📚 AS Physics Unit 2: Experimental Investigations | AS物理单元2：实验探究
Unit 2 of the AS Physics specification puts a strong emphasis on developing practical skills and understanding how experiments are designed, carried out, and analysed. This article revisits the core principles of experimental investigations, providing a detailed guide that mirrors the type of questioning found in past papers such as the January 2022 session. From identifying variables to evaluating uncertainties and plotting graphs, you will be guided through everything you need to master this section.
AS物理单元2十分注重培养实验技能，要求理解实验是如何设计、实施和分析的。这篇文章回顾了实验探究的核心原则，详细指导了类似于2022年1月试卷中的问题类型。从识别变量到评估不确定度，再到绘制图表，你将系统地掌握这一部分所需的所有知识和技能。
1. Designing a Reliable Investigation | 设计可靠的实验
Every solid experiment begins with a clear plan. First, decide on the independent variable (the one you change) and the dependent variable (the one you measure). Next, identify at least three control variables that must be kept constant to ensure a fair test. Without controlling extraneous factors, the data may be invalid.
每个可靠的实验都始于清晰的计划。首先，确定自变量（你改变的变量）和因变量（你测量的变量）。然后，找出至少三个必须保持不变的受控变量，以保证实验公平。如果不控制外来因素，得到的数据可能是无效的。
A well-designed investigation also includes a justified method and an appropriate range of measurements. For example, when investigating the period of a pendulum, you would vary the length over a wide range (e.g., 0.20 m to 1.20 m) and take multiple readings to average out random errors.
精心设计的实验还应包含合理的方法和恰当的测量范围。例如，在探究单摆周期时，你应在较大范围内改变摆长（如0.20米至1.20米），并多次读数以消除随机误差。
2. Identifying and Controlling Variables | 识别与控制变量
In any experiment, clarity on variables is essential. The independent variable is plotted on the x‑axis of a graph; the dependent variable on the y‑axis. Control variables are those that could affect the dependent variable if allowed to change. For instance, when measuring the resistivity of a wire, the temperature must be kept constant because resistance depends on temperature.
在任何实验中，清晰理解变量至关重要。自变量绘制在图的x轴上，因变量在y轴上。控制变量是指那些如果发生改变会影响因变量的因素。例如，在测量导线电阻率时，必须保持温度恒定，因为电阻依赖于温度。
Often, a candidate loses marks by not describing exactly how a control variable is kept constant. Instead of saying ‘keep temperature the same’, you should state, for example, ‘use a water bath and thermometer to maintain the wire at 25 °C’.
考生常常因为未能准确描述如何保持控制变量恒定而丢分。与其说“保持温度相同”，不如具体说明“使用水浴和温度计使导线维持在25°C”。
3. Types of Errors: Random and Systematic | 误差类型：随机误差与系统误差
Random errors cause readings to be scattered around the true value. They can be reduced by taking multiple readings, averaging, and using the best-fit line through points. Systematic errors, on the other hand, shift all readings in the same direction – for example, a zero error on a micrometer or a misaligned scale. These cannot be reduced by averaging; they must be corrected by calibration or by adjusting the experimental setup.
随机误差导致读数分散在真值周围，可通过多次读数、求平均值以及使用最佳拟合直线来减小。而系统误差会使所有读数朝同一方向偏移——例如千分尺的零位误差或刻度未对齐。这类误差无法通过求平均值减小，必须通过校准或调整实验装置来修正。
When analysing your results, you should comment on whether any outliers exist and how they might be handled. An outlier that cannot be explained by a mistake should still be plotted but ignored when drawing the line of best fit.
分析结果时，应讨论是否存在异常值以及如何处理它们。若非由失误造成的异常值，仍应标出但在绘制最佳拟合线时可忽略不计。
4. Uncertainty in Measurements | 测量中的不确定度
Every measurement has an associated uncertainty. For a single reading from a digital instrument, the uncertainty is often taken as the smallest scale division, e.g., ±0.01 g for a balance reading to two decimal places. For analogue instruments, it is usually half the smallest division, e.g., ±0.5 mm on a metre ruler marked in millimetres.
每一次测量都伴有一个不确定度。对于数字仪器的一次读数，不确定度通常取最小分度值，如读到小数点后两位的天平为±0.01g。对于模拟仪器，一般取最小分度的一半，如毫米刻度的米尺为±0.5mm。
When taking multiple readings, the uncertainty can be estimated from the range: half the range (max − min)/2. If you measure the diameter of a wire at five different points and get values of 0.36, 0.38, 0.35, 0.37, 0.36 mm, the uncertainty is (0.38 − 0.35)/2 = ±0.015 mm, which rounds to ±0.02 mm.
当多次测量时，不确定度可以从范围来估计：半极差（最大值−最小值）/2。如果在五个不同点测量导线直径得到0.36, 0.38, 0.35, 0.37, 0.36mm，不确定度为(0.38−0.35)/2 = ±0.015mm，四舍五入为±0.02mm。
5. Combining Uncertainties | 不确定度的合成
When quantities are added or subtracted, absolute uncertainties add. For multiplication or division, we add percentage uncertainties. For example, if a length L = 0.500 ± 0.005 m (1% uncertainty) and a time t = 2.00 ± 0.02 s (1% uncertainty), the speed v = L / t has a percentage uncertainty of 1% + 1% = 2%. The absolute uncertainty in v is then 2% of the calculated value.
当量相加或相减时，绝对不确定度相加。对于乘除运算，则合并百分不确定度。例如，若长度L=0.500±0.005m（1%不确定度），时间t=2.00±0.02s（1%不确定度），则速度v=L/t的百分不确定度为1%+1%=2%，v的绝对不确定度就是该计算值的2%。
Δv/v = ΔL/L + Δt/t
This simple rule allows you to quote final results with a realistic error margin, which is crucial for comparing with accepted values.
这个简单规则可以让你带着现实的误差范围给出最终结果，这对与公认值进行比较至关重要。
6. Plotting and Analysing Graphs | 绘制和分析图表
A well-drawn graph is the heart of data analysis. Use sensible scales that occupy more than half the graph paper in each direction. Label axes with the quantity and its unit (e.g., ‘t/s’ not just ‘time’). Plot points as small crosses or encircled dots, and draw the best-fit straight line – not necessarily through the origin unless justified.
绘制得好的图表是数据分析的核心。使用合理的刻度，让坐标轴在每方向上占据超过半张图纸。坐标轴标注物理量及单位（如’t/s’而非仅仅’时间’）。用小的叉或带圈的点标出数据点，并画最佳拟合直线——除非有充分理由，不一定非经过原点。
Outliers should be identified and excluded from the line fitting. The gradient of the line often gives a physical quantity (e.g., from a voltage‑current graph you obtain resistance). The y‑intercept may reveal a systematic error or a constant term in the equation.
应当识别出异常值并在拟合直线时排除。直线的斜率通常代表某个物理量（例如，电压‑电流图可得到电阻）。y轴截距可能揭示系统误差或方程中的常数项。
7. Using a Graph to Derive Quantities | 利用图表导出物理量
Suppose an experiment follows the relationship T² = k × L, where T is period and L is pendulum length. Plotting T² on the y‑axis against L on the x‑axis produces a straight line through the origin. The gradient is k, and from it you can calculate the acceleration due to gravity, g = 4π² / k. This linearisation technique turns a curved relationship into a straight line, making analysis much simpler.
假设某实验遵循关系式T² = k×L，其中T是周期，L是摆长。以T²为y轴，L为x轴作图，将得到一条过原点的直线。其斜率为k，由此可计算重力加速度g = 4π²/k。这种线性化方法将曲线关系转化为直线，大大简化了分析。
Always show the calculation of gradient clearly using a large triangle drawn on the line. Read the coordinates from the line, not from the data points, to minimise errors.
始终利用在直线上画出的一个足够大的三角形，清晰地展示斜率计算过程。从直线上读取坐标，而不是从数据点，以减小误差。
8. Common Experiment: Determining g by Free Fall | 常见实验：通过自由落体测g
One experiment frequently examined is the determination of g using a trapdoor and an electromagnet, or by analysing a falling object using a timer. The distance fallen s and the time t are related by s = ½gt² if initial velocity is zero. By plotting s against t², the gradient is ½g, so g = 2 × gradient.
经常考察的一个实验是利用电磁铁和接盘测定g，或使用计时器分析下落物体。自由落体的距离s与时间t的关系为s = ½gt²（初速为零）。以s对t²作图，斜率为½g，因此g = 2×斜率。
Sources of error include reaction time if a stopwatch is used manually, air resistance that increases with speed, and the initial release not being perfectly instantaneous. Using electronic timing and light gates reduces random errors significantly.
误差来源包括：手动使用秒表造成的反应时间、随速度增大的空气阻力，以及初始释放不够瞬间。使用电子计时和光闸可大幅减少随机误差。
9. Common Experiment: Resistivity of a Wire | 常见实验：导线电阻率
The resistivity ρ of a metal wire is found from the formula R = ρL/A. By measuring the resistance R for different lengths L (keeping area A and temperature constant), a graph of R against L gives a straight line of gradient ρ/A. The cross‑sectional area A is calculated from the diameter d using A = πd²/4.
金属导线的电阻率ρ由公式R = ρL/A求得。通过测量不同长度L下的电阻R（保持横截面积A和温度恒定），绘出R‑L图，得到过原点直线，其斜率为ρ/A。横截面积A由直径d通过A = πd²/4计算得出。
Measuring the diameter at several points and taking an average reduces the effect of non‑uniformity. The main systematic error could be the contact resistance at the crocodile clips; ensuring tight connections and zeroing the meter helps.
在多个点测量直径并取平均值，可减小导线不均匀的影响。主要的系统误差可能是鳄鱼夹处的接触电阻；确保连接紧密并调零电表有助于消除影响。
10. Evaluating the Experiment and Suggesting Improvements | 实验评估与改进建议
All mark schemes look for specific evaluations. Instead of vague comments like ‘the experiment was done well’, mention whether the trend line was linear as expected, whether the intercept was near zero, and how close the calculated value was to the accepted literature value.
所有评分标准都要求有具体的评估。不要使用模糊的评语，如“实验做得很好”，而应指出趋势线是否如预期呈线性、截距是否接近零，以及计算值有多接近公认文献值。
Improvements could involve using a more precise instrument (e.g., a digital calliper instead of a ruler), taking more readings over a wider range, or controlling a variable that was previously overlooked. Always relate the suggestion to the specific limitation you identified.
改进措施可以包括使用更精确的仪器（例如用数显卡尺代替直尺）、在更大范围内采集更多读数，或控制一个之前忽略的变量。务必将建议与你指出的具体局限联系起来。
11. Skills Tested in Paper 3 (or Unit 2: Experimental Section) | Paper 3（或单元2实验部分）考察的技能
In the AS examination, the experimental investigation may appear as a structured question requiring you to analyse given data, complete a table, calculate uncertainties, plot a graph, and draw conclusions. You might also be asked to critique a student’s method or suggest modifications.
在AS考试中，实验探究可能以结构化问题的形式出现，要求你分析所给数据、完成表格、计算不确定度、绘制图表并得出结论。你还有可能被要求评价某个同学的方法或提出修改建议。
| Skill | What examiners look for |
|---|---|
| Table completion | Consistent decimal places, correct units, significant figures |
| Graph plotting | Suitable scales, labelled axes, accurately plotted points, best-fit line |
| Uncertainty handling | Calculation of absolute and percentage uncertainties, error bars |
| Drawing conclusions | Statement linking the gradient to a physical constant, comparison with true value |
掌握这些技能是取得高分的关键。练习对给定数据的分析，并熟悉不同仪器的不确定度处理。
12. Checklist Before the Exam | 考前检查清单
Review all the standard experiments you have performed. Know the independent, dependent, and control variables for each. Be able to explain how to reduce random errors and identify systematic errors. Practise plotting graphs with error bars and calculating “worst-fit” gradients to estimate uncertainty in the gradient.
复习所有你做过的标准实验。清楚每个实验的自变量、因变量和控制变量。要能够解释如何减小随机误差并识别系统误差。练习绘制带误差棒的图，并计算“最差拟合”线的斜率以估计斜率的不确定度。
Stay calm during the exam, read the stem of the question carefully, and always relate your answer to the physics of the situation. With a solid grasp of the experimental investigation framework, you will be well prepared for any Unit 2 paper, including the January 2022 style of questions.
考试时保持冷静，仔细阅读题干，并始终将你的答案与所涉物理情境相联系。牢牢掌握实验探究的框架，你就能充分应对任何单元2试卷，包括2022年1月卷的题型。
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