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A-level Physics required practicals

Young modulus by a simple method

AQA 3.4.2.2 · RP4

A-level Physics (7408) · Required practical 4 — method, techniques, safety, analysis and uncertainty. Includes errors documented in examiner reports.

Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works

Determine the Young modulus of a wire from its dimensions and its elastic extension under known tensile forces.

Apparatus

  • Long test wire secured to a rigid support, with a reference wire or fixed scale
  • Micrometer screw gauge
  • Metre rule or tape measure
  • Vernier scale, travelling microscope or pointer-and-scale arrangement for extension
  • Mass hanger, slotted masses and a safety tray
  • Eye protection

Apparatus & techniques (AT)

AT a · analogue measurement

A long rule or tape measures the original wire length, and an analogue extension scale supplies displacement readings.

AT c · accuracy methods

A preload, repeated diameter readings and a differential reference improve the accuracy of the small-strain measurement.

AT e · calipers/micrometers

A micrometer measures the wire diameter at multiple positions and orientations before area is calculated.

Safety

Hazard

The wire can snap under tension and recoil.

Control

Wear eye protection, inspect the wire, use modest loads and keep faces out of its line.

Hazard

Slotted masses can fall.

Control

Place a tray beneath the hanger, keep feet clear and add or remove masses only when the system is steady.

Method

  1. 1Apply a small preload to straighten the wire, then measure the original test length between the fixed reference points.
  2. 2Use the micrometer ratchet to measure the diameter at several positions and in two perpendicular directions; calculate a mean diameter.
  3. 3Record the extension reference reading, add known masses in equal steps and allow oscillations to settle before recording each new reading.
  4. 4Keep the load below the elastic limit and, where time permits, unload in steps to check that the wire returns to its original length.
  5. 5Convert mass to force, subtract the reference reading to obtain extension, and plot force against extension over the linear region.

CPAC focus (editorial)

This is an editorial study focus, not an AQA mapping of fixed CPAC competencies to this practical.

  • CPAC 2: Editorial focus: choose a safe elastic load range and measuring instruments suited to a long length and small diameter.
  • CPAC 3: Editorial focus: control falling-load and snapping-wire hazards throughout loading and unloading.
  • CPAC 4: Editorial focus: record repeat diameter, force and extension data with enough points to identify the linear region.
  • CPAC 5: Editorial focus: obtain E from a graph gradient and propagate the length, gradient and squared-diameter uncertainties.

Variables

Independent

Tensile force applied to the wire

Dependent

Extension of the wire

Control

  • The same wire and original measured length
  • Wire temperature and loading history
  • The same extension reference and reading method

Results & processing

  • Calculate cross-sectional area from A = pi d squared / 4 and use the force-extension gradient k = F/delta L.
  • Calculate E = kL/A, equivalently E = FL/(A delta L), and give the unit Pa.
  • Use loading and unloading behaviour to identify the linear elastic region; exclude points only with a stated physical or measurement reason.

Analysis skills

  • Use the force-extension graph gradient with E = gradient x L / A.
  • Calculate area from repeated diameter measurements and identify the linear elastic region from loading and unloading data.

Uncertainty

Sources

  • Micrometer resolution, zero error and real variation in wire diameter
  • Extension-scale resolution, parallax and movement of the support or reference
  • Temperature changes and incomplete settling after a load is added

Calculations

  • For E = kL/A and A proportional to d squared, add percentage uncertainty in k and L to twice the percentage uncertainty in d.
  • Obtain uncertainty in k from maximum and minimum acceptable force-extension gradients through all error bars.

Interpretation

  • The largest percentage contribution often comes from diameter because it is small and its uncertainty is doubled in area.
  • Curvature or failure to retrace on unloading may indicate departure from elastic behaviour rather than random scatter.

Exam angles

  • Adapt the dimension measurements correctly when the sample is a strip rather than a circular wire.
  • Calculate Young modulus from a force-extension gradient and state the unit Pa.
  • Identify the largest uncertainty contribution and test whether the loading remained elastic.

Where students lose marks

Adapting the method to a strip but measuring only one cross-sectional dimension.

Fix: Measure every dimension needed for the relevant area formula and repeat each small dimension across the sample.

  • Examiner report: P3-22 · PDF p. 4

Using the loaded wire length instead of the original measured length in E = FL/(A delta L).

Fix: Measure and label the original gauge length before the loading sequence begins.

Adding the percentage uncertainty in diameter only once when calculating area.

Fix: Because A is proportional to d squared, the percentage uncertainty contribution from diameter is doubled.

Improve the method

  • Use a long wire and a sensitive differential extension reading so extension is large relative to the scale resolution.
  • Measure diameter at several positions and rotations with the ratchet to expose taper or non-circular cross-section.
  • Use a reference wire or nearby fixed scale to reduce the effect of support movement and monitor loading and unloading for elastic return.

Source references

  • Specification: PSpec 3.4.2.2 · PDF p. 27

Try it — exam-style

Hard
ORIGINAL

A wire has L = (2.000 +/- 0.005) m and mean diameter d = (0.400 +/- 0.005) mm. The force-extension gradient is (12.6 +/- 0.3) kN m−1. Calculate E = gradient x L / A, where A = pi d2 / 4, and its percentage and absolute uncertainties.

[6 marks]

Total for this question: 6

Medium
ORIGINAL

State two observations that would show the wire has been loaded beyond the range suitable for finding Young modulus from one straight-line gradient.

[2 marks]

Total for this question: 2

Questions are written in the style of past AQA papers — never copied from them.

Drill it properly

AQA 7408 specification coverage

Materials, stress, strain and every linked 7408 specification point.

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