… Base quantities in physics are the SI base units, which are:
metre (length)
kilogram (mass)
second (time)
ampere (current)
kelvin (temperature)
candela (luminous intensity)
mole (amount of substance)
… To find the units of a quantity in terms of ‘base units’ (e.g. find the base units of Ohms), use formulae from your booklet to ‘break down’ each quantity. For example, the units of resistance (ohms):
R = V/I
and
V = W / Q
and
I = Q/t
so
R = (W/Q) / (Q/t) … remember that if you divide a fraction by a fraction, then flip the second fraction and the divide becomes a multiply:
R = W/Q x t/Q
now replace these quantities with their respective units:
R = J/C x s/C
R = Js/C²
… Prefix notation:
‘large’ prefixes:
kilo (k) = ×10^3
Mega (M) = ×10^6
Giga (M) = ×10^9
Tera (T) = ×10^12
‘Small’ prefixes:
Centi (cm) = ×10^-2
milli (m) = ×10^-3
micro (μ) = ×10^-6
nano (n) = ×10^-9
pico (p) = ×10^-12
femto (f) = ×10^-15
Do make sure BEFORE carrying out any calculations, that you have converted any prefix data to standard units in your data list.
For example:
“34.5kN = 34.5 x 10^3 N”
Exam technique
Here are some ideas on exam technique for those discussion-type questions (usually 6-markers, but can also be used for 2-3 markers too):
1) first underline the important key words or information in the question (not too many – just the really important bits)
2) State general physics facts/principles about the theme of the question. To do this ask,”what do I know about…[keyword or phrase]”. Writing down relevant equations is also a great idea.
Obvious details are often in the mark scheme (e.g. “The LDR’s resistance falls when the light level on it rises”)
3) Read the question again and really focus on the words and the question being asked. Imagine you are explaining a chain of events – a story of what’s happening – to someone who doesn’t know much about physics.
Have you answered everything the question asked for?
4) It is often useful to state an obvious conclusion to sum up (using the question’s wording can help).
Using bullet points is a useful technique to help structure your answer. Try to leave space between each point, just in case you need to add something.
Longer questions will often define quite clearly what they require, so use this to structure your answer.
Once you have answered everything you can, move on and return to the question later just in case you think of something else.
… It’s a good plan to read through an entire question BEFORE starting it. Later parts can often give you clues for earlier parts!
—
For other types of questions – especially those involving calculations:
1) Where possible draw a clear diagram to summarise all the information given in the question. This might be a circuit diagram showing currents and voltages, or a force diagram of the object showing all the forces acting.
Summarising the question in this way gives you a view of the whole situation without having to wade through words and figures in a paragraph of text.
Alternatively, for more calculation-based questions, summarise the question information in a data list, including quantity symbols, units, and the quantity (and unit) that you’re looking for. Make sure you convert data into standard units.
For example:
F = 34.7N
m = 250g = 0.250kg
a = ? m/s²
2) If the next step is not clear, try asking yourself, “what relevant quantities could I find/calculate from the data or graph?” Adding to your diagram or data list in this way often provides a ‘stepping stone’ to the final answer.
… If numbers are given in a ‘describe and explain’ questions, then try to use those numbers in relevant calculations as part of your answer.
—
Questions that ask you to describe an experiment
DO use bullet points to structure your method, but write in full sentences.
A labelled diagram can pick up marks
Explain the quantities you will measure and HOW you will measure them (e.g. “Use a metre rule to measure the new length of the spring”)
Always make repeat readings and take an average to improve the accuracy of your measurements.
Sometimes, you may need to plot a graph and find a best fit line. Then you may need to calculate the gradient or find the y-intercept.
State relevant formulae and how you will use the data. You may need to rearrange the formulae.
Imagine that you are explaining how to do the experiment to a Year 7 student who keeps asking, “How? Why?” 🙂
… Identifying ‘sources of uncertainty’ – type questions:
- read the question (and previous parts) very carefully as the clues are often in the text.
- ask yourself, “in the real world, what could actually happen to affect this experiment?”
- look at the quantities involved in the calculations. Could these quantities differ somehow from the ideal situation?
Practical skills, Measurements and their Uncertainties
… Here’s a useful summary document for AQA:
https://pmt.physicsandmathstutor.com/download/Physics/A-level/Notes/AQA/01-Measurements-and-Errors/Detailed%20Notes%20-%20Section%2001%20Measurements%20and%20their%20Errors%20-%20AQA%20Physics%20A-level.pdf
… An error is the difference between the measured result and the true value.
… An uncertainty is the interval in which the true value can be considered to lie.
… Resolution is the smallest change in the quantity being measured (input) of a measuring instrument that gives a perceptible change in the reading. For example, a typical mercury thermometer will have a resolution of 1°C, but a typical digital thermometer will have a resolution of 0.1°C
… Uncertainties can arise due to:
- the instrument being used to make the measurement (e.g. resolution, zero error)
- the way in which the measurement is made (e.g. parallax error, reaction time)
- the quantity measured not being constant (e.g. a varying diameter of a wire)
… Appropriate instruments for different measuring lengths with good accuracy:
1-10mm … use a micrometer screw gauge
10 – 150mm … use vernier (or digital) callipers
150mm+ … use a mm rule
Measurement vs reading uncertainties
… The uncertainty of a READING (one judgement) is at least ±0.5 of the smallest scale reading.
… The uncertainty of a MEASUREMENT (two judgements) is at least ±1 of the smallest scale reading.
For example, measuring the length of a pencil using a mm ruler needs two readings, one at each end. Each reading carries a ±0.5mm error, so total measurement error = ±1.0mm
… Readings are values found from a SINGLE judgement when using a piece of equipment
… Measurements are the values taken as the DIFFERENCE between the judgements of two values.
Examples:
- When using a thermometer, a student only needs to make one judgement (the height of the liquid). This is a reading. It can be assumed that the zero value has been correctly set.
- For protractors and rulers, both the starting point and the end point of the measurement must be judged, leading to two uncertainties.
… Examples of equipment for Readings and Measurements
Reading (one judgement only, so ±0.5 of smallest scale reading)
thermometer
top pan balance
measuring cylinder
digital voltmeter
Geiger counter
pressure gauge
Measurement (two judgements, so ±1 of smallest scale reading )
Ruler
Vernier calliper
Micrometer
Protractor
Stopwatch
Analogue meter
… When uncertainties are quoted in a measurement, for example, 2.40 ± 0.01V, then quote the uncertainty to the same number of decimal places as the value.
… Keep derived data (calculated data) in a results table to the same number of sig figs as the ‘raw’ data. For example:
λ /m λ² /m²
0.13 0.017
0.32 0.10
Uncertainties in given values
… In all such cases assume the uncertainty to be 1 in the last significant digit.
For example, the value of the charge on an electron is given in the data sheet as 1.60 × 10^–19 C. In this case the uncertainty is ±0.01 × 10^–19 C.
… When you divide a measurement by a number which has no uncertainty on it, the percentage error stays the same. So if diameter = 0.78mm +/- 0.01mm, then:
diameter = 0.78mm +/- 1.3%
radius = 0.39mm +/- 1.3%
radius = 0.39mm +/- 0.005mm
So by dividing by 2, the absolute error is also divided by 2.
Increasing accuracy of a measurement by taking an average
… For example, timing a pendulum over 20 swings.
If t = 15.4s for 20 swings, then the time for 1 swing can be taken as 0.77s (±0.02s).
In this case, there is some uncertainty when measuring both the start time and also the stopping time, resulting from the experimenter’s reflex time (as much as 0.2 s each, i.e. totalling 0.4 s).
Therefore, the uncertainty in the time period = 0.4/20 = ±0.02s
Finding an estimate of uncertainty from repeated measurements
… If measurements are repeated, the uncertainty can be calculated by finding half the RANGE of the measured values.
… There is sometimes confusion over the number of significant figures when READINGS cross multiples of 10. Changing the number of decimal places across a power of ten retains the number of significant figures but changes the accuracy.
For this reason, the same number of DECIMAL PLACES should generally be used, as illustrated below.
0.97 99.7
0.98 99.8
0.99 99.9
1.00 100.0
1.10 101.0
Reading a vernier scale
… The fixed scale is usually in mm intervals. Find the line on the sliding vernier scale which aligns exactly with a line on the fixed scale. Each line on the sliding scale adds 0.1mm. See https://upload.wikimedia.org/wikipedia/commons/1/18/Principle_vernier.png
Error bars in graphs
… The following simple method of plotting error bars is acceptable:
- plot the data point at the mean value
- calculate the range of the data, ignoring any anomalies
- add error bars with lengths equal to half the range on either side of the data point.
Uncertainties from gradients
… To find the uncertainty in a gradient, two lines should be drawn on the graph. One should be the “best” line of best fit. The second line should be the steepest or shallowest gradient line of best fit possible from the data. The gradient of each line should then be found:
Absolute uncertainty = |best gradient – worst gradient|
or
% uncertainty = ( |best gradient – worst gradient| / best gradient ) x 100%
In the same way, the percentage uncertainty in the y-intercept, can be found:
absolute uncertainty = |best y intercept – worst y intercept|
or
% uncertainty = ( |best y intercept – worst y intercept| / best y intercept ) x 100%
…when you add or subtract quantities, then ADD the ABSOLUTE uncertainties of each quantity.
… When you multiply or divide quantities, then ADD the PERCENTAGE uncertainties of each quantity.
… If you are faced with a complicated equation where it is not clear how to combine uncertainties, first calculate the nominal value, then put in the maximum absolute uncertainties and see what ‘comes out’.
You can also put in the minimum absolute values in the same way to see the overall range.
… It’s worth noting that percentage uncertainties increase if the measurement size decreases.
… For some functions, for example cos(x) or √x, the absolute and percentage errors of f(x) become smaller compared to the original x value. There is therefore a fair argument for writing an extra significant figure in the processed f(x) data.
However, a robust approach is to find out what the ‘propagated’ maximum error actually is by determining how much change occurs in the result when the maximum errors in the data combine in the worst possible way.
Example: An angle is measured to be 30°: ±0.5°. What is the error in the sine of this angle?
Solution: Use your calculator. The sine of 30° is 0.5; the sine of 30.5° is 0.508; the sine of 29.5° is 0.492. So if the angle is one half degree too large the sine becomes 0.008 larger, and if it were half a degree too small the sine becomes 0.008 smaller. (The change happens to be nearly the same size in both cases.) So the error in the sine would be written ±0.008.
The size of the error in trigonometric functions depends not only on the size of the error in the angle, but also on the size of the angle. A one half degree error in an angle of 90° would give an error of only 0.00004 in the sine.
… Typical responses to the question of how to improve the accuracy of an experiment:
- increase the number of measurements
- increase the range of measurements
- use measuring equipment with a greater precision (higher resolution)
- take repeat measurements and calculate an average.
- check that there are no systematic errors such as a zero error.
… Data logging (data loggers) instruments have advantages over human-based measuring:
- they can record thousands of data points over short intervals of time
- they remove human errors such as transcription or reading errors
- they can measure in remote and hostile environments
Graph work
… Take care with log scales (graphs where the scale interval distances start large and get smaller between each interval mark). For example, what are the interval values on this log scale?
|——————|—————-|————–|————|———-|——–|——|—-|—|
1.0 x 10^-8 ———————————————————————————– 2.0 x 10^-7
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