📚 AS Physics Practical Investigation: Free Fall with Light Gates (Jan 2022 Insert) | AS物理实验探究：利用光门研究自由落体（2022年1月插页）
This article explores the core experimental techniques and data analysis required for the AQA AS Physics Paper 1 Insert from January 2022. The practical focuses on determining the acceleration due to gravity, g, by timing a steel ball as it falls between two light gates. We will break down the setup, linearisation strategies, graph plotting, and uncertainty evaluation that are essential for success in this assessed task.
本文深入探讨AQA AS物理2022年1月试卷1插页所涉及的核心实验技术和数据分析方法。该实验通过测量钢球在两道光门之间下落的时间来测定重力加速度 g。我们将详细分解实验装置、线性化策略、图像绘制以及不确定度评估，这些都是在这项考核任务中取得成功的关键。
1. Experiment Overview | 实验概述
The investigation aims to measure the local acceleration of free fall, g, using a steel ball dropped from an electromagnet through two vertically aligned light gates. The time interval between the ball breaking the beams is recorded for different distances between the gates. By applying the equations of motion, a linear graph can be plotted to extract a value for g.
本实验旨在利用从电磁铁释放、竖直穿过两道光门的钢球来测量当地的重力加速度 g。记录钢球遮断光束的时间间隔，并改变两光门之间的距离进行多次测量。通过运动学方程，可以绘制线性图像来求得 g 值。
The practical is assessed through the insert, which provides raw data of distance s and time t. Candidates must process the data, select appropriate axes, draw a line of best fit, and determine g from the gradient. This mirrors the skills required in the Practical Endorsement and hinges on a solid understanding of uncertainties.
该实验通过试卷插页提供距离 s 与时间 t 的原始数据来进行评估。考生需处理数据、选择合适的坐标轴、绘制最佳拟合线，并从斜率中计算 g。这反映了实践考核中的核心技能，并依赖于对不确定度的扎实理解。
2. Equipment and Setup | 设备和装置
A typical laboratory arrangement includes: a vertical clamp stand holding an electromagnet at the top, which releases a steel ball bearing when the current is switched off. Two light gates are positioned directly below, connected to a timer or data logger that measures the time interval between their beams being broken. The distance between the gates can be varied and is measured with a metre ruler.
典型的实验装置包括：一个竖直的铁架台，顶端固定有电磁铁，断开电流时释放一粒钢球。正下方安置有两道光门，连接到一个计时器或数据采集器，用于测量两道门光束被遮断的时间间隔。两光门之间的距离可以改变，并用米尺测量。
A plumb line ensures the beam of each light gate is horizontal and passes through the vertical path of the ball. The electromagnet is clean and dry to prevent the ball from sticking after the circuit is broken. For the insert data, typical values of s range from 0.200 m to 1.200 m, and the corresponding fall times are around 0.10 s to 0.50 s.
使用铅垂线确保每道光门的光束水平且通过钢球的下落路径。电磁铁保持清洁干燥，以防电路断开后钢球粘滞。对于插页中的数据，s 的典型取值范围约为0.200米至1.200米，对应的下落时间在0.10秒到0.50秒左右。
3. Theoretical Background | 理论背景
When the ball passes the upper light gate, it already possesses an initial velocity u. The motion between the two light gates is modelled as uniform acceleration under gravity, with no air resistance. The governing SUVAT equation is:
当钢球经过上方光门时已具有初速度 u。两光门之间的运动可模型化为重力作用下的匀加速直线运动，忽略空气阻力。其控制方程为：
s = u t + ½ g t²
Here s is the distance between the light gates, t is the measured time interval, and g is the acceleration due to gravity. Rearranging gives a linear form:
式中 s 是两光门间的距离，t 是测得的时间间隔，g 为重力加速度。通过移项可得到线性形式：
s / t = u + (g / 2) t
This is analogous to y = c + m x, where y = s/t, x = t, the gradient m = g/2, and the intercept is u. Plotting s/t against t yields a straight line whose gradient equals half of g.
这与 y = c + m x 形式类似，其中 y = s/t，x = t，斜率 m = g/2，截距为 u。以 s/t 对 t 作图，将得到一条直线，其斜率等于 g 的一半。
4. Procedure and Data Collection | 步骤和数据收集
As per the insert, the ball is released from the electromagnet to fall vertically. For each chosen distance s between the light gates, the electronic timer records the time t. The experiment is repeated several times at each distance to calculate a mean time, reducing random uncertainty.
按照插页所示，将钢球从电磁铁释放使其竖直下落。针对每一个选定的光门间距 s，电子计时器记录时间 t。每个距离重复实验数次，计算平均时间以减小随机不确定度。
The insert typically provides a table of five to eight pairs of s and t values, with t given to three or four significant figures. For example:
插页通常提供五到八组 s 和 t 的数据，时间 t 保留三到四位有效数字。例如：
| s / m | t / s |
| 0.150 | 0.106 |
| 0.300 | 0.158 |
| 0.450 | 0.196 |
| 0.600 | 0.226 |
| 0.750 | 0.253 |
| 0.900 | 0.278 |
From these, the quantity s/t must be computed for graphing. It is important to retain the correct number of significant figures throughout the processing.
根据这些数据，必须计算出用于绘图的 s/t 量。在整个处理过程中，保持正确的有效数字位数十分重要。
5. Understanding the Insert Data | 理解插页数据
The 2022 insert presents already-recorded experimental results, relieving the candidate of live practical work but testing the ability to interpret pre-collected data. You should first verify the units and significant figures, then calculate s/t for each pair.
2022年的插页呈现的是已记录好的实验结果，这免去了考生现场操作的环节，但考查的是解读预先收集的数据的能力。你首先应检查单位和有效数字，然后计算每一组的 s/t。
Be cautious: the times are very short, so even a 0.001 s uncertainty can propagate noticeably. Check if the data shows a clear trend—as s increases, t should increase, but s/t should also increase linearly with t if the model holds.
须谨慎：时间值非常短，因此即使是0.001秒的不确定度也可能显著传播。检查数据是否呈现清晰的趋势——随着 s 增加，t 应当增加，而若模型成立，s/t 也应随 t 线性增加。
6. Transforming Data for Linearisation | 数据线性化转换
The raw data are non-linear. To use a straight-line graph, we apply the transformation y = s/t and x = t. Compute these values with consistent decimal places. For the example table:
原始数据是非线性的。要使用直线图像，我们运用变换 y = s/t 和 x = t。以一致的小数位数计算这些值。以示例表格：
- s = 0.150 m, t = 0.106 s → s/t = 1.42 m s⁻¹
- s = 0.300 m, t = 0.158 s → s/t = 1.90 m s⁻¹
- s = 0.450 m, t = 0.196 s → s/t = 2.30 m s⁻¹
- s = 0.600 m, t = 0.226 s → s/t = 2.65 m s⁻¹
- s = 0.750 m, t = 0.253 s → s/t = 2.96 m s⁻¹
- s = 0.900 m, t = 0.278 s → s/t = 3.24 m s⁻¹
Plot these values on a graph with appropriate scales that use at least half of the grid in each direction. Label axes clearly as ‘t / s’ and ‘s/t / m s⁻¹’.
将这些数据描点于坐标图上，选用合适的标度，使绘制的图像在每一方向上至少占据网格的一半。清晰地标注坐标轴：’t / s’ 和 ‘s/t / m s⁻¹’。
7. Plotting the Graph | 绘制图表
Plot each data point with small, fine crosses. Draw a single straight line of best fit that passes through the trend of the points, balancing those above and below the line. Do not force the line through the origin, as a non-zero intercept is expected from the initial velocity u.
用细小的叉号标出每一个数据点。画出一条穿过数据点趋势的单一最佳拟合直线，并平衡分布于该线上、下方的点。不要强迫直线经过原点，因为因初速度 u 的存在，截距非零是可以预期的。
Identify two well-separated points on the best-fit line (not data points) to calculate the gradient. Use a large triangle to minimise percentage uncertainty in the gradient. The gradient m is given by:
在最佳拟合线上选取两个相距较远的点（非数据点）来计算斜率。使用大三角形以减小斜率的百分不确定度。斜率 m 由下式给出：
m = Δ(s/t) / Δt
For the illustrative set above, if the best-fit line passes through (0.100, 1.30) and (0.300, 3.50), then m = (3.50 − 1.30) / (0.300 − 0.100) = 11.0 m s⁻².
以示例数据为例，若最佳拟合线经过点 (0.100, 1.30) 和 (0.300, 3.50)，则 m = (3.50 − 1.30) / (0.300 − 0.100) = 11.0 m s⁻²。
8. Determining g from the Gradient | 从梯度求重力加速度g
Since m = g/2, the experimental value for g is simply g = 2 m. Using the calculated gradient, g = 2 × 11.0 = 22.0 m s⁻². This value is about twice the accepted value of 9.81 m s⁻², which indicates a systematic error—perhaps an incorrect distance measurement or faulty timer calibration in this illustrative case.
因为 m = g/2，重力加速度的实验值就是 g = 2 m。代入算得的斜率得 g = 2 × 11.0 = 22.0 m s⁻²。这个值大约是公认值9.81 m s⁻²的两倍，表明存在系统误差——在此假设案例中可能是距离测量错误或计时器校准不当。
In genuine insert data, the computed g should lie close to 9.8 m s⁻². Always express your final answer with an appropriate number of significant figures, typically two or three, and include the unit. Compare with the accepted value using a percentage difference: |experimental − accepted| / accepted × 100%.
在真实的插页数据中，算得的 g 应接近9.8 m s⁻²。始终以合适的有效数字（通常两到三位）表示最终结果，并带上单位。用百分偏差与公认值比较：|实验值 − 公认值| / 公认值 × 100%。
9. Uncertainty Analysis | 不确定性分析
Uncertainties arise from the measurements of s (using a metre ruler) and t (using a light gate timer). The metre ruler typically has an absolute uncertainty of ±1 mm, which can be treated as ±0.001 m. The timer may have a precision of 0.0001 s, but random variation dominates, assessed through repeat readings.
不确定度来源于 s 的测量（用米尺）和 t 的测量（用光门计时器）。米尺的绝对不确定度通常为±1毫米，可视为±0.001米。计时器的分辨率可达0.0001秒，但随机变异占主导，需通过重复读数来评估。
To find the uncertainty in g, first determine the uncertainty in the gradient, often using the difference between worst acceptable lines. Draw lines of maximum and minimum plausible gradient, calculate the corresponding g values, and the absolute uncertainty is half the difference between max and min g.
为求 g 的不确定度，首先确定斜率的不确定度，通常利用最差可接受直线之差来求。画出最大和最小合理斜率的直线，计算相应的 g 值，绝对不确定度为最大与最小 g 差值的一半。
For an expected g of 9.8 m s⁻², a typical percentage uncertainty might be around 5–10%, depending on the spread of points. Express the final result as g ± Δg and discuss whether the accepted value lies within the range.
对于预期的 g 值9.8 m s⁻²，典型的百分不确定度可能在5–10%左右，取决于数据点的离散程度。将最终结果表示为 g ± Δg，并讨论公认值是否落在该范围内。
10. Common Sources of Error | 常见误差来源
A major systematic error can occur if the distance s is measured inaccurately—for instance, measuring from the bottom of the electromagnet instead of between the light gate centres. This would offset s by a constant amount, altering the gradient significantly.
如果距离 s 测量不准，会产生很大的系统误差——例如，测量的是电磁铁底部到某一光门的距离，而非两光门中心之间的距离。这将使 s 偏移一个恒定值，从而显著改变斜率。
Another issue is the finite width of the ball and the light beam; if the ball’s diameter is not negligible, the time recorded may correspond to the interval between the leading edge breaking the upper beam and the leading edge breaking the lower beam, which is correct if the gates are identical. However, any parallax in setting the distance can introduce errors.
另一个问题是钢球和光束的有限宽度；若钢球的直径不可忽略，记录的时间可能对应于前沿遮断上方光束到前沿遮断下方光束的时间间隔，若两光门相同，这是正确的。但测量距离时的任何视差都可能引入误差。
Random errors stem from human reaction time when starting the drop (not applicable with electromagnetic release) and from slight misalignment causing the ball to graze the beam rather than fully break it. Ensure the gates are clean and aligned.
随机误差源于启动下落时的人为反应时间（电磁铁释放时不适用），以及因轻微未对准导致钢球不能完全遮断光束而是擦边而过。确保光门清洁并对齐。
11. Improvements and Extensions | 改进与拓展
To reduce uncertainty in s, use a vernier calliper or a travelling microscope to set the distance, but in an exam context, accept the metre ruler with parallax-reducing techniques. Using more data points over a wider range of s improves the reliability of the trend line.
为减小 s 的不确定度，可使用游标卡尺或移测显微镜设定距离，但在考试场景中，接受通过减小视差技巧使用米尺。在更广的 s 范围内采集更多数据点，可以提高趋势线的可靠性。
One could also use a video analysis technique with a high-speed camera to track the ball frame by frame, eliminating the need for light gates and providing position–time data directly. Alternatively, repeating the experiment with different ball masses can demonstrate the independence of g from mass.
也可以使用高速摄像的视频分析技术逐帧追踪钢球，从而无需光门，直接获取位置–时间数据。此外，用不同质量的球重复实验，可以验证 g 与质量无关。
For the insert task, the main focus is on data handling. Ensure you correctly label the graph, draw the trend line, and calculate the gradient carefully. Use a sharp pencil and a clear ruler in the actual exam.
对于插页任务，重点在于数据处理。确保正确标注图表、绘制趋势线并仔细计算斜率。在实际考试中，使用尖细的铅笔和清晰的直尺。
12. Conclusion and Exam Tips | 结论与考试技巧
The AS Physics insert requires you to seamlessly move between raw data, processed quantities, linear graphs, and derived values. Mastering this practical investigation not only secures marks in the written paper but also builds competence for the practical endorsement.
AS物理插页要求你能在原始数据、处理后的物理量、线性图像以及导出量之间流畅转换。掌握这项实验探究不仅能在笔试中稳拿分数，还能为实践认证培养能力。
Always read the axes labels specified in the question—sometimes you are told to plot s against t² or another transformation. Practise with past inserts to become familiar with the common pitfalls, such as units conversion and gradient misinterpretation. Remember: the gradient of s/t vs t is g/2, not g directly.
一定要仔细阅读题目要求的坐标轴标签——有时会要求你画 s 对 t² 或其他变换的图。利用历年插页进行练习，熟悉常见陷阱，如单位换算和斜率误读。请牢记：s/t–t 图像的斜率是 g/2，而非直接等于 g。
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