6.3 The A2 core practicals

How should you revise the A2 core practicals?

The A2 practical paper changes something in these experiments (a different source, gas or sensor) and asks you to plan, analyse and evaluate. Learn each as a pattern: equation, straight-line graph (often a log graph), limiting measurement. Use the seven AS headings: aim; apparatus with resolutions; method (varied, measured, controlled, range); graph and its gradient or intercept; uncertainties as one percentage; specific safety; an improvement with its reason.

CP9 and CP10: how do you test force, momentum and collisions?

CP9: force and change of momentum

Aim: show that the resultant force equals the rate of change of momentum, F = Δp/Δt, or that the impulse FΔt equals Δp.

Method A (constant force). A trolley on a runway tilted just enough to cancel friction (it rolls at constant speed when pushed) is pulled by a string over a pulley to a hanging mass. A card on the trolley passes through two light gates; the logger gives the speed at each and the time between. The hanging weight accelerates the trolley and the hanging mass, so use their total mass in Δp. Move masses from trolley to hanger to change the force at constant total mass. Graph: F against Δp/Δt is a straight line through the origin, gradient 1.

Method B (force sensor). The trolley runs into a sprung buffer on a force sensor connected to a logger; light gates give the speed just before and after impact. The area under the force–time graph is the impulse; compare it with m(v − u), minding the sign of the rebound velocity.

• Uncertainties: friction compensation; card length; slow sampling misses a short impact's peak.
• Safety: an end stop; padding under the hanging masses.
• Improvements: longer card or slower trolley; repeat and average; a softer buffer lengthens the impact so more points are logged.

CP10: a collision analysed from a video

Aim: use a video camera and analysis software to test conservation of momentum in a collision between two small spheres, and decide whether kinetic energy is conserved. Apparatus: two weighed spheres on a smooth, level surface; a camera looking straight down; a ruler in the spheres' plane as a scale; good lighting. Method: roll A into stationary B off-centre (a glancing collision). Step through the video frame by frame, recording each sphere's centre. Calibrate distances from the scale and times from the frame rate (time between frames = 1 ÷ frames per second). Analysis: x-axis along A's original path; velocity components over several frames; check total momentum in x and in y separately; compare kinetic energy.

• Uncertainties: blurred centres; perspective (a scale out of the spheres' plane); friction, so velocities measured far from the collision are too small.
• Safety: stop spheres reaching the floor (slipping hazard); hot lamps away from cables.
• Improvements: higher frame rate, short exposure; frames just either side of impact; a line fitted to position against time.

CP11: how do you display a capacitor charging and discharging?

Aim: record the p.d. across a capacitor as it charges and discharges through a resistor, with a data logger or oscilloscope, and find RC. Apparatus: d.c. supply, capacitor, resistor, two-way switch, logger with a voltage sensor across the capacitor (or an oscilloscope with a square-wave signal generator).

Logger method: one switch position charges the capacitor through the resistor, the other discharges it through the resistor. Record V against t for at least five time constants, with RC of several seconds or more. Oscilloscope method: a square wave charges and discharges the capacitor repeatedly, giving a steady trace; each half-period must be at least about five time constants. Graph: discharging, \(V = V_0e^{-t/RC}\), so \(\ln V = \ln V_0 - t/RC\): ln V against t is a straight line of gradient −1/RC. Charging, \(V = V_0(1 - e^{-t/RC})\); the time to reach 0.63V₀ is RC.

• Uncertainties: wide capacitor tolerances (often ±10% or ±20%); a sensor resistance not much larger than R adds a second discharge path; reading a fast trace.
• Safety: connect an electrolytic capacitor the right way round and below its rated voltage, or it can overheat and burst; discharge large capacitors before handling.
• Improvements: use the ln-graph gradient, not one time-to-halve reading; repeat with several resistors and plot RC against R: the gradient is C.

CP12: how do you calibrate a thermistor as a thermostat?

Aim: a calibration curve of output p.d. against temperature for a potential divider containing an NTC thermistor, so it can sense and control temperature. Apparatus: sealed thermistor, fixed resistor, low-voltage supply, voltmeter (or logger), water on a hot plate, stirrer, thermometer, ice.

Method. Thermistor and fixed resistor in series across the supply, voltmeter across the fixed resistor, thermistor beside the thermometer bulb in the water. Start with ice and water at 0 °C; heat slowly, stirring, recording V_out every 5 °C or 10 °C up to about 90 °C. Repeat while cooling and average. Graph: V_out against θ is a smooth curve, not a straight line; read the temperature that matches a measured V_out. As a thermostat the output feeds a switching circuit that turns a heater off at a set V_out. Choose the fixed resistor equal to the thermistor's resistance at the set temperature, so the output is half the supply there, near the steepest, most sensitive part of the curve.

• Uncertainties: thermistor and thermometer at different temperatures (heat slowly, stir, wait); self-heating; thermometer resolution.
• Safety: scalds: heat-proof mat, do not move the hot beaker; connections out of the water; low voltage.
• Improvements: a logger with temperature probe reads V_out and θ together; a small supply p.d. limits self-heating.

CP13: how do you measure a specific latent heat?

Aim: the specific latent heat of a phase change, for example fusion of ice, using ΔE = LΔm. Apparatus: two filter funnels of crushed ice over two beakers, a low-voltage immersion heater in one funnel only, joulemeter or ammeter, voltmeter and stopclock, balance.

Method. Pack melting crushed ice round the heater. When both funnels drip steadily, empty both beakers. Switch on and start the clock; after several minutes switch off and weigh the water in each beaker. The second funnel is the control: it shows how much ice the room melts in the same time. The heater's energy VIt melts only the extra mass, so \(L = VIt/(m_{\text{heater}} - m_{\text{control}})\). Vaporisation variant: a heater keeps water boiling on a balance; record mass lost per second at two powers. Losses to the room are the same in both, so L = (P₁ − P₂)/(rate₁ − rate₂).

• Uncertainties: ice below 0 °C (use melting, wet ice); meltwater clinging to ice and funnel; heater energy lost to the air or funnel.
• Safety: never switch on an uncovered heater (it overheats); keep mains supply and meters away from water; mop spills.
• Improvements: run longer; finer ice for better contact; insulate the funnel.

CP14: how are the pressure and volume of a gas related?

Aim: how the pressure of a fixed mass of gas depends on its volume at constant temperature. Apparatus: dry air trapped above oil in a vertical, uniform glass tube with a scale; a Bourdon gauge on the oil reservoir; a foot pump (or a gas syringe with a pressure sensor and logger).

Method. Pump oil up to compress the air, close the valve, wait about a minute, then read the pressure and the air-column length (eye level, bottom of meniscus). Release pressure in steps and repeat. The bore is uniform, so volume = length × area and length can stand in for volume. Why wait: compressing a gas does work on it and warms it; waiting lets it return to room temperature. Graph: pV = NkT, so p against 1/V is a straight line through the origin of gradient NkT; a p–V curve is hard to test by eye.

• Uncertainties: parallax at the meniscus; gauge resolution; a gauge reading above atmospheric rather than absolute pressure gives a line missing the origin.
• Safety: goggles, as the glass tube is under pressure; never exceed the stated maximum pressure.
• Improvements: sensor and logger; a wider range; check pV for every pair.

CP15: how does lead absorb gamma radiation?

Aim: how gamma intensity falls through increasing thicknesses of lead. Apparatus: sealed gamma source (for example cobalt-60) in a holder, GM tube and counter, lead sheets, micrometer, stopclock, tongs, thin aluminium sheet.

Method. With the source in its lead box, count for several minutes for the background rate. Fix source and GM tube a set distance apart; a thin aluminium sheet over the source absorbs any beta particles. Measure each sheet with the micrometer, place sheets between source and tube, and count for a fixed time; repeat and average. Graph: subtract the background from every rate. The corrected rate falls exponentially, \(C = C_0e^{-\mu x}\), so ln C against x is a straight line of gradient −μ. The half-value thickness is ln 2/μ.

• Uncertainties: random decay, so record hundreds or thousands of counts; background matters most at large thicknesses; distance must stay fixed.
• Safety: tongs at arm's length, never pointed at anyone; short exposure; back in the lead box promptly; lead is toxic, so gloves or hand-washing.
• Improvements: longer counts; more thicknesses; a clamp to fix the geometry.

CP16: how do you find an unknown mass from resonance?

Aim: an unknown mass from the resonant frequencies of a mass–spring system loaded with known masses. Apparatus: spring on a vibration generator driven by a signal generator, slotted masses, the unknown mass, clamped stand, oscilloscope to check frequency.

Method. For each known mass, raise the driving frequency slowly to find where the mass's amplitude is largest: the resonant frequency, equal to the natural frequency. Approach from above and below and average. Then do the same for the unknown mass. Graph: \(T = 2\pi\sqrt{m/k}\) and f = 1/T give \(1/f^2 = 4\pi^2 m/k\): 1/f² against m is a straight line of gradient 4π²/k. The spring's own mass adds a little to every load, giving a small positive intercept. Read the unknown mass from the line. Variant: time 10 free oscillations of each mass from a reference mark at the equilibrium position and plot T² against m.

• Uncertainties: damping broadens the peak; the frequency dial; large amplitudes beyond the limit of proportionality.
• Safety: small amplitudes so masses stay on; clamp the stand; goggles in case the spring breaks.
• Improvements: oscilloscope frequency; wider mass range; repeats.

Exam tips for 6.3

Common misconceptions

How this topic connects

Theory pages in Units 4 and 5

Impulse and collisions (4.1), capacitors (4.4), specific latent heat (5.1), the ideal gas (5.2), radioactive decay and absorption (5.4), SHM and resonance (5.5, 5.6). CP12 builds on the Unit 2 potential divider.

6.1 Planning and 6.2 Uncertainties and logarithmic graphs

Choosing a logger, a camera or a control is the planning skill of 6.1; ln graphs and combined uncertainties are in full on 6.2. The seven headings match the AS practicals (3.3).

Key equations

Check your understanding

Specification checklist

• (82) Testing force against change of momentum with light gates or a force sensor and logger.
• (84) Video analysis of a two-sphere collision to test conservation of momentum in two dimensions.
• (103) Showing capacitor charge and discharge on a logger or oscilloscope; RC from ln V against t.
• (126) Calibrating a thermistor in a potential divider and explaining its use as a thermostat.
• (127) Measuring a specific latent heat with a control, and its uncertainty.
• (131) Pressure and volume at constant temperature, using p against 1/V.
• (140) Gamma absorption by lead, background correction and safe use of a radioactive source.
• (149) An unknown mass from the resonant frequencies of a spring loaded with known masses.
• (all) For each practical: main uncertainty, combined uncertainty, a specific safety precaution and an improvement with a reason.