Your handy checklist for practical work
The experiment
1 Taking readings
• Repeat all readings and average. Show all readings.
If timing, measure the period of at least fi ve
oscillations each time. Try for ten if time allows.
Remember, timing uncertainty is 0.1 s with a
hand-held stopclock.
• When taking a set of readings make sure that they
cover the whole range of the readings fairly evenly.
2 The table of results
• Try to arrange for a single table that shows all
readings, even the fi rst, and their averages;
• Use the correct units and quantities for each column.
• Use the same precision (i.e. number of signifi cant
fi gures) for every reading in a particular column.
• Choose a sensible number of signifi cant fi gures for
your readings (usually 2 or 3).
3 The graph
• Label each axis of the graph with both quantity
and unit.
• Make sure your graph occupies at least 5 × 7 squares
(i.e. half the paper) with your plotted points.
• Ask yourself whether the origin should be plotted.
• Do not use an awkward scale, i.e. 1 square =
3, 7, 9 units.
• Plot points neatly, with no large blobs, or crosses.
Circle your points if you plot them as dots.
• Th e line you draw should be clear, thin and even.
4 Measuring the slope
• Use at least half of the drawn straight line.
• Show the coordinates that you use for the slope or
the values of the sides of the triangle that you use.
• Give your answer to 1 or 2 signifi cant fi gures as
appropriate. Don’t forget units.
5 The straight-line formula
for a graph, y = mx + c
• If y 2 = ax 3 then plot y 2 against x 3 and the slope is a.
• If y = ax n then ln ( y) = n ln (x) + ln (a). Plot log10 ( y) or
ln ( y) against log10 (x) or ln (x) and the slope is n.
• If y = a ekx then ln ( y) = kx + ln (a). Plot ln ( y) against x
and the slope is k.
• On tables and graphs the label is ln ( y/m) or log10
( y/m) to show the unit of y as metres,
• Check that you know how to use logs.
6 Checking relationships
When checking, state what should be constant,
perform the calculation and then state whether the
constant was found and whether the relationship is
verifi ed. You may want to refer to the uncertainty.
• y proportional to x y
x should be constant.
y • proportional to 1x
y × x should be constant.
• y proportional to ex y decreases by same factor if x
increases by equal amounts.
Uncertainties
Graphs can be plotted with each point having error
bars on the x-axis and the y-axis to show the expected
absolute uncertainties. Th e worst acceptable line should
be drawn as a dotted line or labelled as worst acceptable
line; it should be the steepest or shallowest line that
goes through the error bars of all the points. If this is
not possible because of one point that point may be
anomalous. Check it – it may be wrong.
Causes of uncertainty in simple
measurements
• Lengths – rulers may have battered ends, or the
zero may not actually be at the end. To avoid
parallax uncertainty, you must view any reading
from directly above. Th e likely uncertainty is ±1 mm
or perhaps ± 0.3 mm.
• Times – stopwatches measure to ± 0.01 s but you
can’t press them that accurately. Th e likely uncertainty
is ± 0.1 s.
• Meters (e.g. ammeter) – uncertainty is the smallest
scale reading, or any fluctuation.
• Graphs – uncertainty in gradient is difference between
gradient of best fi t line and worst acceptable line.
Use similar idea to fi nd uncertainty in y-intercept.
Combining uncertainties
• Th ere are absolute uncertainties and percentage
uncertainties – know the diff erence.
• When adding or subtracting quantities, add absolute
uncertainties.
• When multiplying or dividing quantities, add
percentage uncertainties to get the percentage
uncertainty in the answer.
Describing and improving
an experiment
• State every reading you will take. Do not say, ‘Take the
readings as before.’
• Make clear what is kept constant and what is changed.
• Give sensible values for quantities, particularly those
that are changed. Use your common sense.
• Have at least fi ve sets of readings as a variable changes.
• Say that you will repeat and average each reading.
• Say what the axes will be for a straight-line graph.
Never just say, ‘plot a graph’.
• Set out your account clearly and logically; use any
suggested format if you think it helps.
• Plan your account briefl y before you start writing.
1 Taking readings
• Repeat all readings and average. Show all readings.
If timing, measure the period of at least fi ve
oscillations each time. Try for ten if time allows.
Remember, timing uncertainty is 0.1 s with a
hand-held stopclock.
• When taking a set of readings make sure that they
cover the whole range of the readings fairly evenly.
2 The table of results
• Try to arrange for a single table that shows all
readings, even the fi rst, and their averages;
• Use the correct units and quantities for each column.
• Use the same precision (i.e. number of signifi cant
fi gures) for every reading in a particular column.
• Choose a sensible number of signifi cant fi gures for
your readings (usually 2 or 3).
3 The graph
• Label each axis of the graph with both quantity
and unit.
• Make sure your graph occupies at least 5 × 7 squares
(i.e. half the paper) with your plotted points.
• Ask yourself whether the origin should be plotted.
• Do not use an awkward scale, i.e. 1 square =
3, 7, 9 units.
• Plot points neatly, with no large blobs, or crosses.
Circle your points if you plot them as dots.
• Th e line you draw should be clear, thin and even.
4 Measuring the slope
• Use at least half of the drawn straight line.
• Show the coordinates that you use for the slope or
the values of the sides of the triangle that you use.
• Give your answer to 1 or 2 signifi cant fi gures as
appropriate. Don’t forget units.
5 The straight-line formula
for a graph, y = mx + c
• If y 2 = ax 3 then plot y 2 against x 3 and the slope is a.
• If y = ax n then ln ( y) = n ln (x) + ln (a). Plot log10 ( y) or
ln ( y) against log10 (x) or ln (x) and the slope is n.
• If y = a ekx then ln ( y) = kx + ln (a). Plot ln ( y) against x
and the slope is k.
• On tables and graphs the label is ln ( y/m) or log10
( y/m) to show the unit of y as metres,
• Check that you know how to use logs.
6 Checking relationships
When checking, state what should be constant,
perform the calculation and then state whether the
constant was found and whether the relationship is
verifi ed. You may want to refer to the uncertainty.
• y proportional to x y
x should be constant.
y • proportional to 1x
y × x should be constant.
• y proportional to ex y decreases by same factor if x
increases by equal amounts.
Uncertainties
Graphs can be plotted with each point having error
bars on the x-axis and the y-axis to show the expected
absolute uncertainties. Th e worst acceptable line should
be drawn as a dotted line or labelled as worst acceptable
line; it should be the steepest or shallowest line that
goes through the error bars of all the points. If this is
not possible because of one point that point may be
anomalous. Check it – it may be wrong.
Causes of uncertainty in simple
measurements
• Lengths – rulers may have battered ends, or the
zero may not actually be at the end. To avoid
parallax uncertainty, you must view any reading
from directly above. Th e likely uncertainty is ±1 mm
or perhaps ± 0.3 mm.
• Times – stopwatches measure to ± 0.01 s but you
can’t press them that accurately. Th e likely uncertainty
is ± 0.1 s.
• Meters (e.g. ammeter) – uncertainty is the smallest
scale reading, or any fluctuation.
• Graphs – uncertainty in gradient is difference between
gradient of best fi t line and worst acceptable line.
Use similar idea to fi nd uncertainty in y-intercept.
Combining uncertainties
• Th ere are absolute uncertainties and percentage
uncertainties – know the diff erence.
• When adding or subtracting quantities, add absolute
uncertainties.
• When multiplying or dividing quantities, add
percentage uncertainties to get the percentage
uncertainty in the answer.
Describing and improving
an experiment
• State every reading you will take. Do not say, ‘Take the
readings as before.’
• Make clear what is kept constant and what is changed.
• Give sensible values for quantities, particularly those
that are changed. Use your common sense.
• Have at least fi ve sets of readings as a variable changes.
• Say that you will repeat and average each reading.
• Say what the axes will be for a straight-line graph.
Never just say, ‘plot a graph’.
• Set out your account clearly and logically; use any
suggested format if you think it helps.
• Plan your account briefl y before you start writing.
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