Lesson 17: Required Practicals

A-level physics is an experimental science — the required practicals are examined in every paper, not just as 'describe the experiment' but as data analysis, uncertainty evaluation, and experimental design. This lesson systematises the required practicals (AQA's 12, Edexcel's core practicals, OCR's PAGs) into methods, graphs, and error analysis — plus the general skills: linearisation, percentage uncertainties, and distinguishing random from systematic errors. Learn the patterns and any practical becomes familiar.

The Practical Canon — Mechanics

1. Measuring g by free fall (Lesson 1): electromagnet + trapdoor/timer; plot h vs t², gradient g/2. 2. Young's modulus of a wire: clamp wire, add masses, measure extension (travelling microscope or marker + ruler); stress = F/A (A from micrometer diameter), strain = ΔL/L; plot stress vs strain — gradient = E (linear region only). Copper E ≈ 130 GPa, steel ≈ 200 GPa. Control: long thin wire (large ΔL, small %), avoid exceeding elastic limit (graph curves — the invalidating point). 3. Viscosity by falling ball: time a ball bearing through oil between marks; terminal velocity from Stokes' law, v_t = 2r²g(ρ_ball − ρ_fluid)/9η — or simply compare viscosities relatively.

Common mechanics threads: timing (light gates > stopwatch — human reaction ±0.2 s dominates short timings; repeat and average), length measurement (parallax — eye perpendicular; use set squares), and zero errors (calipers reading 0.02 mm closed — subtract). Every mechanics practical plots a linearised graph: identify y = mx + c form, state what gradient and intercept give. Examiners ask 'what graph?' expecting the linearised choice with justification.

Uncertainty propagation recap: for y = ab/c: Δy/y = Δa/a + Δb/b + Δc/c; for y = aⁿ: nΔa/a; for y = a + b: absolute uncertainties add. Worked: E = FL/(AΔL) with F = 20 ± 0.1 N, L = 2.00 ± 0.01 m, d = 0.50 ± 0.02 mm (A = πd²/4), ΔL = 3.0 ± 0.2 mm. % errors: F 0.5%, L 0.5%, d → A: 2 × (0.02/0.50) = 8%, ΔL 6.7%. Total ≈ 15.7% — diameter and extension dominate (small absolute measurements). Improvements target the largest % error: longer wire (bigger ΔL); a thinner wire gives bigger extension but poorer diameter precision — the trade-off is the experiment's design tension.

The Practical Canon — Electricity and Waves

4. Resistivity of a wire (Lesson 5): R vs L, gradient ρ/A. 5. Internal resistance and EMF (Lesson 5): V vs I, intercept ε, gradient −r. 6. Capacitor discharge: V vs t → ln V vs t, gradient −1/RC (data logger or voltmeter + stopwatch; large C and R for slow discharge). 7. Stationary waves on a string (Lesson 6): f² vs T or direct v = fλ. 8. Double-slit interference (Lesson 7): w vs D, gradient λ/d. 9. Diffraction grating: θ_n measurements, λ = d sinθ_n/n — average over orders.

Electricity practicals share: contact resistance (clean crocodile clips, tight connections — a loose clip is a phantom resistor), temperature drift (resistive heating changes R — use low currents, switch off between readings), and meter limitations (voltmeter draws current — use high-impedance digital meters; ammeter has small resistance — account in precise work). Waves practicals share: measuring across many fringes/wavelengths (÷N reduces random error), and the small-angle or resonance conditions stated explicitly.

Data-logger vs manual: loggers give dense data (capacitor discharge curves, motion sensors) but hide the measurement (know what the sensor actually measures — a motion sensor times ultrasound echoes); manual methods teach uncertainty honesty. A-level accepts both; exam questions probe understanding either way ('why does the data-logger trace curve at the start?' — sensor response time / initial transients).

The Practical Canon — Fields, Thermal, Nuclear, Quantum

10. Magnetic flux density with a Hall probe or current balance: B = F/(IL) — measure force on a wire in a magnet assembly (top-pan balance reads the reaction force — Newton's third law as an instrument!). Vary I, plot F vs I: gradient = BL. 11. Specific heat capacity / latent heat (Lesson 13): electrical method, cooling corrections. 12. Inverse-square law for gamma radiation: GM tube count rate vs distance — plot ln C vs ln r: gradient −2 (background subtracted FIRST — the commonest error). Or light: lux meter vs distance.

13. Photoelectric/LED Planck constant (Lesson 8): LED threshold voltages vs frequency — plot V vs f: gradient h/e. 14. Boyle's law (Lesson 14): p vs 1/V. Each practical follows the template: aim → diagram → measurements (with instruments and precisions) → linearised graph (axes, gradient/intercept meanings) → uncertainties → improvements. Memorise the template, not twelve scripts — the template generates any script.

Safety (examinable!): lasers (never look into beam, terminate beam, warning signs); radioactive sources (ALARP: minimise time, maximise distance, shielding; tongs; no hand-to-mouth); high voltages (Van de Graaff: discharge before touching); projectiles (safety screens, clear range). Risk assessments name hazard → risk → control — three columns, specific controls (not 'be careful').

Uncertainties — The Full Machinery

Reading uncertainty: analogue ± half the smallest division (ruler ±0.5 mm); digital ± the last digit (a 0.01 s timer reads ±0.01 s… plus systematic switch delays). Repeated readings: mean ± (range/2) — use the spread, not the instrument precision, when scatter dominates (timing a pendulum by hand: scatter ±0.2 s >> stopwatch ±0.01 s). Percentage uncertainty = (absolute/mean) × 100%.

Combining: multiplications/divisions — add %; powers — multiply % by the power; additions/subtractions — add absolutes (then convert). Worked full example (Young's modulus above): E = 4FL/(πd²ΔL) with F = 20 N, L = 2.00 m, d = 5.0×10⁻⁴ m, ΔL = 3.0×10⁻³ m. A = π(2.5×10⁻⁴)² = 1.96×10⁻⁷ m². E = 20(2.00)/(1.96×10⁻⁷ × 3.0×10⁻³) ≈ 6.8×10¹⁰ Pa = 68 GPa. % uncertainty ≈ 15.7% → E = (68 ± 11) GPa — low for copper (130 GPa), and the evaluation discusses the discrepancy honestly (alloy wire? elastic limit exceeded? zero error?) rather than hiding it. Lesson: a correctly uncertain answer that flags a discrepancy beats a falsely precise one.

Error bars and best-fit lines: plot points with error bars (x and y where significant); draw the line of best fit AND the steepest/shallowest plausible lines — gradient uncertainty from their spread. Worked: a free-fall plot of h against t² gives best-fit gradient 4.92 m/s²; the steepest line through all error bars has gradient 5.08, the shallowest 4.74. g = 2 × gradient = 9.84 m/s², range 9.48–10.16, so quote g = 9.8 ± 0.3 m/s² (about ±3.5%) — centred on the best fit, with the half-range as uncertainty. A point far off the line: keep it (note as anomaly) or repeat — never silently delete. 'Anomalous result' needs justification (identified procedural slip), not just distance from the line.

Designing Experiments — The Synoptic Skill

Exam 'design' questions give an aim and ask for method: structure as (1) diagram with labels; (2) independent variable (what you change, how, range); (3) dependent variable (what you measure, with what instrument, precision); (4) control variables (kept constant, how); (5) procedure stepwise (including repeats); (6) analysis: the graph, gradient/intercept meanings; (7) safety; (8) uncertainties and improvements. Eight headings, full marks — practice this skeleton until automatic.

Worked design: 'Determine the specific latent heat of vaporisation of water electrically.' Diagram: insulated beaker on scales, immersion heater (known V, I), thermometer. IV: heating time (energy input VIt). DV: mass loss (scales, ±0.1 g). Controls: lagging, constant V/I. Procedure: bring to boiling first (so the measured loss is vaporisation at 100 °C, not warming), start timing, record mass every 60 s for 10 min; plot mass lost vs energy input: gradient = 1/L (from m_lost = VIt/L). Safety: boiling water, electrical safety near water (RCD, dry hands). Uncertainties: mass ±0.1 g over ~10 g loss = 1%; V, I ~1%; heat losses to air (systematic — lagging, correction via measuring the cooling-only baseline rate of mass loss with the heater off… in practice, droplets condensing back and splashing are named too).

The meta-skill: every practical is variables → graph → gradient. If you can name the linearised equation, you can design the experiment. y = mx + c is the most powerful sentence in experimental physics — it turns every law into a straight line and every straight line into a measurement.

Paper 5 Thinking — Planning and Analysis

A-level's practical papers (AQA Paper 3 sections, OCR PAG reporting, CIE-style Paper 5) reward a distinctive style: plan before touching apparatus — state the theory equation you will linearise, predict the graph, and pre-decide how the gradient becomes the answer. Then analyse like a sceptic: maximum and minimum gradient lines, percentage uncertainty in the FINAL quantity (not the raw readings), and a conclusion that compares with the accepted value inside or outside the uncertainty range. Two habits distinguish top scripts: (1) every measured quantity carries its instrument and resolution ('length 1.850 m, metre rule, ±0.001 m'); (2) every improvement targets the LARGEST percentage uncertainty identified — generic 'repeat and average' earns nothing unless tied to a named random error.

Common mistakes

• Confusing precision with accuracy: tiny scatter (precise) around the wrong value (inaccurate — systematic error) is still wrong; repeats fix precision, calibration fixes accuracy.
• Quoting the instrument's resolution as the uncertainty when the scatter is bigger — the observed spread rules. Hand-timed data has ±0.2 s whatever the stopwatch display says.
• Forgetting background subtraction in counting experiments (gamma inverse-square) — the background inflates low count rates most, bending the ln–ln graph exactly where students then 'discover' anomalies.
• Lines forced through the origin when theory doesn't demand it (V vs I for internal resistance HAS an intercept — that's ε!). Forcing zero destroys the physics.
• Vague improvements: 'use a better ruler' scores nothing; 'measure the extension with a travelling microscope (±0.01 mm) instead of a ruler (±0.5 mm), cutting the ΔL uncertainty from 17% to under 1%' scores everything.

Exam Experience — a practical-analysis set

(a) A steel wire of length 1.85 m and diameter 0.46 mm extends by 1.6 mm under a load of 25 N. Calculate the Young modulus. [4] (b) The measurements carry uncertainties: d ±0.01 mm, extension ±0.1 mm, load ±0.5 N, length ±0.01 m. Calculate the total percentage uncertainty in the Young modulus and quote the final result. [4] (c) State the largest single contribution to the uncertainty and one improvement that targets it. [2] (d) A separate free-fall graph of h against t² has best-fit gradient 4.92 m/s²; steepest and shallowest acceptable lines give 5.08 and 4.74 m/s². Quote the measured value of g with its uncertainty. [3]

Mark scheme (a) A = π(0.23×10⁻³)² = 1.66×10⁻⁷ m² [1]; stress = F/A = 25/1.66×10⁻⁷ = 1.50×10⁸ Pa [1]; strain = ΔL/L = 1.6×10⁻³/1.85 = 8.6×10⁻⁴ [1]; E = stress/strain ≈ 1.74×10¹¹ Pa. [1] (b) Contributions: d → 2 × (0.01/0.46) = 4.3%; extension 0.1/1.6 = 6.3%; load 0.5/25 = 2.0%; length 0.01/1.85 = 0.5% [2]; total ≈ 13% [1]; E = (1.7 ± 0.2)×10¹¹ Pa. [1] (c) Extension (6.3%) is largest [1]; measure it with a travelling microscope or a longer wire giving greater extension at the same load — must name a specific instrument/method, not 'measure more carefully'. [1] (d) g = 2 × 4.92 = 9.84 m/s² [1]; half-range = (2 × 5.08 − 2 × 4.74)/2 = 0.34 → g = 9.8 ± 0.3 m/s² [2]. Consistent with 9.81 — that concluding sentence completes the analysis.