1.2.11Development of Practical Skills in Physics

Methods to Increase Accuracy

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Lesson summary

1.2.11 Methods to Increase Accuracy — OCR A Level Physics A notes: Select and justify practical techniques that reduce percentage uncertainty and systematic error in a measurement.Accuracy improves when you reduce the largest percentage uncertainty and remove systematic errors.

Measure multiples
Use larger distances or longer times
Use a larger signal
Choose the instrument with suitable resolution
Repeat and average
Use a graph

Section 1 of 9Where the improvement comes from

Accuracy improves when you reduce the largest percentage uncertainty and remove systematic errors.

Where the improvement comes from

The first step is always to calculate the percentage uncertainty for each measurement (see 1.2.2) and find out which dominates.

A 1 mm uncertainty in a 20 mm length is 5%, much worse than a 0.01 g uncertainty on a 50 g mass (0.02%).

Improving the mass measurement would be pointless; the length is the weak link.

The techniques below fall into three groups: make the measured quantity larger relative to its uncertainty, reduce random scatter, and eliminate systematic effects.

Section 2 of 9Make the measured quantity larger

1Measure multiples

Measure multiples time 20 oscillations instead of one; measure the thickness of a stack of 50 sheets; measure the distance across 10 fringes and divide. The absolute uncertainty stays the same but is shared among many, so the percentage uncertainty falls.

2Use larger distances or longer times

Use larger distances or longer times a free fall from 2 m takes 0.64 s, giving a reaction-time percentage of about 30%; a trolley run lasting 4 s has about 5%.

3Use a larger signal

Use a larger signal a bigger temperature rise (by heating for longer, within limits) reduces the thermometer's percentage uncertainty.

4Choose the instrument with suitable resolution

Choose the instrument with suitable resolution micrometer for wire diameter, vernier for a tube.

Section 3 of 9Reduce random scatter

Reduce random scatter

Repeat and average

Repeat and average the uncertainty in a mean of n readings is about range/n or smaller than for a single reading. Three repeats are a minimum; more if the spread is large.

Use a graph

Use a graph plotting many pairs and drawing a best-fit line averages the scatter, so the gradient is more reliable than a single calculation.

Use electronic timing

Use electronic timing light gates and loggers remove reaction time.

Use a wide range of values

, and take readings at regular intervals so any trend is clear.

Use a fiducial marker

Use a fiducial marker and stop-start at the centre of an oscillation, where the speed is greatest and the timing decision sharpest.

Section 4 of 9Remove systematic errors

Remove systematic errors

Check for zero error

Check for zero error before each experiment and correct every reading.

Calibrate

Calibrate meters and thermometers against known standards, such as an ice and boiling water check at 0 °C and 100 °C.

Avoid parallax

Avoid parallax by viewing at right angles, using a mirror scale or placing a set square beside the pointer.

Control variables

Control variables keep temperature constant in resistance experiments (use low currents so the wire does not heat); keep the same release height; ensure the pendulum swings through small angles, usually under 10°.

Reduce energy losses

Reduce energy losses with lagging, lids, and stirring to even out temperatures.

Compare methods

Compare methods finding a quantity by two different techniques exposes unsuspected systematic effects.

Section 5 of 9Choosing and justifying a method

An examiner wants you to link the technique to the cause: “Timing 20 oscillations rather than one reduces the percentage uncertainty due to reaction time from 12% to 0.6%.” Always give an estimate of the improvement.

Choosing and justifying a method

Remember that some changes involve trade-offs, such as a longer heating time giving a larger temperature rise but more heat lost to the room.

Final reports should say what was done, and how well it worked, as in Evaluating Results and Drawing Conclusions (1.2.4).

Section 6 of 9A short worked comparison of strategies

Suppose a student wants the speed of a trolley over a 1.00 m track.

Using a hand stopwatch on a 0.5 s run gives about 40% uncertainty from reaction time alone.

Increasing the track length so that the run lasts 3 s lowers this to about 7%.

Replacing the stopwatch with two light gates and a timer of resolution 1 ms gives a timing uncertainty well under 1%, so the length measurement (a metre rule, ±1 mm on 1.000 m, 0.1%) now matters as much as the timing.

Repeating the run five times and averaging then tidies up the small random scatter left.

Notice the order of attack: first the largest uncertainty, then the next, and only then the refinements.

A final check for systematic effects, such as a track that is not level or friction that varies along its length, completes the plan.

Write each of these steps with a number to show how much it helps.

Equally, remember that no technique can improve a result beyond the limit set by the weakest link. Once every percentage is below about 1%, further effort is better spent on checking that the method measures what it claims to measure, which is the idea of validity from the evaluation topic.

Section 7 of 9Worked examples

A student times one oscillation of a pendulum as 1.2 s with a reaction uncertainty of 0.2 s. They now time 25 oscillations and get 30.1 s with the same 0.2 s uncertainty. Compare the percentage uncertainties and find the new period.
A wire's diameter is 0.50 mm. Compare the percentage uncertainty using a rule (±0.5 mm) and a micrometer (±0.01 mm). The wire is also measured at 5 places along its length.
In a resistance experiment the current through a wire is 1.5 A and the wire warms up so R increases. Suggest and justify a change to improve accuracy.

Section 8 of 9Key terms

Term	Meaning
Percentage uncertainty	Uncertainty as a percentage of the measured value; used to compare measurements.
Fiducial marker	A fixed reference mark for judging the start or stop of a timing.
Calibration	Checking an instrument against a known standard.
Lagging	Insulating material that reduces heat loss.
Control variable	A quantity kept constant to make a test fair.
Best-fit line	A line through plotted data that averages out the scatter.

Section 9 of 9Exam technique

Suggesting to “repeat the experiment” to remove a systematic error. Repeating does not remove it.

Choosing an improvement without stating which uncertainty it reduces.

Saying “use more accurate instruments” without naming an instrument or its resolution.

Timing a larger number of oscillations but then forgetting to divide by that number.

Making the improvement in the quantity that already has the smallest percentage uncertainty.