📚 Mastering IAL Physics Unit 3: Experimental Investigations (Jan 2020 Insert) | 精通IAL物理Unit 3：实验探究（2020年1月插页）
The January 2020 Unit 3 insert for International A‑Level Physics presents a guided experimental context – typically a mechanics or electricity investigation – complete with raw data, apparatus details and specific instructions. Understanding how to extract, process and critically evaluate this information is essential for achieving top marks in the practical skills paper. This article uses a free‑fall experiment to measure the acceleration due to gravity g as a model, illustrating each skill you will need.
2020年1月的IAL物理Unit 3插页提供了一个引导式的实验情境——通常是力学或电学探究——包含原始数据、器材细节和具体指令。要想在实验技能笔试中取得高分，掌握如何提取、处理并批判性地评估这些信息至关重要。本文以测量重力加速度 g 的自由落体实验为范例，逐一阐释你所需的各项技能。
1. Reading the Insert with Purpose | 有目的地阅读插页
Begin by scanning the insert for the aim, the diagram of the setup and the list of apparatus. Note the resolution of each instrument explicitly stated – for example, a metre rule with 1 mm divisions gives an absolute uncertainty of ±0.5 mm, while a digital timer reading to 0.01 s has a resolution of 0.01 s. Highlight any instructions about repeating measurements and the exact procedure for releasing the object. In a typical free‑fall investigation, the insert might describe dropping a steel ball from rest beside a trapdoor or light gates, measuring the time t for a distance s.
先快速浏览插页，找出实验目的、装置示意图和器材清单。留意每件仪器明确给出的分度值——例如，分度为1 mm的米尺绝对不确定度为±0.5 mm，而读数为0.01 s的数字计时器其分辨率就是0.01 s。划出关于重复测量以及释放物体的确切步骤。在典型的自由落体探究中，插页可能会描述将钢球从静止释放，通过落体门或光门，测量下落距离 s 所需的时间 t。
2. Identifying Types of Uncertainty | 识别不确定度的类型
Measurements carry two main types of uncertainty. Reading uncertainty arises from the instrument’s scale; it is half the smallest division for analogue devices and the last significant digit for digital ones. Random uncertainty is revealed by the spread of repeated readings. You should calculate the mean of several repeat measurements and then find the half‑range, i.e., (max − min)/2, as an estimate of the absolute random uncertainty. For example, if a time reading repeats as 0.52 s, 0.54 s, 0.51 s, the mean is 0.523 s and the half‑range is 0.015 s, which is larger than the timer’s resolution, so the random uncertainty dominates.
测量带有两种主要类型的不确定度。读数不确定度来源于仪器的刻度；模拟仪器的读数不确定度是最小分度的一半，数字仪器则是最后一位有效数字。随机不确定度通过重复读数的分散程度体现。你应该计算多次重复测量的平均值，再用半距（最大值−最小值）/2 作为绝对随机不确定度的估计值。例如，若时间读数重复为 0.52 s、0.54 s、0.51 s，平均值为 0.523 s，半距为 0.015 s，这大于计时器的分辨率，因此随机不确定度占主导。
3. Organising Data in a Table | 用表格整理数据
Construct a clear table with columns for the independent variable, dependent variable and any calculated quantities. Each column heading must include the quantity’s symbol and its unit, separated by a solidus or brackets, e.g., “Distance s / m” or “Time squared t² / s²”. Record all raw values to the instrument’s precision and give calculated values to an appropriate number of significant figures. Below is a typical dataset that might appear in a Jan 2020 insert, showing distance s and the mean time t for a falling ball; the student has added a column for t².
绘制清晰的表格，列出自变量、因变量以及任何计算量。每列表头必须包含量的符号及单位，用斜线或括号分隔，例如“距离 s / m”或“时间的平方 t² / s²”。所有原始值都应按仪器精度记录，计算值则保留适当的有效数字。下表是一个可能出现在2020年1月插页中的典型数据集，显示下落距离 s 和球的平均时间 t ；学生已添加了 t² 列。
| s / m | t₁ / s | t₂ / s | t₃ / s | Mean t / s | t² / s² |
|---|---|---|---|---|---|
| 0.200 | 0.20 | 0.21 | 0.20 | 0.203 | 0.0412 |
| 0.400 | 0.29 | 0.28 | 0.28 | 0.283 | 0.0801 |
| 0.600 | 0.35 | 0.34 | 0.35 | 0.347 | 0.120 |
| 0.800 | 0.40 | 0.40 | 0.41 | 0.403 | 0.162 |
| 1.000 | 0.45 | 0.45 | 0.46 | 0.453 | 0.205 |
4. Calculating Percentage Uncertainty | 计算百分数不确定度
For a derived quantity like t², the percentage uncertainty behaves predictably: when a quantity is squared, its percentage uncertainty doubles. First compute the absolute uncertainty in the mean t as the half‑range, then express it as a percentage: (Δt / t̄) × 100%. Multiply by 2 to obtain the percentage uncertainty in t². For the first row above, if Δt = 0.005 s and mean t = 0.203 s, then %U(t) ≈ 2.46%, so %U(t²) ≈ 4.92%. This estimate is vital for drawing error bars on a graph.
对于像 t² 这样的导出量，百分数不确定度的表现是可预测的：当一个量被平方时，其百分数不确定度加倍。首先计算平均 t 的绝对不确定度（半距），然后表示为百分数：(Δt / t̄) × 100%。再乘以 2 就得到 t² 的百分数不确定度。对于上表第一行，若 Δt = 0.005 s，平均 t = 0.203 s，则 %U(t) ≈ 2.46%，故 %U(t²) ≈ 4.92%。这一估算是绘制图形误差棒的关键。
5. Plotting the Graph with Best‑Fit Line | 绘制最佳拟合线图
Plot s on the vertical axis (dependent) and t² on the horizontal axis (independent), as the equation s = ½ g t² suggests a straight line through the origin with gradient g/2. Mark data points with small crosses. For each point, add error bars on the t² axis using the absolute uncertainty (calculated as %U(t²) × t²). Draw a single, thin best‑fit straight line that passes through the origin and balances the points. Then add a worst‑acceptable line – either the steepest or shallowest reasonable line through the error bars – to determine the uncertainty in gradient later.
将 s 标在纵轴（因变量），将 t² 标在横轴（自变量），因为方程 s = ½ g t² 表明这是一条过原点、梯度为 g/2 的直线。用小的十字标记数据点。为每个点在 t² 轴上添加误差棒，其长度使用绝对不确定度（由 %U(t²)× t² 计算）。画一条通过原点且均衡各点的最细最佳拟合直线。再添加一条最差可接受线——穿过误差棒的合理的最陡或最浅直线——以便随后确定梯度的不确定度。
6. Determining Gradient and Its Uncertainty | 求梯度及其不确定度
Select two widely spaced points on the best‑fit line – not data points – and calculate the gradient Δs/Δ(t²). From the linearised equation, g = 2 × gradient. To find the uncertainty in g, calculate the gradient of your worst‑acceptable line and find the difference from the best gradient. For instance, if the best gradient = 4.90 m s⁻², giving g = 9.80 m s⁻², and the worst gradient = 4.70 m s⁻², then Δg = 2 × |4.90 – 4.70| = 0.40 m s⁻². Quote the final experimental value as g = 9.80 ± 0.40 m s⁻².
在最佳拟合线上选取两个相距较远的点——而非数据点——计算梯度 Δs/Δ(t²)。由线性化方程可得 g = 2 × 梯度。要确定 g 的不确定度，计算最差可接受线的梯度，并求出与最佳梯度的差值。例如，若最佳梯度 = 4.90 m s⁻²，得 g = 9.80 m s⁻²，而最差梯度 = 4.70 m s⁻²，则 Δg = 2 × |4.90 – 4.70| = 0.40 m s⁻²。最终的实验值应表示为 g = 9.80 ± 0.40 m s⁻²。
7. Comparing with the Accepted Value | 与标准值比较
Use the accepted value g = 9.81 m s⁻² to assess accuracy. Calculate the percentage difference: |(experimental – accepted)| / accepted × 100%. With our value, that is |9.80 – 9.81|/9.81 × 100% ≈ 0.10%. Then check whether the accepted value lies within the experimental range (9.80 ± 0.40 gives 9.40 to 10.20 m s⁻²), which it does. This indicates the experiment is accurate. If the percentage difference exceeds your percentage uncertainty, systematic errors are likely present.
使用公认值 g = 9.81 m s⁻² 评估准确度。计算百分差：|（实验值 − 公认值）| / 公认值 × 100%。用我们的值，就是 |9.80 − 9.81|/9.81 × 100% ≈ 0.10%。然后检查公认值是否落在实验范围 (9.80 ± 0.40 给出 9.40 至 10.20 m s⁻²) 内，它确实在范围内。这表明实验是准确的。如果百分差超出了你的百分数不确定度，则很可能存在系统误差。
8. Evaluating Systematic and Random Errors | 评估系统误差与随机误差
Systematic errors shift all readings in one direction. In a free‑fall experiment, a delayed release mechanism could increase every time reading, leading to a reduced value of g. Parallax error when measuring s with a metre rule could also be systematic if the observer consistently reads the scale from the same angle. Random errors cause scatter; timing by hand introduces reaction‑time variation. That scatter is why we draw error bars. To minimise random error, take more readings or use a more precise instrument, such as light gates interfaced with a data‑logger.
系统误差会使所有读数朝一个方向偏移。在自由落体实验中，释放机构延迟会使每次测得的 t 偏大，导致 g 值偏小。用米尺测量 s 时的视差误差，若观察者始终从同一角度读数，也可能是系统性的。随机误差造成数据分散；手动计时会带来反应时间的波动。这种离散正是我们要绘制误差棒的原因。为减小随机误差，可增加读数次数或使用更精密的仪器，如与数据采集器相连的光门。
9. Improving the Investigation | 改进实验探究
Several modifications can reduce uncertainty. Replace the trapdoor with two light gates: the first gate starts the timer as the ball passes, the second stops it, eliminating the delayed release problem. Increase the fall distance to make timing intervals longer; this reduces the percentage uncertainty in t. Use a plumb line to ensure the metre rule is vertical, and record the fall distance from the bottom of the ball to the light gate sensor. Repeat each distance measurement five times and use a set‑square to avoid parallax. These improvements address bias and scatter simultaneously.
若干改进措施能减小不确定度。用两个光门取代落体门：第一个光门在球通过时启动计时器，第二个使其停止，从而消除延迟释放的问题。增加下落距离以延长计时间隔，这能降低 t 的百分数不确定度。使用铅垂线确保米尺竖直，并记录从球的底部到光门传感器的下落距离。每段距离重复测量五次，并使用三角尺以避免视差。这些改进能同时处理偏差和离散。
10. Analysing Anomalous Points | 分析异常数据点
Sometimes a plotted point lies far from the trend. Before discarding it, check the raw data for transcription errors. If the anomalous reading was obtained under different conditions – for instance, a gust of wind or an accidental knock to the setup – it should be excluded, and the reason stated in your evaluation. Remaining anomalies may indicate an unidentified systematic effect, such as air resistance becoming significant at higher speeds, causing the last point to dip below the straight line. Identifying this shows critical thinking.
有时某个绘出的点会远离趋势线。在舍弃它之前，先检查原始数据是否有抄录错误。如果异常读数是在不同条件下获得的——例如，一阵风或装置意外被碰——则应予以剔除，并在评估中说明理由。若仍有异常，可能意味着存在未识别的系统效应，比如在速度较高时空气阻力变得显著，导致最后一个点落在直线下方。识别这一点能展现批判性思维。
11. Safety and Practical Precautions | 安全与实际操作注意事项
Even in a written examination, you may be asked to comment on safety. Dropping a steel ball from height requires a cleared area below; a sand tray or padded box can absorb the impact. If the investigation uses an electromagnet to hold the ball, warn about the hot coil if it is energised for long periods. Mention keeping electrical leads tidy to avoid tripping. These concise, relevant comments earn marks by showing awareness of real laboratory practice.
即使是在笔试中，你也可能被要求对安全事项发表评论。从高处释放钢球需要下方清空区域；可用沙盘或软垫箱来缓冲撞击。如果实验使用电磁铁固定钢球，需警示长时间通电时线圈会发热。还应提及整理好导线以免绊倒。这些简洁而相关的评论能体现你对真实实验室操作的认识，从而获得分数。
12. Exam Technique and Final Checklist | 考试技巧与最终检查清单
When tackling a Jan 2020‑style insert, allocate time to read it twice. Underline the independent and dependent variables, note the apparatus’ resolution, and plan your table before writing. Keep your calculations tidy; a well‑designed table with correct uncertainties impresses the examiner. Always state your final value with an absolute uncertainty and compare it to the accepted one. Finally, review your graph: does it have labeled axes with units, an appropriate scale, and a clear best‑fit line? Mastering these steps transforms the insert from a puzzle into a confident demonstration of practical physics.
在应对像2020年1月这类插页时，留出时间阅读两遍。划出自变量和因变量，记下仪器分辨率，并在动笔前列好表格。保持计算整洁；一张设计良好且正确标注不确定度的表格能给考官留下深刻印象。始终用绝对不确定度表述最终结果，并与公认值进行对比。最后，检查你的图：坐标轴是否标注了单位和物理量、比例是否恰当、最佳拟合线是否清晰？掌握这些步骤，就能把插页从一道难题转变为一篇自信的物理实验能力展示。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导