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
A timing offsetFor a separate single-height estimate g = 2h/t², the timer records a time 0.02 s longer than the true time, while h is correct. How does this affect the estimated g?
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 |
|---|---|---|---|
| 0.162 | 0.179 | 0.18 | 0.181 |
| 0.242 | 0.219 | 0.22 | 0.221 |
| 0.338 | 0.259 | 0.26 | 0.261 |
| 0.45 | 0.299 | 0.3 | 0.301 |
| 0.578 | 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.
Hint
A larger denominator makes 2h/t² smaller.
Worked solution
- Selection: Estimated g is too low.
- A positive time offset increases t², so this single-height estimate is too low.
- Repeats do not remove a constant timing offset. The claim here concerns 2h/t², not an arbitrary fitted graph.
Work through this dataset
- Mean repeated time
- Square the mean time
- Choose linear axes
- Height–time² gradient
- Find g
- Reverse the axes
- Predict a fall time
- Speed before impact
- Timing percentage uncertainty
- Uncertainty in g
- A timing offset (current)
- Release from rest
These tasks keep the same readings. Another question starts a new dataset. Your answers are checked separately.
Question type: A timing offset
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