AS Physics Unit 2 Experimental Investigation (Jan 19) | AS 物理 Unit 2 实验探究 (2019年1月)

📚 AS Physics Unit 2 Experimental Investigation (Jan 19) | AS 物理 Unit 2 实验探究 (2019年1月)

The AS Physics Unit 2 January 2019 examination included an experimental investigation insert that required students to demonstrate a thorough understanding of practical procedures, data handling, and error analysis. This article reconstructs a typical investigation—measuring the acceleration of free fall, g—using an electromagnet and trapdoor, a classic experiment that aligns closely with the skills assessed. By breaking down the core elements of the insert, we explore how to plan an experiment, process raw data, calculate uncertainties, and draw valid conclusions, all essential for high achievement in the practical-based questions of the AQA specification.

2019 年 1 月的 AS 物理 Unit 2 试卷中包含一份实验探究插页，要求学生展现对实验流程、数据处理和误差分析的扎实掌握。本文重构了一个典型实验——利用电磁铁和陷阱门测量重力加速度 g——这一经典实验与所考查的技能高度吻合。通过拆解插页的核心要素，我们将探讨如何规划实验、处理原始数据、计算不确定度并得出有效结论，这些都是在 AQA 考试大纲实践类题目中取得高分的关键。

1. Introduction | 引言

The AQA AS Physics Unit 2 exam frequently embeds a practical scenario in the form of an insert, detailing an experiment that students may have encountered during their course. In January 2019, the insert described an investigation involving the measurement of a fundamental constant, likely the acceleration due to gravity, g. Such an experiment tests not only theoretical knowledge but also the ability to evaluate experimental techniques, identify systematic and random errors, and suggest improvements. Understanding the underlying principles and the standard methodology is crucial for interpreting the insert and answering the associated questions confidently.

AQA AS 物理 Unit 2 考试经常以插页的形式嵌入一个实践场景，详细描述一个学生在课程中可能遇到过的实验。2019 年 1 月的插页描述了一个涉及测量基本常数的探究实验，很可能是重力加速度 g 的测定。这种实验不仅考查理论知识，还考查评估实验技术、识别系统误差和随机误差以及提出改进建议的能力。理解基础原理和标准方法论对于解读插页、自信作答至关重要。

2. Experimental Aim | 实验目的

The primary objective of this investigation was to determine the acceleration of free fall, g, by releasing a steel ball from rest and measuring the time it took to fall through a known vertical distance. The experiment applies the kinematic equation for uniformly accelerated motion, s = ut + ½at², which reduces to s = ½gt² when the initial velocity u is zero. By varying the drop height and recording the corresponding fall time, the value of g could be deduced either by calculation for each trial or, more reliably, from a graph of s against t².

本实验的主要目的是通过从静止释放钢球并测量其下落已知竖直距离所需的时间，来确定重力加速度 g。实验应用了匀加速运动的运动学方程 s = ut + ½at²，当初速度 u 为零时，该方程简化为 s = ½gt²。通过改变下落高度并记录相应的时间，可以推断出 g 的值——既可以通过每次试验计算，也可以更可靠地从 s 对 t² 的图形中获得。

3. Apparatus and Setup | 实验装置与设置

The apparatus typically listed in the insert included an electromagnet, a steel ball bearing, a trapdoor mechanism linked to a timer, a metre rule, a retort stand with clamp, and a power supply for the electromagnet. The electromagnet held the steel ball at a measured height above the trapdoor. When the circuit to the electromagnet was broken, the ball began to fall, simultaneously starting the timer. The collision of the ball with the trapdoor opened a switch, stopping the timer and recording the fall time. A schematic diagram showed the vertical alignment of the ball and trapdoor to ensure the distance measured was precisely the fall distance.

插页中通常列出的设备包括：电磁铁、钢球、连接计时器的陷阱门装置、米尺、带铁夹的铁架台，以及为电磁铁供电的电源。电磁铁将钢球固定在陷阱门上方一个已测量的高度处。当电磁铁电路断开时，钢球开始下落，同时启动计时器。钢球撞击陷阱门时会断开一个开关，停止计时器并记录下落时间。插页中的示意图展示了钢球与陷阱门的竖直对齐，以确保所测量的距离正好是下落距离。

4. Procedure | 实验步骤

The insert outlined a step-by-step method that students had to evaluate. Key steps included:

Set the initial height: Place the bottom of the steel ball a known distance, e.g. 0.800 m, above the trapdoor using a metre rule. Ensure the rule is vertical to minimise parallax error.
Secure the ball: Energise the electromagnet and hold the steel ball against it, confirming the ball is released from rest.
Release and measure: Break the circuit; the timer starts and stops automatically. Record the time displayed.
Repeat trials: Perform three trials at each height to identify any anomalies and calculate a mean time.
Vary the height: Repeat the procedure for at least five different heights, e.g. 0.800, 0.700, 0.600, 0.500, 0.400 m.
Safety precaution: Place a foam pad beneath the trapdoor to prevent the ball from bouncing and causing injury.

插页概述了一个逐步的操作方法，供学生评估。关键步骤包括：

设定初始高度：使用米尺将钢球底部置于陷阱门上方一个已知距离处，例如 0.800 m。确保尺子竖直以减少视差误差。
固定钢球：给电磁铁通电并将钢球吸住，确认钢球从静止开始释放。
释放并测量：断开电路；计时器自动开始和停止。记录显示的时间。
重复试验：在每一个高度上重复三次，以便识别异常值并计算平均时间。
改变高度：至少用五个不同的高度重复上述步骤，例如 0.800、0.700、0.600、0.500、0.400 m。
安全预防措施：在陷阱门下方放置一块泡沫垫，以防止钢球反弹造成伤害。

5. Data Collection | 数据收集

A sample data table from the insert could appear as below. Students were expected to record raw data to an appropriate precision, typically 0.001 m for height and 0.001 s for time if using a digital timer. Each reading must include the absolute uncertainty, often taken as ± the smallest division of the measuring instrument or the resolution of the digital device. The uncertainty in time could be estimated from the spread of repeat readings, calculating the range and dividing by two.

插页中的示例数据表可能如下所示。学生需要以合适的精度记录原始数据，高度通常精确到 0.001 m，若使用数字计时器，时间精确到 0.001 s。每个读数必须包含绝对不确定度，通常取测量仪器最小分度值或数字设备的分辨率作为 ± 值。时间的不确定度可以通过重复读数的分散程度来估计，计算极差并除以二。

Height s / m	± Us / m	t1 / s	t2 / s	t3 / s	Mean t / s	± Ut / s
0.800	0.001	0.404	0.398	0.401	0.401	0.003
0.700	0.001	0.378	0.375	0.381	0.378	0.003
0.600	0.001	0.350	0.347	0.352	0.350	0.003

Note that the uncertainty in the mean time was calculated as half the range of the three readings. The uncertainty in height was taken as the accuracy of the metre rule. These uncertainties would later be used to construct error bars on a graph.

请注意，平均时间的不确定度按三个读数极差的一半计算。高度的不确定度取米尺的准确度。这些不确定度稍后将用于在图形上绘制误差棒。

6. Data Analysis and Calculation | 数据分析与计算

From the kinematic equation s = ½ g t², rearranging gives g = 2s / t². For each row of data, a value of g could be calculated. For example, using the first row: g = 2 × 0.800 / (0.401)² = 1.600 / 0.160801 ≈ 9.95 m s⁻². Repeating for other heights yields slightly different values due to random errors. A better estimate is obtained from a graphical analysis, which minimises the effect of outliers and allows a determination of uncertainty in the final result.

由运动学方程 s = ½ g t² 变形可得 g = 2s / t²。对于每一行数据，都可以计算出一个 g 值。例如，使用第一行数据：g = 2 × 0.800 / (0.401)² = 1.600 / 0.160801 ≈ 9.95 m s⁻²。对其他高度重复计算，由于随机误差，得到的值会略有不同。更好的估计值可通过图形分析得到，因为图形分析能最大限度地减少异常值的影响，并能确定最终结果的不确定度。

It is good practice to complete a table with calculated values of t² and its uncertainty. The uncertainty in t² is found using fractional uncertainties: if t = 0.401 ± 0.003 s, then fractional uncertainty in t is 0.003 / 0.401 ≈ 0.0075. The fractional uncertainty in t² is twice this, i.e. 0.015. The absolute uncertainty in t² is then 0.015 × (0.401)² = 0.015 × 0.1608 ≈ 0.0024 s². This can be approximated to 0.002 s² for plotting.

好的做法是完成一份包含 t² 及其不确定度计算值的表格。t² 的不确定度通过相对不确定度来计算：若 t = 0.401 ± 0.003 s，则 t 的相对不确定度为 0.003 / 0.401 ≈ 0.0075。t² 的相对不确定度是它的两倍，即 0.015。那么 t² 的绝对不确定度为 0.015 × (0.401)² = 0.015 × 0.1608 ≈ 0.0024 s²。作图时可近似取 0.002 s²。

7. Graphical Analysis | 图形分析

A graph of drop height s (on the y-axis) versus t² (on the x-axis) should produce a straight line passing through the origin, according to s = (g/2) × t². The gradient of this line is g/2, so g = 2 × gradient. Plot error bars for both axes—vertical bars for the uncertainty in s and horizontal bars for the uncertainty in t². Draw a best-fit line and, if possible, a worst-fit line to estimate the uncertainty in the gradient. If the best-fit gradient is m and the worst-fit gradient is m’, then the absolute uncertainty in the gradient is |m − m’|, and the percentage uncertainty in g equals that of the gradient.

绘制下落高度 s（在 y 轴上）对 t²（在 x 轴上）的图形，根据 s = (g/2) × t²，应得到一条通过原点的直线。该直线的斜率是 g/2，因此 g = 2 × 斜率。为两个轴都画上误差棒——s 的不确定度用竖直误差棒，t² 的不确定度用水平误差棒。画出最佳拟合线，如果可能的话，再画一条最差拟合线以估算斜率的不确定度。若最佳斜率为 m，最差斜率为 m’，则斜率的绝对不确定度为 |m − m’|，g 的百分不确定度等于斜率的百分不确定度。

For the sample data, the graph yields a gradient close to 4.95 m s⁻², giving g ≈ 9.90 m s⁻². This is slightly above the standard value of 9.81 m s⁻², suggesting systematic errors such as a slight delay in the timer starting or stopping. Students must comment on the agreement between the experimental value and the accepted value by comparing the percentage difference or by checking whether the accepted value falls within the experimental uncertainty range.

对于示例数据，图像给出的斜率接近 4.95 m s⁻²，从而得出 g ≈ 9.90 m s⁻²。这略高于标准值 9.81 m s⁻²，表明可能存在系统误差，例如计时器启动或停止的微小延迟。学生必须通过比较百分差异或检查标准值是否落在实验不确定度范围内，来评论实验值与公认值之间的一致性。

8. Sources of Uncertainty | 不确定度来源

The insert typically prompted students to identify possible sources of error. For this experiment, the main random uncertainties included: reaction time in setting up the exact height, though this was minimal with a metre rule; inconsistency in the release mechanism, where residual magnetism could delay the ball’s release; and the digital timer’s resolution. Systematic errors could arise from the distance measurement if the zero of the rule was not aligned correctly, from air resistance affecting the motion (though negligible for these heights), or from a delay in the timer stopping due to mechanical inertia of the trapdoor.

插页通常会提示学生找出可能的误差来源。就本实验而言，主要的随机不确定度包括：设定准确高度时的反应时间（尽管用米尺时这一问题很小）；释放机构的不一致性，残磁可能延迟钢球的释放；以及数字计时器的分辨率。系统误差可能来源于距离测量中尺子的零刻度未正确对齐、空气阻力对运动的影响（尽管在这些高度下可以忽略不计），或是陷阱门的机械惯性导致计时器停止延迟。

An important systematic effect in the electromagnet method is that the ball may not release immediately when the circuit is broken due to the time taken for the magnetic field to collapse. This ‘release delay’ means the measured time is slightly larger than the true fall time, leading to an underestimate of g. Alternatively, if the timer stops slightly after the trapdoor is triggered, the measured time is too long, again underestimating g. However, in the sample data, the obtained g was larger than the accepted value, which could be caused by a systematic error in the height measurement—perhaps the ball’s diameter was not accounted for, making the actual fall distance shorter than recorded, thereby overestimating g when using g = 2s/t².

在使用电磁铁的方法中，一个重要的系统效应是：当电路断开时，钢球可能不会立即释放，因为磁场消失需要时间。这种“释放延迟”意味着测得的下降时间略大于真实时间，从而导致 g 值低估。或者，如果计时器在陷阱门被触发后稍晚停止，测得的下降时间偏长，同样会低估 g。然而在示例数据中，得到的 g 值大于公认值，这可能由高度测量中的系统误差引起——也许没有考虑到钢球的直径，使得实际下落距离小于记录值，从而在使用 g = 2s/t² 时高估了 g。

9. Reducing Uncertainty | 减少不确定度

The insert asked for suggestions to improve accuracy and reduce uncertainty. Practical modifications could include: using a longer drop distance to increase the time and reduce the percentage uncertainty in timing; employing light gates instead of a mechanical trapdoor for more precise timing; ensuring the ball is a perfect sphere and measuring its diameter to calculate fall distance from its centre of mass; using a plumb line to guarantee verticality of the rule and release path; and taking more repeat readings at each height to reduce random error. Additionally, using a pressure-controlled environment to minimise air resistance could be mentioned for high-precision investigations.

插页要求提出提高准确度和减少不确定度的建议。实际的改进措施可以包括：使用更长的下落距离以增加时间，减小计时的百分不确定度；采用光门代替机械陷阱门以实现更精确的计时；确保钢球是完美的球体，并测量其直径以计算其质心下落距离；使用铅垂线确保尺子和释放路径的竖直性；在每个高度上增加重复读数的次数以减少随机误差。此外，对于高精度探究，可以提及使用压力受控环境以最大程度减少空气阻力。

Another powerful improvement is to use a graph of v² versus s, where v is the instantaneous speed measured by light gates. This method eliminates the need to assume u = 0 and reduces timing uncertainties. Students in the exam were often asked to explain why a particular improvement would reduce a named type of error.

另一个强有力的改进方法是绘制 v² 对 s 的图形，其中 v 是由光门测得的瞬时速度。这种方法无需假设 u = 0，并且减少了计时不确定度。考试中经常要求学生解释为何某项特定的改进能够减少某种指定的误差类型。

10. Safety Considerations | 安全注意事项

While the experiment poses low risk, the insert highlighted standard laboratory safety: secure the electromagnet and retort stand so they do not topple; keep electrical connections away from water; and ensure the falling ball is controlled with a catch box or foam pad. No hazardous chemicals or high voltages were involved, but students must always mention that care should be taken to avoid foot injuries from a dropped steel ball and that all equipment is switched off after use.

尽管实验风险较低，但插页强调了标准的实验室安全事项：固定好电磁铁和铁架台以防倾倒；使电气连接远离水源；确保用接球盒或泡沫垫控制下落的钢球。实验不涉及危险化学品或高电压，但学生必须始终提及要小心避免掉落的钢球砸伤脚，并且所有设备在使用后均应关闭。

11. Extension Ideas | 扩展思路

The investigatory nature of the insert often allowed for an extension into more advanced territory. For example, students could be asked to design an experiment to investigate the effect of air resistance on a falling object of different shapes, or to measure g using a pendulum. A classic AS extension is to use a ticker-tape timer and a free-falling weight to plot a velocity–time graph. Comparing the electromagnet method with the pendulum method highlights that the latter relies on small oscillations and the equation T = 2π√(l/g), providing an independent determination of g. Students should be able to discuss the advantages and limitations of each approach.

插页的探究性质常常允许扩展到更深入的领域。例如，学生可能被要求设计一个实验来研究空气阻力对不同形状物体下落的影响，或者使用单摆测量 g。一个经典的 AS 扩展实验是使用打点计时器和自由下落的重物来绘制速度–时间图。将电磁铁方法与单摆方法进行比较，可以突出后者依赖于小角度摆动和方程 T = 2π√(l/g)，从而为 g 提供一种独立的测定方法。学生应能讨论各种方法的优点和局限性。

12. Conclusion | 结论

The January 2019 AS Physics Unit 2 experimental insert served as a comprehensive test of practical skills, from instrument selection to error propagation and critical evaluation. By concentrating on a well-known experiment like the free-fall determination of g, students could connect their hands-on experience with the theoretical knowledge required to analyse modernised versions of the setup. Mastering such investigations not only secures high marks on the exam but also builds a solid foundation for the A2 practical assessments and future laboratory work in physics.

2019 年 1 月的 AS 物理 Unit 2 实验插页是对实践技能的一次全面考查，涵盖从仪器选择到误差传播以及批判性评价等方面。通过聚焦于一个像自由落体测定 g 这样广为人知的实验，学生能够将自己的实践经验与分析该装置现代化版本所需的理论知识联系起来。掌握此类探究实验不仅能在考试中稳拿高分，还能为 A2 实践评估以及未来的物理实验室工作奠定坚实的基础。

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AS Physics Unit 2 Experimental Investigation (Jan 19) | AS 物理 Unit 2 实验探究 (2019年1月)