Free fall. Measured by light.
Investigate gravitational acceleration with a falling dowel and light gates.
The experimental bench
Single gate| Trial | Gate 1 / ms | Gate 2 / ms |
|---|
Blocked time, not total falling time. Copy the readings or use them directly below.
3Calculate, check, record
For each trial use v = d / (t × 10⁻³), then average the three velocities. Enter your mean to 3 significant figures.
Both methods are retained. Derived velocities come from your checked sets. Export includes every raw interruption time, uncertainty assumptions and session identifier.
| Set | Mode | h / m | s / m | d / mm | Mean v₁ / m s⁻¹ | Mean v₂ / m s⁻¹ | v₁² / m² s⁻² | U(v₁) / % |
|---|
Uncertainties are conservative classroom estimates, not statistical confidence intervals. No automatic rejection of readings.
Tap or move over the graph to read coordinates.
Plan → measure → evaluate
- Choose one gate for a graph, or two gates for a direct estimate of g.
- Measure d and keep the same dowel for the whole investigation. Set h from its released centre to the first infrared beam; measure s between beams.
- Predict how increasing h changes the interruption time. Release from rest without a push.
- Repeat three times at the same settings. Convert milliseconds to seconds, calculate each velocity and then the mean.
- Check your calculation and record the set. In single-gate mode use at least six distinct heights across a wide range. In double-gate mode investigate several separations.
- Use the graph or your two measured velocities to estimate g. Compare accuracy, spread and uncertainty separately.
A real practical requires a stable clamped stand, a suitable release mechanism and a catch tray. This simulation assumes the dowel stays vertical and ignores air resistance.
What the gate measures
Single gate: v² ≈ 2gh
Double gate: g ≈ (v₂² − v₁²) / 2s
A gate measures the time for the entire dowel to cross its beam. d/t is the average velocity during that interval. For constant acceleration it equals the velocity at the midpoint in time. A short dowel makes it a useful approximation to velocity near the gate.
With h measured from the released centre, v² ≈ 2gh. The finite crossing interval introduces a small approximation error; it is retained even in ideal mode. Fit a free intercept. Do not force an experimental line through the origin.
Extension: exact finite-length model
For centre-to-beam distance H and actual length D:
t_in = √[2(H − D/2)/g]
t_out = √[2(H + D/2)/g]
t_block = t_out − t_in.
The rendered beam crossings use these same event times.
Uncertainty belongs in the model
U(v²) / v² ≈ 2 U(v) / v
In experimental mode, use the larger of half the repeat range and the timing allowance (0.02 ms here) for U(t). Ideal mode retains only the ±0.005 ms rounding allowance. Include the length uncertainty even though the same dowel is used repeatedly. A systematic contribution does not disappear when you average.
For the single-gate graph, horizontal bars use ±2 mm in h. Vertical bars propagate length and timing uncertainty. These bars share a length contribution, so they are correlated. A precise fit can still give a biased g.
For two gates, a conservative estimate adds absolute uncertainties in v₂² and v₁², divides by |v₂² − v₁²|, then adds U(s)/s. It may overestimate the result because the length contribution is shared.
A light gate removes human reaction time from timing. It is not automatically more accurate than an electronic trapdoor: compare the full uncertainty budgets and possible systematic errors.
Model notes & references
This is a generic schematic light-gate apparatus, not a calibrated digital twin of one commercial instrument.
- Assumed logger resolution: 0.01 ms. Timing jitter: uniform ±0.015 ms; values round to the displayed resolution.
- Release-height variation: uniform ±1 mm on each drop. A fixed height offset up to ±1 mm and separation offset up to ±1 mm are chosen per session.
- Dowel actual length differs from its measured length by up to ±0.5 mm per session. The same offset is kept for all repeats.
- Ideal mode removes jitter and offsets but keeps 0.01 ms rounding. The displayed times are used for every calculation. A ±0.005 ms rounding allowance remains, along with the finite-length effect.
- g = 9.81 m s⁻²; no drag, rotation, beam width or release impulse. Noise magnitudes are teaching assumptions, not manufacturer specifications.
- Changing session clears results. CSV export is available before clearing.
Curriculum: Pearson Edexcel IAL Physics, Issue 3 — CP1 and Appendix 10. “CP1b” is the IVL method label.
Apparatus principles: PASCO photogate timing and gate and mounting reference. The schematic uses opposed emitter/receiver heads on a common support.
Explain your evidence
Make a checkable choice before revealing each explanation. Then connect it to your own measurements.
Your conclusion is included in the CSV export.