📚 Case Study Masterclass: Practical Exercises for WJEC Year 13 Physics | 案例分析实战演练
Case studies in WJEC Year 13 Physics demand more than just recalling facts — they require you to analyse unfamiliar scenarios, apply physical principles critically, and communicate scientific reasoning clearly. This masterclass offers a set of practical exercises designed to sharpen your case study skills, from decoding data tables to evaluating experimental limitations. By working through these targeted tasks, you will build the confidence and precision needed to excel in the examination.
WJEC 的 A2 物理案例分析题远不止考查知识记忆 — 它要求你分析陌生情境、批判性地运用物理原理，并清晰地表达科学推理。本文提供一套精心设计的实战演练，从解读数据表格到评估实验局限性，帮助你打磨案例分析的各项技能。通过完成这些针对性的练习，你将建立起考试所需的信心与准确性。
1. Understanding the Case Study Brief | 读懂案例分析任务
Every WJEC case study begins with a context — perhaps an engineering application, a medical device, or a natural phenomenon. Start by identifying the key physics themes: is it mechanics, fields, waves, or thermal physics? Underline the quantities given and the specific questions asked. The brief often contains clues about which equations you will need.
每道 WJEC 案例分析题都从一个情境开始 — 可能是工程应用、医疗设备或自然现象。先要识别出核心的物理主题：是力学、场、波还是热物理？圈出题目给出的物理量和具体的问题要求。任务描述中往往藏着需要用到哪些方程的线索。
Exercise: Take a sample case study on ‘Power Transmission Lines’. List all the physics concepts mentioned — e.g., alternating current, step-up transformers, power loss, resistivity of aluminium. Then write a one-sentence summary of what the question is ultimately asking you to explain or calculate.
练习：找一个关于“输电线路”的案例样题。列出其中涉及的所有物理概念 — 例如交流电、升压变压器、功率损耗、铝的电阻率。然后用一句话概括题目的最终要求（解释或计算什么）。
2. Extracting and Organising Data | 提取并整理数据
Case studies often present information in dense paragraphs, tables, or graphs. Practise converting written descriptions into neat labelled tables of numerical values. For instance, a paragraph describing the dimensions and efficiency of a solar panel can be tabulated into columns: area, power output per m2, incident solar radiation, and efficiency.
案例分析常以密集段落、表格或图表呈现信息。要练习将文字描述转化为整洁的带标签的数值表格。例如，一段描述太阳能电池板尺寸和效率的文字可以整理成表格，列出面积、单位平方米输出功率、入射太阳辐射和效率等列。
Exercise: Read the following excerpt and create a data table: ‘A wind turbine blade has a length of 45 m. At a wind speed of 12 m s−1, the turbine generates 2.1 MW. The air density is 1.2 kg m−3. The gearbox efficiency is 92%.’ Identify which values are directly measured and which are derived.
练习：阅读以下摘录并创建数据表：“风力涡轮机叶片长 45 m。风速为 12 m s−1 时，涡轮机发电 2.1 MW。空气密度为 1.2 kg m−3。齿轮箱效率为 92%。”然后区分哪些是直接测量值，哪些是导出值。
3. Applying Physics Principles | 应用物理原理
In WJEC case studies, you are expected to select the correct physical model. For example, when analysing a satellite orbit, you need to decide whether to use Newton’s law of gravitation, Kepler’s third law, or centripetal force equations. Practise matching scenarios to equation sheets and writing down justifications.
在 WJEC 案例分析中，你需要选择合适的物理模型。例如，分析卫星轨道时，你要决定是用牛顿万有引力定律、开普勒第三定律还是向心力方程。练习将场景与公式表匹配，并写出选择的理由。
Exercise: Consider a case about a mass spectrometer. Write the key equation for the radius of a charged particle’s path:
r = (m v) / (B q)
and explain how each variable relates to the instrument’s components. Then calculate the magnetic field strength needed for a proton (m = 1.67×10−27 kg, q = 1.60×10−19 C) moving at 2.0×106 m s−1 to produce a path radius of 0.25 m.
练习：考虑一道关于质谱仪的案例。写出带电粒子轨道半径的关键方程：
r = (m v) / (B q)
并解释每个变量与仪器组件的关系。然后计算：质子（m = 1.67×10−27 kg，q = 1.60×10−19 C）以 2.0×106 m s−1 运动时，要产生 0.25 m 的径迹半径需要多大的磁感应强度。
4. Graph Interpretation and Error Bars | 图表解读与误差棒
Many high-mark questions involve plotting or interpreting graphs. You might be asked to find a gradient that equals a physical constant, or to draw error bars. Always check the units on axes and remember that uncertainty can be estimated from the spread of data points around a best-fit line.
许多高分题目涉及绘制或解读图表。你可能需要求取一个等于某个物理常数的斜率，或者绘制误差棒。务必检查坐标轴单位，并记住不确定度可以根据数据点围绕最佳拟合线的分散程度来估算。
Exercise: The table below shows the stopping potential Vs for different frequencies f of light incident on a metal surface. Plot the data (f on x-axis, Vs on y-axis).
| f / 1014 Hz | 5.5 | 6.0 | 6.5 | 7.0 | 7.5 |
| Vs / V | 0.35 | 0.58 | 0.82 | 1.05 | 1.28 |
Assuming an uncertainty of ±0.05 V in Vs, add error bars. Use the gradient to determine Planck’s constant, given e = 1.60×10−19 C. Compare with the accepted value and discuss systematic errors.
练习：下表给出了不同频率 f 的光照射到金属表面时的遏止电势差 Vs。绘制数据图（x 轴 f，y 轴 Vs）。
| f / 1014 Hz | 5.5 | 6.0 | 6.5 | 7.0 | 7.5 |
| Vs / V | 0.35 | 0.58 | 0.82 | 1.05 | 1.28 |
假设 Vs 的不确定度为 ±0.05 V，添加误差棒。利用斜率，结合 e = 1.60×10−19 C，测定普朗克常数。与公认值进行比较，并讨论系统误差。
5. Uncertainty and Percentage Difference | 不确定度与百分差
WJEC examiners expect you to handle absolute and percentage uncertainties with confidence. When a quantity is calculated from several measured values, you must combine uncertainties using the appropriate rules — adding absolute uncertainties for sums, or adding percentage uncertainties for products and quotients.
WJEC 考官希望你能熟练处理绝对不确定度和百分不确定度。当一个量由多个测量值计算得到时，必须用合适的规则合成不确定度 — 加减运算用绝对不确定度相加，乘除运算用百分不确定度相加。
Exercise: In an experiment to determine Young’s modulus E of a wire, the measurements are: force F = 10.0 ± 0.2 N, length L = 2.000 ± 0.005 m, extension ΔL = 1.50 ± 0.05 mm, diameter d = 0.50 ± 0.01 mm. First calculate the cross-sectional area A = π (d/2)2 and its percentage uncertainty. Then find E using
E = (F L) / (A ΔL)
and propagate the total percentage uncertainty. Express E in the form best estimate ± absolute uncertainty.
练习：在测定金属丝杨氏模量 E 的实验中，测量值为：力 F = 10.0 ± 0.2 N，长度 L = 2.000 ± 0.005 m，伸长量 ΔL = 1.50 ± 0.05 mm，直径 d = 0.50 ± 0.01 mm。先计算横截面积 A = π (d/2)2 及其百分不确定度。然后利用
E = (F L) / (A ΔL)
求出 E，并传播总的百分不确定度。将 E 表示为最佳估计值 ± 绝对不确定度。
6. Evaluating Experimental Design | 评估实验设计
A top-grade response goes beyond calculations to judge the reliability of the method. Ask yourself: Was the range of data sufficient? Were there any uncontrolled variables? Could parallax error affect readings? In a case study about measuring g using a simple pendulum, you might discuss timing precision, the effect of small-angle assumption, and the measurement of length to the centre of mass.
高分回答会超越计算，去评判方法的可靠性。问问自己：数据范围是否足够？是否存在未控制的变量？视差会否影响读数？在一个关于用单摆测量 g 的案例中，你可能要讨论计时精度、小角度假设的影响，以及摆长测量到质心的问题。
Exercise: Critically evaluate the following method: ‘A student drops a ball from rest and uses a stopwatch to measure the time to fall 2.0 m. They calculate g = 2 s / t2, where s = 2.0 m.’ Identify at least three sources of uncertainty and suggest improvements.
练习：批判性地评估以下方法：“一名学生将球由静止释放，用秒表测量其下落 2.0 m 的时间。他使用 g = 2 s / t2 计算 g，其中 s = 2.0 m。”找出至少三个不确定度来源，并提出改进建议。
7. Model Limitations and Real-World Context | 模型局限性与现实情境
WJEC often includes questions about the validity of assumptions. For example, treating a car as a point mass when analysing cornering neglects weight transfer and tyre slip. Learning to spot where an idealised model breaks down and how to refine it is a crucial skill.
WJEC 常包含涉及假设有效性的问题。例如，在分析汽车转弯时将其视为质点，就忽略了重量转移和轮胎滑移。学会识别理想化模型在何处失效以及如何改进它，是一项关键技能。
Exercise: A case study describes the launch of a rocket, modelling it as a projectile with a constant thrust and no air resistance. List three ways the real situation differs from this model and explain how each difference affects the maximum altitude reached. Suggest a more realistic model.
练习：一个案例描述了火箭的发射，将其建模为具有恒定推力且无空气阻力的抛体。列出真实情况与该模型的三点差异，并解释每一点差异如何影响达到的最大高度。提出一个更现实的模型。
8. Drawing Conclusions and Synthesising | 得出结论与综合论述
The final part of a case study often asks for a justified conclusion. Do not simply restate results; link them to the context, discuss whether the evidence is strong enough, and suggest further investigations. Use phrases like ‘The data supports…’ or ‘The large uncertainty in… limits the confidence in…’.
案例分析的结尾部分常要求给出有理有据的结论。不要简单复述结果；要将它们与情境联系起来，讨论证据是否足够有力，并提出进一步研究的建议。使用诸如“数据支持……”或“……中的较大不确定度限制了对……的信心”等表述。
Exercise: From a data set on the efficiency of LED lamps at different currents, a student concludes that ‘higher current always leads to higher light output’. Write a more nuanced conclusion that acknowledges the drop in efficiency at very high currents due to heating effects, and state what additional data would be useful.
练习：根据一组关于不同电流下 LED 灯效率的数据，一名学生得出结论：“更高的电流总能带来更高的光输出”。撰写一个更细致入微的结论，承认由于热效应，在极高电流下效率会下降，并说明哪些额外数据可能有用。
9. Time Management in the Exam | 考试中的时间管理
Case study questions can be long and text-heavy. Allocate your time by first scanning the questions to see what’s asked, then reading the passage with those questions in mind. For a 30-mark case study, spend about 10 minutes reading and planning, 30 minutes writing, and 5 minutes checking calculations and units.
案例分析题可能篇幅长、文字量大。要分配好时间：先快速浏览问题，了解要求，然后带着这些问题去阅读材料。对于 30 分的案例分析题，约用 10 分钟阅读和规划，30 分钟书写，5 分钟检查计算和单位。
Exercise: Simulate exam conditions with a past WJEC case study. Set a timer for 45 minutes. Before you write a full answer, jot down the key principles and equations on a planner sheet. Afterwards, reflect on whether you spent too long on one subsection.
练习：用一道 WJEC 历年真题进行模拟。设定 45 分钟计时。在完整作答之前，先在规划纸上记下关键原理和方程。之后反思是否在某个小题上花费了过多时间。
10. Common Pitfalls and How to Avoid Them | 常见陷阱与规避方法
Many students lose marks by not converting units, misreading scales (e.g., mA vs A, cm vs m), or forgetting to square the diameter in area calculations. Others omit units from final answers, or quote results to an unjustified number of significant figures. Always match your significant figures or decimal places to the least precise measured value.
许多学生因为未换算单位、读错标度（如 mA 与 A、cm 与 m）或在面积计算中忘记将直径平方而失分。另有一些人在最终答案中遗漏单位，或用不合理的有效数字位数来引用结果。始终要将有效数字或小数位数与精度最低的测量值保持一致。
Exercise: Spot the errors in the following answer snippet: ‘The resistivity ρ = R A / L = (2.3 Ω × 0.5 mm2) / 1.2 m = 0.9583 Ω mm2 m−1.’ Provide corrections regarding units, significant figures, and the appropriate SI form for resistivity.
练习：找出以下答案片段中的错误：“电阻率 ρ = R A / L = (2.3 Ω × 0.5 mm2) / 1.2 m = 0.9583 Ω mm2 m−1。”从单位、有效数字以及电阻率合适的 SI 形式方面给出修正。
11. Full-Length Practice Case Study | 完整案例分析模拟
Now combine all these skills in a complete practical exercise. Consider the following scenario: ‘A proposed hydroelectric dam will have a vertical drop of 85 m and an average water flow rate of 320 m3 s−1. The turbine-generator efficiency is quoted as 88%. The electricity is to be transmitted via a 120 km aluminium cable with a resistance of 0.28 Ω km−1 at 400 kV.’
现在将所有技能整合到一次完整的实战演练中。考虑以下情境：“拟建的水力发电大坝垂直落差为 85 m，平均水流量为 320 m3 s−1。涡轮发电机组的效率标注为 88%。电力将通过 120 km 的铝电缆输送，电缆电阻为 0.28 Ω km−1，输电电压为 400 kV。”
Exercise: (a) Calculate the maximum power that can be extracted from the water, given the density of water = 1000 kg m−3. (b) Determine the electrical power output. (c) Find the current in the transmission line and the power loss as heat. (d) Evaluate whether the transmission voltage should be increased, and discuss energy losses and environmental factors.
练习：(a) 已知水的密度为 1000 kg m−3，计算可从水中提取的最大功率。(b) 确定电功率输出。(c) 求输电线路中的电流以及以热量形式损失的功率。(d) 评估是否应提高输电电压，并讨论能量损失和环境因素。
12. Review and Self-Assessment | 复习与自我评估
After completing any case study exercise, use the WJEC mark scheme to self-assess. Note where you lost marks — was it a calculation slip, a missing justification, or a weak evaluation? Keep a log of these errors and revisit them before the exam. Consistent practice with self-assessment turns case studies from intimidating tasks into scoring opportunities.
完成任何案例分析练习后，要用 WJEC 的评分方案进行自我评估。记下失分点 — 是计算失误、缺少论证，还是评估薄弱？建立一个错误日志，并在考前回顾。持续的自我评估练习能将案例分析从令人生畏的题目转变为得分机会。
Exercise: Create a personalised checklist based on WJEC’s assessment objectives (AO2: application, AO3: analysis and evaluation). For the dam case study, tick off what you demonstrated well and highlight areas to improve, such as ‘explicitly linking power loss to voltage’ or ‘quantifying environmental impact qualitatively’.
练习：基于 WJEC 的评估目标（AO2：应用，AO3：分析与评价）创建一份个性化核对清单。针对大坝案例，勾选出你表现良好的内容，并标出需要改进的方面，例如“明确将功率损耗与电压联系起来”或“定性量化环境影响”。
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