📚 AS Physics Experimental Investigation: Insights from Jan 22 Unit 1 | AS物理实验探究：2022年1月单元1试卷精析
Experimental investigations form the core of AS Physics Unit 1, assessing your ability to plan, collect data, analyse results, and evaluate procedures. The January 2022 examination paper featured a classic free-fall experiment to determine the acceleration due to gravity, g, using an electromagnet and a trapdoor switch. This article unpacks the key aspects of that investigation, equipping you with the skills to tackle similar practical-based questions with confidence. Whether you are revising for Edexcel, AQA, or another board, the underlying principles of experimental design, uncertainty handling, and graphical analysis are universal.
实验探究是 AS 物理单元 1 的核心，考查你计划、收集数据、分析结果和评估实验步骤的能力。2022 年 1 月的试卷中，出现了一个利用电磁铁和活板开关测定自由落体加速度 g 的经典实验。本文将拆解该探究的关键方面，帮助你掌握应对类似实验题的技能，充满信心。无论你备考的是 Edexcel、AQA 还是其他考试局，实验设计、不确定度处理和图形分析的底层原则都是相通的。
1. Understanding the Experimental Setup | 理解实验装置
The apparatus typically includes a steel ball bearing held by an electromagnet, a trapdoor switch positioned directly below, and an electronic timer that starts when the ball is released and stops when the ball hits the trapdoor. A metre ruler is used to measure the vertical distance s from the bottom of the ball to the trapdoor. The aim is to measure the time t taken for the ball to fall through this distance, under the sole influence of gravity, so that g can be calculated using the equation of motion s = ut + ½at² with initial velocity u = 0, giving g = 2s / t².
实验装置通常包括一个由电磁铁吸附的钢球、正下方放置的活板开关，以及一个电子计时器——当小球释放时开始计时，小球撞击活板时停止计时。用米尺测量小球底部到活板的竖直距离 s。目的是测量小球仅在重力作用下下落这段距离所用的时间 t，从而利用运动学公式 s = ut + ½at²（初速度 u = 0）算得 g = 2s / t²。
The electromagnet circuit and the timer must be connected correctly so that the timer starts the instant the current to the magnet is cut off. The trapdoor switch must break the timer circuit immediately upon impact. Any delay in these switching actions introduces systematic error.
电磁铁电路与计时器必须正确连接，确保电磁铁断电瞬间计时器立刻启动。活板开关必须在撞击瞬间断开计时电路。这些开关动作中的任何延迟都会引入系统误差。
2. Identifying Variables and Control | 识别变量与控制
In this experiment, the independent variable is the drop distance s, which you deliberately change over a range (e.g. from 0.200 m to 1.000 m in steps of 0.100 m). The dependent variable is the time of fall t. Controlled variables include the mass and shape of the ball bearing, the alignment of the electromagnet and trapdoor, and the absence of air currents—though air resistance cannot be entirely eliminated and becomes a source of error at larger distances.
在这个实验中，自变量是下落距离 s，需有意识地在一定范围内改变（例如从 0.200 m 到 1.000 m，步长 0.100 m）。因变量是下落时间 t。控制变量包括钢球的质量与形状、电磁铁与活板的对中情况以及气流的隔绝——尽管空气阻力无法完全消除，在距离较大时会成为误差来源。
Keeping the ball bearing’s mass constant ensures that air resistance effects are consistent across trials. Using the same ball prevents variations in size or surface that could alter the drag force. It is also important to release the ball without imparting any initial velocity; the electromagnet should simply cut off, letting the ball drop from rest.
保持钢球质量不变可确保各次试验中空气阻力的影响一致。使用同一颗小球可以防止大小或表面变化改变阻力。同样重要的是释放小球时不得施加任何初速度；电磁铁应仅切断电流，让小球从静止下落。
3. Collecting Reliable Data | 收集可靠数据
For each chosen distance s, multiple time readings (at least three repeats) should be taken to minimise random errors. The mean time tₐᵥ is then calculated. Consistent values indicate good precision; large spread suggests random uncertainties such as inconsistent release or timer triggering. The resolution of the timer (typically 0.01 s or 0.001 s) affects the precision of time measurements.
对于每个选定的距离 s，应读取多次时间（至少重复三次）以减小随机误差。然后计算平均时间 tₐᵥ。一致的数值表明精密度良好；发散度大则暗示存在释放不一致或计时触发等随机不确定因素。计时器的分辨率（通常为 0.01 s 或 0.001 s）会影响时间测量的精密度。
The distance s must be measured with care. A metre ruler typically has a resolution of 1 mm, but the uncertainty may be larger due to parallax error when aligning the bottom of the ball with a reference mark. Using a set square or a plumb line can improve alignment and reduce this uncertainty.
距离 s 必须仔细测量。米尺的分辨率通常为 1 mm，但由于小球底部与参考标记对齐时的视差，不确定度可能更大。使用三角板或铅垂线可改善对中，减小这种不确定度。
Record all data in a clear table with columns for s (m), t₁, t₂, t₃, mean t (s), and t² (s²). This facilitates later graphical analysis.
将所有数据记录在清晰的表格中，列名包括 s (m)、t₁、t₂、t₃、平均 t (s) 和 t² (s²)，以便后续进行图形分析。
4. Processing Data and Calculating g | 数据处理与计算 g
From the equation s = ½ g t², rearranging gives g = 2s / t². You could calculate a value of g for each pair of s and mean t, then find the average g. However, this method does not allow easy identification of systematic errors or the validity of the relationship. A superior approach is to plot a graph.
由方程 s = ½ g t² 整理得 g = 2s / t²。可以对每一对 s 和平均 t 计算出一个 g 值，然后求平均 g。然而，这种方法不易识别系统误差或检验关系的有效性。更好的方法是作图。
The expected linear relationship is obtained by plotting s on the y‑axis against t² on the x‑axis. According to s = (g/2) t², this yields a straight line through the origin with gradient = g/2. Hence g = 2 × gradient. Any systematic deviation from the origin indicates a possible error in the timing mechanism or an initial velocity.
将 s 作为 y 轴对 t² 作为 x 轴作图，即可获得预期的线性关系。根据 s = (g/2) t²，这将得到一条过原点的直线，斜率 = g/2。因此 g = 2 × 斜率。任何偏离原点的系统偏差都表明计时机构可能存在误差或小球有初速度。
s = (g/2) t² → gradient m = g/2 → g = 2m
Calculate the gradient from a large triangle drawn on the best-fit line, not from individual data points. Use the gradient to find g and compare with the accepted value of 9.81 m s⁻². Also calculate the percentage difference to evaluate accuracy.
利用最佳拟合线上绘制的大的三角形求斜率，而非个别数据点。用斜率求出 g，并与公认值 9.81 m s⁻² 比较。同时计算百分差异以评估准确度。
5. Uncertainty Analysis and Error Bars | 不确定度分析与误差棒
For a more sophisticated analysis, you can estimate the uncertainty in t² and include error bars on the graph. The absolute uncertainty in t is taken as the greater of the instrument resolution and the spread of repeats (e.g. ± half the range). The percentage uncertainty in t² is double the percentage uncertainty in t, because Δ(t²)/t² = 2 Δt/t. Use this to draw horizontal or vertical error bars depending on which variable has the larger relative uncertainty. Typically, error bars are placed on t².
若要进行更细致的分析，可以估计 t² 的不确定度并在图上加入误差棒。t 的绝对不确定度取仪器分辨率与重复测量范围之半的较大者（例如 ± 极差的一半）。t² 的百分不确定度是 t 的百分不确定度的两倍，因为 Δ(t²)/t² = 2 Δt/t。根据哪个变量的相对不确定度更大，在 t² 上画出水平误差棒，或在 s 上加垂直误差棒。通常误差棒加在 t² 上。
Drawing the worst acceptable line (steepest or shallowest line that still passes through the error bars) allows you to find the uncertainty in the gradient and hence the absolute uncertainty in your value of g. This demonstrates a thorough treatment of experimental errors.
画出最差可接受线（仍然穿过误差棒的最陡或最浅直线），可以得出斜率的不确定度，进而得到 g 值的绝对不确定度。这体现了对实验误差的深入处理。
6. Identifying Sources of Systematic and Random Error | 识别系统误差与随机误差的来源
Systematic errors shift all readings in one direction. In this experiment, a major systematic error arises from the time delay in the electromagnet releasing the ball; residual magnetism may cause the ball to fall slightly later than the timer starts. Similarly, if the trapdoor does not respond instantly, the measured time is too long, leading to an underestimation of g. Parallax error in measuring s, with the experimenter consistently reading from a wrong angle, is also systematic.
系统误差使所有读数朝一个方向偏移。本实验中，一个主要的系统误差源于电磁铁释放小球的时间延迟；剩磁可能导致小球掉落的时间略晚于计时器启动时刻。同样，如果活板不能即时响应，所测时间就会偏长，导致 g 被低估。测量 s 时的视差，如果实验者始终从错误角度读数，也是系统误差。
Random errors are unpredictable fluctuations, such as slight variations in the release mechanism, air turbulence, or the exact moment the trapdoor triggers the timer. These cause the repeated times to scatter. Taking multiple readings and using the mean reduces the effect of random errors, but does not eliminate systematic errors.
随机误差是不可预知的波动，例如释放机构的微小变化、气流扰动或活板触发计时的确切时刻。这会导致重复时间值离散。多次读数并取平均可以减小随机误差的影响，但不能消除系统误差。
7. Methods to Reduce Errors and Improve Accuracy | 减小误差与提高准确度的方法
To minimise the systematic delay from the electromagnet, use a clean, non-magnetised steel ball and ensure the magnet circuit is designed to demagnetise rapidly. A more reliable alternative is to use a mechanical release, or a light gate positioned at the very start of the fall to trigger the timer optically, eliminating the need for an electromagnet altogether.
为减小电磁铁带来的系统延迟，应使用清洁、未被磁化的钢球，并确保磁铁电路能快速退磁。更可靠的方法是采用机械释放，或在起点处使用光门通过光学方式触发计时，完全省去电磁铁。
To reduce parallax errors when reading the ruler, ensure the eye is level with the scale and repeat the measurement with the ball removed, using a fine pointer to locate the trapdoor’s contact point. Using a digital height gauge can further improve precision.
为减小读数视差，应确保视线与刻度水平，并取下小球后用一个细指针标定活板接触点进行重复测量。使用数字高度计可进一步提高精密度。
Air resistance is minimised by using a dense, small-diameter ball bearing and limiting the maximum drop distance. Conducting the experiment in a draught-free room and closing doors can also help.
使用密度大、直径小的钢球并限制最大下落距离，可将空气阻力降至最低。在无风的室内并关好门窗进行实验也有帮助。
8. Evaluating the Experiment and Justifying Modifications | 评估实验与论证改进
An effective evaluation does not simply list errors; it discusses which error is most significant and how it affects the result. For instance, if the graph of s against t² yields a positive intercept on the s-axis, this suggests a systematic zero error where the measured distance is too large or the timer starts late. Propose a specific improvement, such as adding a light gate at the start to provide a more precise zero time and noting how this change would eliminate that particular error.
有效的评估不是简单罗列误差，而是讨论哪种误差最为显著，以及它如何影响结果。例如，若 s-t² 图在 s 轴上有正截距，这就表明存在系统性的零点误差，即所测距离偏大或计时开始偏晚。应提出具体的改进措施，例如在起点加装光门以提供更精确的零时刻，并说明这一改动将如何消除上述特定误差。
When comparing your experimental value of g with the accepted value, comment on whether the difference can be accounted for by the estimated uncertainty. If the percentage difference exceeds the percentage uncertainty in g, there are likely unaccounted systematic errors.
在将实验所得的 g 值与公认值比较时，要说明差异是否能在估计的不确定度范围内得到解释。如果百分差异超过了 g 的百分不确定度，很可能存在未被考虑的系统误差。
9. Common Pitfalls in Exam Responses | 考试作答的常见失分点
Many students lose marks by failing to state variables clearly—for example, saying ‘keep the ball the same’ instead of ‘keep the mass and diameter of the ball bearing constant’. Similarly, when asked to explain how to improve the experiment, vague answers like ‘use a better timer’ without specifying what is better or how it reduces the specific error will not gain credit. Always link the improvement directly to the error it addresses.
许多考生因未能清晰陈述变量而丢分——例如说“保持小球相同”，而不是“保持钢球的质量和直径不变”。同样，当要求解释如何改进实验时，诸如“使用更好的计时器”这样模糊的回答，没有说明好在哪里或它如何降低特定误差，将无法得分。务必使改进措施与其所针对的误差直接关联。
Another typical mistake is confusing precision with accuracy. A set of closely clustered readings is precise, but if there is a systematic error, the value may not be accurate. Specifying that ‘repeat readings improve reliability/precision but do not remove systematic errors’ demonstrates a deeper understanding.
另一个典型错误是混淆精密度与准确度。一组密集的读数精密度高，但若存在系统误差，其值可能并不准确。明确指出“重复读数可提高可靠性/精密度，但不能消除系统误差”，能体现更深层次的理解。
10. Graphical Analysis Checklist | 图形分析要点清单
When plotting any graph for Unit 1 experimental work, ensure you: label axes with quantities and units (e.g. s / m and t² / s²); use sensible scales that spread data over more than half the grid; plot points with small crosses or dots with circles; draw a single, thin best-fit line that goes through as many error bars as possible; and calculate the gradient using a triangle that is at least half the length of the line. State the gradient value with appropriate units and use it to find g.
在为单元 1 实验工作绘制任何图形时，请确保：用物理量和单位标注坐标轴（例如 s / m 与 t² / s²）；选择合理标度，使数据分布在超过一半的网格上；用小十字或带圈圆点描点；画一条细而单一的最佳拟合直线，尽可能多地穿过误差棒；使用跨度至少为直线长度一半的三角形求斜率。给出带合适单位的斜率值，并用其求出 g。
Always include a title for your graph and, if required, draw a second line to show the worst acceptable gradient. Clearly indicate the gradient triangle on the graph and show the calculation steps.
务必为图形添加标题，若要求，还应画出第二条最差可接受斜率线。在图上清晰标出斜率三角形，并展示计算步骤。
11. Linking Theory to the Investigation | 将理论与探究联系起来
The experiment is built on the suvat equation s = ut + ½at². By setting u = 0 and a = g, the relationship simplifies. Understanding why we assume u = 0 is crucial: the ball must be released from rest, and any delay in release or kicking by the electromagnet violates this assumption. Recognising that the equation works only for constant acceleration and that air resistance causes the acceleration to decrease with speed is key to discussing limitations.
该实验建立在匀加速运动公式 s = ut + ½at² 之上。令 u = 0 且 a = g，关系式简化为 s = ½ g t²。理解为何假设 u = 0 至关重要：小球必须从静止释放，任何释放延迟或电磁铁的弹射都会违背这一假设。认识到该公式仅适用于恒定加速度，而空气阻力会导致加速度随速度减小，是讨论局限性的关键。
Additionally, when analysing the graph, a non-zero intercept may indicate that the measured distance s includes a systematic offset, or that the timer started after the ball had already moved. Comparing the experimental result with the textbook value of 9.81 m s⁻² highlights the total effect of uncertainties.
此外，在分析图形时，非零截距可能表明所测距离 s 包含了系统偏移，或者计时器在小球已经运动后才开始计时。将实验结果与课本值 9.81 m s⁻² 比较，可以凸显不确定度的总体影响。
12. Summary of Key Skills for AS Experimental Questions | AS实验题关键技能总结
Success in experimental investigation questions requires a command of: planning (selecting appropriate apparatus, identifying variables, describing a method with steps), data collection (recording measurements with consistent significant figures and calculating means), data presentation (choosing the correct graph to linearise the relationship and plotting accurately), analysis (finding gradient and intercept, linking to physical quantities), and evaluation (identifying sources of error, suggesting specific improvements, and assessing the impact on results).
成功应对实验探究题需要掌握以下技能：计划（选择合适的仪器，识别变量，按步骤描述方法）、数据收集（以一致的有效数字记录测量值并计算平均值）、数据呈现（选择正确图形使关系线性化并准确绘图）、分析（求斜率和截距，与物理量关联）以及评估（识别误差来源，提出具体改进措施，评估对结果的影响）。
Practising with past paper experiments, like the January 2022 free-fall investigation, builds familiarity with common apparatus and expectations. Always read the question carefully to tailor your answer to the specific context—exam boards often include subtle details in the stem that hint at particular errors or refinements.
通过练习历年真题中的实验，如 2022 年 1 月的自由落体探究，可以熟悉常见仪器和考试要求。务必仔细审题，使答案贴合具体情境——考试局常在题干中植入微妙细节，暗示某些特定误差或改进点。
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