Page
1
Links
2
Aims and Objectives + Agenda
3
Learner Profile
4
Combined SL and HL
7
Possible Schedule
10
Data Collection and Processing
24
Conclusion and Evaluation
36
Design
58
Example worksheets
78
Design Ideas
79
Filling out the 4PSOW
83
Sample example
93
Feedback
101
The Exam
118
Extended Essay
127
Group 4 Project
131
TOK Moments
INTHINKING PHYSICS WORKSHOP
Barcelona 2009
This workbook contains exercises and outlines of presentations that will be
used in this course. All other material used can be found on one of the
following internet sites
http://occ.ibo.org
(The IB online Curriculum Centre)
http://occ.ibo.org/ibis/occ/resources/ict_in_physics/
(IB and ICT)
http://www.physics‐inthinking.co.uk/
(IB Physics maintained by me)
www.inthinking.co.uk
IN
T
HINKING
For Teachers New to the IB Diploma
Barcelona, SpainFriday 30th October - Sunday 1st November 2009 Workshop Leader: Chris Hamper
Aims and Objectives
Introduce participants to the DP (incl. the Core & Learner Profile) and allow them to develop their DP subject-specific knowledge.
How the learner profile effects the way we teach Physics •
Why we shouldn’t lose sight of the complete hexagon •
TOK and internationalism •
Provide tools to implement the programme in their subject or school. How to set up a practical programme
•
Sharing methods of delivering the syllabus •
Sharing resources •
What Extended Essay supervision entails •
Engage participants in activities, discussion and reflection about the challenges and rewards of implementing the DP.
What makes IB physics different? •
Gain understanding of methods preparing students for IB assessment. A comprehensive guide to Internal Assessment and its pitfalls •
How to organise your record keeping •
How to get the level right when assessing student work •
Share ideas about ways to incorporate ICT into the classroom. Use of SMARTBOARD • Using simulations • Datalogging • Analysis of data •
Agenda
Session 1 Introductions and the syllabus Session 2 Internal assessment: Data collection Session 3 Datalogging
Session 4 Internal Assessment: Processing data
Session 5 Internal Assessment: Data Presentation and Graphing Session 6 Internal Assessment: Design Labs
Session 7 Internal Assessment: Conclusion and evaluation Session 8 The complete practical programme
Session 9 TOK and the Extended Essay Session 10 Gp 4 Project
The Learner profile
The learner profile is a list of the characteristics that we as IB Diploma teachers should be encouraging in our students but how do we do this in our Physics class?Inquirers
Knowledgeable
Thinkers
Communicators
Principled
Openminded
Caring
Risk takers
Balanced
Reflective
Combined HL / SL classes
A lot of schools do not have enough students to run separate HL and SL classes this means they have to be taught together. If the SL students did the same hours as the HL they would be overloaded so one way of making this fit into a timetable is to teach 2 classes a week with SL and HL then one extra class with HL. One way of making this work is to teach the core with the SL and HL then teach the relevant AHL in the extra classes. Sometimes it might be difficult to achieve continuity with the AHL students but with a bit of planning it’s possible to run a coherent course. The following table shows the areas of overlap with some comments about how the topics might be integrated. Topic 1: Physics and physical measurement HL SL Comments1.1 The realm of physics CORE No need to teach this section first. Most of this will come up in the practical programme or mechanics. 1.2 Measurement and uncertainties CORE 1.3 Vectors and scalars CORE Topic 2 : Mechanics
2.1 Kinematics CORE The projectiles bit is only a short section combined HL students will have to bide their time with extra practicals. 9.1 Projectile motion AHL 2.2 Forces and dynamics CORE 2.3 Work, energy and power CORE 2.4 Uniform circular motion CORE Topic 3 : Thermal physics
3.1 Thermal concepts CORE Quite a lot of AHL here so HL group can be working on thermodynamics in their extra classes. Only have to know basic kinetic theory before they start. 3.2 Thermal properties of matter CORE 10.1 Thermodynamics AHL 10.2 Processes AHL 10.3 Second law of thermodynamics and entropy AHL Topic 4: Oscillations and waves 4.1 Kinematics of simple harmonic motion (SHM) CORE The AHL material in this section is the same as the SL option A (apart from the bit about the eye). Could either get HL students to do this in extra classes or do it with the whole group. 4.2 Energy changes during simple harmonic motion (SHM) CORE 4.3 Forced oscillations and resonance CORE 4.4 Wave characteristics CORE 4.5 Wave properties CORE
11.1 Standing (stationary) waves AHL Op A
11.2 Doppler effect AHL Op A
11.3 Diffraction AHL Op A
11.4 Resolution AHL Op A
11.5 Polarization AHL Op A
5.1 Electric potential difference, current and resistance CORE May seem strange doing this before electric fields but works ok. 5.2 Electric circuits CORE Topic 6: Fields and forces
6.1 Gravitational force and field CORE No overlap here so HL students will have to do the AHL in their extra classes. 9.2 Gravitational field, potential and energy AHL 9.4 Orbital motion AHL 6.2 Electric force and field CORE 9.3 Electric field, potential and energy AHL 6.3 Magnetic force and field CORE 12.1 Induced electromotive force (emf) AHL 12.2 Alternating current AHL 12.3 Transmission of electrical power AHL Topic 7: Atomic and nuclear physics
7.1 The atom CORE Quantum physics AHL is the same as
the SL option B so whole class could do this however it might be more useful to do the AHL in the HL extra classes.
13.1 Quantum physics AHL Op B
7.2 Radioactive decay CORE
7.3 Nuclear reactions, fission and fusion CORE
13.2 Nuclear physics AHL Op B
Topic 8: Energy, power and climate change
8.1 Energy degradation and power generation CORE Everyone does this topic. The theory can be taught quite quickly with the HL but SL need more time. 8.2 World energy sources CORE 8.3 Fossil fuel power production CORE 8.4 Non‐fossil fuel power production CORE 8.5 Greenhouse effect CORE 8.6 Global warming CORE Topic 14: Digital technology
14.1 Analogue and digital signals AHL Op C Same as the SL option C without the mobile phone, and electronics; this is in the HL option F. 14.2 Data capture; digital imaging using charge‐ coupled devices (CCDs) AHL Op C Option E: Astrophysics
E1 Introduction to the universe Op E This would be a good option for a combined class. E2 Stellar radiation and stellar types Op E E3 Stellar distances Op E E4 Cosmology Op E E5 Stellar processes and stellar evolution AHL E6 Galaxies and the expanding universe AHL Option F: Communications
F1 Radio communication Op F If SL did this option and topic 14 with HL then they’d get their two options. Wouldn’t be a very balanced course though. F2 Digital signals Op F F3 Optic fibre transmission Op F F4 Channels of communication Op F F5 Electronics Op C F6 The mobile phone system Op C
Option G: Electromagnetic waves
G1 Nature of EM waves and light sources Op G This would be a good option if you have extra HL classes. G2 Optical instruments Op G G3 Two‐source interference of waves Op G G4 Diffraction grating AHL G5 X‐rays AHL G6 Thin‐film interference AHL Option H: Relativity
H1 Introduction to relativity Op D This is part of the SL
Relativity/Particles option. would work nicely with a combined class if the HL did both particles and relativity. H2 Concepts and postulates of special relativity Op D H3 Relativistic kinematics Op D H4 Some consequences of special relativity Op D H5 Evidence to support special relativity Op D H6 Relativistic momentum and energy AHL H7 General relativity AHL H8 Evidence to support general relativity AHL Option I: Medical physics I1 The ear and hearing Not in the SL course at all, don’t know why. I2 Medical imaging I3 Radiation in medicine Option J: Particle physics
J1 Particles and interactions Op D This is part of the SL
Relativity/Particles option. would work nicely with a combined class if the HL did both particles and relativity. J2 Particle accelerators and detectors AHL J3 Quarks Op D J4 Leptons and the standard model Op D J5 Experimental evidence for the quark and standard models AHL J6 Cosmology and strings AHL Note: All the topics in the SL options, Sight and waves, Quantum and Nuclear, Digital and Relativity and Particle are included in either AHL or HL options. EXCEPT Sight and the eye.
Possible schedule
Based on a ratio of 2 lessons of SL to 3 HL the core could be organised as follows.Mechanics plus Physics and physical measurement
Intro Extra Pracs Intro Kinematics Extra Problems Kinematics Forces Parabolic motion Forces Newtons laws Extra Problems Cons of momentum Work Extra Pracs Energy Circular motion Extra Problems Circular motionThermal Physics
Kinetic model 1st Law of thermodynamics Heat and Temp Sp ht cap Engines Change of stateOscillations and waves
SHM intro 2nd law of thermodynamics SHM equations SHM energy Extra problems DHM, FHM and resonanceWaves intro Standing waves Wave properties Examples of waves Doppler Test
Electric currents
Electricity intro Diffraction V, I and R Electric circuits Resolution TestFields and Forces
Gravitation intro Polarisation G field strength Electric field intro G potential E field strength Magnetism intro Orbits escape velocity ElectromagnetismAtomic and Nuclear
Atom intro E Potential Atomic models The nucleus Faradays law Binding energy Decay AC generator, transformer and transmission Fission and FusionEnergy Power and Climate change
Energy degradation Intro to quantum physics World fuel sources Fossil fuel power Photoelectric effect Non fossil power Non fossil power Wave nature of matter Greenhouse effect Global warming Extra nuclear This now leaves the options for both and Digital for HL An alternative and probably more sensible approach would be to teach the SL core to the whole class followed by the AHL for HL only. This would mean that the SL students would get their free time at the end of the topics rather than once each week. This would make a much more coherent programme but might not fit into all timetable structures.Data collection and Processing
Aspect 1: Recording Raw Data
IB Criteria
Complete/2 Records
appropriate
quantitative and associated
qualitative raw data, including
units and uncertainties where
relevant.
Partial/1 Records
appropriate
quantitative and associated
qualitative raw data, but with
some mistakes or omissions.
Not at All/0
Does not record any
appropriate quantitative raw
data or raw data is
incomprehensible.
Check List
Draw a table (using Excel) with a column for each measurement. This will generally
mean one column for the independent variable and 5 for the repeated measurements
of the dependent. There should be at least 5 rows one for each time you change the
independent variable.
If your data is coming from the gradient of a “data logger graph” or other graphic
computer display include an example of this graph in you report.
The number of decimal places should be the same for all values in a column
Each column must have a heading and the units of the quantity
You should estimate the uncertainty of the measuring instrument this must be in the
header.
Uncertainties should be rounded of to 1 significant figure ±0.2 not ±0.17
The number of decimal places in the data should not exceed the limit of the
uncertainty.
e.g. if uncertainty is ±0.2 the measurement should only be quoted to 1 decimal place
Comment on how you arrived at any uncertainty value in the table
Comment on any observations you made that might be relevant later; there might not
be anything here.
Results
Raw Data Table
Below is a table of the data from the 5 runs performed for each of the 7 different heights.
The Uncertainty in Distance is estimated to be ±5mm due to the difficulty of measuring the
position of the ball and the point at which the landing pad is activated.
Uncertainty in Time is calculated from the (Max Time – Min Time)/2
Distance/m ± 0.005m Time 1 /s Time 2 /s Time 3 /s Time 4 /s Time 5 /s Av. Time /s Time unc. /s ±0.001s ±0.001s ±0.001s ±0.001s ±0.001s 0.090 0.135 0.137 0.136 0.135 0.134 0.135 0.002 0.145 0.172 0.171 0.170 0.170 0.171 0.171 0.001 0.170 0.184 0.185 0.184 0.184 0.185 0.185 0.001 0.235 0.217 0.217 0.218 0.217 0.218 0.217 0.001 0.290 0.241 0.241 0.238 0.240 0.241 0.240 0.002 0.310 0.248 0.248 0.247 0.248 0.249 0.248 0.001 0.365 0.270 0.271 0.271 0.270 0.270 0.271 0.001
Measurements were taken from the bottom of the ball to the depressed landing pad.
Errors and
calculations
explained
Table has consistent
decimal places and
units. Uncertainties
seem reasonable.
Aspect 2: Processing Raw Data
IB Criteria
Complete/2
Processes the quantitative raw
data correctly
Partial/1
Processes quantitative raw
data, but with some mistakes
and/or omissions.
Not at All/0
No processing of quantitative
raw data is carried out or major
mistakes are made in
processing.
Check list
The data should be processed in some way, for example averaging, squaring or
finding the sine. Processed data should be displayed in a table separate to the raw
data table.
The table must have headers that include units and uncertainties
Calculate uncertainties in the repeated measurements by finding the 1/2(max value –
min value) in the spread of data.
Calculate the uncertainties in processed data by calculating the (max value – min
value)/2
e.g. if uncertainty in time is 0.2 then uncertainty in t
2is (t+0.2)
2–(t-0.2)
2/2.
The number of decimal places in each column must be consistent with each other and
the uncertainty.
An extract from a report that completes all requirements
Processed Data
Since the initial velocity is zero, the vertical displacement and time are related by the equation
s=1/2at
2a graph of s vs t
2will give a straight line. The gradient of this line will be 1/2a.
Distance(m) ± 0.005 Av. Time /s Time unc. /s Time² /s² Unc. Time² /s² 0.090 0.135 0.002 0.0183 0.0004 0.145 0.171 0.001 0.0291 0.0003 0.170 0.185 0.001 0.0340 0.0002 0.235 0.217 0.001 0.0472 0.0004 0.290 0.240 0.002 0.0578 0.0007 0.310 0.248 0.001 0.0615 0.0005 0.365 0.271 0.001 0.0732 0.0003
The equation used to calculate the uncertainty in time
2was (Max time
2– Min time
2)/2 where
the max and min values were taken to be the average value + and – the uncertainty.
Table has consistent decimal places
and uncertainties. All columns
have correct units. Calculations
explained.
Aspect 3 Presenting Processed data
IB Criteria
Complete/2
Presents processed data
appropriately and, where
relevant, includes errors and
uncertainties.
Partial/1
Presents processed data
appropriately, but with some
mistakes and/or omissions.
Not at All/0
Presents processed data
inappropriately or
incomprehensibly.
Check List
Processed data should be presented in a graph. This graph should be linearised if
possible. The graph should be drawn using Graphical Analysis. If not possible to
linearise the function then a curve can be plotted, however this makes the analysis
more difficult so the following points are for straight lines only.
The graph must have heading, axis labels and units.
Independent variable should be on the x axis
Graph must include error bars
A best fit line should be plotted automatically
The equation of the line must be displayed (y=mx+c).
Manually fit the steepest and least steep lines that fit the error bars
Quote uncertainty in gradient
An extract from a report that completes all requirements
Graph of s vs t
2Max gradient = 5.198 ms
-2Min gradient = 4.796 ms
-2Uncertainty
in gradient = (5.198 – 4.796)/2 = 0.2 ms
-2Gradient = 5.0 ± 0.2 ms
-2Graph has correct labels, units,
custom error bars, best fit line, and
max and min gradients.
Background on Examples
The following examples are taken from 3 student reports. To clarify the way the different
criteria are applied the reports are split into two parts DCP and CE.
The practical was related to hydro electric power (topic 8).
Student’s worked from the following worksheet which gives some details about the theory but
does not give details on how to collect or process data.
Practical 11 Hydro Power Simulation
Introduction
When water flows from the reservoir (bottle) to the end of the pipe PE is converted to KE, this
causes the water to squirt out of the pipe with velocity v falling in the parabolic path shown in
the diagram below.
Theory
Applying the law of conservation of energy to a mass m of water
1
2
1
2
The water falls with uniform acceleration, applying the equations of uniform acceleration to
the vertical motion:
1
2
1
2
2
The horizontal velocity of the water is constant therefore:
Substituting for t gives
2
2
Substituting into the energy equation gives
1
2 2
4
Method
By measuring the height of the top of the water in the bottle and the distance squirted by the
water confirm this relationship and find y.
Measuring the distance squirted by the water is not easy so introduces some uncertainties into
the measurement which are much greater than the uncertainty in the ruler. Students sometimes
find that their spread of data is zero, this gives something to talk about.
DCP Example 1
Raw data:
The table below contains the data from four measurements of the dependent variable
(distance) for all the five times, the independent variable was changed.
Height
(cm) ± 0,3
cm
Distance 1
(cm) ± 0,5
cm
Distance 2
(cm) ± 0,5 cm
Distance 3
(cm) ± 0,5
cm
Distance 4
(cm) ± 0,5
cm
23,8
1,6
1,7
1,5
1,5
35,8
5,7
5,4
5,3
5,6
47,8
8,5
9,1
8,3
8,2
59,8
10,9
10,8
10,5
10,2
71,8
11,8
11,3
11,2
11,5
• The uncertainty in height was estimated ±0,3 cm because the bar we measured the
height from was circular and we probably didn’t take the measurement of distance
when the water was exactly at the mark.
• The uncertainty in distance was estimated ±0,5 cm because the water
gush was approximately that thick and fluctuated a little.
Processed data:
The table below contains manipulated date, to allow us plotting a graph, in which I can use the
gradient to find out the height of the end of the pipe, above the scale.
Height
(cm) ± 0,3
cm
Average
distance
(cm)
Uncertainty
in distance ±
(cm)
Max
distance
(cm)
(Average
distance)²
(cm)
(max
distance)²
(cm)
Error in
(average
distance)² ±
(cm)
11,8
1,6
0,1
1,7
2,5
2,9
0,4
23,8
5,5
0,2
5,7
30,3
32,5
2,2
35,8
8,5
0,5
9,0
72,7
81,0
8,3
47,8
10,6
0,4
11,0
112,4
121,0
8,6
59,8
11,5
0,3
11,8
131,1
139,2
8,1
DCP Aspect 1
C
P
N
• The average value of distance was found by applying the average function
in Excel to the values in the raw data table.
• The uncertainty in distance was found by applying (MAX value – MIN
value)/2 to the values in the raw data table.
• Max distance was found by adding each uncertainty to the average value
• (Average distance)² and (max distance)² was found by squaring the value
it’s based on
• The error in (average distance)² was found by: [(max distance)²- (Average distance)²]
Processed data:
Graphical Analysis
•
Manually fit, steepest and least steep line, to find out the uncertainty in the
answer could not be plotted due to inaccuracy
in the data.DCP Aspect 2
C
P
N
DCP Aspect 3
C
P
N
DCP Example 2
Results
Raw Data Table
Below is a table of the data from the 5 runs performed for each of the 5 different heights.
The uncertainty in Height is estimated to be ½ the smallest division of the meter stick (1mm).
The uncertainty in Horizontal Displacement (Hor.disp.) is calculated by the (Max Disp. – Min
Disp.)/2.
Height(cm)
±0.05cm
Hor.disp.
1 (cm)
Hor.disp.
2 (cm)
Hor.disp.
3 (cm)
Hor.disp.
4 (cm)
Hor.disp.
5 (cm)
Avg.hor.
disp.(cm)
Hor.disp
unc.(cm)
80
11.0 11.9 11.0
11.0
10.9
11.2 0.5
100
13.5 13.1 13.0
12.8
12.9
13.1 0.3
115
14.0 13.7 14.2
14.3
14.0
14.0 0.3
120
16.2 16.0 17.0
16.5
16.4
16.4 0.5
205
20.9 21.4 21.1
21.0
21.1
21.1 0.25
There was no system for which side of the stream of water would be used to measure the
x-value, which was approximately 1cm in diameter. This may have affected the variation in the
measurements.
Processed Data
The height and the horizontal displacement are related by the equation h=x
2/4y, and so a
graph of h vs. x
2will have a gradient of 4y.
Height(cm)
±0.05cm
disp.(cm)
Avg.hor.
Hor.disp
unc.(cm)
disp.
Avg.hor.
2(cm
2)
Avg.hor.disp.
2unc.(cm
2)
80 11.2
0.5
125
11.4
100 13.1
0.3
171
9.21
115 14.0
0.3
196
8.40
120 16.4
0.5
269
16.5
205 21.1
0.25
445
10.6
DCP Aspect 1
C
P
N
DCP Aspect 2
C
P
N
Graph of Height vs. Distance
2DCP Aspect 3
C
P
N
DCP Example 3
RAW DATA AND UNCERTAINTY
Below is a table of the data from the 5 runs performed for each of the five different heights.
The uncertainty in the measurement of the height of water in the bottle is estimated to be ½ of
the smallest division of ruler (1mm). However, the design of the experiment and the manner
in which the equipment had been set up did not allow me to hold the ruler close enough to the
bottle. Thus the ruler had to be held at a distance of 3-4 cm away from the bottle and I had to
rely upon eye measurement. The uncertainty can thus be assumed to be 0.5 cm.
The distance was measured using eye measurement and thus wasn’t very precise. The ruler
used to measure the distance lay on top of the bucket, while I measured where the water hit
the bottom of the bucket, which was approximately 30 cm below. Due to this the maximum
precision I was able to make was up to 0.005 m. Also, the water was constantly running and
filling up the bucket, making it harder to accurately measure the distance squirted by water.
Thus the uncertainty in the measurement of the different runs is 0.005m.
PROCESSED DATA
Height of water (m) ±
0.005 m
Average Distance
(m)
Uncertainty
(m)
Distance²
(m²)
Uncertainty
Distance²
(m²)
0.620
0.262
0.008
0.069
0.004
0.600
0.249
0.008
0.062
0.004
0.580
0.245
0.005
0.060
0.002
0.560
0.243
0.005
0.059
0.002
0.530
0.228
0.005
0.052
0.002
The equation used to calculate the uncertainty in distance was (Max distance – Min
distance)/2.
Height of water
(m) ± 0.005 m
Distance squirted
(m) Run1 ± 0.005m
Run2
±0.005m
Run 3
±0.005m
Run 4
±0.005m
Run 5
±0.005m
Average
Distance
(m)
Uncertainty
(m)
0.62
0.260
0.265
0.255
0.270
0.260
0.262
0.008
0.60
0.250
0.250
0.240
0.250
0.255
0.249
0.008
0.58
0.245
0.240
0.245
0.250
0.245
0.245
0.005
0.56
0.240
0.245
0.240
0.250
0.240
0.243
0.005
0.53
0.230
0.230
0.220
0.230
0.230
0.228
0.005
DCP Aspect 2
C
P
N
DCP Aspect 1
C
P
N
The uncertainty in distance² is found using (Max²-Min²)/2 where the maximum and minimum
values for distance² are calculated using the average value + and – the uncertainty.
From the theory we know that
Meaning that
Therefore,
Resultantly, we will get a graph of x² against h will give a gradient equal to 4y.
GRAPH
DCP Aspect 3
C
P
N
Conclusion and Evaluation
Aspect1: Concluding
IB Criteria
Complete/2
States a conclusion, with
justification, based on a
reasonable interpretation of the
data.
Partial/1
States a conclusion based on a
reasonable interpretation of the
data.
Not at All/0
States no conclusion or the
conclusion is based on an
unreasonable interpretation of
the data.
Check List
State whether your graph supports the theory. E.g. Is the relationship between the
quantities linear? This is only true if the line touches all error bars, don’t say it is if it
isn’t.
Are there any points on the graph that appear to be due to mistake (outliers), maybe
it’s best to remove these and plot the line again?
Normally the data will be arranged so that the gradient will give you some value (e.g.
“g”) calculate this value from the gradient.
Calculate the uncertainty in this value from the steepest and least steep lines.
Don’t forget units.
Compare your result with an accepted value, say where this value is from and quote
uncertainty if known.
An extract from a report that completes all requirements
Conclusion
From the graph it can be seen that within the uncertainties in the experiment s is proportional
to t
2. Since the acceleration is therefore constant we can apply the equation s=1/2at
2so the
gradient of the line can be deduced to be 1/2a where a is the acceleration of free fall.
From the graph the gradient = 4.966ms
-2so the acceleration g=9.932ms
-2The uncertainty in the gradient can be found from the steepest and least steep lines
Max value = 2x5.198 = 10.396ms
-2Min Value = 2x4.796 = 9.593ms
-2Uncertainty = (Max-min)/2 = ±0.4ms
-2The final value obtained for g is therefore 9.9 ±0.4 ms
.2The accepted value established by the 3
rdGeneral Conference on Weights and Measures is
9.80665 ms
-2, this lies within the limits of uncertainty of the experimental value obtained,
although it should be noted that g is not the same all over the world so this is an average
value. The value in Oslo is 9.819 ms
-2(Wikepedia)
Here is the graph referred to in this conclusion
Value of g
calculated from the
gradient.
Uncertainty
calculated from max
and min lines. Value
compared.
Aspect 2: Evaluation
IB Criteria
Complete/2 Evaluates
weaknesses
and
limitations.
Partial/1 Identifies
some
weaknesses
and limitations, but the
evaluation is weak or missing.
Not at All/0
Identifies irrelevant
weaknesses and limitations.
Check List
This is where you say if the conclusion is reasonable or not, you must have evidence
for anything you write here, this can be from your results (the graph) or the
observations you made during the experiment. You shouldn’t say friction was a
problem without evidence. It might help to do a small experiment to show that
something was a problem.
Comments do not have to be negative.
Comment on whether your graph shows a trend; is it clearly a curve even though the
line passes through the error bars? Are the errors reasonable, are they obviously too
big or too small
Comment on whether the intercept tell you anything, if it is supposed to be (0,0) and
isn’t it might suggest a systematic error.
Comment on whether you manage to keep the “controlled variables” constant?
Comment on the equipment used and the method in which you used it.
Comment on the range of values and the number of repetitions.
Comment on time management
Extract from a report that completes all requirements
Evaluation
Looking at the graph I can see that the data points lie very close to the best fit line although
there is some small deviation. The small error bars realistically reflect the accuracy of the
measurement. The final value was quite close to the accepted value supporting this
deduction.
Air resistance was not seen to be a problem; if there had been air resistance the graph would
not have been a straight line
Although the experiment gave a good value the random uncertainty could be reduced by
repeating the measurements more times or using a wider range of heights. In this case air
resistance would start to be a problem so a smaller ball could be used.
They intercept was very close to the theoretical value of 0, this shows that the height
measurement was carried out accurately with no zero error.
Graph referred to:
Evaluation based on results,
error bars and intercept
Aspect 3: Improving the Investigation
IB Criteria
Complete/2 Suggests
realistic
improvements in respect of
identified weaknesses and
limitations.
Partial/1
Suggests only superficial
improvements.
Not at All/0
Suggests unrealistic
improvements.
Check List
List ways of improving the investigation (I.e. reducing the uncertainties). Anything
you write here must be related to something you mentioned in the evaluation. This in
turn should be linked to the results. Think like a detective, look for evidence.
If possible do a calculation or a small experiment to show how the improvement
might improve the accuracy of the result.
If you had a more reading (wider range or more repetitions) would it improve your
result?
Is there any modification to the apparatus that would make the results better?
If you made any modification to the original method then mention it here, you will
then get credit for suggesting improvements.
Extract from a report that completes all requirements
Improvements
The method gave good results but the uncertainty ±0.4m/s
2could be reduced. The weak point
of the experiment was the positioning of the ball and the release mechanism. This was not
completely stable and even though we could measure the height to ± 0.5mm the ball could
easily move after the measurement, a more solid support would reduce this error.
To reduce the uncertainty in the height measurement would have to replace the ruler with
something more accurate, perhaps a vernier calliper could be used to position the ball
however if the support was not made more stable this would be pointless.
A bigger range of values is often seen as a way of reducing the uncertainty however if we
dropped the ball from higher up then air resistance may be a problem since it is related to the
speed of the ball which would in this case be higher.
As stated early there was no evidence that air resistance was a problem, probably due the
short drops used, repeating the experiment in a vacuum would therefore not lead to a
significant improvement.
All improvements supported
by evidence either from the
results or observation.
CE Example 1
Conclusion and evaluation:
Conclusion:
From looking at the graph we can see that (distance)
2and height seem to be proportional.
However, I cannot confidently state that, due to the inaccuracies in the data. The linear graph
does not pass through all the error bars.
If I assume that the relationship is proportional, I can apply the equation that was
presented in the theory part earlier.
From this
equation, we can divide the gradient by 4 and the result of that
should be equal to the real height of the pipe above the scale, 12 cm
(y).
The results of that calculation is on the other hand:
We can clearly see that there is a mistake in the data collection or in the theory the calculations
are based on.
Things that could have made the results inaccurate:
• The path that the water flowed through the pipe did clearly affect the power
at which the water squirted out of it.
o
The evidence for this statement is the fact that when we changed the
path from how it is on picture A to how it is on picture B, the distance
that the water squirted increased. More energy is used on the way
through A than B.
C
P
N
CEAspect 2
C
P
N
o
When the independent variable, height was change, the path of the pipe
changed significantly (Picture C) and from my observation connecting power
and path of the water, I can state that this is a factor that could easily influence
the results.
Picture
C
• The bucket where the scale was placed on (see picture c) might have moved slightly
between measurements, even we market the place on the table
o
This was found out by measuring two times during the experiment, how far
over the bucket, the end of the pipe was.
o
The scale also moved slightly and it was difficult to adjust it with the curved
edge of the bucket.
• The reason for the points being scattered around the best fit line is probably the
different paths of the pipe (the difference, in how we held it), combined with the
factors just mentioned.
o
Another possibility is that, by holding the pipe it is possible that I made it
narrower and caused more energy to be used up on the way, in some of the
cases.
• The reasons for the interception being -31,42 are not known but might suggest a
systematic error
Improvements:
• What we did:
o
Marked the place on the table where the bucket should stand, to decrease the
inaccuracies in distance.
• What we could have done:
o
Wrapped the pipe around a horizontal wheel that would make sure that there
were never sharp curves on it and that we are not making the pipe narrower in
some of the cases.
The difference would then always have the same effect and the points
would therefore not be scattered but with a systematic uncertainties.
o
Get the bucket and the scale into a position where it would not be necessary to
move it. Pump the water out of the bucket, when it has to be emptied.
• Because the reasons for the error in the result of this experiment are not known, I can’t
suggest any improvements for it.
CE Aspect 3
C
P
N
CE Example 2
Conclusion
From the graph it can be seen that the linear fit is nearly within the uncertainties of the
experiment. It seems as though the uncertainty was not large enough or for an unknown
reason the measurements at h=120cm were taken consistently incorrectly. Otherwise, the
slope appears to be constant, and so the equation h=x
2/4y can be applied.
From the graph the gradient=2.574cm, so the vertical displacement y=0.6435cm
The uncertainty in the gradient can be found in the steepest and least steep lines
Max value = ¼x2.738 = 0.6845cm
Min value = ¼x2.477 = .61925cm
Uncertainty = ½(Max - Min) = ±0.03cm
The final obtained for y is therefore 0.64±0.03cm
The value measured with the meter stick for y was 0.65cm; this lies within the limits of
uncertainty of the experimental value obtained.
Improvements
The measurements could be taken from a constant position in order to minimize parallax
error.
CE Aspect 3
C
P
N
CE Aspect 2
C
P
N
CE Aspect 1
C
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N
CONCLUSION
As the height of the open end of the pipe from the table upwards, wasn’t changed; y was held
constant throughout the experiment. Therefore, a linear relationship should exist. However,
since the line doesn’t touch all the error bars, this is not the case for this particular experiment.
We know that the gradient, taken from the first graph, is equal to 4y.
Therefore
The uncertainty in the gradient can be found from the steepest and least steep lines.
Max value
Min value
Uncertainty
The final value obtained for y is therefore 0.042 m ± 0.010
EVALUATION
This conclusion seems unreasonable as I was unable to prove, through the experiment, that a
linear relationship exists between the two variables, even though such a relationship should
exist. This may be due to the imprecision of the uncertainties in my measurements, which
could have been greater than was accounted for.
Also, the y-value originally measured in order to obtain the height of water in the bottle, being
approximately 30 cm, was significantly higher than the value that was calculated through the
experiment itself. The y-intercept was not (0,0) i.e. the line did not pass through the equation
y=x, as can be seen from the graph, so a systematic error could have occurred. The y-intercept
not being (0,0) obviously does not make sense, for there cannot be a value for y when there is
in fact no height (h) from which to spurt water.
The position of the clamps to which both the bottle (reservoir) and the end of the pipe were
clamped, was not changed throughout the experiment. Thus I was able to control my
controlled variables.
The equipment used made it extremely difficult to measure:
• The height of water since the shape of the bottle clamped to the stand was hard to
measure precisely with the use of a ruler
• The distance that water was spurted was imprecisely measured since the only means
of measuring it was a ruler placed on top of the bucket. The distance of the ruler from
the top to the bottom of the bucket (which is where the water fell) was 30 cm; this
distance between the place from which distance of water spurted was measured, and
from where it should have been measured, made the measurement itself inaccurate
• The shape of the bucket too was a problem. Since the bucket was circular, instead of
being uniformly shaped, with a smaller diameter at the bottom than at the top, it was
difficult to measure exactly where the water spurted out and touched the bucket. So a
human error in measurement may have led to a repeated systematic error in the
experiment, thus contributing to a shift in the y-intercept
• The pipe was stretched by the use of clamps, since without the use of them, the pipe
contracted. Fastening the pipe to the clamp may have resulted in the clamp squeezing
CE Aspect 1
C
P
N
the pipe. This may have induced pressure applied on the pipe which wasn’t accounted
for in the experiment and thus may have led to a spurt of water to a greater distance
than might actually be the case if the pipe wasn’t squeezed at all
As I spilled water everywhere in the beginning of the experiment, I had to carry out the whole
experiment again. Also the fact that I realized after having carried out 2 runs, that the clamp
was squeezing the pipe and thus the values were more likely to be imprecise, meant that I
used more time on this experiment than was originally allotted.
IMPROVEMENTS
The uncertainty of ±0.010 m being too high could be reduced by improving the experiment in
the following ways:
• Use of digital equipment, such as a digital camera with which the whole experiment
could be filmed may enable a more precise measurement for the distance that the
water spurts
• Using a smaller ruler at the bottom of the bucket may give a more exact value for x
• Using a cuboid bucket for the water to spurt in, would make it easier to measure x and
rid the experiment of the systematic error
The h-values chosen could have had a greater difference in between them. This may have
made it easier for me to find a systematic trend in the results. The amount of repetitions was
appropriate. Further repetitions probably wouldn’t have made a significant difference since
the element of systematic and human error due to eye measurement could not be erased even
through more runs.
I carried out certain improvements, though, when going through the experiment for the second
time:
• I used a pen to mark the bottle (reservoir) in order to measure “h” easily
• I tried to clamp the end of the pipe to the stand in such a manner that it would squeeze
the pipe as little as possible
• I also emptied the bucket each time a run was carried out so that I could measure the
distance the water was spurted (x) more accurately
CE Aspect 2
C
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N
CE Aspect 3
C
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N
Design
Aspect 1:Research Question
IB Criteria
Complete/2
Formulates a focused
problem/research question and
identifies the relevant
variables.
Partial/1
Formulates a problem/research
question that is incomplete or
identifies
only some relevant variables.
Not at All/0
Does not identify a
problem/research question and
does not identify any relevant
variables.
Check List
State the research question clearly under the heading “Research question”. It should
be phrased in the form “how is y dependant on x”. If the topic is not obvious it is
wise to write a paragraph introducing the topic before you state the research question.
Identify and list the independent variable (this is the one you are changing, x) and
dependent variable (the one that changes, y).
Identify and list the controlled variables. These are all the other quantities that you
could change but that are being kept constant.
You will not be graded on writing a hypothesis but it is good practice to say what you
expect to happen.
Extract from a report that competes all requirements
Introduction
This practical is an investigation into a rubber bung connected to an elastic band. The free
end of the elastic band is clamped to a stand and the bung hung vertically from it. When the
bung was lifted and released the elastic band stretched (as shown in the diagram below). I
decided to investigate the relationship between the maximum stretch of the elastic band and
the height of release.
Research Question
How does the extension of the elastic band (x) depend upon the height of release (h)?
Independent Variable
: The height of release
Dependent Variable
: The stretched length of the elastic
Controlled Variables
:
• The mass of the bung • The length of the elastic band • The type of elastic band • The initial velocity of the bungHypothesis
Applying the law of conservation of energy I expect that the GPE at the top will equal the
EPE at the bottom. mgh=½kx
2Since mg and k are constant I expect that x will be
proportional to √h
h
x
Good idea to introduce topic since
it’s not obvious what this is about
from the research question alone
Clear Research question
Diagram helps clarify research
question
Variables listed
Controlled variables
listed
Hypothesis included but
not necessary for a
complete score
Design Aspect 2 Controlling variables
IB Criteria
Complete/2
Designs a method for the
effective control of the
variables.
Partial/1
Designs a method that makes
some attempt to control the
variables
Not at All/0
Designs a method that does not
control the variables.
Check List
List the apparatus used
Draw a labelled diagram of the apparatus, a photo is also a good idea
Describe how you are going to change and measure the independent variable
Describe how you are going to measure the dependent variable.
Extract from a report that completes all requirements
Method
Measuring the variables
To measure the height of release and extension a ruler was mounted next to the elastic. It is
important that the ruler is vertical so it was positioned using
a plumb line.
All measurements were made from the bottom of the bung; I
decided to do this because it was a straight line therefore
easy to line up with the ruler.
The bung was lifted so that it lined up with a cm mark on the
ruler and released. To reduce parallax errors I positioned
my head in line with the bung when I took the reading. The
ruler was positioned close to the bung but not touching.
After release the lowest position of the bung was measured
using the same ruler. I found that if I did this a couple of
times I could position my head in line with the lowest point
before release again minimizing parallax error.
Controlling the controlled variables
The same bung and elastic band was used throughout the experiment.
After each run I waited a few seconds so that the elastic would lose any heat generated.
I was careful to make sure that the bung was released from rest each time.
Apparatus List Plumb line Ruler Rubber bung Elastic cord
Apparatus list
Details on how
variables are varied
and measured
Details on how each of
the controlled
Design Aspect 3 Developing a method for collection of data
IB Criteria
Complete/2
Develops a method that allows
for the collection of sufficient
relevant data.
Partial/1
Develops a method that allows
for the collection of
insufficient relevant data.
Not at All/0
Develops a method that does
not allow for any relevant data
to be collected.
Check List
State the range of values of the independent variable that you are going to use
State how many times you are going to repeat the measurements of the dependant
variable
Extract from a report that competes all requirements
The experiment was repeated 5 times for each of 8 different heights ranging from 4cm above
the “at rest” position to 12cm above. The elastic supplied by the teacher wasn’t long enough
to give the range that I wanted so I swapped it for a longer one.
I decided only to use initial positions where the elastic was slack. This is because I didn’t
want the elastic to have any elastic PE before release.
The student has chosen a
good range of values and
repeated each
Background on Examples
Sponge
In this practical students were given a large piece of foam rubber. It was actually an old
mattress from one of the student houses.
All they were told was that they must think of a research question related to some property of
the sponge (squashiness, absorbency, bounciness etc.)
The research question must be in the form “how is y related to x”.
An experiment to test the relationship between x and y is then designed and carried out.
Students work in pairs but only one of the pair writes up the experiment.
Practical Report. Sponge
Introduction
This practical is an investigation about a sponge. The Investigated material is used for
making mattresses, such as those used for beds. This material can absorb some energy from
an object which is dropped on it so the surface under the sponge experiences smaller force
than it would without the sponge. It can also be soaked in water, it bounces when dropped,
objects bounce when dropped on the sponge... I decided to investigate the first characteristic:
the change of energy absorbed by the surface under the sponge when an object is dropped on
it.
Research question
How the percentage change in the force exerted when a mass is dropped on the sponge and
without the sponge is related to the mass dropped onto it.
In order to investigate my research question I will measure the force applied on the surface of
the plate attached to a force sensor; once with and once without the sponge (without changing
the mass of the plasticine).
Independent variable:
Weight of the object (plasticine).
Dependent variable:
Energy absorbed by the surface of the force sensor plate.Controlled variables:
• Height from which the object is dropped • Elasticity of the sponge (type of sponge, shape of sponge) • The initial velocity • Surface under the spongeMethod
Measuring the variables
Apparatus List:
• Sponge (cuboid shape) • Plasticine • Triangular holder • Ruler • Force sensor + wooden plate adjustage • Digital scale I set the apparatus as shown on the picture on the right:Sensor without a
sponge
Sensor with
a sponge
plasticine
D Aspect 1
C
P
N
I used plasticine for this experiment because I can easily change its mass without changing other characteristics of it. I used the triangular holder for making sure that I will drop the plasticine always from the same height. Then I used a pendulum to make sure that the end of the upper metal stick ‐the place from which I will later drop the plasticine‐ is ideally above the force sensor, so after I drop the plasticine, it will precisely fall on the sensor. I made sure during the measurements that the position from which is the plasticine dropped is always the same, so the lower edge of the plasticine was in the same level as the end of the upper metal stick. I used a ruler to measure the height difference between the end of the metal upper stick and the surface of the force sensor (not the surface of the sponge). After I set the apparatus up, I did not move it in any way. I used a knife to shape the sponge to an appropriate shape. It could not be too think because then the possibility of measuring small masses could be restricted and also if the sponge would be too thin, measurements for greater masses may not be very clear and distinctive. I also tried to make the cut surface of the sponge as even as possible so that the measurement is as precise as possible. For making sure that the sponge will stay on the force sensor plate and will not slip aside, I used a thin –so that it will effect the measurement as little as possible‐ layer of sticky plasticine to stuck it there.
Controlling the controlled variables
: The same sponge was used during the whole experiment I did not move the triangular holder or the force sensor after I set the apparatus so that the height difference will not change. I made sure that I am releasing the plasticine from rest – without any initial velocity. There was a small mechanical problem with the force sensor; sometimes when a greater mass hit the surface of the sensor, the plate which is connected to the sensor itself became more loose. Therefore after every impact I made sure that the adjustage is fasted enough. The measurements were done for 5 different masses. I first repeated the measurement ´without sponge´ 10 times in order to decrease the uncertainty as I find my human factor in the setting up the experiment very crucial and also highly inclined to cause systematic error. Further I did not repeat the measurement ´without sponge´. The experiments ´with the sponge´ were repeated at least 4 times as I observed huge differences in measured values after the first set of measurements. I will discuss this problem later in my report.D Aspect 2
C
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N
D Aspect 3
C
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