140 HSW-The Use of Tables in Pracical Work

Physics Factsheet www.curriculum-press.co.uk

Number 140

How Science Works - The Use of Tables in Practical Work Almost every time you carry out practical work you need to produce a table of results. • • •

Getting the table right is important both to make your results useful and to make sure you get good marks in an exam! There are a number of points to think about when drawing up your table:

Always do at least two repeats and make sure your results table shows you have done this. This may mean you will have to carry out the experiment three times under the same conditions. When you have done your repeats, take an average for each value of the dependent variable and show this average in your table.

First of all ‘the basics’ : – make sure each column has: • •

Layout Headings Units Independent variable first

The correct heading The correct units

This means, that even before you start collecting results, your table should look something like this:

Also, the independent variable should be shown in the first column of your results table. Name of independent variable

Name of dependent variable Reading 1

Name of dependent variable Reading 2

Name of dependent variable Reading 3

Name of dependent variable Average of readings 1, 2 & 3

(unit of independent variable)

(unit of dependent variable)

(unit of dependent variable)

(unit of dependent variable)

(unit of dependent variable)

First value Second value Third value Fourth value Fifth value Sixth value Seventh value At ‘A‘ level, you should be investigating a minimum of 5 values for each variable – ideally more. This is so you will have enough readings to be able to draw a good graph – and also so you can investigate a big enough range of values for the independent variable. If the range you choose is too small then your conclusions may not be valid.

• • • • •

So how would this look in practice?

Gathering results Minimum of 5 values of the independent variable Each value tested 3 times Average values taken Appropriate range of independent variables investigated. Appropriate interval between values of the independent variable

Let’s imagine you have been investigating a cooling curve for water. You have first carried out a preliminary experiment to gauge how long it takes boiling water to cool to room temperature – this allows you to decide the time period that will need to be covered in your experiment. You have concluded that it takes about 20 minutes to reach room temperature so you decide to take measurements every 2 minutes.

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Physics Factsheet

140. How Science Works - The Use of Tables in Practical Work Only part of the data gathered is shown in the table below. Time Temperature 1 (mins) (°C)

Temperature 2 (°C)

Temperature 3 (°C)

Average temperature (°C)

0

98.5

2

90.0

4

82.1

…….. 18

23.2

20

22.4

Exam Hint:- It’s worth doing a trial run to decide on an appropriate range of values for your independent variable and also to decide on the best interval between values e.g. do you take readings every 10 seconds, every minute etc.

If you had only taken measurements for 10 minutes you might have missed important information about the change in the rate of cooling as time goes on.

Averaging Let’s look a little more at averaging your results. Sometimes you use your results to calculate the value of a quantity. For example, you may measure the current through a resistor and the voltage across it in order to measure its resistance.

At which point do you take your averages? You could: • do your resistance calculations first then average them or • you could average your current and voltage values then use the average values to calculate resistance. The second method is better – to illustrate this: Supply voltage (V)

Current 1 Current 2

Current 3

(A)

(A)

(A)

0 2 4 6 …… 12

0.00 0.25 0.49

0.00 0.23 0.49

0.00 0.24 0.49

Average current (A)

Voltage 1 Voltage 2

Voltage 3

(V)

(V)

(V)

Average voltage (V)

0.00 0.24 0.49

0.0 1.8 3.6

0.0 1.8 3.8

0.0 1.8 3.7

0.0 1.8 3.7

The value of resistance for each value of supply voltage would then be calculated by dividing the average voltage across the resistor by the average current through it – using the figures in bold in the table above.

Supply Voltage 1 voltage (V) (V) 0 2 4 6 …… 12

The table above has all the measurements you have taken and all the values you need together in one place. It’s much better to do this than to have several tables that you then have to keep cross-referencing. So – for example, the set up below is not as useful as the composite table we had above. Supply Current 1 voltage (V) (A) 0 2 4 6 …… 12

0.00 0.25 0.49

Current 2 Current 3 (A) (A) 0.00 0.23 0.49

0.00 0.24 0.49

0.0 1.8 3.6

Supply Average voltage (V) current (A)

Average current (A)

0 2 4 6 …… 12

0.00 0.24 0.49

0.00 0.24 0.49

Resistance (Ω)

Voltage 2 Voltage 3 (V) (V) 0.0 1.8 3.8

Average voltage (V)

0.0 1.8 3.7

Average Voltage (V) 0.0 1.8 3.7

Resistance (Ω)

0.00 1.8 3.7

If you have to have information shown in separate tables then you must make sure that common information appears on all the tables. For example, in this set of three, all the tables have the “Supply Voltage” column included.

Composite tables Composite tables are usually better than a series of separate tables.

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Physics Factsheet

140. How Science Works - The Use of Tables in Practical Work Anomalous readings

Identifying an anomaly is easier if your readings are arranged in a logical order – by going from the lowest value of the independent variable to the highest (or, sometimes, from the highest to the lowest). Taking your results in a random order is not good practice and it makes your results table much harder to interpret - so don’t do it!

What do you do if any of your readings seem to be anomalous? Repeating your readings helps you identify anomalous results. Once you have identified them, you need to decide whether to ignore them or not. You can really only make this decision if you know they really are anomalous.

So what if you find that you need to investigate a particular section of your results further - let’s say you have found that something odd seems to be happening when the supply voltage is 4V in the experiment above so you decide (very sensibly) to see what happens when the supply voltage is 3V and 5V.

How do you know if a result is anomalous? • • •

Repeat the reading. Is the result the same every time you repeat for that value of independent variable? If it is, it may not be an anomalous result but it may be a feature of the effect you are investigating. If it is not repeatable, then assume it is anomalous and ignore it – do not include it when you average your readings.

Supply voltage (V)

Current 1 Current 2

Current 3

(A)

(A)

(A)

0 2 3 4 5 6 …… 12

0.00 0.25

0.00 0.23

0.49

0.49

Supply voltage (V)

Current 1 Current 2 (A)

(A)

(A)

0 2 4 6 …… 12 3 5

0.00 0.25 0.49

0.00 0.23 0.49

0.00 0.24 0.49

You will need to redraw your table to put the 3V and 5V readings in the right place – don’t just tag them onto the end!

Average current (A)

Voltage 1 Voltage 2

Voltage 3

(V)

(V)

(V)

Average voltage (V)

0.00 0.24

0.00 0.24

0.0 1.8

0.0 1.8

0.0 1.8

0.0 1.8

0.49

0.49

3.6

3.8

3.7

3.7

Current 3

Average current (A)

Voltage 1 Voltage 2

Voltage 3

(V)

(V)

(V)

Average voltage (V)

0.00 0.24 0.49

0.0 1.8 3.6

0.0 1.8 3.8

0.0 1.8 3.7

0.0 1.8 3.7

Exam Hints: anomalies • always check out anomalies • you may need to redraw your table if you investigate new values of the independent variable – to keep the values in the independent variable column in a logical order.

• • •

Resistance (Ω)

Resistance (Ω)

Numbers Make sure the number of decimal places is consistent within each column. The number of decimal places should be consistent with how accurately you can measure a quantity. Use a sensible number of significant figures

And what about the numbers themselves? Things to look out for include: • make sure the numbers in every column are written to the same number of decimal places. The number of decimal places should reflect how accurately you can measure the quantities. For example, if you can measure mass to within 0.01 of a gramme, then a mass of two grammes should be written as 2.00g not 2g. •

Take care in deciding how many significant figures to use when you write each value. Keep this realistic and in line with the advice above rounding up or down as appropriate when filling in values you have calculated.

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140. How Science Works - The Use of Tables in Practical Work

Physics Factsheet

Problems on improving results tables

So, did you find these errors? The tables below have something wrong with them. Can you identify Table 1 what’s wrong with each table, and suggest how it could be improved?

• The numbers within each column of a table should be shown to the same number of decimal places. In this table, this is only true for the first column. The number of decimal places should reflect how accurately you can measure. • The final column not only shows a huge range of decimal places – there are also far too many significant figures in the numbers shown. Could you really measure to this degree of accuracy?

Table 1 These results are from an experiment to measure the resistance of a resistor. Supply Average voltage (V) current (A) 0 2 4 6 8 10

Average voltage (V)

0 0.24 0.49 0.5 1.2 1.68

0 1.25 3.7 4.8 7.2 9.05

Resistance (Ω) 5.2083333 7.5510204 9.6 6 5.3869047

Table 2

• The 30 second reading has just been tagged on at the end of the table. The table should have been redrawn so that this reading appeared between the 20 second and 40 second readings. • The units in the final column are not Volts – how could they still be Volts when the numerical values are different from those in the column before? They should be lnVolts or lnV.

Table 2 These results follow the change in voltage as a capacitor discharges. Table 3 • Units again – suddenly the count rate has become measured in Time Average voltage Natural log of average voltage ‘counts per second’ rather than in ‘counts per minute’ ! (s) (V) (V)

• There is an anomaly (shown in bold on the table). This anomalous figure has been included when the average count rate for 0.15m was found – it should have been omitted – or better still a further result obtained for this distance and that value used to calculate the average instead. • Decimal places are not consistent within the first column. The figures should be: Table 3 0.10 These are results for an experiment to measure the penetration of a 0.15 beta source. 0.20 Distance Count Count Count Average 0.25 from source rate 1 rate 2 rate 2 Count rate 0.30 and (m) (c.p.m) (c.p.m) (c.p.m) (c.p.s) 0.35 0 20 40 60 30

12.4 9.2 7.4 5.8 7.6

0.1 0.15 0.2 0.25 0.3 0.35

2.517 2.219 2.001 1.758 2.028

255 200 180 168 159 154

282 165 178 163 157 153

264 214 182 170 161 149

267 193 180 167 159 152

Table 4

• Not enough readings taken – only four values of the independent variable (mass) have been tested. • Units again - the mass would need to be in kilogrammes to give an answer in Newtons.

Table 5 Table 4 • More unit problems! These results relate to an experiment where mass and acceleration ×103 and • You need to be consistent. Really it should be V× -3 were measured and force calculated from the readings using F = ma. ×10 OR kV and mA A× • When you divide kV (103V) by mA (10-3A) you don’t get Ω! Mass (g) Average acceleration (ms-2) Force (N) 60 40 30 20

0.42 0.72 0.83 1.40

You actually get MΩ (106Ω).

25.2 28.8 24.9 28.0

So, to summarise. Take care with:

• Headings • Units Table 5 • Range Here, voltage and current were measured and resistance calculated • Number of values of variables from the results. • Repeats Voltage (M×103) Average current (mA) Resistance (Ω) • Averages • Anomalies 0 0.00 • Decimal Places 2 0.24 8.333 • Significant figures 4 0.49 8.163 • The order of your results. 6 0.50 12.000 Acknowledgements: 8 1.20 6.667 This Physics Factsheet was researched and written by Beverly Rickwood 10 1.68 5.952 The Curriculum Press,Bank House, 105 King Street,Wellington, Shropshire, TF1 1NU

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