Experimental and laboratory skills: measurement, uncertainty, data analysis, experimental design
Experimental and laboratory skills
This domain tests measurement, uncertainty, graphical analysis and experimental design. You are expected to report a result with a realistic uncertainty, identify random and systematic errors, and choose a graph that linearises a relationship.
Core rules
- Recording data: include the instrument resolution and use consistent significant figures. For a digital scale, the reading uncertainty is usually ±1 in the last digit; for an analogue scale, it is often ±half the smallest division.
- Random vs systematic: repeating readings reduces random scatter but does not remove a zero error or calibration bias. Compare with a known value or plot residuals to expose systematic error.
- Combining uncertainties: for sums and differences, add absolute uncertainties; for products and quotients, add relative uncertainties. For a power y=xⁿ, the relative uncertainty is |n| times that of x.
- Graphs: a linear graph gives the most reliable slope. For T=2π√(L/g), plot T² against L; the slope is 4π²/g. Label axes with quantity and unit, and draw a line of best fit rather than joining points.
- Design: identify independent, dependent and controlled variables; use a control where appropriate; choose a range that gives a measurable change and repeat at each setting.
Worked example
A pendulum of length L=0.800±0.002 m gives T=1.79±0.01 s. Using g=4π²L/T²: g=4π²(0.800)/(1.79²)=9.86 m/s². The relative uncertainty is Δg/g=ΔL/L+2ΔT/T=0.002/0.800+2(0.01/1.79)=0.0025+0.0112=0.0137. Thus Δg=0.135, and the result is g=(9.86±0.14) m/s². The dominant error is timing, so timing many swings would improve precision.
Traps
Adding percentage uncertainties for a sum; quoting more digits than the uncertainty justifies; treating a zero error as random; forcing a line through the origin when the theory does not require it; forgetting to convert units before graphing; using the range instead of the standard deviation as the uncertainty of repeated readings.