Laboratory Practice and Experimental Skills: Measurement, Errors, Data
The laboratory section tests whether you can read an instrument, quote an uncertainty honestly, combine uncertainties correctly, and extract physics from a graph. It is examined both as short structured questions and as the interpretation of a set of readings, so precision in presentation matters as much as the arithmetic.
Instruments and readings
A metre rule reads to 1 mm; a vernier caliper to 0.1 mm or 0.05 mm; a micrometer to 0.01 mm. For analogue scales, record to half the smallest division where that is the convention taught, and always subtract any zero error before use. Repeat readings and average them to reduce random error; systematic error (a zero error, a mis-calibrated scale) shifts every reading the same way and is not removed by averaging.
Uncertainty analysis
Absolute uncertainty carries the unit; relative uncertainty is the ratio; percentage uncertainty is relative × 100. For sums and differences, add absolute uncertainties. For products and quotients, add percentage uncertainties. For a power, multiply the percentage uncertainty by the exponent. Quote the final uncertainty to one significant figure (two at most) and give the value to the same decimal place, for example 2.60 ± 0.08 g/cm³.
Graphs and data interpretation
Plot the quantity that linearises the relation: T² against l for a pendulum (gradient 4π²/g), V against I for a resistor (gradient R), 1/v against 1/u for a lens. Read the gradient from a large triangle on the line of best fit, never from two data points, and give its unit. The intercept often has physical meaning - an internal resistance or a zero error. Error bars indicate uncertainty, and the line should pass through as many bars as possible.
Worked example
A metal block has mass 12.5 ± 0.1 g and volume 4.8 ± 0.1 cm³. Find the density with its uncertainty. ρ = m/V = 12.5/4.8 = 2.604 g/cm³. Percentage uncertainties: mass 0.1/12.5 = 0.8 %, volume 0.1/4.8 = 2.1 %. Adding them for a quotient gives 2.9 %, so the absolute uncertainty is 0.029 × 2.604 = 0.075 g/cm³. Rounding: ρ = 2.60 ± 0.08 g/cm³.
Traps that cost marks
- Adding percentage uncertainties for a sum instead of absolute ones.
- Forgetting the factor of 2 when a quantity is squared, or the power when it is cubed (volume from a diameter).
- Writing more decimal places in the answer than the uncertainty justifies.
- Reading a vernier without checking the zero error.
- Taking the gradient from the raw curve rather than from a linearised graph, or leaving the gradient without units.