📚 9630 PH01 Specimen: Experimental Determination of g | 9630 PH01样卷：重力加速度的实验测定
In the International AS Physics Unit 1 specimen paper (9630 PH01), a classic investigation involves measuring the acceleration due to gravity, g, using a freely falling steel ball and an electronic timer. This experiment links core mechanics concepts such as kinematics, uniform acceleration, and data analysis, and is representative of the practical skills assessed in the qualification.
在国际AS物理第一单元样卷（9630 PH01）中，一项经典实验是通过自由落体的钢球和电子计时器测量重力加速度 g。该实验将运动学、匀加速运动和数据分析等核心力学概念联系起来，代表了该资格评估中考察的实践技能。
1. Core Principle of the Experiment | 实验的核心原理
An object falling freely under gravity near the Earth’s surface experiences uniform acceleration, assuming air resistance is negligible. The relationship between displacement (s), initial velocity (u), acceleration (a), and time (t) is given by the kinematic equation: s = ut + ½at². By releasing a steel ball from rest (u = 0) and measuring the time it takes to fall a known vertical distance, we can determine a — the acceleration due to gravity.
在地球表面附近，若空气阻力可忽略，自由下落的物体会作匀加速运动。位移（s）、初速度（u）、加速度（a）和时间（t）之间的关系由运动学方程给出：s = ut + ½at²。将钢球从静止释放（u = 0），并测量其下落已知垂直距离所用时间，即可求出加速度 a，即重力加速度。
For u = 0, the equation simplifies to s = ½gt², which can be rearranged to g = 2s / t². A more robust approach uses multiple values of s and t, plotting a graph of s against t², where the gradient equals ½g.
当 u = 0 时，方程简化为 s = ½gt²，重新整理可得 g = 2s / t²。更可靠的方法是使用多组 s 和 t 值，绘制 s 对 t² 的图像，其斜率等于 ½g。
2. Apparatus Required | 所需器材
The typical setup described in the PH01 specimen includes an electromagnet to hold and release the steel ball, a trapdoor switch placed at a measured distance below, and an electronic timer or data logger connected to both. A metre rule or measuring tape is used to set the fall distance, and a plumb line ensures vertical alignment.
PH01 样卷中描述的典型装置包括：用于固定和释放钢球的电磁铁、置于其下方一定距离处的陷阱门开关，以及连接二者的电子计时器或数据采集器。米尺或卷尺用于设定下落距离，铅垂线用于确保竖直对准。
Other essential items: a steel ball (to reduce air resistance effects), clamp stands, bosses, and a switch to reset the timer. The trapdoor is a hinged plate that opens when the ball strikes it, breaking an electrical contact to stop the timer.
其他必备物品：钢球（以减小空气阻力影响）、铁架台、铁夹以及复位计时器的开关。陷阱门是一个铰接板，当球击中时会打开，从而断开电接触使计时器停止。
3. Experimental Setup and Procedure | 实验设置与步骤
First, suspend the electromagnet from a clamp stand and connect it to a low-voltage DC supply. Position the trapdoor switch directly underneath, aligned using a plumb line. Measure the vertical distance s from the bottom of the ball (when held by the magnet) to the top of the trapdoor. This distance should be varied systematically, e.g., from 0.500 m to 1.500 m in steps of 0.100 m.
首先，将电磁铁悬挂在铁架台上，并连接到低压直流电源。用铅垂线对准下方的陷阱门开关。测量从球（被磁铁吸住时）底部到陷阱门上表面的垂直距离 s。该距离应有系统地改变，例如从 0.500 m 至 1.500 m，步长 0.100 m。
After setting each distance, reset the timer. Switch off the electromagnet to release the ball; the timer starts when the ball leaves the magnet. When the ball hits the trapdoor, the timer stops, recording the fall time t. Repeat the measurement at least three times for each s to calculate a mean time and reduce random error.
设定每个距离后，将计时器复位。断开电磁铁电源释放钢球，计时器在球离开磁铁瞬间启动。球击中陷阱门时计时停止，记录下落时间 t。对每个 s 值至少重复测量三次，以计算平均时间并减小随机误差。
4. Variables and Control | 变量与控制
The independent variable is the vertical displacement s. The dependent variable is the fall time t (or t² for graphical analysis). Key controlled variables include the initial velocity (kept at zero by releasing from rest), the alignment to ensure purely vertical motion, and the electronic equipment to avoid systematic timing delays.
自变量是竖直位移 s。因变量是下落时间 t（或用于图像分析的 t²）。关键控制变量包括初速度（通过静止释放保持为零）、确保纯竖直运动的对准情况，以及电子设备以避免系统性的计时延迟。
Air resistance is minimised by using a dense, spherical steel ball and limiting the maximum fall height. The same ball and the same electromagnetic release mechanism must be used throughout to maintain consistency.
通过使用密度大的球形钢球并限制最大下落高度，空气阻力被降至最低。整个实验必须使用同一钢球和同一电磁释放机制以保持一致性。
5. Data Collection Table | 数据记录表
A suitable table for recording raw data and processed values is shown below. It includes columns for distance s, fall times t₁, t₂, t₃, mean time tₘₑₐₙ, and tₘₑₐₙ².
适合记录原始数据和处理值的表格如下所示，包括距离 s、下落时间 t₁、t₂、t₃、平均时间 tₘₑₐₙ 和 tₘₑₐₙ²。
| s / m | t₁ / s | t₂ / s | t₃ / s | Mean t / s | t² / s² |
|---|---|---|---|---|---|
| 0.500 | 0.32 | 0.33 | 0.32 | 0.323 | 0.104 |
| 0.700 | 0.38 | 0.39 | 0.38 | 0.383 | 0.147 |
| 0.900 | 0.43 | 0.44 | 0.43 | 0.433 | 0.187 |
| 1.100 | 0.48 | 0.47 | 0.48 | 0.477 | 0.228 |
Always record raw times to the precision of the timer (typically 0.01 s). Repeat measurements help identify anomalies and improve the reliability of the mean.
务必将原始时间记录到计时器的精度（通常为 0.01 s）。重复测量有助于识别异常值并提高平均值的可靠性。
6. Graphical Analysis and Determination of g | 图像分析与 g 的确定
Plot a graph of s on the vertical axis against t² on the horizontal axis. Since s = ½gt², the graph should be a straight line passing through the origin. The gradient of this line is equal to ½g, so g = 2 × gradient. Use a line of best fit and calculate the gradient from a large triangle; do not use data points directly.
绘制 s 为纵轴、t² 为横轴的图像。由于 s = ½gt²，该图像应是一条通过原点的直线。该直线的斜率等于 ½g，因此 g = 2 × 斜率。使用最佳拟合线，并通过大三角形计算斜率；切勿直接使用数据点。
For the sample data above, the gradient might be approximately 4.8 m s⁻², giving g ≈ 9.6 m s⁻². Many specimen mark schemes expect a value within ±1 m s⁻² of the accepted 9.81 m s⁻², with percentage difference discussed.
对于上述示例数据，斜率可能约为 4.8 m s⁻²，得出 g ≈ 9.6 m s⁻²。许多样卷评分方案期望得到的值在公认值 9.81 m s⁻² 的 ±1 m s⁻² 范围内，并讨论百分比差异。
Gradient = Δs / Δ(t²) = (1.100 – 0.500) / (0.228 – 0.104) = 0.600 / 0.124 ≈ 4.84 m s⁻²
g = 2 × 4.84 ≈ 9.68 m s⁻²
The intercept should be close to zero. A non-zero intercept suggests a systematic error, such as an incorrect zero for the distance measurement.
截距应接近于零。非零截距表明存在系统误差，例如距离测量的零点不正确。
7. Mathematical Verification Using Motion Equations | 利用运动方程进行数学验证
An alternative method calculates g for each pair of s and t directly, using g = 2s / t². Take the average of the results and evaluate the spread. This is less robust than the graphical method because it doesn’t compensate for random errors as effectively, and an outlier distorts the mean significantly.
另一种方法是用 g = 2s / t² 直接对每对 s 和 t 计算 g。取结果的平均值并评估离散度。此方法不如图像法可靠，因为它无法有效补偿随机误差，且异常值会显著扭曲平均值。
For the first data point: g = 2 × 0.500 / 0.104 = 9.62 m s⁻². For the last: g = 2 × 1.100 / 0.228 = 9.65 m s⁻². The consistency indicates small random errors. Always quote final g to an appropriate number of significant figures, typically 2 or 3.
对于第一个数据点：g = 2 × 0.500 / 0.104 = 9.62 m s⁻²。对于最后一个：g = 2 × 1.100 / 0.228 = 9.65 m s⁻²。一致性表明随机误差很小。最终 g 值通常应给出 2 或 3 位有效数字。
8. Sources of Uncertainty and Error | 不确定度和误差来源
Several factors contribute to experimental uncertainty. Reaction time is eliminated by the electronic timer, but there may be a delay between the electromagnet switching off and the ball actually releasing due to residual magnetism. This causes the measured time to be slightly too short, leading to an overestimate of g.
有几个因素会导致实验不确定度。电子计时器消除了反应时间，但电磁铁断开后，由于剩磁，球实际释放可能存在延迟。这会导致测得的时间略短，从而高估 g。
The distance s may be measured with a metre rule, introducing an uncertainty of ±1 mm or more. Parallax error when aligning the trapdoor and electromagnet can be significant. Furthermore, air resistance reduces the acceleration, causing g to be underestimated, although this effect is small for short drops with a steel ball.
距离 s 可能使用米尺测量，引入 ±1 mm 或更大的不确定度。对准陷阱门和电磁铁时的视差也可能很明显。此外，空气阻力会降低加速度，导致 g 被低估，不过对于钢球的短距离下落，此影响较小。
The timer itself has a precision limit (e.g., ±0.01 s). Expressing the combined uncertainty in g requires calculating percentage uncertainties: %U(g) = %U(s) + 2 × %U(t).
计时器本身有精度限制（如 ±0.01 s）。表示 g 的合成不确定度需要计算百分不确定度：%U(g) = %U(s) + 2 × %U(t)。
9. Suggested Improvements to Increase Accuracy | 提高精度的改进建议
To reduce the effect of residual magnetism, a mechanical release mechanism or a sharper magnetic cut-off could be used. Placing the trapdoor and electromagnet farther apart allows a longer fall time, reducing the percentage uncertainty in time – however, air resistance becomes more significant at greater speeds, so a balance must be struck.
为减小剩磁影响，可使用机械释放装置或更灵敏的磁力切断。增加陷阱门与电磁铁之间的距离可延长下落时间，降低时间的百分不确定度——但速度更大时空气阻力更显著，因此需要权衡。
Use a digital camera or light gates to record time more accurately and to verify that the ball passes a precise point. Conducting the experiment in a vacuum would eliminate air resistance, but is impractical in a school lab. Instead, use a heavier, denser ball and limit the maximum height to about 1.5 m.
使用数码相机或光闸可更准确地记录时间，并验证球通过精确位置。在真空中进行实验可消除空气阻力，但在学校实验室不切实际。取而代之，可使用更重、密度更大的球，并将最大高度限制在约 1.5 m。
Repeating the entire experiment with different electromagnets or timers can help identify systematic errors. Finally, always check that the trapdoor is clean and pivots freely to avoid a delay when the ball strikes.
使用不同的电磁铁或计时器重复整个实验有助于识别系统误差。最后，务必检查陷阱门是否清洁且转动自如，以避免球击中时延迟。
10. Common Mistakes and Pitfalls | 常见错误与陷阱
A typical mistake in the PH01 specimen investigation is treating the distance s as the separation between the electromagnet and the trapdoor, ignoring the diameter of the ball if it is not aligned carefully. Always measure from the bottom of the suspended ball to the trapdoor surface.
PH01 样卷实验探究中的一个常见错误是将距离 s 视为电磁铁与陷阱门之间的间距，而忽略未仔细对准时球的直径。务必从悬挂的球底部量到陷阱门表面。
Students may forget to account for the fact that t² is plotted on the x-axis, leading to confusion in gradient calculation. The gradient must be Δs / Δ(t²), not Δs / Δt. Additionally, using too few data points or not drawing a best-fit line reduces the reliability of the determined g.
学生可能忘记 t² 绘制在 x 轴上，从而导致斜率计算混乱。斜率必须是 Δs / Δ(t²)，而非 Δs / Δt。此外，使用过少的数据点或不画最佳拟合线会降低所得 g 值的可靠性。
11. Linking to the Specimen Mark Scheme | 联系样卷评分标准
The 9630 PH01 specimen mark scheme typically awards marks for: identifying the variables, describing a valid method with a clear diagram, recording measurements with appropriate precision, presenting data in a table, computing t², plotting a graph, determining gradient, calculating g, and commenting on sources of error and limitations.
9630 PH01 样卷评分方案通常对以下方面给分：识别变量、用清晰示意图描述有效方法、以适当精度记录测量值、以表格呈现数据、计算 t²、绘制图像、确定斜率、计算 g，以及评论误差来源和局限性。
It also rewards understanding that the graph should pass through the origin, and that gradient = ½g. Using the phrase ‘systematic error due to residual magnetism’ and proposing a sensible improvement can earn the higher-band marks.
理解图像应通过原点以及斜率 = ½g 也能得分。使用“剩磁引起的系统误差”这一表述并提出合理的改进建议，可赢得高分段的分数。
12. Conclusion | 结论
The free-fall experiment is a cornerstone of AS Physics practical work. It beautifully demonstrates the relationship between displacement, time, and acceleration, while teaching students how to handle real data, minimise errors, and draw conclusions from a linear graph. The specimen paper 9630 PH01 captures these skills precisely, guiding learners to think critically about both theoretical and experimental physics.
自由落体实验是 AS 物理实践工作的基石。它完美地展示了位移、时间和加速度之间的关系，同时教会学生如何处理真实数据、最小化误差并从线性图像中得出结论。样卷 9630 PH01 精确捕捉了这些技能，引导学习者批判性地思考理论与实验物理。
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