Combining uncertainties
Choose when to add absolute uncertainties, add percentages or include powers.
Free fall practical questions
Process repeated timings, find g from squared-time graphs and evaluate timing errors.
Practise
Height–time² gradientCalculate the supplied h–t² line gradient from the first and last mean-time readings. Give 3 significant figures.
Practical setup and assumptions
A ball is released from rest. Electronic timing measures release to impact; h is the vertical displacement of the same reference point on the ball. Ignore drag and use constant downward acceleration.
These are generated practice readings. Their mean times follow h = ½gt² exactly. Use any stated uncertainties; do not estimate uncertainty from the spread of these readings.
Readings for this dataset
| h / m | t₁ / s | t₂ / s | t₃ / s |
|---|---|---|---|
| 0.15552 | 0.179 | 0.18 | 0.181 |
| 0.23232 | 0.219 | 0.22 | 0.221 |
| 0.32448 | 0.259 | 0.26 | 0.261 |
| 0.432 | 0.299 | 0.3 | 0.301 |
| 0.55488 | 0.339 | 0.34 | 0.341 |
The linked tasks use the same readings. These are generated practice data: treat them as exact unless an uncertainty is stated. Use the stated uncertainty rather than estimating it from scatter.
Larger graph
Graph values
| Point | Mean time² / s² | Height / m |
|---|---|---|
| 1 | 0.0324 | 0.15552 |
| 2 | 0.0484 | 0.23232 |
| 3 | 0.0676 | 0.32448 |
| 4 | 0.09 | 0.432 |
| 5 | 0.1156 | 0.55488 |
Hint
Gradient = Δh/Δ(t²).
Worked solution
- Gradient = (0.55488 − 0.15552)/(0.1156 − 0.0324) m s⁻².
- Answer: 4.80 m s⁻² (3 significant figures).
Work through this dataset
- Mean repeated time
- Square the mean time
- Choose linear axes
- Height–time² gradient (current)
- Find g
- Reverse the axes
- Predict a fall time
- Speed before impact
- Timing percentage uncertainty
- Uncertainty in g
- A timing offset
- Release from rest
These tasks keep the same readings. Another question starts a new dataset. Your answers are checked separately.
Question type: Height–time² gradient
Report a problem
Mean time and graph orientation
For a ball released from rest with negligible drag, h = ½gt². Calculate the mean time at each height, then square that mean. A graph of h vertically against t² has gradient g/2. Reversing the axes gives gradient 2/g.
Timing and release errors
The timer must measure the fall from release to impact. Measure displacement between matching reference points. A downward push adds an initial-velocity term ut. A positive timing offset makes a single-height 2h/t² estimate too low; repeats do not remove that offset.
Uncertainty
For the stated first-order maximum method, percentage uncertainty in g = 2h/t² is the height percentage plus twice the time percentage. Use the separately quoted uncertainties; the synthetic repeat spread is not a universal instrument rule. These tasks cover selected data skills, not a full laboratory procedure.
A-level relevance
AQA 7408: 3.4.1.3; required practical 3 (selected); OCR A H556: 3.1.2(a–b) (selected). Tasks cover the selected skills listed above.
AQA mechanics and materials specification · OCR A specification · AQA practical handbook · OCR practical skills handbook