Methods of Scientific Inquiry and Experimental Data Analysis
Core concepts
Experimental physics requires careful measurement, uncertainty analysis, and clear presentation. Distinguish systematic errors (consistent bias, e.g., a zero error in an instrument) from random errors (scatter that averages out with repeated trials).
When reporting a measurement, include the value and its uncertainty with matching precision, e.g., (2.54 ± 0.02) cm. For sums and differences, absolute uncertainties add. For products and quotients, relative (percentage) uncertainties add. For a power, multiply the relative uncertainty by the exponent.
Graphs are powerful tools: plot the independent variable on the x-axis and the dependent variable on the y-axis. A linearized graph (e.g., T² vs. ℓ for a pendulum) lets you extract parameters from the slope and intercept. Always label axes with units and draw a best-fit line, not point-to-point connections.
Estimation (order-of-magnitude reasoning) tests physical intuition: choose reasonable values, keep units consistent, and check that the answer is physically plausible.
Traps
- Adding absolute uncertainties when multiplying quantities (should add relative).
- Reporting too many significant figures.
- Confusing systematic and random errors.
- Drawing a line through every data point instead of a best fit.
- Forgetting unit conversions in estimates.
Worked rule of thumb
If a length is measured as 10.0 ± 0.1 cm (1%) and a time as 2.0 ± 0.1 s (5%), a computed speed has about 6% relative uncertainty - add relative uncertainties.