Wait, What? A falling object can give you the wrong value of g even when gravity is behaving perfectly.

The problem is usually the measurement chain. A release mechanism can give the object a tiny initial push. A timer can start at the wrong physical event. A light gate can infer speed from a flag width entered incorrectly. A short drop can make timing resolution dominate the whole result. The experiment is therefore not simply “drop something and use s = ½gt².” It is an exercise in deciding whether the motion you measured really matches the motion described by the model.

The experimental model

For an object released from rest and falling vertically with approximately constant gravitational acceleration:

s = ½gt²

so:

g = 2s/t²

This equation assumes initial vertical velocity is zero, acceleration is approximately constant and air resistance is small enough to neglect over the chosen interval.

Release is part of the measurement

If the object is pushed downward or upward as it is released, the simple released-from-rest equation no longer applies. A mechanical or electromagnetic release can improve repeatability because the object starts from a defined position without a hand impulse.

But even an electromagnet introduces a timing question: does the timer begin when current switches off, when the object physically detaches, or when a separate sensor detects the object? Those events may differ by milliseconds, which matters for short falls.

Why short drops are deceptively difficult

If a fall lasts 0.20 s and timing uncertainty is ±0.005 s, the fractional timing uncertainty is about 2.5%. Because time is squared in the denominator of g = 2s/t², timing uncertainty has an amplified effect on g.

A longer safe drop increases fall time and usually reduces fractional timing uncertainty. But longer drops can increase alignment demands and may make air resistance more important for light or high-area objects.

Light gates do not measure acceleration directly

A light gate detects interruption of a beam. If a card of known width L passes through in time Δt, speed is inferred as approximately:

v ≈ L/Δt

Two gates at different heights can provide two speeds or two timing events. From these, acceleration can be calculated using kinematic relationships. Entering the wrong flag width creates a systematic speed error even though the timer is functioning perfectly.

A graph can test the model more strongly

Measure fall time for several distances from the same release condition. Since:

s = ½gt²

a plot of s against t² should be approximately linear with gradient g/2.

This is stronger than calculating g from one drop because the graph reveals whether the relationship is linear and whether there is a non-zero intercept suggesting release/timing offsets.

Quantitative window

Suppose an object falls 0.80 m in 0.405 s.

g = 2(0.80)/(0.405²) ≈ 9.75 m s⁻²

This is close to the familiar local value near 9.8 m s⁻². But numerical closeness is not enough. If the distance was measured from the wrong reference point or the timer started before release, the agreement could be partly accidental.

Distance must have a defined reference point

Measure from the same physical point on the falling object at release and detection. If the release position is defined by the object’s lower edge but the sensor responds to its centre or flag edge, the nominal fall distance can contain a fixed offset.

A graph intercept can sometimes reveal this kind of geometry mismatch more clearly than repeated one-point calculations.

Air resistance: choose the object intelligently

A dense compact object experiences a smaller drag-to-weight ratio than a light object with large area. A metal ball is therefore usually a better free-fall object than a sheet of paper.

At school drop heights, air resistance on a small dense ball is often small enough to neglect to first approximation. The evidence boundary should still be stated: the measured acceleration is an approximation to gravitational acceleration in air, not a vacuum determination.

Observation versus inference

Observation: “A ball travelled 0.80 m between the defined release and detection events in 0.405 s.”

Transformation: “Using the released-from-rest model gives g ≈ 9.75 m s⁻².”

Inference: “The data are consistent with approximately constant downward acceleration close to local gravitational acceleration over this interval.”

Failure modes that cap standards

• Hand release: the object gains unknown initial velocity.
• Timer event mismatched to physical release: a fixed timing offset enters every result.
• Short fall time: timer resolution becomes a large fractional uncertainty.
• Wrong flag width: light-gate speed is systematically wrong.
• Distance measured from inconsistent points: geometry offset contaminates s.
• Large-area object: air resistance becomes significant.
• One-drop calculation only: model failure and intercept effects remain hidden.

Unfamiliar transfer: using video instead of light gates

High-frame-rate video can provide position at known time intervals. But video introduces scale calibration, perspective, frame-rate accuracy and point-tracking choices. The underlying RFE remains the same: identify the event and geometry connecting the raw signal to motion.

Secondary → JC → deeper Physics

Secondary: measure distance and time, use constant-acceleration equations, repeat readings and recognise release/timing limitations.

JC: use s–t² or velocity–time graphs, analyse intercepts, propagate uncertainty and compare alternative sensing methods.

Deeper Physics: free-fall measurements extend to vacuum drops, atom interferometry, absolute gravimeters, local gravitational anomalies and precision metrology.

Checkpoint

A student measures g from a 0.10 m drop and obtains 8.9, 10.7, 9.2 and 10.4 m s⁻². The timer resolution is 0.01 s. What is the first design improvement?

Answer key and WHY reasoning

Increase the safe fall distance and use a controlled release. The longer time interval reduces fractional timing uncertainty, while the controlled release reduces initial-velocity variation. Simply taking more decimal places in the calculation cannot repair poor timing resolution.

How to study this practical

Write the chain release event → distance definition → timing event → kinematic model → g. Then attack each arrow: what could shift it, by how much, and in which direction? High-standard practical revision is model auditing, not memorising apparatus names.

Evidence boundaries

A classroom free-fall experiment estimates local gravitational acceleration under its release, timing and drag assumptions. It does not test the universality of free fall across material composition, which is a different scientific job, nor does it establish g as exactly identical at every location on Earth.

Authoritative next steps

• Institute of Physics practical Physics resources
• NIST Physical Measurement Laboratory
• SEAB O-Level syllabus directory
• SEAB A-Level syllabus directory

Teaching Guide

For teachers and parents: give students the same timer but two drop heights and ask which experiment has lower fractional timing uncertainty. Then deliberately add a small push at release and ask what equation assumption has failed. The learning target is not “g = 9.8”; it is knowing why the apparatus deserves to estimate g at all.