# AS physics unit 3 revision notes (prt 4 - uncertainty)

Part 4 and Final!

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Guidance notes on experimental work.
Section 1 ­ Treatment of uncertainties in Physics at AS and A2 level
Preamble
One of the main aims of the practical work undertaken in GCE Physics is for candidates to
develop a feeling for uncertainty in scientific data. Some of the treatment that follows may
appear daunting. That is not the intention. The estimates of uncertainties that are required in
this specification are more in the nature of educated guesses than statistically sound
calculations. It is the intention that candidates be introduced early in the course to estimating
uncertainties so that by the time their work is assessed, they have a relaxed attitude to it. The
sections in PH1 on density determinations and resistivity are ideal for this.
Definitions
Uncertainty
Uncertainty in measurements is unavoidable and estimates the range within which the answer
is likely to lie. This is usually expressed as an absolute value, but can be given as a
percentage.
The normal way of expressing a measurement x0, with its uncertainty, u, is x0 ± u. This means
that the true value of the measurement is likely to lie in the range x0 - u to x0 + u.
Note: The term "error" is used in many textbooks instead of uncertainty. This term implies
that something has gone wrong and is therefore best avoided.
Uncertainties can be split up into two different categories:
- Random uncertainties ­ These occur in any measured quantity. The uncertainty of
each reading cannot be reduced by repeat measurement but the more measurements
which are taken, the closer the mean value of the measurements is likely to be to the
"true" value of the quantity. Taking repeat readings is therefore a way of reducing the
effect of random uncertainties.
- Systematic uncertainties ­ These can be due to a fault in the equipment, or design of
the experiment e.g. possible zero error such as not taking into account the resistance
of the leads when measuring the resistance of an electrical component or use of a ruler
at a different temperature from the one at which it is calibrated. The effect of these
cannot be reduced by taking repeat readings. If a systematic uncertainty is suspected,
it must be tackled either by a redesign of the experimental technique or theoretical
analysis. An example of this sort of uncertainty, the origin of which remains
mysterious, is in the determination of stellar distances by parallax. The differences
between the distances, as determined by different observatories, often exceeds the
standard uncertainties by a large margin.
Percentage uncertainty
This is the absolute uncertainty expressed as a percentage of the best estimate of the true
value of the quantity.
Resolution
This is the smallest quantity to which an instrument can measure

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Mistake
This is the misreading of a scale or faulty equipment.
Suspect results
These are results that lie well outside the normal range e.g. points well away from a line or
curve of best fit. They often arise from mistakes in measurement. These should be recorded
and reason for discarding noted by the candidate.
How is the uncertainty in the measurement of a quantity estimated?
1. Estimation of uncertainty using the spread of repeat readings.…read more

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Estimation of uncertainty from a single reading
Sometimes there may only be a single reading. Sometimes all the readings may be
identical. Clearly it cannot be therefore assumed that there is zero uncertainty in the
With analogue instruments, it is not expected that interpolated readings will be taken
between divisions (this is clearly not possible with digital instrument anyway).…read more

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The period of oscillation of a Pendulum/Spring
The resolution of a stop watch, used for measuring a period, is usually 0.01s. Reaction time
would increase the uncertainty and, although in making measurements on oscillating
quantities it is possible to anticipate, the uncertainty derived from repeat readings is likely to
be of the order of 0.1 s. To increase accuracy, often 10 (or 20) oscillations are measured. The
absolute error in the period [i.e.…read more

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Determining the uncertainties in derived quantities.
Please note that candidates entered for AS award will now be required to combine
percentage uncertainties.
Very frequently in Physics, the values of two or more quantities are measured and then these
are combined to determine another quantity; e.g. the density of a material is determined using
the equation:
m
=
V
To do this the mass, m, and the volume, V, are first measured.…read more

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So T2 = 961 ± 4%.
4% × 961 = 40 (to 1.s.f)
So the period is expressed as T = 960 ± 40 s.
-
Note: x 1 is the same as 1/x. So the percentage uncertainty in 1/x is the same as that in x.
Can you see why we ignore the - sign?
Note: the percentage uncertainty in x is half the percentage uncertainty in x.
3. Multiplying by a constant
In this case the percentage uncertainty is unchanged.…read more

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Notes for purists:
1. When working at a high academic level, where many repeat measurements are taken,
scientists often use "standard error" , a.k.a. "standard uncertainty".…read more

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GRAPHS [derivation of uncertainties from graphs is only expected in A2]
The following remarks apply to linear graphs:
The points should be plotted with error bars. These should be centred on the plotted point and
have a length equal to ymax - ymin [for uncertainties in the y values of the points]. If identical
results are obtained the precision of the instrument could be used. If the error bars are too
small to plot this should be stated.…read more

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Section 2 ­ Ideas for practical work
Prac Context
Density of regular solids [cuboids, cylinders] Use of metre rule, callipers, micrometer,
Identification of material using density. balance
Initial work on uncertainties
Density of liquids and irregular solids Use of measuring cylinders
Weighing a rule by balancing a loaded rule Use of P of M
Acceleration of a trolley on a ramp [lots of Use of equations of motion ­ graphs to
variants here] determine acceleration
Determination of g by simple pendulum N.B.…read more

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Section 3 ­ Experimental techniques
The following is a selection of experimental techniques which it is anticipated that candidates
will acquire during their AS and A2 studies. It is not exhaustive, but is intended to provide
some guidance into the expectations of the PH3 and PH6 experimental tasks.
Measuring instruments
The use of the following in the context of individual experiments:
· micrometers and callipers. These may be analogue or digital.…read more