Determination of g

Stand and clamp: To hold the electromagnet and position the ball for release.
Electromagnet: Used to initially hold the steel ball bearing in place.
Steel ball bearing: The object that will undergo free fall.
Light gates: Two gates are used to measure the time taken by the ball to pass between two points.
Stopwatch: To manually verify timing (if required).
Metre ruler: To measure the height $h$ between the release and detection points.

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Set Up Apparatus: Assemble the apparatus as shown in the diagram, ensuring the stand is secure with a counterweight if necessary to prevent toppling.
Adjust Initial Height: Position the lower light gate so that the height $h$ between the release point (electromagnet) and this gate is 0.500 m, measured with the metre ruler.
Release and Record Time:

Switch on the electromagnet to hold the steel ball bearing in place.
Reset the stopwatch, if used, and then turn off the electromagnet to release the ball.
The ball will pass through the lower light gate, which will record the time $t$ taken to fall from the initial height $h$ .

Decrease Height in Intervals: Reduce $h$ by 0.050 m by raising the lower light gate, and repeat the timing measurement for each new height, down to a minimum height of 0.250 m.
Repeat for Accuracy: Repeat each measurement twice more and record the mean time $t$ for each height $h$ to improve reliability.

Plot a graph with $\frac{2h}{t}$ on the y-axis and time $t$ on the x-axis.
Draw a line of best fit through the data points.

h = ut + \frac{1}{2}gt^2

Since $u = 0$ (the ball starts from rest), rearranging gives:

\frac{2h}{t} = 2u + gt

The y-intercept corresponds to $2u$ , where $u$ is the speed of the ball when it reaches the upper light gate, but this is not needed for calculating $g$ .

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Securing the Stand: Use a counterweight or clamp to ensure the stand is stable and will not tip over, preventing injuries.
Protecting the Ball Bearing: Place a soft pad or tray at the bottom to safely cushion the ball after it falls.

Consistent Release Position: Ensure that the starting position of the ball relative to the upper light gate remains constant to prevent inconsistencies in timing.
Air Resistance Minimisation: The steel ball bearing should be dense and compact to reduce the effects of air resistance, which could affect timing accuracy.
Reducing Parallax Error: To ensure accurate height measurement, position the ruler directly beside the light gates or use a set square.

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Free-Fall Motion: The ball bearing is under uniform acceleration due to gravity, and we use the time taken over a set height to measure this acceleration.
Equation of Motion for Free Fall: Since initial velocity $u = 0$ , the simplified equation $h = \frac{1}{2}gt^2$ describes the relationship between height, time, and acceleration due to gravity.
Graphical Analysis: By plotting $\frac{2h}{t}$ against $t$ , we can derive $g$ from the gradient of the best-fit line.

Determination of g Simplified Revision Notes for A-Level AQA Physics