Planning and evaluating experiments (A2) flashcards

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Accuracy
How close a measurement or result is to the true value. Limited by systematic errors.
Precision
How closely repeated measurements agree with each other: a precise set has very little spread about its mean. Limited by random errors.
Sensitivity of an instrument
The change in its reading (output) per unit change in the quantity being measured (input), e.g. 25 mV per mT.
Resolution of an instrument
The smallest change in the quantity that the instrument can show — one scale division or the last digit of a display.
Calibration
Comparing an instrument's readings with known values (fixed points, known fields, known masses) and using the result to correct its readings.
Background count rate
The count rate recorded with no source present, from cosmic rays and natural radioactivity; subtracted from every measured count rate.
Anomalous reading
A reading that does not fit the pattern of the others: a repeat far from the other repeats, or a point well off the best-fit line.
Relevant dimension
The particular length the equation needs, measured between the right points — e.g. pendulum length to the centre of the bob.
Smallest detectable change of a sensor + meter
Resolution of the meter ÷ sensitivity of the sensor. (No — derive it)
Corrected count rate
Measured count rate − background count rate (both in s⁻¹, from counts ÷ counting time). (No — learn it)
Sensitivity from two readings
Δ(output) ÷ Δ(input), e.g. (3.92 V − 3.40 V) ÷ 10 K = 0.052 V K⁻¹. (No — learn it)
Period of a simple pendulum
T = 2π√(l/g), with l measured to the centre of the bob. Plot T² against l: gradient 4π²/g. (Yes)
Capacitor discharge (for judging time scales)
V = V₀e^(−t/RC); the time constant RC sets how fast readings must be taken. (Yes)
Effect of a zero error on a straight-line graph
The line shifts up or down: intercept changes, gradient does not — so a result from the gradient is unaffected.
Effect of a scale (gradient) error in an instrument
Readings are wrong in proportion; differences do not cancel it. Correct with a calibration line.
Which graph finds a hidden source offset d₀ if C = k/(d + d₀)²?
Plot C^(−1/2) against d: a straight line crossing the d axis at −d₀.
Precise but inaccurate results on a dot plot
Tightly grouped values whose mean is shifted from the true value: a systematic error.
Calibration line for a thermometer
Plot reading against true temperature using two fixed points (melting ice, steam); read true values back from the line.
When should you use a data logger?
When the change is too fast to read by hand, needs many readings at exact times, needs two quantities at once, or lasts a long time.
How do you choose a data-logger sampling rate?
Estimate the time scale (time constant, period, pulse length) and choose a rate giving at least 10–20 readings within it.
Precautions with a sealed radioactive source
Long tongs, held at arm's length pointing away from people; minimum time out of the lead-lined box; return and store securely.
Precautions with high-voltage supplies (kV)
Current-limited supply; connect and change leads only with it switched off; shrouded leads; never touch terminals when on.
Precautions with hot liquids
Heat-proof mat, stable clamp, do not carry hot beakers, let liquids cool before emptying, keep leads away from water.
Dealing with an anomalous reading
Spot it during the experiment and repeat it; if that is impossible, keep it in the table, marked, and leave it out of the mean and the line.
Where to put a fiducial mark
At the centre of the oscillation, where the object moves fastest, so each pass is sharply timed.
Number, range and spacing of readings at A2
At least 6–8 values, widest safe range, spread evenly along the axis you will plot; for decays cover 2–3 time constants.
Repeats vs longer counts for radioactivity
Decay is random: count for longer (several hundred counts or more) and/or repeat, to improve precision.
Why can a more sensitive sensor still be inaccurate?
Sensitivity only sets how big the output change is; accuracy depends on calibration and systematic errors.
220 µF discharges through 2.2 kΩ. Stopwatch or data logger?
RC = 0.484 s; a 0.2 s reaction time is 41% of it → data logger (e.g. 50 samples per second).
Pendulum: pivot to top of bob 0.842 m, bob diameter 24.6 mm. Length to use?
0.842 + 0.0123 = 0.8543 m (to the centre of the bob).
1520 counts in 60.0 s; background 186 counts in 5.00 min. Corrected count rate?
25.3 − 0.62 = 24.7 s⁻¹.
Sensor sensitivity 25 mV K⁻¹, voltmeter resolution 0.01 V. Smallest detectable change?
0.01 ÷ 0.025 = 0.40 K.
Thermometer reads 2.0 in melting ice and 96.0 in steam. True temperature for a reading of 60.0?
(60.0 − 2.0) ÷ 0.94 = 61.7 °C.
Hall probe gives 0.126 V in a known 5.03 mT field. Sensitivity?
0.126 ÷ 5.03 × 10⁻³ = 25.1 V T⁻¹.
Naming an instrument in an A2 plan
Give range, resolution and exactly what is measured, between which points: a name alone is not a specification.
Table headings
Quantity / unit, e.g. C / s⁻¹ or T² / s². Units in the heading, never after each value; work out units of derived columns.
Inconsistent decimal places in a column
Record every raw reading to the instrument's resolution: 0.050, 0.075, 0.100 m — not 0.05, 0.075, 0.1.
“Wear gloves” with a gamma source
Gloves do not stop gamma rays. Use distance (tongs), short exposure time and shielding.
Suggesting an improvement
Name the apparatus, link it to a specific source of uncertainty, and say what it improves — not “use better equipment”.

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