Practical and Experimental Skills
What this domain tests
Instrument choice and reading, precision versus accuracy, random versus systematic error, combination of uncertainties, graph plotting and interpretation, and experimental design. Marks come from quoting a correct uncertainty with a sensible number of significant figures and from explaining why a procedure reduces error.
Measurement and uncertainty
- Read each instrument or supplied specification to determine resolution; familiar scale intervals are examples, not universal values for every device. Record calibration corrections and distinguish display resolution from total measurement uncertainty.
- State your uncertainty convention - commonly ± half the smallest division for a single reading, and the full division for a difference of two readings.
- Random errors scatter readings about a mean and are reduced by repeats; systematic errors shift every reading the same way (zero error, calibration) and are removed by correction, not averaging.
- For first-order worst-case bounds, add absolute contributions for sums and differences, and relative contributions for products, quotients and powers. Independent standard uncertainties are instead commonly propagated in quadrature; correlations require additional terms. State the convention.
Graphs and experimental design
- Plot the quantity that gives a straight line, label axes with quantity and unit, draw error bars where asked and a best-fit line with points balanced above and below.
- Gradient = Δy/Δx taken from two well-separated points on the line, with units.
- Reduce error by: repeating and averaging, timing many oscillations and dividing, using fiducial markers to avoid parallax, setting a micrometer to zero first, and controlling all variables except the one under test.
Worked example
A metal cylinder has mass 25.0 ± 0.1 g, diameter 10.00 ± 0.02 mm and height 40.0 ± 0.1 mm. Find its density with uncertainty.
V = πd²h/4 = π(10.00)²(40.0)/4 = 3142 mm³ = 3.142 cm³. Using first-order worst-case uncertainty bounds: mass 0.4%, diameter 0.2% (doubled to 0.4%), height 0.25%. Total = 0.4 + 0.4 + 0.25 ≈ 1.05%. ρ = 25.0/3.142 = 7.96 g cm⁻³; absolute uncertainty = 0.0105 × 7.96 ≈ 0.08. Result: ρ = (7.96 ± 0.08) g cm⁻³.
Traps that cost marks
- Quoting 7.95843 g cm⁻³ from data good to three significant figures.
- Adding absolute uncertainties for a multiplication instead of adding percentages.
- Forgetting the factor of 2 when a quantity is squared.
- Ignoring a vernier or micrometer zero error.
- Reading a meniscus or pointer without eye-level alignment.
- Extrapolating far beyond the measured range and presenting it as data.