Laboratory Practice, Measurement and Data Analysis, Applications of Physics in Technology and Engineering
Scope of the domain
This domain covers units and prefixes, measurement uncertainty, graphical analysis, and the engineering application of physics ideas. The exam asks you to record and process data with correct precision, combine uncertainties, interpret gradients and intercepts, and relate physical principles to devices and systems.
Core rules
- Convert all quantities to SI base units before calculating: mm to m, g to kg, mA to A, cm³ to m³.
- Uncertainty of an analogue scale is typically ± half the smallest division; for a digital display it is ± the last digit. Repeat readings reduce random error.
- Absolute uncertainty has the same unit as the quantity. Fractional uncertainty = absolute ÷ value; percentage uncertainty = fractional × 100%.
- When adding or subtracting, add absolute uncertainties. When multiplying or dividing, add percentage uncertainties. For a power, multiply the percentage uncertainty by the power.
- Random errors scatter readings about the true value and are reduced by averaging; systematic errors shift all readings in one direction and are not removed by averaging.
- On a graph, label axes with quantity and unit, draw a best-fit line, and calculate the gradient using widely spaced points. The gradient's unit is the unit of the y-axis divided by that of the x-axis.
- Accuracy is closeness to the true value; precision is closeness of repeated readings to each other.
- Applications include sensors such as thermistors and LDRs, efficiency of machines, mechanical advantage, and energy sources.
Worked example
A metal block has mass 24.6 ± 0.1 g and volume 8.0 ± 0.2 cm³. Density = 24.6 ÷ 8.0 = 3.075 g/cm³. Percentage uncertainty in mass = 0.1 ÷ 24.6 × 100% = 0.41%; in volume = 0.2 ÷ 8.0 × 100% = 2.5%. Total percentage uncertainty = 2.9%. Absolute uncertainty = 3.075 × 0.029 = 0.089 g/cm³. The result is quoted as 3.1 ± 0.1 g/cm³, with the uncertainty rounded to one significant figure and the value matched to it.
Traps that cost marks
- Adding percentage uncertainties when quantities are added; absolute uncertainties should be added instead.
- Rounding the uncertainty to several figures, or quoting the result more precisely than the data allow.
- Reading a gradient without units, or using points too close together.
- Treating a systematic zero error as random scatter that averaging will remove.
- Forgetting to convert cm³ to m³ (1 cm³ = 10⁻⁶ m³) in density calculations.
- Confusing accuracy with precision when evaluating an experiment.