📚 IB CCEA Physics: Experimental Operations Guide | IB CCEA 物理：实验操作指南
Mastering experimental techniques is essential for success in IB Physics and CCEA A‑level practical assessments. This guide explains how to plan, carry out, analyse and evaluate experiments, focusing on data handling, uncertainty calculations and safe practice. Whether you are preparing for the IB Internal Assessment or the CCEA practical exam, these principles will help you work like a real physicist.
掌握实验技术是 IB 物理和 CCEA A‑level 实践考核成功的关键。本文指导你如何设计、实施、分析和评估实验，重点讲解数据处理、不确定度计算与安全操作。无论你在准备 IB 内部评估还是 CCEA 实验考试，这些原则都能帮助你像真正的物理学家一样工作。
1. Planning the Investigation | 实验设计
Start by defining a clear research question that includes the independent, dependent and control variables. A well‑posed question leads to a focused experiment, e.g. 'How does the length of a pendulum affect its period for small amplitudes?'.
首先明确一个包含自变量、因变量和控制变量的研究问题。一个好问题能让实验有重点，例如“摆长如何影响小振幅下的单摆周期？”
Write a step‑by‑step method that allows another student to repeat your work exactly. Include a labelled diagram of the apparatus and specify how you will vary the independent variable, measure the dependent variable and keep other factors constant.
写出一步一步的方法，让其他同学能完全重复你的工作。包含带有标注的装置示意图，并说明如何改变自变量、测量因变量以及保持其他因素不变。
Always conduct a risk assessment. Identify hazards such as hot surfaces, moving masses or electrical circuits, and state the precautions you will take to minimise risk.
一定要进行风险评估。识别热表面、移动重物或电路等危险源，并说明将采取的预防措施以将风险降至最低。
2. Measuring Instruments and Their Use | 测量仪器及使用
kness, whereas a vernier caliper (±0.1 mm) suits lengths up to about 15 cm. A metre rule is sufficient for longer distances but has a typical uncertainty of ±1 mm.
为每个量选最合适的仪器。千分尺精度为 ±0.01 mm，适合测量导线直径；游标卡尺（±0.1 mm）适合约 15 cm 以内的长度。米尺适用于更长距离，但典型不确定度为 ±1 mm。
For electrical measurements, digital multimeters often have an accuracy quoted as a percentage of the reading plus a number of least‑significant digits. Analogue meters require you to interpolate between scale divisions, giving an uncertainty of half the smallest division.
对于电学测量，数字万用表的准确度通常表示为读数的百分比加几个最低有效位。模拟电表需要你在刻度间估读，不确定度为最小分度值的一半。
Always zero the instrument before use and, where possible, take repeat readings to reduce random error. Record the raw data immediately in a clearly designed table.
使用前务必调零，并尽可能重复读数以减少随机误差。立即将原始数据记录在设计清晰的表格中。
3. Data Tables and Record Keeping | 数据表与记录
Design a results table before starting the experiment. Each column should have a heading that includes the quantity and its unit, separated by a forward slash, e.g. 'Length / m'. This follows IBO and CCEA conventions and avoids ambiguity.
实验开始前设计结果表格。每列应有表头，包含物理量及单位，用斜线分隔，如 “长度 / m”。这遵循 IBO 和 CCEA 惯例，避免歧义。
Record all measured values to the same number of decimal places consistent with the instrument’s precision. If you read a balance to 0.01 g, write 15.00 g, not 15 g. Include columns for derived quantities if needed, but clearly mark which are calculated.
所有测量值按仪器精度保留一致的小数位数。如果天平读到 0.01 g，就记作 15.00 g 而非 15 g。必要时可加入导出量的列，但要清楚注明哪些是计算值。
Leave space for notes on conditions such as room temperature or unexpected observations. These details are valuable when evaluating the experiment.
留出空间记录室温等环境条件和意外观察结果。这些细节在评估实验时很有价值。
4. Understanding Uncertainty | 理解不确定度
al instrument, it is ± the resolution, e.g. ±0.01 V for a voltmeter displaying two decimal places, unless the manufacturer states otherwise.
每个测量都有不确定度。单次读数的绝对不确定度通常为 ± 最小刻度的一半。对于数字仪器，则为 ± 分辨率，例如显示两位小数的电压表为 ±0.01 V，除非厂家另有说明。
When several repeat readings are taken, the best estimate is the mean, and the absolute uncertainty can be taken as half the range or the standard deviation of the mean, depending on the level of study. For IB and CCEA, half the range (max − min)/2 is commonly used.
当有多次重复读数时，最佳估计值为平均值，绝对不确定度可取半区间宽度（最大值−最小值）/2 或平均值的标准偏差，视学习阶段而定。IB 和 CCEA 常用半区间宽度。
Propagate uncertainties through calculations using simple rules. For addition and subtraction, add absolute uncertainties. For multiplication and division, add percentage uncertainties. For powers, multiply the percentage uncertainty by the power.
使用简单规则传递不确定度。加减运算时，绝对不确定度相加；乘除运算时，百分比不确定度相加；幂运算则用百分比不确定度乘以幂指数。
5. Calculating Percentage and Absolute Uncertainty | 计算百分比与绝对不确定度
Percentage uncertainty = (absolute uncertainty / measured value) × 100% th of 25.0 cm with an absolute uncertainty of 0.1 cm gives a percentage uncertainty of 0.4%.
百分比不确定度 = (绝对不确定度 / 测量值) × 100%。这便于比较不同测量的相对精确度。例如，长度 25.0 cm，绝对不确定度 0.1 cm，百分比不确定度为 0.4%。
nificant figures in the uncertainty should match the last significant digit of the main value.
当实验得出最终结果，如 g = 9.78 m s⁻²，绝对不确定度 ±0.05 m s⁻²，应表示为 9.78 ± 0.05 m s⁻²。不确定度的有效数字位数应与主值最后一位对齐。
Always quote uncertainties to 1 significant figure unless the first digit is 1, in which case 2 significant figures may be kept. Never state a calculated value with greater precision than the uncertainty allows.
除非首位是 1（此时可保留两位），不确定度一般保留一位有效数字。计算值的精度绝不能超过不确定度所容许的范围。
6. Graphical Analysis: Plotting | 图表分析：绘图
Plot graphs using a sharp pencil on graph paper or with software like Logger Pro or Excel. The independent variable goes on the x‑axis, the dependent on the y‑axis. Label axes with the quantity and unit in the format 'Period² / s²' if you are plotting the square of a period.
用削尖的铅笔在坐标纸上绘图，或使用 Logger Pro、Excel 等软件。自变量在 x 轴，因变量在 y 轴。轴标签格式为 “周期² / s²”，如果你绘制的是周期的平方。
Choose scales that make the best use of the paper – the plotted points should occupy more than half the grid. Scales should be easy to read: multiples of 1, 2, 5 or 10. Do not use awkward divisions like 3 or 7.
选择能充分利用图纸的刻度——数据点应占据一半以上网格。刻度应易于读取：选用 1、2、5、10 的倍数，不要用 3 或 7 等别扭的分度。
Plot each point with a small cross or a dot in a circle. Add error bars to show the absolute uncertainty in each coordinate, if required. Draw a clear best‑fit straight line or smooth curve through the points.
每个点用小十字或带圈圆点标出。如果需要，添加误差棒以显示每个坐标的绝对不确定度。穿过各点画一条清晰的最佳拟合直线或光滑曲线。
7. Analysing Graphs: Gradient and Intercept | 图表分析：斜率与截距
exactly on the line. Gradient = Δy / Δx. Include units by dividing the units on the axes.
求斜率时，在最佳拟合线上选取距离较远的两点。除非数据点恰好落在线上，否则不要直接使用。斜率 = Δy / Δx。单位由两轴单位相除得到。
The y‑intercept is read directly from the graph where the line crosses the y‑ adient gives a value related to the physics quantity you seek, such as g = 4π² / gradient.
y 截距直接从图中直线与 y 轴交点读取。如果图形已线性化（如单摆的 T²–L 图），斜率可给出与所求物理量相关的值，如 g = 4π² / 斜率。
Calculate the uncertainty in the gradient by drawing lines of maximum and minimum slope that still reasonably fit the data. The half‑range of these slopes gives the absolute uncertainty in the gradient.
通过画出仍能合理拟合数据的最大和最小斜率线，计算斜率的不确定度。这些斜率值的半区间即为斜率的绝对不确定度。
8. Evaluating Results and Percentage Difference | 结果评估与百分差
Compare your result to the accepted value using percentage difference: |experimental − accepted| / accepted × 100% nce suggests good accuracy, but this must be judged against your experimental uncertainty.
用百分差将你的结果与公认值进行比较：|实验值 − 公认值| / 公认值 × 100%。小百分差意味着好准确度，但必须结合实验不确定度进行判断。
s⁻² and the accepted value is 9.81 m s⁻², the result agrees within the stated uncertainty.
如果公认值落在你的实验不确定度范围内，结果就是一致的。例如，你测得 g = 9.8 ± 0.2 m s⁻²，公认值为 9.81 m s⁻²，则该结果在给定不确定度内吻合。
Identify the main sources of systematic and random error. Systematic errors, such as a zero error or a mis‑calibrated scale, shift all readings in one direction. Random errors cause scatter and can be averaged out by repetition.
识别系统误差和随机误差的主要来源。系统误差（如零误差或刻度未校准）使所有读数朝一个方向偏移。随机误差造成离散，可通过重复测量取平均减小。
9. Electrical Circuit Practicalities | 电路实验注意事项
When building circuits, always connect the voltmeter in parallel across the component and the ammeter in series. Start with the highest range to avoid damaging the meters, then reduce for a more precise reading.
搭建电路时，电压表始终并联在元件两端，电流表串联。先用最高量程以免损坏仪表，然后调低以获得更精确的读数。
Keep connecting leads short and use clean terminals to minimise contact resistance. For IV characteristic experiments, vary the voltage smoothly using a potential divider rather than a variable resistor in series, as it gives a wider range down to zero volts.
连接线尽量短，接线端子保持清洁以减小接触电阻。做 IV 特性实验时，用分压电路而不是串联变阻器平滑改变电压，因为它能提供从零伏起的更宽范围。
Allow components to cool between readings if they heat up, as resistance changes with temperature. In investigating Ohm’s law, take pairs of I and V quickly and then switch off the circuit.
若元件发热，应在读数间让其冷却，因为电阻随温度变化。探究欧姆定律时，迅速读取 I 和 V 配对值后立即断开电路。
10. Handling Mechanics and Waves Experiments | 力学与波动实验处理
For free‑fall measurement of g, use a trapdoor and electromagnet to reduce reaction‑ . Drop the object several times and calculate the mean time. Use s = ut + ½at² with u = 0.
用自由落体测 g 时，使用捕集器和电磁铁减少反应时间误差，或用光电门电子计时器。多次释放物体并计算平均时间。使用 s = ut + ½at²，其中 u = 0。
In pendulum experiments, keep the amplitude small (θ < 10°) so that the period is independent of displacement. Measure the time for at least 20 complete swings to reduce the fractional uncertainty in the period.
单摆实验中，保持振幅较小（θ < 10°）以使周期与位移无关。至少测量 20 个完整摆动的时间，以减小周期的不确定度占比。
When investigating standing waves on a string, use a vibration generator at a fixed frequency and adjust the length or the tension. Measure the distance between several adjacent nodes and divide by the number of half‑wavelengths to obtain the wavelength.
研究弦上驻波时，用固定频率的振动源，调节弦长或张力。测量多个相邻波节间的距离，除以半波长数目即可得到波长。
11. Thermal and Gas Law Experiments | 热学与气体定律实验
For Boyle’s law, use an oil‑filled glass tube or a syringe connected to a pressure sensor. Trap a fixed mass of air and keep the temperature constant by waiting after each volume change for thermal equilibrium. Plot p against 1/V to obtain a straight line through the origin.
验证波意耳定律时，使用油封玻璃管或连有气压传感器的注射器。封闭一定质量空气，每次改变体积后等待热平衡以保持温度恒定。绘制 p–1/V 图，得到过原点的直线。
In specific heat capacity determinations, insulate the container well and stir continuously. Record the highest temperature reached, not the temperature at the moment you stop heating. Correct for heat loss by plotting a cooling curve if time permits.
测定比热容时，容器要充分绝热并持续搅拌。记录达到的最高温度，而非停止加热瞬间的温度。时间允许时，可绘制冷却曲线进行热损失修正。
Always handle mercury‑in‑ llows, and state the uncertainty, typically ±0.5 °C for a standard laboratory thermometer.
小心使用水银温度计，或使用数字温度探头。若仪器允许，温度记录到 0.1 °C，并给出不确定度，标准实验室温度计通常为 ±0.5 °C。
12. Writing the Conclusion and Evaluation | 结论与评估撰写
A strong conclusion states the findings clearly, quotes the key result with its absolute and percentage uncertainty, and relates it back to the research question. For example, 'The period T of the pendulum is proportional to √L 81 ± 0.10 m s⁻², which agrees with the accepted value within the experimental uncertainty.'
强有力的结论要清晰陈述发现，给出带绝对和百分比不确定度的关键结果，并联系研究问题。例如，“单摆周期 T 与 √L 成正比，所得常数值 g = 9.81 ± 0.10 m s⁻²，在实验不确定度内与公认值吻合。”
Discuss the significance of the uncertainty and mention the largest sources of error. Suggest realistic improvements: e.g. using a light gate instead of a stopwatch, or taking more readings at small displacements to better define the line of best fit.
讨论不确定度的意义并指出最大的误差来源。提出切实可行的改进：例如用光电门代替秒表，或在小位移下采集更多数据以更好定义最佳拟合线。
Link your evaluation to the method and the equipment used. Avoid vague comments like 'human error'; instead, state ' roduced a ±0.2 s uncertainty, which could be reduced by using an electronic timing device.'
评估要与方法和所用仪器挂钩。避免“人为误差”等模糊表述，而应该说“启动和停止秒表时的反应时间引入了 ±0.2 s 的不确定度，可通过电子计时装置减小。”
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图