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Core Practical 1b — Determine g Using a Light Gate

CP1b · AS Physics · Method B

Theory & Background

Light gate principles, instantaneous velocity and determining g

Objectives

  • Determine g using a light gate and falling dowel — Method B of CP1
  • Understand how a light gate measures instantaneous velocity using v = d/t where d is the dowel length
  • Use a single gate setup: plot v² against h and find g from the gradient
  • Use a double gate setup: directly calculate g from two velocity measurements
  • Compare precision with the trapdoor method (CP1 Method A)

How a Light Gate Works

A light gate consists of an infrared beam across a narrow gap. When an object passes through, it interrupts the beam. A data logger records the interruption time t. If the falling object is a dowel of known length d, the instantaneous velocity as it passes through the gate is:

v = d / t

d = length of dowel (measured with a ruler, e.g. 2.0 cm = 0.020 m)
t = time the beam is interrupted (recorded by data logger, typically milliseconds)

This gives a much more precise value of velocity than the trapdoor method because the data logger measures time to ±0.1 ms, far better than a stopwatch.

Single Gate — v² vs h Graph

A single gate at height h below the release point measures velocity v at that point. Using SUVAT (u = 0):

v² = u² + 2as   →   v² = 2gh Plotting v² (y-axis) against h (x-axis) gives a straight line through the origin Gradient m = 2g   ∴   g = m/2

Use at least 6 different heights. The graph must pass through the origin since v = 0 when h = 0.

Double Gate — Direct Calculation of g

Two gates separated by a known distance s measure velocities v₁ (upper gate) and v₂ (lower gate). Using SUVAT:

v₂² = v₁² + 2as   →   g = (v₂² − v₁²) / (2s)

s = vertical separation between the two gates (measured with a metre rule)
This method calculates g directly from one drop — no graph needed.

Method A vs Method B — Comparison

Method A — Trapdoor

Uses an electronic timer started by the electromagnet and stopped by the trapdoor. Timing resolution ~1 ms. Prone to bounce and mechanical delay errors. Plots t² vs h → g = 2/gradient.

Method B — Light Gate

Uses a data logger measuring interruption time to ±0.1 ms. Much lower timing uncertainty. Can measure instantaneous velocity directly. Plots v² vs h → g = gradient/2. More precise, fewer systematic errors.

Step-by-Step Procedure

Follow these steps in the Simulation tab

Equipment

Falling dowel (2 cm long, 10 cm is also used) · Light gate(s) and data logger · Retort stand · Metre rule · Mechanism to hold and release dowel from rest · Guide tube or curtain track to keep dowel vertical

1
Choose gate mode: Single or Double

Select Single Gate to plot a v² vs h graph (recommended for full analysis). Select Double Gate to calculate g directly from one drop.

2
Set the dowel length

In a real experiment, measure the dowel length d with a ruler to the nearest mm. The simulation uses a fixed 20 mm dowel. The data logger measures interruption time t and computes v = d/t automatically.

v = d / t    e.g. d = 0.020 m, t = 12.4 ms → v = 1.613 m/s
3
Set the drop height h

Use the slider to set height h from the release point to the upper gate. In a real experiment, measure h with a metre rule from the bottom of the dowel to the top of the light gate.

4
Drop the dowel — repeat 3 times

Click Drop Dowel. The data logger records the interruption time t and calculates v = d/t with realistic noise. Repeat 3 times to get a mean velocity at this height.

5
Record the reading

Click Record Reading. The simulation logs h, v̄, and v̄² (single gate) or v₁, v₂, and calculated g (double gate).

6
Repeat for at least 6 heights (single gate)

Change h and repeat. For double gate mode, repeat at several gate separations s to get a mean g with uncertainty.

7
Analyse

Single gate: Go to Graph tab → plot v² vs h → g = gradient/2. Double gate: Go to Data tab → mean g is calculated directly from all drops.

Single: g = m/2 from v²–h graph   |   Double: g = (v₂²–v₁²)/(2s)

Controls

Gate mode
Dowel length d 20.0 mm
10 mm40 mm
Drop height h 0.50 m
0.10 m1.00 m
— ms
— ms
— ms
—

Results Data Table

Single gate mode — plots v² vs h. Need ≥6 different heights.

No data yet — go to Simulation tab.

Graph & Analysis

Single gate: v² vs h — gradient = 2g

Calculated g

—Collect ≥3 readings first

Graph Parameters

Gradient m = 2g—
R²—
Accepted g9.81 m s⁻²
% Difference—

Uncertainty

Avg %U in t—
%U in v—
%U in v²—

%U in v² = 2 × %U in v (power rule). Error bars shown in y-direction.

Interpretation

Complete your experiment to see analysis.

Mean g (double gate)

—Collect ≥3 readings first

Statistics

Mean g—
Std deviation—
Half range—
Accepted g9.81 m s⁻²
% Difference—

Interpretation

Complete your experiment to see analysis.

Discussion Questions

Write your answers and reveal model answers when ready.

Question 1
Explain how a light gate measures the instantaneous velocity of a falling dowel. Why is this more precise than using a stopwatch?
A light gate uses an infrared beam across a narrow gap. When the dowel passes through, it interrupts the beam. A data logger records the interruption time t to the nearest 0.1 ms. Since the dowel length d is known, the instantaneous velocity at the gate is v = d/t. This is more precise than a stopwatch because: (1) the data logger has a resolution of ~0.1 ms compared to ~0.1–0.2 s for a human reaction time; (2) the measurement is automatic so there is no reaction time error; (3) the time measured is very short (milliseconds) so it genuinely represents the velocity at that instant rather than an average over a long time.
Question 2
For the single gate method, show that plotting v² against h gives a straight line through the origin with gradient 2g.
Using SUVAT with u = 0, a = g, s = h: v² = u² + 2as → v² = 2gh. This is of the form y = mx where y = v², x = h, and m = 2g is constant. Since g is constant, v² is directly proportional to h — giving a straight line through the origin. The gradient m = 2g, so g = m/2. Any non-zero intercept would suggest the object was not released from rest, or that h was not measured from the correct reference point.
Question 3
For the double gate method, derive the expression g = (v₂² − v₁²) / 2s and state what each symbol represents.
Using SUVAT between the two gates: v₂² = v₁² + 2as, where v₁ = velocity at upper gate (m/s), v₂ = velocity at lower gate (m/s), a = g (acceleration due to gravity, m/s²), s = vertical separation between the two gates (m). Rearranging: v₂² − v₁² = 2gs → g = (v₂² − v₁²) / 2s. This allows g to be calculated directly from a single drop without needing to plot a graph, though repeating drops gives a mean and allows uncertainty to be estimated from the spread.
Question 4
The percentage uncertainty in v is approximately equal to the percentage uncertainty in t. Explain why, and state what the percentage uncertainty in v² would be.
Since v = d/t, and d (dowel length) is measured carefully with a ruler to give a very small percentage uncertainty (e.g. 1 mm in 20 mm = 5%, but this is systematic and constant), the random uncertainty in v comes mainly from the uncertainty in t. Using the division rule: %U(v) ≈ %U(d) + %U(t). For small timing uncertainty: %U(v) ≈ %U(t). For v²: since v is raised to the power 2, by the power rule %U(v²) = 2 × %U(v) = 2 × %U(t). This means timing precision is doubly important when computing v².
Question 5
Discuss two advantages of the light gate method over the trapdoor method for determining g, and one situation where the trapdoor method might be preferred.
Advantages of light gate method: (1) Timing precision — the data logger measures to ±0.1 ms compared to ~±1 ms for an electronic timer with a trapdoor, giving much lower %U in t and therefore in g. (2) No mechanical errors — the trapdoor method suffers from bounce delays and mechanical trigger errors; the light gate measures the beam interruption electronically with no moving parts. Advantage of trapdoor method: It directly measures the time of fall over a known distance without needing a calibrated object (dowel). If no suitable dowel is available, or if the falling object's length cannot be measured precisely, the trapdoor method is more practical. The trapdoor method also allows very large drop heights without needing multiple gates.