IB PHYSICS WORKSHOP Berlin 2009 - "You cannot teach a...

IB PHYSICS WORKSHOP Berlin 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 site.

http://occ.ibo.org (The IB online Curriculum Centre)

http://occ.ibo.org/ibis/occ/resources/ict_in_physics/ (IB and ICT)

http://www.rcnuwc.org/ibphysics/index.html (Chris Hamper's website)

Berlin 2009 Chris Hamper

1

Contents

Section Page no. Workshop Schedule 3

Syllabus overview 5Possible teaching schedule 8Data Collections and processing 11Conclusion and Evaluation 23Design 38Examples of worksheets 50Design Practicals 74Preparing the Sample 76TOK Moments 77Extended Essay 81EE Hints 88Gp 4 Project 90


2

Workshop leader Agenda

DP Workshops for New Teachers to the programme

06 to 08 July 2009

Event: DP Workshops in Berlin Workshop : Physics Workshop leader: Chris Hamper

Day 1 Time Agenda per session

Plenary session 08.30 – 08.45

Session 1 09.00 ‐ 10.30 Introduction and the IB Hexagon

Coffee break 10.30 – 11.00

Session 2 11.00 – 12.30 Learner Profile and Resources

Lunch 12.30 ‐ 13.30

Session 3 13.30 – 15.00 Teaching the syllabus


Session 4 15.30 – 17.00 IA Data Collection

Official Reception 17. 15 – 18.15


Session 5 08.30 ‐ 10.00 IA Datalogging


Session 6 10.30 – 12.00 IA Processing Data and Graphing

Lunch 12.00 ‐ 13.00

Session 7 13.00 – 14.30 IA Design


Session 8 15.00 – 16.30 IA Conclusion and Evaluation


Session 9 08.00 ‐ 09.30 IA The complete Programme


Session 10 10.00 – 11.30 The Exam

Lunch 11.30 ‐ 12.30

Session 11 12.30 – 14.00 TOK and Extended Essay

Coffee break 14.00 ‐ 14.30

Session 12 14.30 – 15.30 Group 4 project


3

Aims and Objectives

• Introduce participants to the DP (incl. the Core & Learner Profile) and allow them to develop their DP subject-specific knowledge. • Provide tools to implement the programme in their subject or school. • Engage participants in activities, discussion and reflection about the challenges and rewards of implementing the DP. • Gain understanding of methods preparing students for IB assessment.


4

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 Comments 1.1 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 CORE1.3 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 CORE2.3 Work, energy and power CORE2.4 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 CORE10.1 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 CORE4.4 Wave characteristics CORE4.5 Wave properties CORE11.1 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 Topic 5: Electric currents


5

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 CORE9.3 Electric field, potential and energy AHL 6.3 Magnetic force and field CORE12.1 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 CORE7.3 Nuclear reactions, fission and fusion CORE13.2 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 CORE8.3 Fossil fuel power production CORE8.4 Non‐fossil fuel power production CORE8.5 Greenhouse effect CORE8.6 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


6

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.


7

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 motion

Thermal Physics

Kinetic model 1st Law of thermodynamics Heat and Temp

Sp ht cap Engines Change of state

Oscillations and waves

SHM intro 2nd law of thermodynamics SHM equations

SHM energy Extra problems DHM, FHM and resonance


8

Waves intro Standing waves Wave properties

Examples of waves Doppler Test

Electric currents

Electricity intro Diffraction V, I and R

Electric circuits Resolution Test

Fields and Forces

Gravitation intro Polarisation G field strength

Electric field intro G potential E field strength

Magnetism intro Orbits escape velocity Electromagnetism

Atomic and Nuclear

Atom intro E Potential Atomic models

The nucleus Faradays law Binding energy

Decay AC generator, transformer and transmission

Fission and Fusion


9

Energy 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.


10

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.


11

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.


12

DCP Aspect 1 Raw Data Examples

Example 1 Raw Data Table Below is table of the data for the four run performed for each of 4 diffrent destance. The uncertainty in the time is calculated from: (Max.t-Min.t)/2

Time 1 (s) Time 2 Time 3 Time 4 Average Time Uncertainty in time(cm) (s) (s) (s) (s) (s) (s) ±.0001 ±.0001 ±.0001 ±.0001 ±.0001 ±.0001

100 0.0196 0.0196 0.0193 0.0196 0.0195 0.000290 0.0204 0.0204 0.0202 0.0207 0.0204 0.000280 0.0218 0.0222 0.0223 0.0225 0.0222 0.000470 0.0237 0.0238 0.0237 0.0237 0.0237 0.0001

Example 2 Measurements: These are our raw datas. We estimated that our uncertainty in the distance or height would be about ±0.005m, even though the smallest unit on the ruler is 0.001m. The reason for the rather huge uncertainty is that we noticed how difficult it was to the ruler strait up and also to measure at the same place at the ball each time. Distance (m) ±0.005m Time1(s) Time2(s) Time3(s) Time4(s) Time5(s)

0,200 0,165 0,191 0,181 0,184 0,2010,250 0,208 0,220 0,220 0,203 0,2230,300 0,225 0,119 0,221 0,231 0,2230,350 0,239 0,242 0,255 0,258 0,2630,400 0,263 0,265 0,241 0,268 0,2080,450 0,288 0,268 0,292 0,300 0,2830,500 0,298 0,302 0,289 0,311 0,2960,550 0,323 0,326 0,314 0,309 0,3130,600 0,337 0,337 0,335 0,331 0,3400,650 0,358 0,360 0,348 0,354 0,330

C P N

C P N


13

Example 3

Raw Data

Distance to counter ±.005 m

Actual distance fallen ±.005 m

Time 1 ±.001s

Time 2 ±.001s

Time 3 ±.001s

Time 4 ±.001s

0.200 0.118 0.155 0.153 0.156 0.1560.250 0.168 0.183 0.182 0.183 0.1820.300 0.218 0.208 0.205 0.210 0.2110.350 0.268 0.236 0.235 0.237 0.2390.400 0.318 0.250 0.254 0.255 0.2500.450 0.368 0.276 0.277 0.276 0.2780.500 0.418 0.292 0.293 0.294 0.2910.550 0.468 0.310 0.310 0.303 0.3000.600 0.518 0.322 0.328 0.330 0.3280.650 0.568 0.342 0.341 0.343 0.343

(The original report had 9 runs all together, these aren’t shown here) The distance to the counter was the height from the top of the dropping device to the counter. The uncertainty in the distance to the counter was in based on half of the smallest increment initially, but it was estimated to be half a centimetre instead because of the wobble in the apparatus, and the imminent variation of the dropping height. The actual distance fallen is the distance from the point on the device where the ball was dropped to the top of the stopping plate. This was obtained by finding the height of the stop plate and the height from the top to the dropping point of the timing device, then subtracting that from the distance to the counter. The uncertainty of this was the combined absolute uncertainty of the distance to the counter and the difference between that and the actual distance fallen. The uncertainty in the time was based on the smallest digit on the timer used.

Example 4 Results Distance (m)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Time 4 (s)

Time 5 (s)

Avg. Time² (s²)

Error in Time²

±.05 ±0.019 ±0.019 ±0.019 ±0.019 ±0.019 0.163 0.162 0.163 0.180 0.176 0.178 0.030 0.0090.306 0.235 0.235 0.233 0.231 0.230 0.054 0.0020.459 0.267 0.295 0.267 0.251 0.287 0.075 0.0120.505 0.306 0.307 0.299 0.305 0.308 0.093 0.0030.556 0.304 0.292 0.283 0.309 0.306 0.089 0.0080.617 0.324 0.349 0.349 0.315 0.352 0.114 0.0120.634 0.352 0.343 0.353 0.353 0.317 0.118 0.0120.704 0.349 0.365 0.372 0.373 0.359 0.132 0.0090.752 0.365 0.391 0.378 0.353 0.360 0.137 0.0140.802 0.366 0.373 0.358 0.360 0.362 0.132 0.005

The uncertainty in distance was found by dividing the smallest unit of measurement (0.1m) on our measuring tool (a meter stick) by 2. The uncertainty in time was found through an estimation based on previous trials.

C P N

C P N


14

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 t2 is (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.

Any calculation must be explained


15

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=1/2at2 a graph of s vs t2 will 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 time2 was (Max time2 – Min time2)/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.


16

DCP Aspect 2 Data Processing Examples

Example 1 Processed Data Since the velocity is the displacement/ time taken. It is given that the displacement is 2.5 cm. the average time is calculated below as the following: 2.5/average time - then the velocity2 is found to present it the graph. The uncertainty in velocity2 : (max.velocity2 – min velocity2) Average V. max. V Min. V Uncertainty in V. Average of V2 uncertainty in v2

(cm/s) (cm/s) (cm/s) (cm/s) (cm2/s2) (cm2/s2)±.001 ±.001 ±.001 ±.001 ±.001 ±.001

128.041 129.032 127.065 0.984 16394.491 251.930122.399 123.305 121.507 0.899 14981.520 220.071112.613 114.417 110.865 1.776 12681.601 400.069105.374 105.597 105.153 0.222 11103.696 46.802

Example 2 These are our processed datas. To find the uncertainty in the time, we took the (max time-min

time)/2. ± the answers became our uncertainties. We also calculated the average times by

adding up all the times and dividing them by 5.

Distance (m) ±0.005m Average Time(s)

Uncertainty, time(±s,) Time^2(s^2)

0.200 0.184 0.02 0.0340.250 0.215 0.01 0.0460.300 0.204 0.06 0.0420.350 0.251 0.01 0.0630.400 0.249 0.03 0.0620.450 0.286 0.02 0.0820.500 0.299 0.01 0.0900.550 0.317 0.01 0.1000.600 0.336 0.00 0.1130.650 0.350 0.02 0.123

C P N

C P N


17

Example 3

Processed Data Actual distance fallen ±.001 m

Avg Time (s)

Uncertainty in time (s)

Average time² (s²)

Maximum time (s)

Minimum time (s)

Uncertainty in time² (s²)

0.118 0.152 0.005 0.023 0.157 0.147 0.0020.168 0.183 0.004 0.034 0.187 0.179 0.0010.218 0.210 0.004 0.044 0.214 0.205 0.0020.268 0.235 0.004 0.055 0.239 0.231 0.0020.318 0.255 0.005 0.065 0.260 0.251 0.0020.368 0.276 0.003 0.076 0.279 0.274 0.0010.418 0.293 0.003 0.086 0.296 0.291 0.0010.468 0.308 0.006 0.095 0.314 0.302 0.0040.518 0.327 0.004 0.107 0.331 0.323 0.0030.568 0.343 0.007 0.117 0.350 0.335 0.005

Uncertainty in time was calculated by finding the range of the times in on particular height, and dividing that by 2, i.e. (Max time-Min time)/2, or by using the uncertainty of the scale, whichever was bigger. Time squared is calculated because acceleration due to gravity is to be found using the relationship s=ut+(1/2)at².The uncertainty in time squared was found by finding the maximum time then minimum time, squaring them, and finding half the difference of the two. i.e. (Max time²– Min time²)/2.

Example 4 Processing raw data Now it will be shown the data with square time and its uncertainty, according with equation relating the height and time 2

21 atuth += which will allow us to graph a straight line, since the initial

velocity is 0 this simplifies to 22

1 ats = s is therefore proportional to t² so a graph of s (y axis) against t² (x axis) will give a straight line. The slope of this line will be ½a. The uncertainty in time2 was by (higest reading ²-lowest reading ²)/2

Average time2 Uncertainty in time2

0.0492 0.0010

0.0591 0.0011

0.0694 0.0011

0.0784 0.0018

0.0890 0.0004

0.0994 0.0017

0.194 0.0014

0.1194 0.0028Table 2- The square time and its uncertainty

C P N

C P N


18

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


19

An extract from a report that completes all requirements

Graph of s vs t2

Max gradient = 5.198 ms-2 Min gradient = 4.796 ms-2

Uncertainty in gradient = (5.198 – 4.796)/2 = 0.2 ms-2 Gradient = 5.0 ± 0.2 ms-2

Graph has correct labels, units, custom error bars, best fit line, and max and min gradients.


20

DCP Aspect 3 Presenting Data Examples

Example 1 Graph distance and velocity2

Example 2

C P N

C P N


21

Example 3 Graph of Processed Data

Example 4 Graph On the graph below t² is on X-axis and height on Y-axis representing the independent and dependent variable respectively.

Distance Fallen Vs. Time2

C P N

C P N


22

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.


23

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 t2. Since the acceleration is therefore constant we can apply the equation s=1/2at2 so 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 = 4.966m/s2 so the acceleration g=9.932m/s2 The uncertainty in the gradient can be found from the steepest and least steep lines Max value = 2x5.198 = 10.396m/s2 Min Value = 2x4.796 = 9.593m/s2

Uncertainty = (Max-min)/2 = ±0.4m/s2 The final value obtained for g is therefore 9.9 ±0.4 m/s2 The accepted value established by the 3rd General Conference on Weights and Measures is 9.80665 m/s2, this lies within the limits of uncertainty of the experimental value obtained. 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.


24

CE Aspect 1 Conclusion Examples

Example 1 Graph distance and velocity2

Conclusion From the graph above. It noticed that the acceleration is uniform. Because the relationship between the distance and velocity2 is shown with linear. Since the acceleration can be presented by the the following equation that relates distance and velocity2:

asuv 222 += u2 = 0 In other words v² is proportional to 2as a = v2/2s so acceleration = the slope/ 2 a = 184.5/2 a = 92.5 cm2/s2

C P N


25

Example 2

Conclusion and evaluation:

The slope is supposed to be a/2 in, which means that the gradient is supposed to be about 5 if this happened in vacuum, since the acceleration is gravity (9.8N/kg) when we drop something. We can certainly see from the graph that this is not the case. The graph says that the gradient is 2.6m/s ±0,375m/s (max.gradient-min.gradient/2). One of the obvious reasons

C P N


26

Example 3

Graph of Processed Data

Conclusion and Evaluation

Conclusion

The graph above has a slope of s/t². The equation s=ut+(1/2)at² shows us what it equates to. In this case, the initial speed of the ball bearing is 0, thus our expression becomes s=(1/2)at². By rearranging, we find that s/t²=a/2. Therefore, a=(2s)/t². Or a=2m, where m=the gradient.

Slope of graph = 4.99m/s²

a=2m

=2(4.806m/s²)

=9.612m/s²

Uncertainty = (Maximum-minimum)/2

= (2m1-2m2)/2=(2(4.980m/s²)-2(4.627m/s²))/2

=0.353m/s²

Final Acceleration Found: 9.6m/s² ±0.4m/s²

C P N


27

Example 4

Conclusion From the graph it is clear that there is a direct proportionality between the height and the square of time during the fall; It, in other way, tell us that the acceleration must be constant. Looking at our graph we see that the gradient is approximately 4.978 m/s², so we can see if it agrees what we have been learning so far about free fall of bodies.

We know that the equation relating height and time is 22

1 atuth += since the initial

velocity is 0 this simplifies to 22

1 ath = . We also know that in this case we have, at least, two different facts:

1st: The height is directly proportional to t² 2nd: The expression ½ a is the constant of proportionality

But in free fall of bodies, in ideal conditions, the unique acceleration existent is the gravitational acceleration, therefore: a=g Then: slope = ½ a, as a = g, we have:

Slope = ½g, but, slop = 4.978m/s² then: 4.978 m/s²= ½g, g = 9.956 m/s² that is approximately the value of gravitational acceleration!!!

Therefore we can conclude that our experiment our acceleration was almost truly constant.

C P N


28

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


29

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


30

CE Aspect 2 Examples

Example 1 Evaluation It was expected that distance and velocity2 are positivly related( when the distance increases the velocity2 increases as well) One of the run of distance (110cm) is deleted due to the mistak of measuring during the experment. The curve almost fit as linear and plotting the steepest and least steep line manually is not shown as cross lines because the distances between the points are not exact. Therefore, its points might be included a human mistake that can be avoided next time.

Example 2 Evaluation One of the obvious reasons for this is the air resistance, but that can impossibly be everything.

The weak point of this practical was the release mechanism, and it would be likeable to think

that it didn’t always start the timer exactly when we dropped the ball. We experienced quite a

lot of misreadings in the experiment (which we did not write down), so it could be very

possible that the graph is far from linear of this reason. It is the readings from 0.3m and 0.4m

that lay the most from the linear graph. This can be because it was difficult to measure the

height properly (it was not always easy to get the ruler to stand strait up), and that it was on

those heights we had the most difference from the height we thought be measured and our

actual height. We also see that the graph becomes straiter as the height increases.

C P N

C P N


31

Example 3

Evaluation

The value of the acceleration due to gravity found seems reasonable. The literature value of the acceleration due to gravity is 9.8 m/s² (sourced from http://en.wikipedia.org/wiki/Standard_gravity), which is within the uncertainties found. The origin was within the range of error, which complies with the expression s=ut+(1/2)at². In this case, initial velocity is 0, so s=(1/2)at2. If the displacement is 0, then no time should have passed, so it makes sense that the origin should be the close to our data. The fact that our graph showed a linear relationship meant it complied with the equation s=ut+(1/2)at² , suggesting that acceleration was uniform. However, when we place the graph of the actual value of the acceleration due to gravity on this data, we find the values at longer falling distances (specifically, the last five) are below this line, except for one with an exceptionally large error bar. Furthermore, the fact that the acceleration found was lower than the accepted value may indicate a force other than gravity was acting on this ball, slowing its acceleration as it went faster. This suggests that acceleration is in fact not uniform, and that further investigation into air resistance should be performed.

A major problem with this investigation was the dropping device used did not have a mechanism to ensure the ball fell without having any extra kinetic energy being added to it or that it began falling exactly when the timer started. Several times, we noticed that the timer failed to start at all when the ball was dropped, and that our range of data was well over 5/100ths of a second, which was unreasonable when most of our measurements were under 3/10th of a second. The error was so bad that we had to redo measurement at several heights because the range of data was unreasonably large, and some individual timing were rejected

Comparing Accepted Value of g to Data Collected


32

because the technique used to drop was obviously affecting the speed of the ball, or the timer visibly started after the ball was released. What's more, the actual apparatus was unstable. The stand, which was screwed into the base, wobbled because it did not fit perfectly. During our trials, our movements made it move in turn, so it was impossible to even find a point of equilibrium. Measuring the distance to the ground was also problematic. It was impossible to ensure that the ruler used was an exactly perpendicular to the ground since we had nothing to compare it to. (The stand was unstable, thus never properly upright.) The round stand was also difficult to take a measurement from. One had to assure they were exactly eye level with it, which was at times difficult to confirm.

Example 4

The estimates of uncertainties were reasonable because I used the same decimal the availed methods to find uncertainties and explained how I found them. However, as I worked not in really ideal conditions, there were some aspects that might to be considerate, as the air resistance, although we know that our object is small but it still has some influence.

C P N

C P N


33

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.


34


Improvements The method gave good results but the uncertainty ±0.4m/s2 could 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.


35

CE Aspect 3 Examples

Example 1 Evaluation It was expected that distance and velocity2 are positivly related( when the distance increases the velocity2 increases as well) One of the run of distance (110cm) is deleted due to the mistak of measuring during the experment. The curve almost fit as linear and plotting the steepest and least steep line manually is not shown as cross lines because the distances between the points are not exact. Therefore, its points might be included a human mistake that can be avoided next time.

Example 2 One of the obvious reasons for this is the air resistance, but that can impossibly be everything.

The weak point of this practical was the release mechanism, and it would be likeable to think

that it didn’t always start the timer exactly when we dropped the ball. We experienced quite a

lot of misreadings in the experiment (which we did not write down), so it could be very

possible that the graph is far from linear of this reason. It is the readings from 0.3m and 0.4m

that lay the most from the linear graph. This can be because it was difficult to measure the

height properly (it was not always easy to get the ruler to stand strait up), and that it was on

those heights we had the most difference from the height we thought be measured and our

actual height. We also see that the graph becomes straiter as the height increases.

One improvement of the experiment can be to do it with bigger heights, since we se from the

graph that those readings are most accurate. We could also have dropped the ball more than 5

times from each height. The small misreadings will matter less, when we get an average of

more readings.

We can conclude with that the acceleration is constant, if we look away from the readings at

0.3m and 0.4m. Then the acceleration would be 6m/s (reading from the steepest line*2). This

is less than the gravity would say it should be, but we are not in vacuum and the release

mechanism was not acting properly all the time.

C P N

C P N


36

Example 3 A major problem with this investigation was the dropping device used did not have a mechanism to ensure the ball fell without having any extra kinetic energy being added to it or that it began falling exactly when the timer started. Several times, we noticed that the timer failed to start at all when the ball was dropped, and that our range of data was well over 5/100ths of a second, which was unreasonable when most of our measurements were under 3/10th of a second. The error was so bad that we had to redo measurement at several heights because the range of data was unreasonably large, and some individual timing were rejected because the technique used to drop was obviously affecting the speed of the ball, or the timer visibly started after the ball was released. What's more, the actual apparatus was unstable. The stand, which was screwed into the base, wobbled because it did not fit perfectly. During our trials, our movements made it move in turn, so it was impossible to even find a point of equilibrium. Measuring the distance to the ground was also problematic. It was impossible to ensure that the ruler used was an exactly perpendicular to the ground since we had nothing to compare it to. (The stand was unstable, thus never properly upright.) The round stand was also difficult to take a measurement from. One had to assure they were exactly eye level with it, which was at times difficult to confirm. Improving the investigation Attaching a spring‐release mechanism to the dropping device would reduce the error involved in dropping the ball inconsistently. One would have to be careful to attach this spring in a way such that it does not apply a force to the ball, only pushes away the flap holding it in order to avoid further systematic error. A more consistent system like such would also work together with the circuitry to ensure the timer was started at the appropriate time because the ball would lose contact with the flap after the same amount of time, thus the electrical circuit would break, and timing would begin. Using a one‐piece stand, though it would impractical to store, would reduce the wobble. Using a thicker piece would also reduce how much it could potentially bend. Moreover, making this stand in the shape of a rectangular prism rather than round and cylindrical would make taking measurements more easily. Moreover, ssing a ruler with a flat, stable base would ensure that it stayed perpendicular during measurement.

Example 4

The estimates of uncertainties were reasonable because I used the same decimal the availed methods to find uncertainties and explained how I found them. However, as I worked not in really ideal conditions, there were some aspects that might to be considerate, as the air resistance, although we know that our object is small but it still has some influence. The experiment could be improved if the ruler had big base, because it hadn’t the same vertical at each run I were measuring. Also the ruler didn’t start to measure at its first edge, there was a small space before start to count and it didn’t help to have a precise measurement. Although we have a digital equipment to measure the time, it is quite difficult to have the exact precision to stop the time exactly when the run stops. When we were doing our experiment we didn’t have an exact measurement of height we just did approximation of the ruler and the height. To improve the experiment we could be more careful with the position of the ruler at each run. We measure the height of the first space of the ruler without scale and then subtract by the total in each run. And we could use more accrued equipments to measure the time.

C P N

C P N


37

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.


38

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 bung

Hypothesis Applying the law of conservation of energy I expect that the GPE at the top will equal the EPE at the bottom. mgh=½kx2 Since 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


39

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. Describe what you did to make sure the controlled variables remained constant.


40


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 variables is kept


41

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


42

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


43

Design lab examples Since it can be difficult to mark the different aspects in isolation the following examples include all 3 aspects. In all 3 examples students were given a balloon and asked to develop a research question related to it.

Example 1 Research Question

What is the relationship between the weight of a mass held by a balloon and the time it stays stuck to the wall (by electrostatic charge)? Introduction In this experiment we are going to investigate the relationship between the weight of a mass held by a balloon and the time it stays stuck to the wall. We are going to give electrostatic charge to the balloons (by rubbing them against the wall) and then stick them to the wall. The balloons will have a piece of thread attached to them, from which, a mass will be held. We are going to apply our previous knowledge on electrostatics and mechanics to formulate a hypothesis and predict what the results will be. Hypothesis: The heavier the mass held by the balloon, the shorter the time it will stay stuck to wall. Taking into account the following “free body” diagram of the balloon:

According to Newton’s first law, since the body is not moving, all the

forces need to be balanced. Therefore, the Normal force (N) is equal to the Electrostatic force (Ef) and the Frictional force (Ff) is equal to the weight (W). Moreover, the Frictional force is dependant on the Normal force (Ff=µN).

Aspect 1 C P N


44

As time runs, the balloon will eventually lose (transfer to the surrounds) its charge. The latter will cause a decrease in the Electrostatic force, which will lead to a decrease in the Normal force. As we stated before, the Frictional force depends on the Normal thus this one will also decrease. Hence, it will get to a point where the Frictional force will not be enough to hold the weight, and the balloon will fall. The greater the weight held by the balloon, the greater the Frictional force needed to hold it. Assuming that the charge given to the balloon will always be the same, and that it will decrease by the same rate each time: The heavier the mass held by the balloon, the shorter the time it will stay stuck to wall. Variables:

• Independant: Weight of the mass attached to the balloon.

• Dependant: Time that the balloon remains stuck to the wall.

• Controlled:

o Charge given to the balloons.

o Size, weight, and color of the ballons.

o Thread’s length.

Materials: ‐ Five balloons ‐ Thread ‐ A wall ‐ Weights ‐ Stop watch

Procedure:

• From experience, we noticed that once a balloon was used it would not charge in the same way as the first time. In order to avoid this, therefore, we decided to use different balloons for each trial.

• To control any differences that could arise from using different balloons, we used five balloons of the same color, weight (before and after we had inflated them) and approximately the same size after we had inflated them.

Aspect 2 C P N


45

• We attached a piece of thread of the same length to each balloon, from which the different masses will be held.

• Then, we stuck the balloon, with the mass attached to it, to the wall. • To charge them, we rubbed each balloon, for 20 seconds, against the

wall (in both directions up and down). By controlling the amount of time and rhythm of rubbing them, and using the same surface every time, we tried to keep the charge of the balloons constant for each trial.

• Furthermore, since the human body works as a conductor and could have taken electrostatic charge from the balloons, we released them as fast as we could after charging them.

• As soon as we stuck the balloon to the wall, we started running the stop watch.

• As soon as the balloon moved, we stopped the watch. • After gathering the data for one balloon, we attached a mass with a

different weight to another balloon and repeated the whole process again.

• The whole procedure was performed within an hour and in the same room; so that, factors such as: humidity and temperature were controlled. This was important because such factors can affect the charge of the balloons.

Aspect 3 C P N


46

Example 2 Balloon Practical

Aim The aim of this practical is to investigate how the air flow influences levitating balloon when balloon is in different sizes.

Introduction The balloon was held by air flow created by hair dryer. We were changing the size of the balloon.

Research question Finding a relation between length of the balloon and height it reaches with air flow.

Stand

Hair dryer with holders

Interface

Motion sensor

Balloon

PC

Aspect 1 C P N


47

Hypothesis I suppose that the balloon the bigger the higher it levitates, since the area of the applied force by the air flow is bigger. The mass of the balloon increases with much smaller ratio than its volume so more force applied should lift balloon higher. Variables:

a) Dependant: - a mass and a size (length) of the balloon

b) Independent: - distance between motion sensor and balloon ( a height balloon reaches)

c) Constant:

- the same balloon - The output speed of the air flow

Procedure

1. Apparatus is set up as in the picture above. 2. The hairdryer is being put on (always the same mode) and then balloon put above it (it

levitates) 3. Motion sensor connected to the computer is recording the height of the balloon. 4. Change the size of the balloon (record its length) and measure the height of levitation

(actually the distance of the balloon form the motion sensor). Repeat with several different sizes.

5. We took measurement of uncertainties in height (drawing a graph and recording max and min points).

Aspect 2 C P N

Aspect 3 C P N


48

Example 3 Research question What is the relation between a gas’ increase in volume and its rise in temperature? Hypothesis As the temperature rises the volume increases. The higher the temperature gets the smaller will the reaction of the change of volume be. This is because Charles’ law states that when pressure of a fixed mass is constant, the volume is directly proportional to its absolute temperature. Hence, the volume will increase as temperature increases, but we have no way of making sure the pressure remains constant, therefore the rise might not be proportional. Method Variables: Independent- temperature, as it rises due to the activity of the kettle. Dependent- height of water, and consequently air’s volume Controlled- mass of system (though some of the water might have evaporated; expansion of water+ material of kettle, as this was separately calculated and subtracted; rate of rise in temperature (the kettle was turned on and off as necessary to carry out measurement). Attach a balloon filled with air in the bottom of a kettle filled with water and mark the water level in the kettle. Turn the kettle on and measure the change of height of the water on different temperatures. From that calculate the difference of the volume of the water. Since we didn’t add any water, this is the difference of the volume of the balloon. From that we can then conclude the nature of the relationship between volume and temperature of the balloon (after subtracting the rate of expansion of water). Diagram

Balloon filled with air Water Kettle

Initial water level

Increase in water level as temperature increases

Aspect 1 C P N

Aspect 2 C P N

Aspect 3 C P N


49

Examples of practicals This section includes some examples of practical worksheets I have used at RCNUWC.

Practical 00 Introduction to datalogging Practical 0 Introduction to Data analysis and uncertainties Practical 1 Measuring acceleration Practical 2 Measuring g Practical 5 Specific Heat capacity Practical 6 The pendulum Practical 8 Video Analysis of waves Practical 9 Conducting paper Practical 10 Keplers Laws


50

Practical 00 Introduction to using Data Studio The first two practicals introduce students to datalogging and the analysis of data. They are not used for internal assessment.

Introduction In this practical you will be measuring the temperature of water using a temperature sensor connected to the computer via a Pasco Interface. The aim of the experiment is to learn how to use the equipment rather than to understand the physical principles.

Setting up the interface You will be using the following apparatus:

0

Temperature Sensor

USB connector


51

• Connect the power supply to the back of the interface then connect it to the mains plug using a power lead (hanging on the cupboard door)

• Connect the USB connector to the back of the interface, do this very carefully so you don’t break any of the pins, ask me to do it if not sure.

• Connect the USB connector to the USB port on your computer. • Connect the Temperature sensor to “Analog Channel A”. • Start the program “Data Studio”. • When asked “How would you like to use data studio?” click “create experiment” • You will get a window like the one below. Make sure the interface looks like the one you are using,

if not change it as instructed below. Add temperature sensor by double clicking chsnnel A on gthe interface picture (we have two types ordinary and stainless steel). Finally drag the graph icon to “channel A”. You are now ready to start.

Note: If you have a yellow triangle next to the picture of the interface ( like above) ask Chris for help.

• To see if everything is working click the start button and see if you can see the temperature recorded on the graph. Try rubbing the sensor in your hand to make the temperature go up.

• Try changing the “sampling rate”, this is on the right hand side of the window. This changes how often the computer measures temperature.


52

Taking Measurements. You are going to investigate how the temperature rise of water is related to it’s mass.

• Put a known mass of water into the kettle/water boiler. • Start measuring the temperature by clicking the start button • Switch on the heater and measure how much the temperature goes up in 1 minute. • Repeat the experiment with 5 different masses of water, enter your results in a table like the one

below.

Mass (kg) Temperature (ºC)

Plotting the Graph (Analysing the Data) You are going to plot the graph using the computer programme “Graphical Analysis”. Open the programme and you will see a blank table on the left and a blank graph on the right as shown below.

Copy the data from your table of results into the Graphical analysis table, you can do everything in one go. To add titles to the columns double click the column header, you will get a box like the one shown below. Fill in the title and units.


53

The graph will be plotted automatically if you can’t see it click the autoscale button You should now have a graph like the one below

Next lesson you will find out how to add a smooth curve and deal with uncertainties.


54

Practical 0 Introduction to Data Analysis and Uncertainties

Part 1 Uncertainties Physical measurements are never exact. For example, when you use a ruler you can estimate the length to within 0.05cm. So if we use a ruler to measure a piece of string and find it to be 5cm then we should say that it is 5 ± 0.05 cm. We say the uncertainty or error is ±0.05cm. If you are simply using a scale then the uncertainty is ± half the smallest division. Sometimes it’s not so simple, then you should repeat the measurement several times, the uncertainty is found from (highest reading – lowest reading)/2 To find the uncertainty in the water heating experiment

• Heat the same amount of water 4 times. • Calculate the temperature difference for each run. • Calculate the average value. • Find the uncertainty from (highest reading – lowest reading)/2

Part 2 Data analysis You have already used graphical analysis (GA) to draw a simple graph. You can see that the graph is not linear. To get the labels double click the table headers and fill out the form.

Temperature rise is in fact inversely proportional to mass so the equation of the line is something like y=k/x where k is some constant


55

Curve plotting You can plot a curve using GA but first remove the line joining the dots by double clicking on the graph. You will then see a message box like this:

Untick the connect points option and then Done.

To plot a curve click this button You will get the following message box:

Choose A/X (Inverse) and OK


56

What does the line look like? It might not be very good, why doesn’t the line pass through all the points?

Plotting error bars An error bar is a line that is drawn on each point on a graph to show the maximum and minimum values. Below is an example of a graph with error bars

Now you can see that although the line doesn’t pass through all the points it does touch all the error bars. To plot error bars for mass double click the table header on the mass column. You will get a message box, click the options tab. You will now get the following message

Tick the Error Bar Calculations box then the Fixed value and Error Constant boxes as above. Enter the error in the mass reading. This is 0.1g due to the balance. Do the same for the Temperature column and enter the uncertainty that you calculated in part 1.

• Does your line pass through all the error bars?


57

Plotting a Straight Line Instead of plotting mass vs temperature you could have plotted mass vs 1/temperature this would have given a straight line graph. You are now going to use EXCEL to manipulate the data.

• Copy and paste the table Into Excel

Add a third column called 1/Temperature. To do the calculation follow these steps

• Click the first cell in the new column • Write =1/ then click the first cell in the temperature column. The equation should now read =1/B2. • Press return • Now hold the cursor on the bottom corner of the first cell until you get a cross like the one below

• Pull this down like a blind, the equation will now copy into all the other cells automatically

calculating 1/Temp for all the values. • You can now copy the mass and 1/temperature back into GA • Remove the line connecting the points as before

• Add a best fit straight line by clicking this button ’

Note: the numbers in the columns have the same number of significant figures as the uncertainties.


58

Your graph should look like this:

If you want to adjust the scale of the graph then you can put your cursor near the axis labels to get the wiggly arrow shown below, You can then slide this up and down to adjust the scale.

To move the graph sideways or up and down then use the arrows next to the labels.

To automatically scale the graph to fit the page click this button on the tool bar

Plot a best fit line by clicking the linear fit button


59

Plotting error bars on the 1/Temp graph Go back to the Excel table and add columns as below

• The max temp is the temp + the uncertainty, fill this in by writing the equation=B2+(uncertainty) and

filling down as before In the 1/Max ΔT column write an equation =1/C2 and fill down In the 1/Min ΔT column write an equation =1/D2 and fill down

• The error in 1/temp is found by subtracting (1/MinΔT – 1/MaxΔT)/2 • The following table has been filled in assuming error in temp was 1ºC

• Notice that the error in 1/temp is not the same for all the values; this means that they have to be plotted in a different way.

• Also note that the number of significant figures in the error has been reduced to 1 and the number of decimal places in 1/ΔT is the same as the error.


60

Back to GA • From the Data menu choose “New data set” • This will add two new columns onto the table, add the heading “error in 1/T” to one of these and cut

and paste the data from excel.

• Double click the 1/temp column select the option tab. Again tick the Error bar calculations box but

this time “use column”. • Select the Data set 2“error in 1/T “ option from the list • Add the error bars to the mass column as before. • You should now have a graph like this


61

Plotting the Least Steep and Steepest lines. The best fit line that you have drawn is not the only line you can draw through the error bars. It is useful to plot the steepest line and least steep line to give you some idea of the uncertainty in the

gradient, to do this open the curve fit window by clicking the curve fit button .

This time select Linear then press Try Fit. This will place a best fit line on you graph. Now select manual (top right) and use the arrows to the right of m1(Slope) and b(Y‐intercept) to place the steepest line through the error bars. The best way to do this is to get the line to pass through the top of the right hand bar and the bottom of the lefthand bar as shown below.

Now press OK and the line will appear on your graph. Repeat the process but with the least steep line. Your finished graph will look like the one below. This is difficult so I will demonstrate it to the class.


62

The gradient of the best fit line is 0.2829 kg‐1°C‐1 The uncertainty in the gradient is (max grad – min grad)/2 = (0.47 – 0.15)/2 = 0.16 kg‐1°C‐1 rounding down to 1sf = 0.2 kg‐1°C‐1 So the gradient = 0.3 kg‐1°C‐1 ± 0.2 kg‐1°C‐1

Note that the gradient is only given to 1 decimal place since the uncertainty is 0.2 kg‐1°C‐1

In this example the error bars have been exaggerated so that you can see what is being done, you probably won’t get such large uncertainties in a real experiment. This is a lot to take in but you will get more practice over the next few months, if you want more help you can ask me or one of the peer tutors, alternatively go to my website http://occ.ibo.org/ibis/occ/resources/ict_in_physics/ and look under graphplotting.


63

Practical 1 Measuring acceleration This practical is the next stage in introducing analysis of data. Students are instructed what to do so this practical is not used in assessment; it is however marked according to the criteria so students get some idea of how the marking works.

Introduction In this practical you will be using the time for a rectangular marker to pass through a photo gate to measure the velocity of a trolley rolling down a sloping track.

The photo gate is connected to a computer via an interface.

Setting up the apparatus Make sure the interface is switched on and plugged into the USB port of your computer. Open Data Studio Press “set up” Choose interface “science workshop 500” Click “digital channel 1” double click “photogate” Select Time in gate and de‐select velocity in gate From the “displays list” select “Digits” You are now ready to go, click “start” and perform a trial run sending the trolley down the slope.

Collecting the Data You are going to measure the final velocity after the trolley has travelled a measured distance. Set the photo gate a measured distance down the slope then let the trolley roll down the slope starting from the top and measure the time taken for the marker to pass through the photo gate.

• Which two points should you measure between?

Di


64

Prepare a table in excel like the one below:

Distance m ± ?

Time 1 s ± ?

Time 2 s ± ?

Time 3 s ± ?

Time 4 s ± ?

Av. Time s ± ?

Uncertainty in time (s)

Repeat the procedure for 5 different distances; fill in the table as you go. Estimate the uncertainties in s and t Calculate the average time and the uncertainty in time, this is found from the (Max time – Min time)/2. This will probably be bigger than the measurement uncertainty that you have already estimated, use this new uncertainty from now on.

Processing the Data You want to know the velocity of the trolley so must divide the distance travelled through the photo gate by the time taken. The distance travelled through the gate is the size of the marker (2.5cm) so the velocity = (2.5/time) cms‐1 The uncertainty in velocity can be found by calculating (Max velocity – Min velocity)/2, you find Max and Min by adding and subtracting the uncertainties (think about it). Fill in a table like the one below, this will help you to organise the values and uncertainties. Don’t make a new table, just add columns to your existing excel spreadsheet.

Average velocity ms‐1

Max velocity ms‐1

Min Velocity ms‐1

Uncertainty in velocity ms‐1

The velocity and distance are related by the equation asuv 222 +=

Since the initial velocity is 0 this simplifies to asv 22 =

In other words v² is proportional to 2as

If you plot a graph of v² on the y axis against s on the x axis the gradient will be equal to 2a. The next stage is to process the results, add the following columns to your spreadsheet and calculate the values. The uncertainty in velocity2 is found from [(Max velocity)2 – (Min velocity)2 ]/2

Average velocity ms‐1

Max velocity ms‐1

Min Velocity ms‐1

Uncertainty in velocity ms‐1

Average velocity2

m2s‐2

Uncertainty in velocity2

m2s‐2


65

Presenting the Data You are now ready to present the data in a graph. Copy the distance and velocity2 columns into Logger Pro (or graphical analysis) and plot a graph. Then copy the uncertainty in velocity2 to a new data set so that you can use it for plotting the error bars like you did in practical 0. Find the acceleration from the gradient of the line. Now plot the steepest and least steep line manually so that you can determine the uncertainty in the acceleration. Refer to my website ICT and IB physics if you have forgotten what to do.

Conclusion and Evaluation Looking at your graph of results answer the following questions:

• Do you think the acceleration was uniform? • Are the results what you expected? • Are there any improvements that you could have made to the experiment?

Photo of apparatus


66

Practical 2 Measurement of g This practical is also part of a circus of 4 in which students develop their skills in data analysis. I have used this as an example on my website and I openly tell the students to use this to help them with their write up. This practical is of course not part of the assessment

Introduction In this practical the acceleration due to gravity will be calculated by using an electronic timer to measure the time taken for a small steel ball to fall a known distance.

Procedure The apparatus is set up as in the diagram. Find out how the release mechanism works and make a couple of trial runs to see if it works properly. Measure the time for the same height and see if you get the same reading. Estimate the uncertainty in the time measurement from the last decimal place of the time reading (If you have 4 digits e.g.0.3214s then the uncertainty is ±0.0001s). This is the uncertainty in the measuring device however you will probably find that the spread of results is much bigger. The height is to be measured using a meter rule; the uncertainty in this measurement depends upon how well you can read the scale, the best you can do with a ruler is ± 0.5mm but you probably won’t be that accurate. Copy the table below ready for your results fill in the uncertainties. Now fix the height of the ball at a convenient level and measure its height. Release the ball and measure the time of fall. Repeat to make sure that no mistake was made. Enter the distance and time in your table, repeat for 10 different heights. To calculate the uncertainty in time find (Max time – Min time )/2, this is the uncertainty in your measurement rather than the device, this is the value you will use from now on.

Distance m ±?

Time1 s ±?

Time2 s ±?

Time3 s ±?

Time4 s ±?

Time5 s ±?

Average time s

Uncertainty Time s

Hi


67

Processing the data

The equation relating distance and time is 22

1 atuts +=

Since the initial velocity is 0 this simplifies to 22

1 ats =

s is therefore proportional to t² so a graph of s (y axis) against t² (x axis) will give a straight line. The slope of this line will be ½a Add the columns below to your spreadsheet and calculate the time2 and the uncertainty in time2, uncertainty in time2 = (Max time2 ‐ Min time2)/2

Average time2

s2 Uncertainty in time2

s2

Presenting Data You are now ready to present your data in a graph. Copy the distance and time2 columns into loggerPro (or Graphical Analysis) and plot the best fit line and find the acceleration due to gravity from the gradient of the line. Create another data set and use the “uncertainty in time2” Column to plot the error bars. Plot the steepest and least steep lines manually to find the uncertainty in the acceleration. If you can’t remember how to do this see the ICT and IB Physics website. On my website you will also find this practical used as an example.

Conclusion and evaluation Use your graph to answer the following questions

• Is the acceleration truly constant? • Were your estimates of uncertainties reasonable? • Is there any way that this experiment could be improved?

Photo of apparatus


68

Practical 4 Specific Heat Capacity This is the first assessed practical. By this time students have learnt how they should construct tables and analyse data, now they have to do it alone.

Introduction In this experiment the specific heat capacity of water will be determined by heating different quantities of water in an electric kettle. The method used is far from ideal, try to think of ways to make your result as accurate as possible and modify the method as appropriate (don’t forget to write about these modifications in your report).

Method Pour some water into the electric kettle and determine it’s mass. Switch on the kettle and measure the rate of temperature rise using a temperature sensor connected to the computer. Repeat the procedure with at least 5 different masses of water. Enter your results into an appropriate table.

Theory The rate of temperature rise of the kettle ΔT/Δt is related to the power of the kettle, P by the following equation:

⎟⎠⎞

⎜⎝⎛ΔΔ

=tTmcP

Find out the power rating of the kettle then using a graphical method find the specific heat capacity of the water.

m= mass c= specific heat capacity of water


69

Practical 5 The pendulum This is a practical that is used for assessing for DCP and CE. It is also an introduction to designing an experiment since they have to choose how to measure the time period

Introduction In this investigation the relationship between the time period and the length of a simple pendulum will be investigated.

Method There are many different ways to measure the time period of a pendulum. Using one of the following devices: Photogate Motion sensor Rotational motion sensor Force sensor

Design a method to measure the time period and carry out an experiment to measure the time period for at least 5 different lengths of pendulum. Enter your results into a suitable table.

Theory The time period, T is related to the length, l by the equation

glT π2=

Use a graphical method to show that T is proportional to √l and use your graph to find the acceleration due to gravity (g).


70

Practical 8 Measuring the velocity of a wave using video analysis This practical is used to introduce the video analysis. It is an example of how simulations can be used in the programme but is not used in assessment.

Introduction In this practical the Phet simulation “waves in a string” will be used to investigate the relationship between the tension in the string and the wave speed. This is not really an experiment since you are not measuring real physical quantities but simulated ones, however it will introduce you to the use of loggerpro to analyse videos, and this might be useful later in the course.

Method Open loggerpro, this is very similar to graphical analysis but can also be used to collect data using the vernier interface and analyse video. Open the video by selecting movie from the insert menu. The movie is in my public drive (ac90cham). I have already prepared the video to save time. You should see something like this

Run the video by clicking the arrow at the bottom of the video window. To analyse the video got to http://home.no/champer/ict/Home/Home.html “video analysis”. Here you will find step by step instructions on how to do it. When setting the scale assume the length of the string is 1m.

Analysis The video shows the wave travelling through the string at different tension setting. The actual tension is not given but assume the tension scale is in Newtons (ON ‐ 10N). Using loggerpro draw a graph of the displacement of the wave at each Tension setting (4N – 10N), find the wave velocity by plotting a best fit line for each graph and recording the gradient of the line. You should enter your results into a suitable table. Don’t forget to estimate the uncertainties.

The velocity, v of the wave is given by the formula T = Tension and µ = mass per unit

length. By plotting a suitable graph show that v is proportional to √T and find µ.


71

Practical 9 Resistivity of conducting paper

Introduction Conducting paper is a special type of paper that conducts electricity; it has a fairly high resistance so the current through it is small. In this practical the pd along a piece of current carrying conducting paper will be measured using a voltmeter. Given the resistivity it is then possible to find the current flowing through it.

Method Set up the circuit as in the diagram

When not taking measurements disconnect the battery so that it doesn’t run down. Using the multimeter adjusted to a suitable range measure the pd across different lengths of the conductor (L). Enter your results into an appropriate table with all the usual additions.

Theory Making the following assumptions:

• The voltmeter has an infinite resistance so takes no current

• The current is small so the pd across the internal resistance is negligible

• The paper strip is uniform

The pd across a length L of paper, V= IR Where R is the resistance of the length of paper L. But R =ρL/A where ρ = resistivity of the paper and A=Cross sectional area

So V=IρL/A Given that ρ/A= 200kΩ/cm use a graphical method find the current flowing through the paper.


72

Practical 10 Kepler’s Law This is an example of a practical that uses a database. it is not used to assess any of the criteria

Introduction This isn’t really a practical but it is an exercise in using data from a database. A database is a computer programme that allows you to make connections between different bits of data. The college timetable uses a database to make lists of the students in different classes, the teachers in different rooms and what time the different classes happen. When teachers mark a student absent the database makes a list for the advisor so they know when the student missed a class. In this exercise a database containing data about the solar system will be used to plot a graph verifying Kepler’s law.

Kepler’s Law For many years before Newton thought of his “Universal Law of Gravity” man was interested in the movement of the planets, this interest led to very precise measurement of their time periods and orbital radii. By manipulating this data Kepler found out that the square of the Time period was proportional to the cube root of the radius. r³αT² Later Newton showed how this could be derived from the “Universal law of Gravity”. We know that if a body moves in a circle the force acting toward the centre = mv²/r Newton’s Law said that this force = GMm/r² where M is the mass of the sun. So

But the speed of the body v = 2πr/T where T= time period

• Substitute this into the equation above and show that

• Using the data about the solar system found here (press ctrl and click to open link), plot a graph of r³ against T².

• Use your graph to find the mass of the sun.

• More info about databases can be found on the ICT site.


73

Design Practicals One of the nice thing about doing design practicals is that you don’t need to prepare a worksheet, all you do is give the students a topic to work with and off they go. However you do need to make sure that the topic has a lot of possibilities, its best if all the students in a class have different research questions so the topic has to be fairly broad, alternatively you could give a variety of different topics. To test out a topic I try to think of 10 different research questions in 10 minutes, if I can’t do that I abandon the idea. Here are some of the topics I have tried with a sample of research questions.

Jelly In Norway you can by blocks of readymade jelly as well as powder that can used to make you own, I give students both to increase the possibilities.

• What is the relationship between the intensity of a laser beam and the thickness of a slab of jelly?

• What is the relationship between the number of beta particles passing through a slab of jelly and its thickness?

• What is the relationship between the electrical resistance of a slice of jelly and the amount of jelly powder mixed with a constant volume of water?

• What is the relationship between the volume of a cube of jelly and its natural frequency?

• What is the relationship between the temperature of jelly and its frequency of vibration?

• What is the relationship between the elastic constant of jelly cube of jelly and the amount of jelly powder used to make the jelly?

Balloons I have used this example after we have done mechanics, thermal physics, SHM, electrical ccts and fields. I don’t restrict students to a particular topic. Some of the research questions are a bit obscure; it is therefore a good idea for students to always write an introduction to the topic before writing their research question.

• What is the relationship between the radius of a balloon and its terminal velocity?

• What is the relationship between the amount of air in a balloon and the charge it gains after being rubbed the same number of times?

• What is the relationship between the volume of a balloon and its temperature?

• What is the relationship between the height reached by a balloon and the distance that the end is pulled down?

• What is the relationship between the deflection of two charge balloons and time?


74


75

Internal Assessment Sample

Before entering grade Have students have submitted enough examples Have you have marked them properly Have you got a copy? Were the practicals suitable?

Selecting sample You must send 2 examples of practicals with the highest grade achieved in each sample Much better if you have a choice Select the best examples Show your range of practicals Don’t send the same Design prac for all the sample Don’t send the same Research question for whole sample Check for duplicates Substitute if non typical

Notes for the Moderator Explain using the criteria why you awarded the marks you did Include worksheet or explain what the students were told or given Organise the sample well, attach worksheets, 4PSOW cover sheets etc. Submit on time

If it all goes wrong Ask Diploma coordinator to contct IB Ask for feedback


76

TOK Moments We can bring up TOK in every physics lesson but here are a few memorable moments.

Topic 1: Physics and physical measurement 1.1 The realm of physics Measurement vs perception.

How we define quantities. What if the standard meter kept changing. Why is everything based on numbers? Is there such a thing as a non physical world?

1.2 Measurement and uncertainties Can we ever measure exactly, if we can’t how can we really know anything? Why do we use graphs? Anscombes quartet.

1.3 Vectors and scalars Is everything really a vector or a scalar? Topic 2 : Mechanics 2.1 Kinematics Using graphs to aid understanding.

Using equations to models what the physical world.

9.1 Projectile motion 2.2 Forces and dynamics Why do we call “Newton’s Laws” laws.

How are physics laws different to other laws Using laws to make predictions

2.3 Work, energy and power Misuse of the word energy. 2.4 Uniform circular motion Does centrifugal force exist? Topic 3 : Thermal physics 3.1 Thermal concepts Does heat mean the same thing in other

contexts? 3.2 Thermal properties of matter Particles, the recurring theme. 10.1 Thermodynamics Laws make strong arguments. 10.2 Processes Using graphs to visualise the invisible. 10.3 Second law of thermodynamics and entropy

Isothermal changes, not practically possible or impossible. Decreasing entropy, impossible or unlikely. Arrows of time

Topic 4: Oscillations and waves 4.1 Kinematics of simple harmonic motion (SHM)

Patterns in physics

4.2 Energy changes during simple harmonic motion (SHM)

4.3 Forced oscillations and resonance Learning the hard way, Tacoma Narrows. 4.4 Wave characteristics Patterns again 4.5 Wave properties 11.1 Standing (stationary) waves


77

11.2 Doppler effect Using physics to cheat the speed trap. 11.3 Diffraction 11.4 Resolution When we use an electron microscope are we

seeing? 11.5 Polarization Topic 5: Electric currents 5.1 Electric potential difference, current and resistance

Analogies in physics

5.2 Electric circuits Does it matter what’s happening in the wire as long as the light goes on?

Topic 6: Fields and forces 6.1 Gravitational force and field How can things accelerate without anything

touching them? 9.2 Gravitational field, potential and energy 9.4 Orbital motion Galileo and the church. 6.2 Electric force and field The symmetry of the physical world 9.3 Electric field, potential and energy 6.3 Magnetic force and field Monopoles and dipoles 12.1 Induced electromotive force (emf) Rules not Laws 12.2 Alternating current 12.3 Transmission of electrical power Health hazards and the media. Topic 7: Atomic and nuclear physics 7.1 The atom The development of models through

experiment. Is this History?

13.1 Quantum physics How can something be a particle and a wave? Paradigm shifts.

7.2 Radioactive decay Ethics of using data from Hiroshima. Radioactive dating and religion.

7.3 Nuclear reactions, fission and fusion Ethics of research to make bombs 13.2 Nuclear physics Is the WWW the only thing that CERN has done? Topic 8: Energy, power and climate change 8.1 Energy degradation and power generation 8.2 World energy sources How do we know how much oil is left? 8.3 Fossil fuel power production 8.4 Non‐fossil fuel power production Is it physics or economics? 8.5 Greenhouse effect 8.6 Global warming International problem and international

solutions. What does 99% certain mean? Politics and physics

Topic 14: Digital technology 14.1 Analogue and digital signals Chinese alphabet and ASCII 14.2 Data capture; digital imaging using charge‐coupled devices (CCDs)

The effects of developments in Physics on society.


78

Option E: Astrophysics E1 Introduction to the universe Mans obsession with the stars.

Horoscopes. E2 Stellar radiation and stellar types Based on a small amount of light.

How bright is a star, early measurements. E3 Stellar distances Can we have a feel for these distances. E4 Cosmology Recreating the big bang at CERN. E5 Stellar processes and stellar evolution Graphs and charts.

How can we know what happened when we only see what is there today.

E6 Galaxies and the expanding universe Cosmology and religion What was there before the big bang? Chance discoveries. Justifying the expense of research.

Option F: Communications F1 Radio communication F2 Digital signals The digital revolution.

Redundant technology. Sampling and the interpretation of signals

F3 Optic fibre transmission Optical fibres everywhere, who decides? F4 Channels of communication Satellites and space law. F5 Electronics Can anyone comprehend the electrical ccts in a

computer? F6 The mobile phone system Mobile phones and society.

Can a mobile cook your brain? Option G: Electromagnetic waves G1 Nature of EM waves and light sources EM radiation and Health. G2 Optical instruments G3 Two‐source interference of waves G4 Diffraction grating G5 X‐rays G6 Thin‐film interference Does knowing why a bubble is coloured make it

more beautiful? Option H: Relativity H1 Introduction to relativity H2 Concepts and postulates of special relativity The use of postulates in science.

To prove it wrong you must prove the postulate wrong.

H3 Relativistic kinematics The use of though experiments H4 Some consequences of special relativity Is this all just made up by physicists?

Do things get shorter or is it an optical illusion? H5 Evidence to support special relativity Uncertainties H6 Relativistic momentum and energy H7 General relativity How can we visualise curved space time? H8 Evidence to support general relativity Is it a field or a curved space?


79

Option I: Medical physics I1 The ear and hearing Perception and measurement I2 Medical imaging Technology for the rich. I3 Radiation in medicine Benefits outweigh the risk.

No safe limit Ethics of testing.

Option J: Particle physics J1 Particles and interactions J2 Particle accelerators and detectors Is CERN worth the expense?

exploding black boxes Technology and knowledge

J3 Quarks Is the simplest model necessarily the right one? When numbers are not enough. If a quark cannot exist on its own does it exist? Strangeness and Charm, language in physics.

J4 Leptons and the standard model J5 Experimental evidence for the quark and standard models

Is this physics or stamp collecting?

J6 Cosmology and strings Are we getting closer to the truth or simply digging a deeper hole? Do we have to know everything?


80

The Extended Essay This is an unedited extract from the soon to be published HL Physics book by Heinemann.

Extended Essay The extended essay is a 4000 word piece of independent research on an IB topic of your choice. Tackling an extended essay in physics can be a frightening prospect but your physics teacher will be given the task of supervising your research and will be on hand to give guidance and help solve any practical problems that you might come across. Your supervisor will also give you a booklet; ”the extended essay guide” giving guidance on how to construct the essay with some specific recommendations for physics.

Choosing a Topic If you have a good topic then writing an extended essay in Physics can be quite straight forward, choose a bad topic and it could be a nightmare, your supervisor will help guide you but here are some guidelines to help:

• Don’t be too ambitious, simple ideas often lead to the best essays. Students often don’t believe that they can write 4000 words on something as simple as a ball of plasticene being dropped on the floor but end up struggling to reduce the number of words.

• Make sure its physics, avoid anything that overlaps with chemistry or biology and keep well away from metaphysics or bad science.

• Although the essay does not have to be something that has never been done before it mustn’t be something lifted straight from the syllabus.

• Avoid a purely theoretical based essay unless you have specialist knowledge. The essay must include some personal input; this is very difficult if you write about some advanced topic like “black holes” or “super strings”.

• It is best if you can do whatever experiments you require in the school laboratory under the supervision of your supervisor. If you do the experiments at home during the holiday keep in contact with your supervisor so your research is kept on the right track.

• Choose a topic that interests you then it will be easier to keep motivated when the going gets tough.

Photo 1 Roberto Carlos’ free kicks are an interesting phenomenon but can you do them in the lab?


81

• Sports offer a wide range of interesting research questions but sometimes it is very difficult to perform experiments. Roberto Carlos’ famous free kick is a fascinating topic for an extended essay but not even he can do it every time let alone with different amounts of spin. If you are keen to do this sort of research try to think how you can simplify the situation so it can be done in the laboratory not on the football pitch.

• You mustn’t do anything dangerous or unethical.

The Research Question Once a topic has been decided upon you will have to think of a specific research question, this normally involves some experimental trials and book research. The title of the essay often poses a question that could be answered in many ways; the research question focuses in on the way that you are going answer the question. It is important that as you write the essay you refer back to the original topic and don’t get lost in the intricacies of your experimental method.

Examples of topics and research questions Does the depth of a swimming pool affect the maximum speed achieved by a swimmer? Rather than trying to measure the speed of swimmers in different depth pools experiments were performed in the physics lab pulling a floating ball across a ripple tank. This led to the research question “What is the relationship between the depth of water and the drag experienced by a body moving across the surface?” Why isn’t it possible to charge a balloon that isn’t blown up? This topic led to the research question “what is the relationship between the electron affinity of rubber and the amount that the rubber is stretched”. To perform the experiment a machine was built that could rub different samples of stretched rubber in the same way. Why does my motorbike lean to the left when I turn the handle bars to the right? Rather than experimenting on a motorbike experiments were performed in the lab with a simple gyroscope. The research question was “how is the rate of precession of a spinning wheel related to the applied torque?”

Photo 2 Giovanni Braghieri IB physics student and EE writer riding his motorbike.


82

Performing the practical work Most extended essays will involve some practical work, you should start this as early as possible, if it doesn’t work or you find you don’t have the right equipment then you might want to change the research question. You don’t have to spend hours and hours on the experiment (although some students do) the whole essay is only supposed to take 40 hours so keep things in perspective. Make sure the experiments are relevant to the research question and that you consider possible sources of error like you would in any other piece of practical work. If you get stuck ask your supervisor for help, they can’t do it for you but can help you solve problems.

Research Remember that you’re doing research not a piece of internal assessment, this means that you should find out what other people have done and compare their findings with your own. This might be difficult if you have chosen a particularly novel topic but most things have been done before. You can try the internet but Science journals found in University libraries are often the best good source of information.

Writing the Essay Once you have done some research and conducted your experiment you are ready to write the essay. Remember you are trying to answer a research question so get straight to the point, there is no need to tell a story about how this has been your greatest interest since you were a small child or something of that nature, you are expected to make some personal input but not like that. Make a plan of how you want your essay to be, the thread running through it is the research question, don’t lose sight of this. Here is a plan of the essay mentioned above about the balloon:

• Introduction of the topic and research question, how the electron affinity of rubber is connected to the charging of a balloon.

• The theory of charging a balloon and electron affinity

• Hypothesis based on the theory

• How I am going to test the hypothesis

• Details of experimental technique

• Results of experiment

• Interpretation of results including evaluation of method.

• Conclusion, how my results support my hypothesis and the findings of others.

• Why a balloon that is inflated cannot be charged.


83

What can go wrong In the real world things are rarely as simple as they first appear and you might find that your data does not support you original hypothesis, this can be disappointing but shouldn’t ruin your chances of writing a good essay. First make sure that you haven’t made any mistakes in your initial assumptions or analysis of data then try to think what why the experiment doesn’t match the theory and write this in the conclusion. Don’t pretend that it does if it doesn’t.

Extended Essay Assessment The extended essay is marked by experienced Physics teachers against 11 criteria it is important that you understand the criteria since if your essay doesn’t satisfy them it won’t score well even if it’s really good. A Research Question Most importantly your research question must be physics and not just loosely related to physics. “Did Isaac Newton’s mother influence his laws of motion”? Isn’t physics. “An investigation into the relationship between the thickness of Jelly and the attenuation of a laser beam” is. Assuming you have a good research question make sure you emphasise it in the introduction of your essay, the first paragraph would be good. Introduction The introduction puts your research question in context; it is not supposed to be a story. Give some background information about the topic you are investigating to help the reader to understand the research question. For example if your research question is “the relationship between the velocity of a toy hedgehog and the angle of the slope” you had probably better explain how the toy hedgehog works, however don’t bother telling a story about the day you bought it and how your love of physics blossomed from that day forth. Investigation This mark is for the practical work that you carried out or in the case of a theoretical essay the research. Include enough detail so that the reader can understand what you did but don’t get bogged down in detail. Remember it is an essay not a lab report, don’t whatever you do use titles like “Data collection and Processing”. If you have used

secondary data make sure you reference the sources and give some indication of their reliability. If you have got the idea for your experimental design from a book or the internet then quote the source. Make sure you estimate the uncertainties in all of your measurements and propagate then correctly through any calculations; all graphs should include error bars.

Photo 3 Simple toys based on complex physics are often a good source of ideas


84

Knowledge and Understanding of Topic Studied To gain marks in this criteria you must show that you understand the physics that you are using. It is almost impossible to write an essay that shows you understand something if you don’t understand it so choose a topic that you either understand or think you will be able to understand if you read up on it. This is why it’s not a good idea to write an essay on something like string theory (unless you are brilliant of course), it’s also why interesting applications of Newtonian mechanics to novel situations often lead to good essays. Reasoned Argument To have a reasoned argument that runs through an essay requires a good essay plan. When you have your data and know your conclusions plan how you are going to tell the story. The introduction should lead into the experiment, the results should imply the conclusion, and the evaluation should be based on evidence that can be seen in the results. Essays in Physics can become unconnected sections, think carefully about how it fits together, if something takes you away from the main argument leave it out. Application of Analytical and evaluative skills appropriate to the subject Most essays in physics will include some mathematics, make sure you understand what you are doing, don’t just copy derivations from a book or use computer software blindly. Analyse your data properly; some of the approximations for calculating errors used in the internal assessment are not good enough if using large amounts of data. Evaluate your experimental technique honestly, don’t try to hide mistakes, it shows you understand what you are doing if you can spot mistakes. Use of Language appropriate to the subject In physics words don’t have two meanings, use the language of physics carefully. If you use symbols to represent quantities define them clearly and be consistent. Always give the units of any quantity. If you don’t know what a term means then don’t use it, stick to what you know. Conclusion The results of your experiment should lead logically to the conclusion; this is part of the development of the argument mentioned previously. When you first thought of your research question you may already have thought of the conclusion, try to forget this and base the conclusion on what your experiment tells you not on what you thought would happen. Your conclusion will be have greater validity if your uncertainties are small, if they are large then explain how they affect your conclusion. If your results are


85

inconclusive say what further investigation could be done to resolve the problem. Formal presentation Make sure you have included all of the components listed in the official extended essay guide: Title page Abstract Table of contents Page numbers References Bibliography Abstract The abstract is an overview of the whole essay including the research question method of research and conclusion, here is an example: The Relationship between the Depth and the Drag of Water The aim of the essay is to investigate the relationship between the depth of water and the resisting force caused by the water on a floating object that is being pulled parallel to the surface of the water. The experiment only deals with a small spherical object that is being pulled with a constant force, on a low velocity and on shallow depths to limit the scope. According to the developed hypothesis the resisting force, drag, is proportional to 1/depth² because the movement of the sphere pushes the water towards the bottom which means that the bottom is also pushing the water towards the sphere. The longer the distance between the sphere and the bottom the more the force is dispersed to other directions. A method of measuring the acceleration of the sphere at a certain velocity but different depths was used to examine the relationship. From the acceleration, the masses and the gravitational force involved it is possible to calculate the drag. The conclusion of the experiment is that the hypothesis does hold true for the conducted experiment i.e. the drag is proportional to 1/depth² for the limited scope of situation that the experiment deals with. There are also certain reservations about the accuracy of the experiment. Joonas Govenius RCNUWC


86

Holistic Judgement These marks are awarded to the essay as a whole to reward intellectual initiative, Insight, originality and creativity. Even if the essay isn’t well written it can still gain marks here if you have for example shown original thought in devising an ingenious way of solving a practical problem.


87

Some Extended Essay Hints (From Geoff Neuss)

Research Question The research question MUST be clearly worded and sharply focused. Without this the whole EE will be on very shaky ground as the whole essay should be based on the RQ. It’s not a “normal Lab” Students must not just follow the IA criteria. They must address ALL the EE criteria.

Research The EE is about research. Students must find out and report what others have done in the area. It is no good just doing 'an investigation' into some problem without putting it into proper context.

Sources The quality of the sources must be analyzed. Students do this ad nauseam for the equipment they use to produce their own results but often they do not question the veracity of internet sources nor do they tend to question the underlying physical assumptions in their own work.

Development of Argument Students must develop an argument rather than just write a narrative account. It can be particularly helpful to try to arrive at a solution to a problem by two independent routes as then the merits of the two routes can be compared.

Address Criteria Don't lose marks by failing to address all the criteria correctly. The checklist to be found in my IB Study Guide is extremely useful here. Students must be able to check 'yes' to every point.

Initiative Students must demonstrate personal input and initiative.


88

Enough detail When giving experiment details give enough information so that the work could be repeated by others. Acknowledge where the basic experimental method was obtained from. Detail specific equipment such as the make of a visible spectrometer but do not give spurious lists of basic equipment. Also do not include unnecessary photographs.

Explain It is not necessary to explain basic physics that is covered in the core or AHL programme, but the student must ensure that it is clear that they understand the underlying physics and use the correct terminology. Physics that is not on the core/AHL etc should be explained and the physics underlying specialized techniques should also be explained.


89

Group 4 Project

Why? Encourage an understanding of the relationships between scientific disciplines and the overarching nature of the scientific method. (Aim 10) Encourage students to work as a team. The ability to be a good team member is seen as a positive attribute by most employers and universities.

The Team A group of students from different scientific disciplines.

How many? Cooperation – each team member doing a part Collaboration – The end result is produced by the team Give guidance on team management

Designing the task Clearly defined outcome Assessment Criteria A variety of roles and responsibilities Scope for creativity Group product Requirement for cooperation Give enough time

Assessment must understand the assessment criteria and how they will be applied. Assessing individual contributions.

Not easy to do if you aren’t there all the time Difficult to judge as an outsider

Assessing the final product. Should all team members get the same mark? Don’t expect the final product to be high quality.


90

Assessment Criteria

Peer Assessment The team members know more about who contributed most than you do. Students don’t like giving their friends low marks Moderated Teacher Assessment Give a mark for each student. Get each student to grade their peers. Moderate your mark based on the peer assessment. Assessment Example Teachers mark + average of peer marks


91

Group 4 Project 2008 Assessment Name_______________________________

Project title___________________________

Using the following criteria grade yourself and the members of your team

Self Member 1 Member 2 Member 3 Member 4 Member 5 Name: Motivation Teamwork Reflection

Evaluation:

On the IB scale of 1‐7 (1 Bad ‐ 7 Excellent) rate the following

1. The day overall 2. The topic of the project 3. The organisation of the day 4. The Information given

Any other comments:


92


93

IB PHYSICS WORKSHOP Berlin 2009 - "You cannot teach a...

Documents

Transcript of IB PHYSICS WORKSHOP Berlin 2009 - "You cannot teach a...