A graph of s against t squared has best gradient 4.91 m s−2. The steepest and shallowest acceptable gradients are 5.03 m s−2 and 4.79 m s−2. Determine g and its absolute uncertainty.
[4 marks]
Total for this question: 4
A-level Physics required practicals
Determine g by free fall
AQA 3.4.1.3 · RP3
A-level Physics (7408) · Required practical 3 — method, techniques, safety, analysis and uncertainty. Includes errors documented in examiner reports.
Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works
Determine the local gravitational field strength from the motion of an object released from rest.
Apparatus
- Dense falling object and an electromagnet or other repeatable release
- Light gates with a data logger, or a strobe/video record with a visible scale
- Metre rule and set square
- Clamp stands and impact tray or soft landing pad
Apparatus & techniques (AT)
AT a · analogue measurement
A metre rule or image scale supplies the displacement measurements along the free-fall path.
AT c · accuracy methods
A repeatable release, long useful fall and scale in the motion plane improve the accuracy of the motion coordinates.
AT d · stopwatch/light gates
Light-gate timing or known strobe intervals provide elapsed times without hand-operated reaction delay.
AT k · ICT/data logging/processing
A data logger or image-processing system converts timed positions into the graph used to determine g.
Safety
Hazard
The falling object can strike a person or damage equipment.
Control
Keep the drop zone clear, secure all stands and use an impact tray or soft landing pad.
Hazard
A tall arrangement can topple.
Control
Use a stable base or bench clamp and adjust the apparatus only while the object is removed.
Method
- 1Arrange a release that lets the object fall vertically from rest without a push, and place a protected landing area below it.
- 2If using light gates, measure their reference positions and record the logged times or velocities; if using images, place a scale in the plane of motion and record the known time between frames or flashes.
- 3Collect displacement and elapsed-time data over a range large enough that timer and position resolution are not dominant.
- 4Repeat releases from the same reference position and reject a reading only for an identified fault, such as a clipped gate or unclear image.
- 5Plot s against t squared for a release from rest, or v against t when the logging system provides velocity directly.
CPAC focus (editorial)
This is an editorial study focus, not an AQA mapping of fixed CPAC competencies to this practical.
- CPAC 2: Editorial focus: choose a release, range and coordinate system that test the free-fall model without an uncontrolled push.
- CPAC 4: Editorial focus: record sufficient timed positions or velocities with stated spatial and temporal resolution.
- CPAC 5: Editorial focus: extract g from a gradient, quantify its uncertainty and distinguish precision from accuracy.
Variables
Independent
Elapsed time t (frame or light-gate interval)
Dependent
Displacement s, or velocity v from the logger
Control
- The same object and release mechanism
- The same vertical path and position reference
- The imaging scale position or light-gate configuration
Results & processing
- For s against t squared, the gradient is g/2; for v against t, the gradient is g.
- A small intercept may expose a position or timing zero rather than being forced through the origin.
- Compare the measured g with the accepted local value using the gradient uncertainty and the likely systematic effects.
Analysis skills
- Transform displacement data by plotting s against t squared so the gradient equals g/2.
- Alternatively fit v against t and use the gradient directly as g while interpreting the intercept as initial velocity or timing offset.
Uncertainty
Sources
- Light-gate or frame timing resolution
- Position resolution, parallax and uncertainty in the reference point on the object
- Release delay, a small initial speed and air resistance
Calculations
- Use half the difference between maximum and minimum acceptable graph gradients for the gradient uncertainty.
- When g is twice the s-versus-t-squared gradient, its absolute uncertainty is twice the gradient's absolute uncertainty while its percentage uncertainty is unchanged.
Interpretation
- An offset intercept is evidence to investigate rather than a reason to force the fit through the origin.
- Repeats reduce uncertainty in the mean but do not remove a scale calibration error, release bias or air resistance.
Exam angles
- Explain how a scale and known strobe or frame interval generate numerical coordinates.
- Extract g and its uncertainty from best, maximum and minimum gradients.
- Distinguish a more precise imaging method from a more accurate result and identify the evidence for each claim.
Where students lose marks
Saying that software automatically gives more accurate coordinates without explaining the scale and timing information.
Fix: State how pixels are converted to distance, how frame or flash spacing gives time, and what limits each reading.
- Examiner report: P3-23 · PDF p. 3
Using a hand release that gives the object an unknown initial speed.
Fix: Use an electromagnet or mechanical release and check whether the graph intercept supports the assumption u = 0.
Calling a tightly clustered value accurate without comparison to an accepted value.
Fix: Use repeat scatter to discuss precision and the discrepancy from accepted g to discuss accuracy.
Improve the method
- Use an electronic release and data logging so reaction time does not set the start or stop time.
- Use a longer measured fall where safe, so fixed position and timing resolution become smaller percentages.
- Place the calibration scale in the plane of motion to avoid parallax in image coordinates.
Source references
- Specification: PSpec 3.4.1.3 · PDF p. 23
Try it — exam-style
Medium
ORIGINAL
Medium
ORIGINAL
A strobe photograph shows a falling ball beside a metre rule. Explain how the student obtains a displacement-time data point and name one systematic error that the software cannot remove automatically.
[3 marks]
Total for this question: 3
Questions are written in the style of past AQA papers — never copied from them.
Drill it properly
Stuck on determine g by free fall?
Free-fall questions are won on the graph transformation and on explaining what the logger actually measures — I drill both. Free intro call, then a free first lesson.