3.3 The AS core practicals

How should you revise a core practical?

The practical paper rarely asks you to repeat a method word for word. It changes the object, the liquid, the wire or the source and expects you to adapt. So learn each practical as a pattern under the same seven headings:

• Aim: the quantity to be found, in one line.
• Apparatus: each instrument with its resolution (metre rule 1 mm, vernier calipers 0.1 mm, micrometer 0.01 mm).
• Method: what is varied, what is measured, what is kept constant, how many readings and repeats.
• Graph: the axes that give a straight line, and what the gradient or intercept means.
• Uncertainties: which measurement limits the result, and whether the error is random or systematic.
• Safety: a specific hazard and a specific precaution.
• Improvements: a change that reduces the main uncertainty, with the reason.

The AS uncertainty rules (page 3.2) apply throughout: a single reading has an uncertainty of half the resolution, repeats have half the range, and percentage uncertainty = uncertainty ÷ measured value × 100%. At AS you find the percentage uncertainty of a single quantity and say which measurement dominates; combining uncertainties belongs to Unit 6.

CP1: how do you measure the acceleration of free fall?

• Aim: determine g by timing a body falling from rest.
• Apparatus: small steel ball, electromagnet, trapdoor switch (or a light gate), electronic timer, metre rule, set square.
• Method: switching off the magnet releases the ball and starts the timer; the ball opens the trapdoor and stops it. Measure h from the bottom of the ball to the trapdoor, using the set square to keep the rule vertical. Use five or six heights over the widest range possible (for example 0.20 m to 1.20 m) and repeat each three times.
• Graph: from rest, \(h = \tfrac12 g t^2\), so h against t² is a straight line through the origin with gradient g/2. A gradient of 4.87 m s⁻² gives g = 2 × 4.87 = 9.74 m s⁻², 0.71% below 9.81 m s⁻².
• Variant: a light gate measures the speed v = (ball diameter) ÷ (time the beam is blocked) after a fall h; then v² = 2gh and the gradient of v² against h is 2g.
• Uncertainties: the magnet holds the ball for a moment after switch-off (residual magnetism), making every time slightly too long, a systematic error; reading h to ±0.5 mm and parallax at the scale.
• Safety: catch the falling steel ball in a box of sand or cloth; the magnet coil can get warm, so switch it off between drops.
• Improvements: use the smallest magnet current that holds the ball; use larger heights so the times are longer and their percentage uncertainty smaller; replace the trapdoor by two light gates.

CP2: how do you find the viscosity of a liquid?

• Aim: find the viscosity η of a liquid such as glycerol from the terminal velocity of a small sphere.
• Apparatus: tall, wide tube of the liquid, small steel balls, micrometer, three rubber bands round the tube, metre rule, stopwatch, thermometer, balance and measuring cylinder (for the densities), a magnet on a string to retrieve the balls.
• Method: measure each ball's diameter with the micrometer in several directions. Place the first band well below the surface so the ball has reached terminal velocity before timing starts. Release the ball gently on the axis of the tube and time it from A to B and from B to C: equal times confirm a constant (terminal) velocity. Repeat, and record the temperature.
• Analysis: at terminal velocity the forces balance, W = U + F, with F = 6πηrv (Stokes' law).
• Graph: with balls of several sizes, v against r² is a straight line through the origin of gradient \(2g(\rho_s - \rho_f)/9\eta\).
• Uncertainties: starting and stopping the stopwatch by eye (reaction time, parallax at the bands); the small radius, which is squared; the temperature, because viscosity falls steeply as the liquid warms.
• Safety: wipe up spills at once, as glycerol and oils make the floor slippery; clamp the tall tube so it cannot topple.
• Improvements: view the bands at eye level, or film the fall next to a scale and step through the frames; use a longer distance between bands; use a wide tube so the walls do not slow the ball; keep the liquid in a water bath at a known temperature.

Writing the weight and upthrust in terms of the ball's volume and the two densities, then solving for η:

F = 6πηrv is in the formulae list; the expression for η is not, so derive it. Stokes' law holds only for a small sphere moving slowly through the liquid in laminar flow.

CP3: how do you find the Young modulus of a wire?

• Aim: determine the Young modulus E of a metal in the form of a long wire.
• Apparatus: a wire 2–3 m long clamped at one end and passing over a pulley at the edge of the bench; mass hanger and slotted masses; a small flag of tape on the wire next to a fixed metre rule (or a vernier scale); micrometer; tape measure; safety goggles.
• Method: hang a small load first to straighten the wire and take its reading as zero. Measure the original length l from the clamp to the flag. Measure the diameter at several points and in two directions at right angles; average. Add equal loads, recording the flag position each time; then remove them to check the wire returns (it stayed elastic).
• Graph: stress = F/A against strain = Δx/l; the gradient of the straight section is E. Points that curve away at the top show the limit of proportionality has been passed, so leave them out of the gradient.
• Uncertainties: the extensions are only a few millimetres, so their percentage uncertainty is large; the diameter of about 0.4 mm read to 0.01 mm is also a few per cent; temperature changes and the wire settling in the clamp.
• Safety: goggles, because a loaded wire may snap and whip back; a box of sand or foam under the masses; keep feet clear.
• Improvements: a longer wire gives a larger extension for the same strain; a vernier scale reads extensions to 0.1 mm; a second, unloaded reference wire hung alongside (Searle's arrangement) cancels sag and temperature effects.

CP4: how do you measure the speed of sound with an oscilloscope?

• Aim: measure the speed of sound in air using v = fλ.
• Apparatus: signal generator, loudspeaker, two microphones, two-beam (dual-trace) oscilloscope, metre rule.
• Method: drive the loudspeaker at a few kilohertz. Connect one microphone to channel 1 and the other to channel 2, both in line with the speaker. Start with the microphones side by side so the traces are in phase. Slide microphone 2 away along the rule: the traces drift out of phase and come back into phase each time the separation grows by one wavelength. Record the position after each of n = 1, 2, 3 … wavelengths.
• Graph: distance moved against n is a straight line of gradient λ. Read the period from the screen (divisions × timebase) to find f, then v = fλ. Alternatively, change f and plot λ against 1/f: the gradient is v.
• Uncertainties: judging exactly where the traces are in phase; sound reflected from the bench and walls distorting the traces; the frequency dial of the generator.
• Safety: keep the sound level low and the session short to protect hearing.
• Improvements: move through many wavelengths and divide; measure f from the oscilloscope rather than the dial; use the X–Y mode, where in-phase signals give a sloping straight line that is easier to judge; work away from hard surfaces.

CP5: what sets the frequency of a vibrating string?

• Aim: investigate how the frequency of the first harmonic depends on the length l, tension T and mass per unit length μ of a string.
• Apparatus: string or wire passing over a pulley to a mass hanger (T = mg), two bridges, a vibration generator driven by a signal generator, metre rule, balance.
• Method: fix the vibrating length between the bridges. Raise the frequency slowly until the string vibrates in one loop with the largest amplitude (the first harmonic) and read f. Change one variable at a time: move a bridge to change l; add masses to change T; change the string to change μ, finding each μ by weighing a long measured length.
• Graph: for the first harmonic λ = 2l, so \(f = \dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}}\). Plot f against 1/l (gradient \(\tfrac12\sqrt{T/\mu}\)), f² against T (gradient \(1/4l^2\mu\)), or f against \(1/\sqrt{\mu}\).
• Uncertainties: deciding where the amplitude is largest, because resonance covers a range of frequencies; measuring l between the contact points of the bridges; the calibration of the generator.
• Safety: the masses fall if the string breaks, so keep feet clear and use a box underneath; wear goggles with a wire under high tension.
• Improvements: approach resonance from above and from below and average the two readings; check the frequency on an oscilloscope; use a wider range of lengths.

CP6: how do you measure a wavelength with a diffraction grating?

• Aim: determine the wavelength of laser light using a grating with a known number of lines per millimetre.
• Apparatus: laser, diffraction grating, screen, metre rule and tape measure.
• Method: set the grating at right angles to the beam and the screen parallel to the grating, a distance D of 1–2 m away. Measure the distance between the two first-order spots (2x₁), then between the two second-order spots, and so on. Halve each distance; tan θ = x/D; then nλ = d sin θ with d = 1/(lines per metre).
• Graph: sin θ against n is a straight line through the origin with gradient λ/d.
• Uncertainties: locating the centre of each spot; measuring D; the grating not being exactly perpendicular to the beam.
• Safety: never look along the beam or at its reflections; remove watches and rings and keep shiny surfaces out of the beam path; use a low-power laser and a warning sign.
• Improvements: measure across opposite orders rather than from the centre; use a larger D so the spots are further apart; use higher orders; darken the room so the spot centres are easier to see.

CP7: how do you find the resistivity of a wire?

• Aim: determine the resistivity ρ of the metal of a wire.
• Apparatus: about 1 m of thin wire taped along a metre rule, a sliding clip (crocodile clip or jockey), cell, switch, ammeter, voltmeter, micrometer.
• Method: measure the diameter at several points and in two directions; average and find A. Connect the wire in series with the cell, switch and ammeter, with the voltmeter across the length l between the fixed end and the clip. For lengths from about 0.20 m to 0.90 m, close the switch briefly, read V and I, open it again; R = V/I.
• Graph: R = ρl/A, so R against l is a straight line of gradient ρ/A; ρ = gradient × A.
• Uncertainties: the diameter, which is squared in A; contact resistance at the clip and the leads (a systematic error that gives an intercept); the wire warming, which raises its resistance.
• Safety: a thin wire carrying a large current gets hot, so keep the current small and switch off between readings.
• Improvements: use a small p.d. so the temperature stays constant; clean the wire where the clip touches it; use the gradient, not a single reading, so a constant contact resistance does not matter.

CP8: how do you find the e.m.f. and internal resistance of a cell?

• Aim: determine the e.m.f. ε and internal resistance r of a cell.
• Apparatus: the cell, variable resistor, ammeter, voltmeter, switch (a fixed protective resistor in series is useful).
• Method: connect the cell in series with the variable resistor, ammeter and switch, with the voltmeter directly across the cell terminals. Close the switch, read V and I, open it; repeat for at least six settings covering the widest range of current.
• Graph: ε = I(R + r) gives V = ε − Ir, so V against I is a straight line: intercept on the V-axis = ε, gradient = −r.
• Uncertainties: the cell warms, so its internal resistance and e.m.f. drift while current flows; the resolution of the meters at small currents.
• Safety: never short-circuit the cell; avoid rechargeable cells with very small r, which can deliver large currents and become hot.
• Improvements: switch off between readings so the cell does not heat; take readings quickly; repeat with the readings in reverse order and average.

Exam tips for 3.3

Common misconceptions

How this topic connects

The theory pages in Units 1 and 2

Each practical belongs to a topic page: free fall (1.1), viscosity (1.7), the Young modulus (1.9), progressive and stationary waves (2.1, 2.2), diffraction gratings (2.4), resistivity (2.8) and e.m.f. (2.9).

3.1 Planning and 3.2 Uncertainties and graphs

Choosing the micrometer for a wire diameter or a set square for a vertical rule is the same skill in every practical here; gradients from large triangles, half-range uncertainties and percentage uncertainty turn the results into numbers.

The A2 core practicals (Unit 6)

The same seven-heading approach carries on to Core Practicals 9–16, where uncertainties are combined and logarithmic graphs are used.

Key equations

Check your understanding

Specification checklist

• (11) I can describe the free-fall experiment, plot h against t² and find g from the gradient.
• (26) I can describe the falling-ball method, explain why timing starts below the surface and calculate a viscosity from a terminal velocity.
• (31) I can describe how to measure the Young modulus of a long wire and find it from a stress–strain graph.
• (38) I can describe how two microphones and a two-beam oscilloscope give the wavelength and speed of sound.
• (43) I can describe how the first-harmonic frequency of a string varies with length, tension and mass per unit length, and choose the graph that tests it.
• (52) I can describe how to find a wavelength with a laser and a diffraction grating, including working safely with lasers.
• (72) I can describe how to measure the resistivity of a wire and find it from a graph of resistance against length.
• (78) I can describe how to find the e.m.f. and internal resistance of a cell from a graph of terminal p.d. against current.
• (all) For each practical I can name the main source of uncertainty, a specific safety precaution and an improvement with a reason.