AS Physics: Experimental Investigations | AS 物理：实验探究

📚 AS Physics: Experimental Investigations | AS 物理：实验探究

Practical work lies at the heart of physics. In the AS Physics course (9630), experimental investigations not only reinforce theoretical ideas but also develop essential skills in planning, measurement, data analysis and evaluation. This article walks you through the key aspects of experimental work, from choosing apparatus to assessing uncertainties, so that you can approach any investigation with confidence.

实验是物理的核心。在 AS 物理课程（9630）中，实验探究不仅巩固理论知识，还培养计划、测量、数据分析和评估等关键技能。本文带你梳理实验工作的各个重要环节，从选择仪器到评估不确定度，让你游刃有余地面对任何探究任务。

1. Planning the Investigation | 制定探究计划

Before any practical work begins, you must identify the independent variable (the one you change), the dependent variable (the one you measure) and the control variables (the ones you keep constant). A clear plan ensures the data you collect is reliable and relevant to the physics relationship you are testing.

在做任何实验之前，你必须确定自变量（你改变的物理量）、因变量（你测量的物理量）和控制变量（需要保持不变的量）。清晰的计划能确保收集到的数据可靠，并与你要验证的物理关系相关。

Independent variable: for instance, the length of a pendulum or the voltage across a component.

自变量：例如单摆的长度或元件两端的电压。
Dependent variable: the quantity you measure as a result, such as time period or current.

因变量：你作为结果测量的量，比如周期或电流。
Control variables: aspects like temperature, mass or initial conditions that should stay the same so they do not affect the outcome unfairly.

控制变量：温度、质量或初始条件等应保持不变的方面，以免对结果产生额外影响。

2. Measurements and Uncertainties | 测量与不确定度

Every measurement carries uncertainty. Accuracy tells you how close a result is to the true value, while precision reflects the spread of repeated readings. Understanding the difference is crucial for evaluating experimental data.

每一次测量都带有不确定度。准确度表示结果与真实值的接近程度，而精密度反映重复读数的分散程度。理解两者的区别对评估实验数据至关重要。

Systematic errors (e.g. a zero error on a meter) shift all readings in one direction; random errors (e.g. reaction time when using a stopwatch) cause scatter but can be reduced by averaging.

系统误差（如仪表零位误差）使所有读数朝同一方向偏移；随机误差（如使用秒表时的反应时间）造成数据散布，但可通过取平均值减小影响。

You will often express an absolute uncertainty (e.g. ±0.1 cm) and a percentage uncertainty. The percentage uncertainty in a calculated quantity is found by adding the percentage uncertainties of the measured quantities – for multiplication or division – or adding absolute uncertainties for addition/subtraction.

你通常会给出绝对不确定度（如 ±0.1 cm）和百分比不确定度。通过乘除计算得到的物理量，其百分比不确定度等于各测量量百分比不确定度之和；若为加减运算，则需合并绝对不确定度。

3. Using Measuring Instruments | 使用测量仪器

Metre rules, vernier callipers and micrometer screw gauges are standard length-measuring tools. A metre rule reads to the nearest millimetre (±1 mm), a vernier calliper to 0.1 mm (±0.05 mm typically), and a micrometer to 0.01 mm (±0.005 mm typically). Choosing the right instrument depends on the size of the object and the precision required.

米尺、游标卡尺和螺旋测微器是标准的长度测量工具。米尺可读到最接近的毫米（±1 mm），游标卡尺可读到 0.1 mm（通常不确定度为 ±0.05 mm），螺旋测微器则可读到 0.01 mm（通常不确定度为 ±0.005 mm）。选择何种仪器取决于物体的尺寸和所需的精度。

For mass, a top-pan balance usually reads to 0.01 g or 0.001 g. Digital meters for voltage and current often give readings with an uncertainty quoted by the manufacturer, e.g. ±(0.5% of reading + 1 digit). Always record the reading to the full resolution of the instrument and note any zero errors before use.

对于质量的测量，上皿天平通常能读到 0.01 g 或 0.001 g。数字电压表和电流表的读数不确定度常由制造商给出，比如 ±（读数的 0.5% + 1 个字）。始终记录仪器全分辨率的读数，并在使用前检查零位误差。

4. Timing and Motion Experiments | 计时与运动实验

When investigating motion, you often use a stopwatch (uncertainty ≈ 0.1–0.3 s due to human reaction time) or electronic timing gates (reducing human error). For oscillations, it is good practice to time multiple swings (e.g. 20) and then divide to find the period – this reduces the relative uncertainty.

在研究运动时，你常用秒表（考虑到人的反应时间，不确定度约为 0.1–0.3 s）或电子计时门（可减小人为误差）。对于摆动实验，最好多次计时（如 20 次全振动）然后除以次数得到周期——这能减小相对不确定度。

Light gates connected to a data logger can measure times to the nearest millisecond, allowing velocities and accelerations to be determined from known distances. Always check that the object cuts the beam cleanly and that friction is minimised.

连接数据采集器的光电门可以测量到接近毫秒级别的时间，从而结合已知距离求出速度和加速度。务必确保物体干净地切断光束，并尽量减小摩擦力。

5. Electrical Circuit Investigations | 电路实验探究

Ammeters (connected in series) and voltmeters (in parallel) are the workhorses of electrical experiments. The ideal ammeter has zero resistance; real ones have a small but finite resistance that can affect low-resistance circuits. Voltmeters should have very high resistance so they draw negligible current.

电流表（串联）和电压表（并联）是电学实验的核心工具。理想电流表的内阻为零；真实的电流表有很小但有限的内阻，可能会影响低电阻电路。电压表应有很高的内阻，以使其分流电流可以忽略。

When investigating Ohm’s law or the I–V characteristics of a filament lamp, you should vary the voltage using a variable resistor (rheostat) or a potential divider circuit, and take plenty of readings. Always check the zero of analogue meters and allow components to cool when investigating temperature-dependent resistors.

在探究欧姆定律或灯丝的 I–V 特性时，应通过可变电阻器（变阻器）或分压电路来改变电压，并采集大量读数。使用模拟电表时要先调零，研究热敏电阻时需让元件冷却后再读数。

6. Recording Data and Significant Figures | 记录数据与有效数字

All measured data should be recorded in a properly headed table. Each column heading must include the quantity and its unit, for example ‘Length l / cm’. Use consistent significant figures: if a ruler reads to 0.1 cm, write 12.0 cm rather than 12 cm, to show the precision.

所有测量数据都应当记录在正确表头的表格中。每列的表头必须包含物理量和单位，比如“长度 l / cm”。有效数字应前后一致：如果一把尺子能读到 0.1 cm，就写作 12.0 cm 而不是 12 cm，以体现精度。

Calculated quantities should be given to the number of significant figures determined by the least precise measurement in the calculation. Avoid rounding during intermediate steps; round only at the final answer.

计算得到的量应取到与计算中最不精确测量值相同的有效数字。中间步骤避免过早舍入，只在最终答案处取整。

7. Drawing Graphs | 绘制图表

Plotting a graph is one of the most powerful ways to analyse experimental data. Use sharp pencil, label axes clearly with quantity and unit, and choose sensible scales that use more than half the graph paper in both directions. Plot data points with small crosses or circled dots. Do not join points dot-to-dot; instead, draw a line of best fit – a single straight line or a smooth curve that passes as close to as many points as possible.

绘制图表是分析实验数据最强大的方法之一。用尖铅笔绘图，清楚标明坐标轴物理量与单位，并选择合适的分度，使图形在两方向上占据超过一半的坐标纸。数据点用小十字或带圆圈的实点标出。不要逐点连接，而应画一条最佳拟合线——一条尽可能多地贴近数据点的单一直线或平滑曲线。

If the theory predicts a straight line through the origin, your best-fit line should be judged accordingly. You may need to draw a worst-fit line as well to estimate the uncertainty in a gradient or intercept.

如果理论预言一条过原点的直线，你的最佳拟合线也应当依此判断。你可能还需要画一条最差拟合线，以评估斜率或截距的不确定度。

8. Using Gradients and Intercepts | 利用斜率与截距求物理量

Many physical relationships can be expressed in the form y = mx + c. By plotting the right variables, the gradient m and the y-intercept c give direct information about physical constants. For example:

许多物理关系可以表示为 y = mx + c 的形式。通过选取恰当的变量作图，其斜率 m 和 y 轴截距 c 能直接给出物理常数的信息。例如：

Resistivity: plot R against L for a wire, gradient = ρ/A → ρ = gradient × A.

电阻率：对金属丝画 R 随 L 变化的图，斜率 = ρ/A → ρ = 斜率 × A。
Acceleration under uniform force: plot v² against s, gradient = 2a.

恒力作用下的加速度：画 v² 随 s 变化的图，斜率 = 2a。
Young modulus: plot stress against strain, gradient = Young modulus E.

杨氏模量：画应力-应变图，斜率 = 杨氏模量 E。

Always calculate the gradient using a large triangle that covers at least half the plotted line, and read the coordinates from points on the line of best fit, not from data points.

计算斜率时，应使用覆盖至少一半拟合线的大三角形，并从最佳拟合线上的点读取坐标，而不是从原始数据点。

9. Sources of Error and Improvements | 误差来源与改进方法

Evaluation is a skill examined in depth. For each experiment, list the main sources of uncertainty and state whether they are systematic or random. Suggest realistic improvements: for instance, using a longer timing interval to reduce percentage error from reaction time, or using a set square to align a ruler vertically when measuring pendulum length.

评估是被深入考察的一项技能。对每个实验，列出主要的不确定度来源，并说明是系统误差还是随机误差。提出切实可行的改进方案：例如，采用更长的计时区间来减小反应时间带来的百分比误差，或者使用三角尺确保测量单摆长度的直尺竖直放置。

Common mistakes include blaming ‘human error’ vaguely – always be specific. If a graph shows a systematic deviation from the expected linear relationship, comment on whether a zero offset or a change in a supposedly constant variable might be the cause.

常见错误是笼统地归咎于“人为误差”——一定要具体指出。如果图形偏离预期的线性关系，需评论是否由零点偏移或某个本应保持恒定的变量发生改变所导致。

10. Writing the Practical Report | 撰写实验报告

A well-structured report typically contains: aim, apparatus, method, results (including tables and graphs), calculations, conclusion and evaluation. The conclusion should compare the experimental value with the accepted value, quoting the percentage difference and discussing whether the ranges of uncertainty overlap with the accepted value.

一份结构清晰的报告一般包括：目的、器材、方法、结果（含表格与图表）、计算、结论和评估。结论中应比较实验值与公认值，给出百分比差异，并讨论不确定度区间是否与公认值有重叠。

For example: “The measured value of g was (9.65 ± 0.15) m s⁻². The accepted value of 9.81 m s⁻² lies just outside the uncertainty range, suggesting a small systematic error, possibly due to a consistently late start of the stopwatch.”

例如：“测量所得的 g 值为 (9.65 ± 0.15) m s⁻²。公认值 9.81 m s⁻² 恰好在不确定度范围之外，表明可能存在小的系统误差，或许由秒表启动持续偏迟引起。”

11. Representative AS Experiments | AS 物理典型实验

Below are a few classic investigations from the 9630 syllabus, each combining several of the skills outlined above.

以下为 9630 大纲中的几个经典探究实验，每个实验都综合了上述多项技能。

Determination of g by free fall: Drop a steel ball from different heights, measure time of fall using a timer or trapdoor switch. Plot height h against (time)²; gradient = ½ g.

通过自由落体测 g：从不同高度释放钢球，用计时器或陷阱门开关测量下落时间。画下落高度 h 对 (时间)² 的图；斜率 = ½ g。
Resistivity of a wire: Use a metre bridge or four-wire measurement to get resistance R for different lengths L of a uniform wire. Graph R vs L; gradient = ρ/A. Measure the wire diameter with a micrometer to calculate A.

金属丝的电阻率：利用滑线电桥或四线法测量均匀金属丝不同长度 L 对应的电阻 R。作 R–L 图；斜率 = ρ/A。用螺旋测微器测量线径以计算截面积 A。
Young modulus of a wire: Add known masses to a vertical wire, measure the extension with a travelling microscope or a Vernier scale. Plot force F against extension ΔL; gradient = EA/L₀, so E can be found.

金属丝的杨氏模量：在竖直悬挂的金属丝上增加已知质量，用移测显微镜或游标尺测量伸长量 ΔL。画拉力 F 对 ΔL 的图；斜率 = EA/L₀，由此可求出 E。

12. Safety in the Laboratory | 实验室安全

Safety must never be an afterthought. When working with falling masses, keep feet clear and use a soft landing surface. In electrical experiments, use low voltages (typically under 12 V) unless specifically instructed, and check for frayed wires. When heating substances, use tongs and wear safety goggles. Always stand up during practical work and tidy the workspace after you finish.

安全绝不能事后才考虑。做落体实验时，双脚要避开落点，并在下方放置软垫。电学实验中，除非特别说明，一般使用低压（通常低于 12 V），并检查电线是否破损。加热物质时，要使用钳子并佩戴护目镜。实验过程中务必站立操作，结束后整理工作台。

Following these practical guidelines and understanding the logic behind each step will not only boost your practical skills assessment but also deepen your grasp of the physical concepts involved. Keep asking yourself: why does this method work, and what is the physics behind it?

遵循这些实验指南并理解每一步背后的逻辑，不仅能提升你的实验技能评估成绩，还能加深你对相关物理概念的理解。不断问自己：这个方法为什么有效？背后隐藏着怎样的物理原理？

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AS Physics: Experimental Investigations | AS 物理：实验探究