Complete Physics Experimental Investigations | 完整物理实验探究

📚 Complete Physics Experimental Investigations | 完整物理实验探究

Mastering experimental physics is essential for any student tackling practical examinations in IGCSE or A-Level science courses. This guide covers the complete process of planning, conducting, analysing, and evaluating experiments, with an emphasis on key skills such as controlling variables, handling uncertainties, and interpreting data. From mechanics to electricity and waves, you will gain a solid foundation in experimental methodology that can be applied across all topics.

掌握物理实验探究对于任何参加IGCSE或A-Level科学课程实践考试的学生都至关重要。本指南涵盖了从实验规划、实施、分析到评估的完整过程，重点在于控制变量、处理不确定度和解释数据等关键技能。从力学到电学再到波动，你将获得可应用于所有主题的实验方法的坚实基础。

1. Designing an Experiment | 设计实验

A well-designed experiment starts with a clear aim or research question. The aim should be specific, measurable, and based on a scientific hypothesis. For example: ‘Investigate how the length of a pendulum affects its period.’ Before writing a detailed method, identify the independent variable (the factor you change) and the dependent variable (the factor you measure).

一个设计良好的实验始于明确的实验目的或研究问题。该目的应具体、可测量并基于科学假说。例如：“探究摆长如何影响单摆的周期。”在撰写详细方法之前，应先确定自变量（你改变的因素）和因变量（你测量的因素）。

Next, list all equipment needed, including measuring instruments, and decide on a suitable range and number of readings. A minimum of five readings for the independent variable is recommended to establish a trend. Always include a fair test plan: keep control variables constant. For the pendulum, control variables might include the mass of the bob and the amplitude of swing.

接下来，列出所有所需设备，包括测量仪器，并确定合适的自变量范围和读数次数。建议至少采集五组自变量数据以确定趋势。始终安排公平测试方案：保持控制变量不变。对于单摆，控制变量可能包括摆锤的质量和摆动幅度。

2. Variables and Controls | 变量与控制

Independent variable: The factor you deliberately change. In a pendulum experiment, it is the length of the string. Plot this on the x-axis of a graph unless the relationship is not straightforward.

自变量：你有意改变的因素。在单摆实验中，它是绳长。除非关系不是直接的，否则通常将它绘制在图的x轴上。

Dependent variable: The factor you measure as a result. Here, it is the period (T). This is plotted on the y-axis.

因变量：你作为结果测量的因素。此处，它是周期（T）。这绘制在y轴上。

Control variables: Factors that must be kept the same to ensure a fair test. For the pendulum, keep the bob mass constant, the initial displacement (small angles only, less than 10°) constant, and avoid air drafts. Record the values of control variables so the experiment can be replicated.

控制变量：为确保公平测试而必须保持不变的因素。对于单摆，保持摆锤质量不变，初始摆角不变（仅小角度，小于10°），并避免气流。记录控制变量的值，以便实验可以重复。

3. Measurement Techniques | 测量技术

Use instruments appropriate to the required precision. A metre ruler is fine for pendulum length (±0.1 cm or ±0.5 mm depending on scale). For time, a digital stopwatch provides a resolution of 0.01 s, but human reaction time introduces a larger uncertainty, typically ±0.2 s.

使用适合所需精度的仪器。米尺适用于测量摆长（根据刻度，不确定度可为±0.1 cm或±0.5 mm）。对于时间，数字秒表提供0.01 s的分辨力，但人的反应时间会引入更大的不确定度，通常为±0.2 s。

To reduce random errors, repeat measurements and take an average. For the period, measure the time for 10 or 20 complete swings and then divide by the number of swings to find the period. This technique reduces the impact of reaction time uncertainty per swing.

为减少随机误差，应重复测量并取平均值。对于周期，可以测量10次或20次完整摆动的时间，然后除以摆动次数来求得周期。此技巧降低了每次摆动反应时间不确定度的影响。

For length, measure from the point of suspension to the centre of the bob. Mark the centre clearly. For small amplitudes, the effective length is the distance to the centre of mass.

对于长度，应从悬挂点测量到摆锤的中心。清楚标记中心。对于小振幅，有效长度是到质心的距离。

4. Data Collection and Recording | 数据收集与记录

Record raw data in a clearly labelled table, using correct units in headings (e.g., Length l / cm). Do not write units inside the data cells. Include columns for independent, dependent, and any derived quantities (e.g., time for 10 swings, period). Show repeated readings and averages.

在标注清晰的表格中记录原始数据，表头使用正确的单位（例如，长度 l / cm）。不要在数据单元格内写入单位。包括自变量、因变量和任何派生量（例如，10次摆动的时间、周期）的列。展示重复读数和平均值。

All data should be recorded to the same decimal place consistent with the measuring instrument’s precision. For example, if using a metre ruler with mm marks, record length as 25.0 cm, not 25 cm.

所有数据应记录到与测量仪器精度一致的小数位。例如，如果使用带毫米刻度的米尺，应将长度记录为25.0 cm，而非25 cm。

If anomalous results occur, identify them and repeat those measurements if time permits. Do not erase anomalous data; instead, circle them and note possible reasons.

如果出现异常结果，识别它们并在时间允许的情况下重复这些测量。不要擦除异常数据；而是将其圈出，并注明可能的原因。

5. Tables and Graphs | 表格与图表

When plotting a graph, use a sharp pencil for points and line of best fit. Label axes with quantity and unit (e.g., Period squared T² / s²). Choose a sensible scale that uses more than half of the graph paper in both directions, avoid awkward scales like intervals of 3 or 7.

在绘制图表时，用削尖的铅笔描点和画最佳拟合线。坐标轴标注物理量和单位（例如，周期平方 T² / s²）。选择合理的刻度，使图形在双向都占满半张坐标纸以上，避免使用像3或7这样棘手的间隔。

Plot data points as small crosses (×) or encircled dots. Draw a best-fit straight line or smooth curve. For a straight line, use a transparent ruler. If the line does not pass through the origin, it may indicate a systematic error or an intercept.

将数据点画为小叉号（×）或带圈的点。画一条最佳拟合直线或平滑曲线。对于直线，使用透明直尺。如果直线不通过原点，可能表明存在系统误差或截距。

Calculate gradient using a large triangle; do not use plotted data points for the gradient triangle. Show coordinates on the graph. State the gradient with units. If the relationship is linearised (e.g., T² vs l for a pendulum), the gradient has physical meaning: g = 4π² / gradient.

使用大三角形计算斜率；不要将绘制的数据点用于斜率三角形。在图上显示坐标。说明斜率并带单位。如果关系已线性化（例如，单摆的 T² 对 l），则斜率有物理意义：g = 4π² / 斜率。

6. Error Analysis and Uncertainty | 误差分析和不确定度

Uncertainty in a single measurement is often half the smallest scale division (e.g., ±0.5 mm for a metre ruler). For a digital instrument, it is the resolution (e.g., ±0.01 s for stopwatch), but remember human reaction time dominates for timing.

单次测量的不确定度通常是仪器最小刻度的一半（例如，米尺为±0.5 mm）。对于数字仪器，它是分辨力（例如，秒表为±0.01 s），但要记住对于计时，人的反应时间起主要作用。

For repeated measurements, uncertainty can be estimated as half the range: (max − min)/2. Express the result as (mean ± uncertainty) with units.

对于重复测量，不确定度可用极差的一半来估算：(最大值 − 最小值) / 2。将结果表示为（平均值 ± 不确定度）并带单位。

When calculating a derived quantity, propagate uncertainties. For addition/subtraction, add absolute uncertainties. For multiplication/division, add percentage uncertainties. For example, speed v = s/t, if s has an uncertainty of 2% and t has 3%, then v has 5% uncertainty.

在计算导出量时，需传递不确定度。对于加减，将绝对不确定度相加。对于乘除，将百分比不确定度相加。例如，速度 v = s / t，若 s 的不确定度为2%，t 为3%，则 v 的不确定度为5%。

Use percentage difference to compare an experimental value with an accepted value: % difference = |experimental − accepted| / accepted × 100%. Comment on accuracy and possible systematic errors.

使用百分比差异将实验值与公认值比较：%差异 = |实验值 − 公认值| / 公认值 × 100%。评价准确度和可能的系统误差。

7. Drawing Conclusions | 得出结论

State whether the results support the hypothesis. Refer directly to the graph, gradient, or data trend. For a pendulum, if T² ∝ l, then the period squared is directly proportional to length, in accordance with the theoretical equation T² = (4π²/g) l.

说明结果是否支持假说。直接引用图表、斜率或数据趋势。对于单摆，如果 T² ∝ l，则周期平方与摆长成正比，符合理论方程 T² = (4π²/g) l。

Use the equation of the line (if linear) to extract constants, e.g., calculate g from gradient. Report the experimental value with its uncertainty and compare with 9.81 m/s².

使用直线方程（如果是线性的）提取常数，例如，从斜率计算 g。报告实验值及其不确定度，并与9.81 m/s² 比较。

Avoid definitive statements like ‘proves’; use ‘supports the theory’ or ‘within experimental uncertainty, the relationship is valid’.

避免使用“证明”等确定性的陈述；使用“支持该理论”或“在实验不确定度范围内，该关系成立”。

8. Evaluation and Improvements | 评估与改进

Identify sources of error: random errors (reaction time, parallax) and systematic errors (zero error on a measuring device, incorrectly marked scale). Suggest practical improvements: using a fiducial marker for timing oscillations, measuring length with a vernier caliper for greater accuracy, or using a light gate to remove reaction time.

识别误差来源：随机误差（反应时间、视差）和系统误差（测量装置零误差、刻度标记不正确）。提出切实可行的改进：使用基准标记来计时摆动，使用游标卡尺测量长度以获得更高准确度，或使用光闸消除反应时间。

Discuss reliability: more data points, repeated measurements, and checking consistency. If the line of best fit has outliers, suggest repeating those measurements. State whether the method could be modified to reduce uncertainty or extend the investigation.

讨论可靠性：更多数据点、重复测量和检查一致性。如果最佳拟合线有离群值，建议重复这些测量。说明是否可以修改方法以减少不确定度或扩展研究。

Always relate improvements to specific errors identified earlier. For instance, to minimise reaction time, use a light gate connected to a data logger; to improve length measurement, use a travelling microscope for small distances.

始终将改进与之前识别的具体错误联系起来。例如，为了使反应时间最小化，使用连接数据记录仪的光闸；为了改进长度测量，使用移测显微镜测量小距离。

9. Common Experiments – Mechanics | 常见实验——力学

Free fall to determine g: Drop a steel ball from various heights and use a trapdoor or light gates to measure time of fall. Plot height h against (time)², gradient = g/2. The equation h = ½ g t² is used if initial velocity is zero.

自由落体测定 g：从不同高度释放钢球，使用活动门或光闸测量下落时间。绘制高度 h 对 (时间)² 图，斜率 = g/2。如果初速度为零，使用方程 h = ½ g t²。

Newton’s second law: Use a dynamics trolley pulled by a falling mass over a pulley. Vary the accelerating force (mass hanger) while keeping total mass constant, or vary mass and keep force constant. Plot acceleration a against force F to obtain 1/m as gradient.

牛顿第二定律：使用一个由绕过滑轮的落体牵引的动力小车。改变加速力（砝码挂架）但保持总质量不变，或改变质量并保持力不变。绘制加速度 a 对力 F 的图，得到斜率为 1/m。

Investigate momentum or conservation of energy using light gates

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