Laboratory Methods and Data Analysis
Laboratory Methods and Data Analysis on ORT Physics tests whether you can design a valid measurement, treat uncertainties honestly, and extract a physical result from a graph. It rewards precision of language as much as arithmetic.
Core rules
- SI base units are kg, m, s, A, K, mol and cd. Check that equations are homogeneous in units before substituting numbers.
- Precision is repeatability; accuracy is closeness to the true value. Random errors scatter readings and are reduced by averaging; systematic errors shift all readings in the same way and are not reduced by repeating.
- For addition or subtraction, add absolute uncertainties. For multiplication or division, add percentage uncertainties. For a power, multiply the percentage uncertainty by the exponent.
- Quote a result as value ± uncertainty with the uncertainty to one significant figure and the value to the same decimal place.
- Graphs: choose axes that should give a straight line, label units, use a line of best fit rather than joining points, and interpret the gradient with its units.
- Good practice includes control variables, repeat readings, calibration checks and correcting for zero error.
Worked example
A block has mass 25.0 ± 0.1 g and volume 10.0 ± 0.2 cm³. Density = 25.0/10.0 = 2.50 g/cm³. Percentage uncertainty in mass is 0.1/25.0 = 0.4%; in volume it is 0.2/10.0 = 2.0%. Because density is a quotient, add percentages: total = 2.4%. The absolute uncertainty is 0.024 × 2.50 = 0.06 g/cm³, so the result is 2.50 ± 0.06 g/cm³, or 2.5 ± 0.1 g/cm³ at two significant figures.
Traps
- Adding absolute uncertainties when dividing quantities.
- Reporting ten digits from a calculator when the data justify three.
- Extrapolating a best-fit line beyond the measured range.
- Treating precision and accuracy as synonyms.
- Ignoring a zero error or a calibrated offset.