Laboratory practice and data analysis
The laboratory-practice domain tests experimental design, measurement, uncertainty, graphical analysis and error treatment. In the PAU it often appears as a question about a pendulum, a lens, a resistor or a falling body, asking you to identify variables, process data and justify a conclusion.
Core rules
- Design: identify independent, dependent and controlled variables; repeat measurements; use the smallest suitable instrument; avoid parallax and zero error.
- Uncertainty: for a single reading, use the instrument resolution or half the smallest division as appropriate. For repeated readings, use the standard deviation or half the range, and state the result as value ± uncertainty with consistent units.
- Propagation: for sums and differences add absolute uncertainties; for products and quotients add fractional uncertainties; for powers multiply the fractional uncertainty by the exponent.
- Graphs: plot the dependent variable against the independent variable, draw a best-fit line, and use the gradient and intercept to extract constants. Linearise the relation first, for example T² against L for a pendulum.
- Error treatment: random errors scatter and are reduced by averaging; systematic errors shift all readings and require calibration or correction.
Worked example
A simple pendulum is timed for different lengths L. The theoretical relation is T = 2π sqrt(L/g), so a graph of T² against L should be a straight line through the origin with gradient 4π²/g. Suppose the best-fit gradient is 4.05 s²/m. Then g = 4π²/4.05 = 9.75 m/s². If the accepted value is 9.81 m/s², the discrepancy is about 0.6%. A small positive intercept would suggest a systematic timing or length offset; scattered points about the line suggest random error.
Traps
Do not quote more significant figures than the data justify. Do not add percentage uncertainties when quantities are multiplied; add them, then convert back. A best-fit line need not pass through every point, and forcing it through the origin can hide a systematic error. Keep units on gradients. Distinguish reaction time from instrument resolution. When measuring a length with a ruler, record the uncertainty once, not on every repeated calculation. Finally, never describe a systematic error as something averaging will remove.