📚 Practical Skills at AS Level | AS 物理实验技能
Mastering practical skills is essential for success in CIE AS Physics Paper 3, where you will perform experiments, record measurements, and analyse data. This article covers everything you need to know: from identifying sources of uncertainty to plotting graphs and evaluating your conclusions. By understanding these core concepts, you will gain confidence in handling apparatus, processing results, and presenting findings in a clear, logical manner.
掌握实验技能对于在 CIE AS 物理 Paper 3 中取得成功至关重要，在这张试卷中你将进行实验、记录测量并分析数据。本文涵盖了你需要了解的所有内容：从识别不确定度的来源到绘制图表并评估你的结论。通过理解这些核心概念，你将能够自信地操作仪器、处理结果并以清晰、有逻辑的方式呈现发现。
1. Understanding Experimental Uncertainties | 理解实验不确定性
urement and in a set of repeated readings. The uncertainty reflects the range within which the true value is expected to lie. For a single reading taken from a digital instrument, the uncertainty is usually taken as ± the smallest scale division, whereas for an analogue scale, it is typically ± half the smallest division. When multiple readings are taken, the uncertainty can be estimated by calculating the half-range (½ × (maximum − minimum)) or the standard deviation of the data.
没有任何测量是完全精确的；每次读数都带有不确定度。在 AS 物理中，你必须学会估计单次测量和一组重复读数的不确定度。不确定度反映了真实值预期所在的范围。对于从数字仪器读取的单个读数，不确定度通常取作 ± 的最小刻度值，而对于模拟刻度，通常取 ± 最小刻度的一半。当进行多次读数时，可以通过计算半距（½ ×（最大值 − 最小值））或数据的标准偏差来估计不确定度。
a micrometer screw gauge, the reading may be 0.54 mm, with an uncertainty of ±0.01 mm. When you repeat the measurement and obtain 0.53 mm, 0.55 mm, and 0.54 mm, the range is 0.02 mm, so the half-range uncertainty becomes ±0.01 mm. Always state the uncertainty alongside your measured value, such as (0.54 ± 0.01) mm. This practice is fundamental to all subsequent data analysis.
清楚地理解不确定度可以让你评估结果的可靠性。例如，如果用千分尺测量一根金属丝的直径，读数可能是 0.54 mm，不确定度为 ±0.01 mm。当你重复测量并得到 0.53 mm、0.55 mm 和 0.54 mm 时，范围是 0.02 mm，因此半距不确定度变为 ±0.01 mm。始终将不确定度与测量值一同表述，例如（0.54 ± 0.01）mm。这种做法是所有后续数据分析的基础。
2. Types of Errors: Systematic and Random | 误差类型：系统误差与随机误差
Experimental errors are categorised as either systematic or random. Systematic errors shift all readings in one direction by a constant amount; they can be caused by poorly calibrated instruments or a zero error. For instance, a mass balance that reads 0.2 g when empty gives every mass reading a systematic offset. Such errors affect the accuracy of the experiment but can often be eliminated by adjusting the apparatus or subtracting the zero error from each reading.
实验误差分为系统误差和随机误差。系统误差会使所有读数向一个方向恒定偏移；它们可能是由校准不良的仪器或零点误差引起的。例如，一个空载时显示 0.2 g 的天平会使每次质量读数产生系统偏移。这种误差会影响实验的准确度，但通常可以通过调整仪器或从每个读数中减去零点误差来消除。
Random errors, on the other hand, cause readings to be scattered around the true value, sometimes above and sometimes below. These arise from unpredictable fluctuations in the environment, the reaction time of the experimenter when using a stopwatch, or the difficulty of judging a scale correctly. Random errors can be reduced by taking many repeat readings and calculating a mean value. The spread of the data then gives an indication of the random uncertainty. While systematic errors affect accuracy, random errors mainly influence the precision of the results.
另一方面，随机误差会导致读数分散在真实值周围，有时偏高，有时偏低。这些误差来源于环境中不可预测的波动、使用秒表时实验者的反应时间，或难以正确判断刻度。通过多次重复读数并计算平均值可以减少随机误差。数据的分散程度则提供了随机不确定度的指示。系统误差影响准确度，而随机误差主要影响结果的精密度。
3. Accuracy, Precision, and Sensitivity | 准确度、精密度与灵敏度
Accuracy refers to how close a measured value is to the true value. A highly accurate experiment has small systematic error. Precision describes the consistency of repeated measurements; a precise set of readings shows very little spread. However, results can be precise but not accurate if a systematic offset is present. In AS practicals you must be able to judge the accuracy and precision of your measurements by comparing them with known constants or calculating the range of repeats.
准确度指的是测量值与真实值的接近程度。一个高度准确的实验具有很小的系统误差。精密度描述的是重复测量的一致性；一组精密的读数显示出非常小的分散。然而，如果存在系统偏移，结果可能精密但不准确。在 AS 实验考试中，你必须能够通过与已知常数比较或计算重复读数的范围来判断测量的准确度和精密度。
Sensitivity is the smallest change that an instrument can detect. A sensitive balance might respond to a change of 0.001 g, while a less sensitive one only resolves 0.1 g. Choosing the right instrument for a measurement depends on the required uncertainty. For example, measuring the thickness of a sheet of paper requires a micrometer rather than a metre rule because the micrometer’s sensitivity (0.01 mm) is far better. In your write‑up, always note the sensitivity of each instrument used, as it directly affects your stated uncertainties.
灵敏度是仪器能检测到的最小变化。一台灵敏的天平可能对 0.001 g 的变化做出反应，而不太灵敏的天平只能分辨 0.1 g。为某项测量选择合适的仪器取决于所需的不确定度。例如，测量一张纸的厚度需要使用千分尺而不是米尺，因为千分尺的灵敏度（0.01 mm）要好得多。在实验报告中，务必注明所用每种仪器的灵敏度，因为它直接影响你所表述的不确定度。
4. Reading Scales and Significant Figures | 读数与有效数字
Taking a correct reading from an analogue scale requires care: your eye must be directly in line with the scale to avoid parallax error. When using a ruler, a protractor, or a voltmeter with a needle, always view the scale perpendicularly. Some instruments, such as thermometers and burettes, are often read from the bottom of the meniscus. For digital displays, simply record every digit shown, including any trailing zeros, as these indicate the instrument’s precision. Never round a reading before recording it.
从模拟刻度正确读数需要格外小心：眼睛必须与刻度正对，以避免视差。使用尺子、量角器或带有指针的电压表时，始终垂直观察刻度。有些仪器，如温度计和滴定管，通常从液面的底部读取。对于数字显示，只需记录显示的所有数字，包括末尾的零，因为这些零表明了仪器的精密度。切勿在记录读数之前进行四舍五入。
asured value should match the same decimal place. For instance, if you calculate a density as 2.7125 g cm⁻³ with an uncertainty of ±0.032 g cm⁻³, you should round the uncertainty to ±0.03 g cm⁻³ and the density to 2.71 g cm⁻³. In calculations, keep extra figures until the end, but present final results in the correct number of significant figures. This demonstrates careful data processing.
有效数字必须一致处理。最终引用的不确定度通常应保留 1 位有效数字，测量值应与其小数位数相匹配。例如，如果你计算出的密度为 2.7125 g cm⁻³，不确定度为 ±0.032 g cm⁻³，则应先将不确定度四舍五入为 ±0.03 g cm⁻³，再将密度四舍五入为 2.71 g cm⁻³。在计算过程中可以保留多余的数字直到最终，但最终结果应以正确的有效数字位数呈现。这表明了细致的数据处理。
5. Absolute, Fractional, and Percentage Uncertainties | 绝对、相对和百分不确定度
5 cm. This is the simplest form to record on a data table. The fractional uncertainty is Δx / x, and the percentage uncertainty is (Δx / x) × 100%. For the length above, the percentage uncertainty is (0.05/5.00) × 100% = 1.0% ferent measurements are, or when combining uncertainties in multiplications and divisions.
绝对不确定度 Δx 与被测量 x 具有相同的单位。如果你测得的长度为 (5.00 ± 0.05) cm，绝对不确定度就是 ±0.05 cm。这是在数据表上记录的最简单形式。相对不确定度是 Δx / x，而百分不确定度是 (Δx / x) × 100%。对于上述长度，百分不确定度为 (0.05/5.00) × 100% = 1.0%。当你需要比较不同测量的精密度，或在乘除运算中合并不确定度时，百分不确定度非常有用。
Always calculate percentage uncertainties for key measurements, especially those that will be raised to a power or multiplied together. For example, if you determine the period T of a pendulum as 1.2 s with an uncertainty of 0.1 s, the percentage uncertainty is about 8.3%. This is large, so you should consider how to reduce it, perhaps by timing 20 oscillations instead of one. Showing a clear awareness of percentage uncertainties in your practical write‑up demonstrates a mature understanding of experimental science.
始终为关键测量计算百分不确定度，尤其是那些将被乘方或相乘的量。例如，如果你测得单摆的周期 T 为 1.2 s，不确定度为 0.1 s，则百分不确定度约为 8.3%。这个数值很大，所以你应该考虑如何减小它，或许可以通过计时 20 个振荡而不是一个。在实验报告中清晰地展示对百分不确定度的认识，体现了对实验科学成熟的的理解。
6. Combining Uncertainties | 合并不确定度
When you use measured values in an equation, the final result will have an uncertainty that depends on the individual uncertainties. The rules for combining them depend on the operation. For addition and subtraction, you add the absolute uncertainties:
当你将测量值用于公式时，最终结果的不确定度将取决于各个独立的不确定度。合并不确定度的规则取决于运算类型。对于加法和减法，你将绝对不确定度相加：
If Z = A + B or Z = A − B, then ΔZ = ΔA + ΔB
对于 Z = A + B 或 Z = A − B，有 ΔZ = ΔA + ΔB。
For multiplication and division, you add the percentage (or fractional) uncertainties:
对于乘法和除法，你将百分（或相对）不确定度相加：
If Z = A × B or Z = A ÷ B, then %ΔZ = %ΔA + %ΔB
若 Z = A × B 或 Z = A ÷ B，则 %ΔZ = %ΔA + %ΔB。
When a quantity is raised to a power n, its percentage uncertainty is multiplied by n:
当一个量被进行 n 次方运算时，其百分不确定度需乘以 n：
If Z = Aⁿ, then %ΔZ = n × %ΔA
若 Z = Aⁿ，则 %ΔZ = n × %ΔA。
lute one. Practice these combinations with sample data to ensure you can quickly determine the uncertainty in calculated quantities such as resistance (R = V/I) or acceleration (a = 2s/t²).
应用这些规则之前，务必先将绝对不确定度转换为百分数，最后再将百分不确定度转换回绝对形式。用示例数据练习这些组合，以确保你能快速确定计算量（如 R = V/I 或 a = 2s/t²）的不确定度。
7. Recording Data in Tables | 在表格中记录数据
A well‑organised table is the backbone of effective data presentation. Each column must have a clear heading, with the quantity and its unit separated by a slash or given in brackets, e.g. “Length l / cm” or “Time t (s)”. The units should not appear next to each numerical entry. Repeat readings should be recorded side‑by‑side, with a final column for the mean value and another for the absolute uncertainty, if relevant. All raw readings must be written to the precision of the instrument, including trailing zeros.
一个组织良好的表格是有效数据呈现的支柱。每一列都必须有清晰的表头，物理量和单位用斜线分隔或用括号给出，例如 “Length l / cm” 或 “Time t (s)”。单位不应出现在每个数字条目的旁边。重复读数应并排记录，最后一列用于平均值，如果相关的话再增加一列用于绝对不确定度。所有原始读数必须按照仪器的精密度书写，包括末尾的零。
tension e = (L − L₀) / mm, and the uncertainty in e. Points to remember: use the same number of decimal places for all values in a column, round the average to the same precision as the raw data, and clearly indicate if an entry is a repeat or a derived quantity. A neat, systematic table makes it easy to detect anomalies and shows the examiner that you understand good experimental practice.
例如，在研究弹簧的伸长时，你的表格可能会有力 F / N、初始长度 L₀ / mm、最终长度 L / mm、伸长量 e = (L − L₀) / mm 以及 e 的不确定度这几列。需要记住的要点：一列中的所有数值应使用相同的小数位数，平均值四舍五入到与原始数据相同的精密度，并清楚地指示某一条目是重复读数还是导出量。一个整洁、系统的表格便于发现异常值，并向考官展示你理解良好的实验规范。
8. Plotting Graphs and Drawing Lines of Best Fit | 绘制图表和最佳拟合线
on and that is easy to read, e.g. multiples of 1, 2, 5 or 10. Plot the independent variable on the x‑axis and the dependent variable on the y‑ d a simple scale mark. Plot each data point as a small, sharp cross (×) or a circled dot (⊙), and do not join the points with a line.
AS 物理实验中的图表几乎都是在坐标纸上手绘的。选择一个能在每个方向至少使用坐标纸一半的刻度，并且易于读数，例如 1、2、5 或 10 的倍数。将自变量放在 x 轴，因变量放在 y 轴。给两条轴标上物理量、单位和简单的刻度标记。将每个数据点绘制成小而清晰的十字 (×) 或带圆圈的圆点 (⊙)，不要用直线连接这些点。
The line of best fit should be drawn as a single, thin, straight line that passes through as many error bars as possible and has an equal number of points above and below it. If the relationship is clearly non‑linear, you may need to draw a smooth curve instead. For a straight line, use a transparent ruler and do not force the line through the origin unless the theory explicitly demands it, or if the data strongly suggest it. Show the examiner your line is genuine by marking it with a subtle label like “best fit”. A well‑drawn graph often reveals unexpected trends or outliers.
最佳拟合线应绘制成一条单一、细且直的线，使之尽可能多地穿过误差棒，并使得线上方和下方的点数大致相等。如果关系明显是非线性的，你可能需要绘制平滑曲线而不是直线。画直线时，使用透明直尺，除非理论明确要求，或数据强烈表明可以，否则不要强制让直线通过原点。通过在线上标注 “best fit” 之类的微妙标签，向考官展示你的线是真实的。一张绘制良好的图表常常能揭示意想不到的趋势或异常值。
9. Determining Gradients and Intercepts | 确定梯度和截距
Calculating the gradient of a straight‑line graph is a central skill in AS practical analysis. Select two points that lie exactly on your line of best fit, not necessarily experimental points. The two points should be as far apart as possible to minimise uncertainty; using the coordinates (x₁, y₁) and (x₂, y₂), the gradient m is:
计算直线图的梯度是 AS 实验分析的核心技能。选择恰好位于最佳拟合线上的两点，而不一定是实验点。这两个点应尽可能远，以最小化不确定度；使用坐标 (x₁, y₁) 和 (x₂, y₂)，梯度 m 为：
m = (y₂ − y₁) / (x₂ − x₁)
梯度 m = (y₂ − y₁) / (x₂ − x₁)。
graph is a straight line passing through the origin, y = mx, and the gradient gives a physical constant, e.g. the spring constant from a force–extension graph. If the line does not pass through the origin, the y‑ ld also be determined. The intercept is simply the value of y where the line crosses the y‑ s unit, and discuss whether it represents a systematic error or a genuine physical effect.
小心地从坐标轴上读取坐标，并在作图纸上展示你的计算过程。梯度的单位由 y 和 x 的单位推导得出。如果图形是一条通过原点的直线，y = mx，梯度就给出了一个物理常数，例如力–伸长图中的弹簧常数。如果直线不通过原点，还必须确定 y 轴截距。截距就是直线与 y 轴（x = 0）相交处的 y 值。务必连同单位一起表述截距，并讨论它代表的是系统误差还是真实的物理效应。
10. Evaluating Conclusions and Limitations | 评估结论与局限性
xperimental value with the accepted value, if known, and calculate a percentage difference: |(experimental − accepted) / accepted| × 100% uss the most significant sources of uncertainty and whether they are random or systematic.
一旦分析了数据，你必须说明结果是否支持假设或预期的物理关系。如果已知公认值，将实验值与公认值进行比较，并计算百分比差：|(实验值 − 公认值) / 公认值| × 100%。如果差值大于你的实验不确定度，则表明可能存在系统误差。务必讨论最主要的不确定度来源，并说明它们是随机的还是系统的。
In your evaluation, identify practical limitations of the procedure, such as heat loss to the surroundings, friction not accounted for, or difficulties in accurately starting and stopping a stopwatch. Then, suggest realistic improvements that address those limitations directly. For example, if timing a free‑falling object gives a large uncertainty because of reaction time, you might propose using an electronic timer triggered by light gates. This shows the examiner you can critically assess your own experiment and think like a physicist. Never suggest vague improvements such as “use better equipment”; be specific and explain how the change would reduce uncertainty.
在你的评估中，要指出实验步骤的实际局限性，例如向周围环境的热损失、未计入的摩擦力，或难以准确地启动和停止秒表。然后，提出能直接解决这些局限性的现实可行的改进建议。例如，如果由于反应时间导致自由落体计时产生较大的不确定度，你可以提议使用光门触发的电子计时器。这向考官展示了你能够批判性地评估自己的实验并像物理学家一样思考。绝不要提出诸如“使用更好的设备”之类的模糊建议；要具体，并解释这一改变如何减小不确定度。
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