19; CP1MechanicsCore

Core Practical 1: Measuring Free-Fall Acceleration

Measure a motion that lasts a fraction of a second without letting reaction time dominate the result. The graph and height reference must match the chosen release and timing method.

40 min 2.1 Motion

What you'll be able to do

Choose an electronic timing method
Determine g from a graph
Evaluate trigger delays and distance uncertainty

Define exactly what is timed

For one suitable method, release a ball from rest using an electromagnet or release switch and stop an electronic timer when it reaches a trapdoor. Measure the vertical fall between the release reference and the detection reference. A manual stopwatch usually gives a large fractional timing uncertainty over such a short fall.

With appropriate light gates, a short flag’s interruption time can estimate speed as flag length divided by time. State whether you measure fall time or speed: the analysis is different. The speed estimate is an average during interruption, so a shorter flag can improve its instantaneous-speed approximation but increase fractional timing uncertainty.

Choose the graph before collecting data

For release from rest with negligible air resistance, h=gt²/2. Plot height vertically against squared fall time horizontally; the gradient is g/2. Use a range of heights and repeat timings independently at each height. A dense compact ball helps make drag small.

If using measured speed after a fall, v²=2gh for zero initial speed, so a v² against h graph has gradient 2g. Do not use the wrong gradient just because both methods involve gravity. Record original readings and units, then calculate squared quantities with appropriate precision.

h=\frac12gt^2,\qquad v^2=2gh

Separate scatter from systematic bias

An electromagnet can introduce a delay between timer start and actual release. A consistent offset in the measured fall distance or a non-zero release speed can also distort the result. A fitted intercept and the pattern of residuals help identify problems; do not force every graph through zero without considering the apparatus.

Use a secure stand and a catch arrangement, and keep the fall path clear. Repetition assesses random variation but does not eliminate a fixed timer delay. Improving the height reference or release mechanism addresses a different problem from merely taking more readings.

Work through the reasoning

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.

Example 1A height against t² graph has gradient 4.90 m s⁻². Determine g.

1Gradient

=g/2

g=2(4.90)=9.80

m s⁻².

Answer9.80 m s⁻².

Example 2A 0.50 s fall is timed with uncertainty ±0.002 s and height with 1% uncertainty. Estimate the percentage uncertainty in g=2h/t².

1Timing contributes

2(0.002/0.50)\times100\%=0.8\%

2Add the height contribution for the usual worst-case estimate:

1.0+0.8=1.8\%

AnswerAbout 1.8%, excluding additional systematic effects.

Equation recap

h=\frac12gt^2,\qquad v^2=2gh

Equation recap

Common mistakes to avoid

Using a graph gradient without comparing its axes with the equation.

Write the linear model explicitly.

Saying repetition removes all error.

Distinguish random scatter from consistent bias.

Key takeaways

Define distance and timing references precisely.
Different timing methods require different graph gradients.
Check systematic effects as well as scatter.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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