Free Fall Virtual Lab: Measuring g with Light Gates

This free fall virtual lab matches the AQA A-level Physics required practical on determining g by a free-fall method. Students release a steel ball from an electromagnet, time its fall to a light gate at six heights and take three readings at each. The gradient of 2h against t̄² is g. The lesson covers means of repeats, a gradient, percentage difference, and random versus systematic error. Every value below was read from the simulation.

Curriculum links

• AQA A-level Physics (7408), required practical 3: determination of g by a free-fall method.
• AP Physics 1, Unit 1 (Kinematics): motion with constant acceleration, analyzed from experimental data and graphs.
• IB Diploma Physics, A.1 Kinematics: equations of motion for uniform acceleration, linearizing data to find a constant.

Simulic is not affiliated with or endorsed by AQA, the College Board or the International Baccalaureate.

Before the lab (5 min)

Ask students to commit to a prediction, on paper or as question 1 of the class link:

"A ball falls from rest. You move the light gate so the ball falls four times as far. How does the fall time change?"

Many students say "four times longer".

Method in the simulation

1. The page opens on Drop two objects. Click the Lab tab and keep g with light gates.
2. Set Drop height h to 0.20 m with the slider, or drag the light gate in the picture. h runs from the bottom of the ball to the beam.
3. Press Switch off magnet: the timer runs from release until the ball breaks the beam. Wait for the ball to land; take three readings.
4. Repeat at 0.40, 0.60, 0.80, 1.00 and 1.20 m. The table adds t̄, t̄² and 2h.
5. Since h = ½gt², 2h = g·t²: the gradient of 2h against t̄² is g. Calculate it from the 0.20 m and 1.20 m rows and compare with the best-fit line under the graph.
6. Percentage difference = |g − 9.81| ÷ 9.81 × 100.

The timer readings follow a fixed random sequence: on a freshly opened page, or after Clear table, the same presses in the same order give the same readings.

h (m)	t₁ (s)	t₂ (s)	t₃ (s)	t̄ (s)	t̄² (s²)
0.20
0.40
0.60
0.80
1.00
1.20

Expected results

Our run, heights in the order above on a freshly opened page:

h (m)	0.20	0.40	0.60	0.80	1.00	1.20
t̄ (s)	0.2033	0.2853	0.3507	0.4037	0.4510	0.4953
t̄² (s²)	0.0413	0.0814	0.1230	0.1629	0.2034	0.2454

The three readings at 0.80 m were 0.404, 0.404 and 0.403 s.

• Best-fit line: gradient g = 9.82 m/s², intercept −0.003 m, a 0.1% difference from 9.81 m/s².
• Two-point gradient: (2.40 − 0.40) ÷ (0.2454 − 0.0413) = 9.80 m/s².
• Square-root law: four times the height (0.20 to 0.80 m) only doubles the time (0.203 to 0.404 s).

Questions for students

1. (Prediction, asked again after the lab) How does the fall time change when the drop height is four times larger?
2. Which is the independent variable?
3. What is the mean fall time t̄ at h = 0.80 m?
4. Calculate the gradient of 2h against t̄² from the 0.20 m and 1.20 m rows.
5. Explain the random error in the readings, how repeats and the graph reduce it, and name one systematic error a real electromagnet adds.

Answers for teachers: (1) It doubles. (2) The drop height h. (3) About 0.404 s (accept 0.398–0.410). (4) About 9.80 m/s² (accept 9.50–10.10). (5) Readings at one height differ by a few milliseconds: random timing error, reduced by averaging repeats and by drawing a best-fit line through six points. A real electromagnet releases the ball a little after the timer starts. That makes every time too long, and repeating cannot remove it.

Common misconceptions

• "Heavier objects fall faster." On Drop two objects, untick Air resistance: the 5 kg and 0.2 kg objects fall side by side, and the readout gives one fall time, 3.03 s from 45 m, for any mass.
• "A graph that misses the origin is wrong." If every h were measured to the top of the ball instead, each 2h would grow by the same amount. The line would shift up, but its gradient, g, would not change.

Extension

• Terminal velocity with coffee filters: choose Drag on coffee filters, press Clear table, then Drop filters and Record for n = 1, 2, 4 and 8. Our run gave terminal velocities of 1.11, 1.57, 2.21 and 3.08 m/s. Four times the mass only doubles v_t, so drag ∝ v². Choose the graph (Terminal velocity)² against m: the line through the origin gives c = 0.0090 kg/m.

FAQ

Why do my students get slightly different times?

Each timer reading has a random error of about 2 ms from a fixed sequence, so a different order of presses gives slightly different values. The ranges for questions 3 and 4 held in all 20,000 model runs we tried, where the best-fit g stayed between 9.59 and 10.00 m/s².

Can I set the lab up for my students?

Yes. In the class link's starting values, set Screen to Lab and Experiment (Lab screen) to Measuring g with light gates. The page then opens on the light gates.

Does this replace the required practical?

No. AQA students must still do it by hand. Use the simulation to rehearse the analysis. See virtual labs vs physical labs.

Related simulations and guides

Measuring g with a simple pendulum Projectile motion – trajectory and air resistance

To measure g from motion images, see the projectile motion virtual lab. The reaction time virtual lab uses the same equation, d = ½gt², with a falling ruler.