Data test skills
G5.2 G5.3 G5.4
A data test gives you an unseen data set (usually from a practical you have done) and asks short questions about it. The physics is the theory you already know; the marks come from handling data carefully and quoting it as evidence. Your teacher will tell you when the data test is (see QLearn).
Theory first, then data
Every data set in this course comes from a practical you do after the theory lesson. Before a data test, revise the formula behind each practical: it tells you what to plot and what the gradient means.
The cognitive verbs
| Verb | What it asks you to do | Show working? |
|---|---|---|
| Identify | Name or state it (a value, an anomaly, a relationship). | Usually no |
| Calculate | Work out a number using a formula or the data. | Yes |
| Determine | Find a value from the data, a graph or a calculation. | Usually yes |
| Deduce | Reach a value or statement from the data plus a known relationship (e.g. use the gradient to find g). | Yes |
| Predict / interpolate / extrapolate | Give a value inside (interpolate) or outside (extrapolate) the measured range, from the pattern or your line. | Yes |
| Draw a conclusion | Answer the research question, using data as evidence. | Evidence, yes |
| Evaluate | Judge the quality of the data or method, with reasons. | Reasons |
The full definitions are in the glossary of the QCAA Physics syllabus.
Eight moves that earn most of the marks
- Mean of trials. Add the trials and divide by how many. Leave out an anomaly (and say so).
- Uncertainty of a mean. Absolute uncertainty = half the range of the trials: \(\Delta x = \tfrac{1}{2}(x_{max} - x_{min})\). If all trials agree, use the instrument uncertainty instead.
- Percentage uncertainty. \(\%\,\text{uncertainty} = \dfrac{\Delta x}{\bar{x}} \times 100\).
- Spot the anomaly. Compare each trial with the other trials at the same value. An anomaly is clearly out of line with them, not just the biggest number in the table.
- Identify the relationship with evidence. Name it (linear, directly proportional, inverse, inverse square, maximum at …) and quote numbers: "When F increases by a factor of 4 (0.39 N → 1.57 N), T halves (0.74 s → 0.37 s), so F ∝ 1/T²."
- Linearise. Choose axes that give a straight line (table below). The gradient then means something physical.
- Use the gradient. Gradient = rise ÷ run from two points on your line, far apart (not data points). Then match it to the formula to deduce a quantity.
- Conclude. Answer the research question in one or two sentences, with the relationship, the key value (with uncertainty) and any limitation.
What to plot (Unit 3)
| Practical / situation | Plot y | against x | Gradient means |
|---|---|---|---|
| Range at different launch angles (level ground) | \(R\) | \(\sin 2\theta\) | \(u^2/g\) |
| Falling from rest | \(s\) | \(t^2\) | \(\tfrac{1}{2}g\) |
| Force to hold a trolley on a ramp | \(F_\parallel\) | \(\sin\theta\) | \(mg\) (intercept: friction) |
| Acceleration down a ramp | \(a\) | \(\sin\theta\) | \(g\) |
| Whirling bung: tension vs period | \(F\) | \(1/T^2\) | \(4\pi^2 m r\) |
| Whirling bung: radius vs period | \(T^2\) | \(r\) | \(4\pi^2 m / F\) |
| Gravitational force vs distance | \(F\) | \(1/r^2\) | \(GMm\) |
| Kepler's third law | \(r^3\) | \(T^2\) | \(GM/4\pi^2\) |
| Force on a current-carrying wire | \(F\) | \(I\) | \(BL\) |
Practice: tension and period in circular motion
A rubber bung (mass 12 g) is whirled in a horizontal circle on a string through a tube, with a hanging mass providing the tension (\(F = Mg\)). A marker keeps the radius constant. The time for 10 revolutions is measured three times for each hanging mass (stopwatch ±0.1 s). The experiment uses \(F = \dfrac{4\pi^2 m r}{T^2}\).
| Hanging mass M (g) | Tension F (N) | 10 rev, trial 1 (s) | Trial 2 (s) | Trial 3 (s) | Mean period T (s) | 1/T² (s⁻²) |
|---|---|---|---|---|---|---|
| 40 | 0.392 | 7.3 | 7.4 | 7.3 | 0.733 | 1.86 |
| 80 | 0.784 | 5.2 | 5.2 | 4.3 | 0.490 | 4.16 |
| 120 | 1.176 | 4.2 | 4.2 | 4.3 | ? | 5.58 |
| 160 | 1.568 | 3.6 | 3.7 | 3.6 | 0.363 | ? |
| 200 | 1.960 | 3.3 | 3.3 | 3.2 | 0.327 | 9.37 |
(a) Determine the mean period \(T\) for the 120 g mass (3 decimal places).
(b) Calculate the missing value of \(1/T^2\) for the 160 g mass.
(c) Identify the anomaly.
(d) Plot \(F\) (y) against \(1/T^2\) (x), leaving out the anomaly. Determine the gradient of your line of best fit.
(e) Deduce the radius of the circle.
(f) Predict the period for a 250 g hanging mass. Is this interpolation or extrapolation?
Worked solutions
(a) Mean of the three 120 g times ÷ 10 = 0.423 s. (b) \(1/T^2 = 1/0.363^2 = 7.58\) s⁻². (c) 80 g, trial 3: about 0.9 s shorter than 5.2 s and 5.2 s (probably a miscounted revolution). (d) The points lie on a straight line close to the origin. Gradient ≈ 0.207 N s² (intercept ≈ 0.011 N). (e) Gradient = \(4\pi^2 m r\), so \(r = 0.207 / (4\pi^2 \times 0.012) = 0.44\) m. (f) \(F = 0.250 \times 9.8 = 2.45\) N; \(T = \sqrt{\text{gradient}/F} = 0.291\) s. This is extrapolation (250 g is beyond the data), so it is less certain.
Relationship with evidence: a model answer
\(F\) is inversely proportional to \(T^2\). When the hanging mass increases by a factor of 4 (40 g → 160 g), the period halves (0.733 s → 0.363 s), and the graph of \(F\) against \(1/T^2\) is a straight line through (close to) the origin.
More practice with feedback is in your QLearn course (data test practice sets after each practical).