the experiment. For example, in mea-

suring the thermal capacity of an object, insulating the sys-

tem 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 elim-

inate 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


37/37


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 mea-

surement 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 re-

sult, the instrumental uncertainty in time would be reduced to

t=0.01s, and that of position tos=0.001m.

You may use the Internet in finding information about the instru-

ments. 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 tem-

perature 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.
http://www.vernier.com/files/manuals/md-btd.pdfhttp://www.vernier.com/files/manuals/md-btd.pdfhttp://www.vernier.com/support/manuals/http://www.vernier.com/support/manuals/http://www.vernier.com/support/manuals/http://www.vernier.com/files/manuals/md-btd.pdf

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