Aim
To determine the value of gravitational acceleration g by timing a steel ball falling freely through measured heights.
Variables
- Manipulated: Height of fall, h
- Responding: Time of fall, t
- Constant: The same steel ball and release mechanism
Apparatus & materials
- Steel ball
- Electromagnet
- Electronic timer
- Trapdoor (release-to-timer switch)
- Metre rule
- Retort stand
- Low-voltage power supply
- Connecting wires
Procedure
- Mount the electromagnet at the top of the stand so it holds the steel ball, with a trapdoor switch directly below.
- Adjust the height of fall to h = 0.400 m, measured with the metre rule from the bottom of the ball to the trapdoor.
- Switch off the electromagnet to release the ball; this starts the timer, and the ball stops it on hitting the trapdoor.
- Record the time of fall t; repeat three times and take the average.
- Repeat for h = 0.500, 0.600, 0.700 and 0.800 m.
- Record h, t and calculate t² for each height.
Tabulating results
Record the height h in m, the three timings and their average t in s, and the derived value t² in s². Head each column with the quantity and unit.
The graph
Plot h (y-axis) against t² (x-axis). A straight line through the origin shows h is directly proportional to t².
Analysis
For free fall from rest, h = ½gt², so the gradient of the h–t² graph equals ½g. Therefore g = 2 × gradient.
Precautions
- Measure h precisely from the bottom of the ball to the trapdoor.
- Make sure the ball is released cleanly and falls straight onto the trapdoor.
- Repeat each timing and average to reduce random error.
Force and Motion I · Graph skills
Sample results and what they show
These are example readings, not a mark scheme. For heights h = 0.400, 0.500, 0.600, 0.700, 0.800 m the time of fall t rose from about 0.286 s to 0.404 s, giving t² of about 0.082, 0.102, 0.122, 0.143 and 0.163 s².
The times are short, so the electronic timer matters: a hand-held stopwatch could not resolve 0.286 s reliably. Notice that t does not rise in proportion to h, increasing h from 0.400 m to 0.800 m only raises t from about 0.29 s to 0.40 s, not double, because h depends on t².
It is t² that is proportional to h: t² almost exactly doubles from 0.082 s² to 0.163 s² as h doubles. Repeat each drop three times and average, because a stray reading from a late release or the ball clipping the trapdoor will otherwise shift a point off the line.
Reading the graph and finding the answer
Plot h / m on the y-axis against t² / s² on the x-axis. The points should lie on a straight line through the origin, showing h is proportional to t².
Take the gradient from a large triangle on the best-fit line. Using (0.082 s², 0.400 m) and (0.163 s², 0.800 m): gradient = (0.800 − 0.400) m ÷ (0.163 − 0.082) s² = 0.400 m ÷ 0.081 s² = 4.94 m s⁻².
For free fall from rest h = ½gt², so the gradient equals ½g and therefore g = 2 × gradient = 2 × 4.94 m s⁻² = 9.88 m s⁻², close to 9.81 m s⁻². If the line has a small positive intercept on the h-axis, suspect that the ball began to move slightly before the timer started.
Marks examiners look for
State the variables: manipulated h / m, responding t / s, with the same steel ball and release mechanism kept constant. Measuring h from the bottom of the ball to the trapdoor is the point most often lost, measuring to the centre or the top introduces a systematic error.
Tabulate h / m, the three timings t₁, t₂, t₃ / s, the average t / s and t² / s², with units in the headings and consistent decimals. Repeating each timing and averaging is the fair-test move that earns credit, because it reduces the random error in a very short time.
On the graph, plot t² on the x-axis and draw a single best-fit line; a line forced through the origin when the points suggest otherwise loses the plotting mark. Finish with g quoted to a unit and sensible significant figures, and a conclusion linking the straight line to h ∝ t².
Do not treat air resistance as significant for a dense steel ball over these small heights.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)