Experimental Methods and Data Analysis
Experimental methods questions test measurement uncertainty, significant figures, instrument resolution, graph linearisation and interpretation, and experimental design.
Core rules
- For y = a ± b, absolute uncertainties add. For y = ab or a/b, relative (percentage) uncertainties add. For y = aⁿ, the relative uncertainty is |n| times that of a.
- Analogue instruments: uncertainty is often half the smallest division; digital instruments: ±1 in the last displayed digit.
- A result should not have more significant figures than the least precise input.
- Linearise to find constants: for a pendulum, plot T² against L; the gradient is 4π²/g, so g = 4π²/gradient.
- Random errors are reduced by repeating and averaging; systematic errors shift all readings and are not reduced by averaging.
- Always give units for gradients and intercepts.
Worked example
A mass is measured as 50.0 ± 0.1 g and a volume as 10.0 ± 0.2 cm³. Density = 50.0/10.0 = 5.00 g/cm³. Relative uncertainties: 0.1/50.0 = 0.2% and 0.2/10.0 = 2.0%, total 2.2%. Absolute uncertainty = 0.022 × 5.00 ≈ 0.11 g/cm³, so ρ = 5.00 ± 0.11 g/cm³.
Traps
Adding percentage errors when quantities are multiplied rather than added; quoting 5.003 g/cm³; omitting units on a gradient; ignoring a zero error; treating a systematic offset as random scatter.