📚 Case Study Practice in Physics | 物理案例分析实战演练
Case studies in physics require you to connect scientific knowledge with everyday situations. You will practice identifying relevant principles, interpreting data, and applying equations to reach a conclusion.
物理案例分析要求你将科学知识与日常情境联系起来。你将练习识别相关原理、解读数据并应用方程来得出结论。
1. What is a Case Study in Physics? | 什么是物理案例分析？
A case study presents a real-life scenario where physics can explain what is happening. You must break down the problem, decide which laws apply, and then carry out calculations or qualitative analysis.
案例分析呈现一个现实生活场景，可以用物理学来解释所发生的事情。你必须分解问题，判断适用哪些定律，然后进行计算或定性分析。
The process typically involves these steps: observe the situation, identify the physics concepts, gather and organise data, apply equations or reasoning, and finally evaluate your answer.
这个过程通常包括以下步骤：观察情境、识别物理概念、收集并整理数据、应用方程或推理，最后评估你的答案。
Common topics for KS3 case studies include forces and motion, energy transfers, electricity, waves, and properties of matter. You will see examples covering these areas.
KS3 案例分析的常见主题包括力与运动、能量传递、电学、波和物质的性质。你将看到覆盖这些领域的示例。
2. Case Study 1: The Speeding Car | 案例一：超速的汽车
A car passes two sensors on a road with a speed limit of 50 km/h. The sensors are 500 metres apart. The car covers this distance in 30 seconds. Determine whether the driver has broken the speed limit.
一辆汽车驶过一条限速 50 km/h 道路上的两个传感器。传感器相距 500 米。汽车在 30 秒内通过这段距离。判断司机是否超速。
| Quantity | Value |
|---|---|
| Distance (s) | 500 m |
| Time (t) | 30 s |
| Speed limit | 50 km/h |
pare with the speed limit, we convert to km/h by multiplying by 3.6: 16.7 × 3.6 ≈ 60 km/h.
我们使用 v = s / t 计算平均速度。结果以 m/s 表示为 500 m ÷ 30 s = 16.7 m/s。为了与限速比较，乘以 3.6 转换为 km/h：16.7 × 3.6 ≈ 60 km/h。
Since 60 km/h is greater than 50 km/h, the car was indeed speeding. This assumes the speed was constant; real-world factors like traffic or acceleration might affect the result, but the average speed alone proves the limit was exceeded.
既然 60 km/h 大于 50 km/h，汽车确实超速了。这假设速度是恒定的；现实因素如交通或加速度可能影响结果，但仅平均速度就证明超过了限速。
The key physics principle is the relationship between distance, time and speed. This is an example of using quantitative data to make a decision about safety.
关键的物理原理是距离、时间和速度之间的关系。这是利用定量数据做出安全决策的一个例子。
3. Case Study 2: The Electric Kettle | 案例二：电热水壶
An electric kettle is rated at 2000 W. It takes 4 minutes to bring 1 litre of water to the boil from 20 °C. We want to find the efficiency of the kettle. The specific heat capacity of water is 4200 J/(kg °C).
一个电热水壶的额定功率为 2000 W。将 1 升水从 20 °C 烧开需要 4 分钟。我们想求出热水壶的效率。水的比热容是 4200 J/(kg °C)。
| Input / Useful output | Calculation | Result |
|---|---|---|
| Electrical energy supplied | Eₑ ₌ P × t = 2000 W × (4 × 60 s) | 480 000 J |
| Heat gained by water | Q = m × c × Δθ = 1 kg × 4200 × (100 − 20) | 336 000 J |
Efficiency = (useful energy output / total energy input) × 100% = (336 000 / 480 000) × 100% = 70%. The remaining 30% he energy is lost to the surroundings, mostly as heat warming the kettle body and the air.
效率 = (有用能量输出 / 总能量输入) × 100% = (336 000 / 480 000) × 100% = 70%。剩余的 30% 能量散失到周围环境中，主要是加热壶体和空气的热量。
This case study highlights energy transfer and the principle of conservation of energy. Even though the kettle is efficient, some energy is always wasted, which leads to the design of insulated kettles to reduce loss.
这个案例分析突出了能量传递和能量守恒原理。尽管热水壶效率较高，但总有一部分能量被浪费，这促使人们设计保温壶以减少损失。
4. Case Study 3: The Floating Boat | 案例三：漂浮的小船
A small wooden boat has a volume of 0.50 m³ and a mass of 300 kg. Will it float when placed in fresh water? The density of fresh water is 1000 kg/m³.
一艘小木船体积为 0.50 m³，质量为 300 kg。把它放进淡水中，它会漂浮吗？淡水的密度是 1000 kg/m³。
00 kg / 0.50 m³ = 600 kg/m³. Since 600 kg/m³ is less than 1000 kg/m³, the boat will float.
首先，求船的密度：密度 = 质量 / 体积 = 300 kg / 0.50 m³ = 600 kg/m³。由于 600 kg/m³ 小于 1000 kg/m³，船会浮起来。
pthrust = weight of displaced fluid, so displaced water mass = 3000 N / 10 N/kg = 300 kg. Displaced volume = 300 kg / 1000 kg/m³ = 0.30 m³, which is less than the boat's total volume, so 0.20 m³ remains above water.
对于漂浮物体，重力等于浮力。可以计算排开水的体积：重力 = 质量 × g = 300 kg × 10 N/kg = 3000 N。浮力 = 排开液体的重量，所以排开水的质量 = 3000 N / 10 N/kg = 300 kg。排开体积 = 300 kg / 1000 kg/m³ = 0.30 m³，小于船的总体积，所以有 0.20 m³ 露出水面。
This demonstrates Archimedes' principle and the concept of density. Understanding buoyancy helps naval architects design safe vessels.
这展示了阿基米德原理和密度概念。理解浮力有助于船舶建筑师设计安全的船只。
5. Case Study 4: The Noisy Classroom | 案例四：嘈杂的教室
During a group activity, the noise level in a classroom reaches 85 dB. A student complains of headache and difficulty concentrating. The school's health and safety guideline states that prolonged exposure above 70 dB can cause harm.
在一次小组活动期间，教室里的噪音水平达到 85 dB。一名学生抱怨头痛和难以集中注意力。学校的健康与安全指南指出，长时间暴露在 70 dB 以上会造成伤害。
| Sound level (dB) | Typical source | Effect |
|---|---|---|
| 30 | Whisper | Very quiet |
| 60 | Normal conversation | Comfortable |
| 70 | Vacuum cleaner | Irritating over time |
| 85 | Busy classroom | Potential damage after 8 h |
The decibel scale is logarithmic: an increase of 10 dB means the sound intensity becomes 10 times greater. So 85 dB is roughly 3.2 times as intense as 80 dB, making it much more than just a small jump in perceived loudness.
分贝标度是对数的：增加 10 dB 意味着声强增加 10 倍。因此 85 dB 的声强大约是 80 dB 的 3.2 倍，这使得它远不止是感知响度上的一小步跳跃。
To reduce noise, the school could install soft furnishings, use acoustic panels, or change classroom management strategies. The physics of sound absorption and reflection explains how these measures reduce echo and background noise.
为了减少噪音，学校可以安装软装潢、使用吸音板或改变课堂管理策略。声音的吸收和反射物理原理解释了这些措施如何减少回声和背景噪音。
6. Case Study 5: The Magnetic Door Lock | 案例五：磁力门锁
A security door uses an electromagnet to hold the door closed. When a current of 2 A flows through a coil with 200 turns, the electromagnet can support a steel plate of mass 15 kg before the door can be pulled open. The gravitational field strength is 10 N/kg.
一扇安全门利用电磁铁来保持门关闭。当 2 A 电流流过 200 匝的线圈时，电磁铁能吸住一块 15 kg 的钢制板，门才能被拉开。重力场强度为 10 N/kg。
force must be at least 150 N to hold it. This force results from the magnetic effect of the current; increasing the current or the number of turns would strengthen the magnetic field and increase the holding force.
钢板的重力为 W = m × g = 15 kg × 10 N/kg = 150 N。电磁力至少需为 150 N 才能吸住它。这个力源于电流的磁效应；增大电流或增加匝数会增强磁场并增大力。
This case links electricity and magnetism. A simple calculation shows the minimum force needed, but real designs must apply a safety factor, perhaps holding twice that weight, to ensure security.
这个案例将电与磁联系起来。简单的计算显示了所需的最小力，但实际设计必须应用安全系数，也许要吸住两倍重量，以确保安全。
7. How to Structure Your Case Study Answer | 如何构建案例分析答案
A clear structure helps you earn marks even if the final number is wrong. Follow these steps:
清晰的结构有助你得分，即使最终数字有误。请遵循以下步骤：
Step 1 – Read and underline the physics quantities given (distance, time, power, mass, etc.) and the quantity you need to find.
步骤 1 – 阅读题干并在给出的物理量（距离、时间、功率、质量等）以及你需要求的物理量下划线。
Step 2 – n. Use symbols and check that you have the correct form. For example, v = s / t for speed.
步骤 2 – 写下相关方程。使用符号并确认使用了正确的形式。例如，求速度用 v = s / t。
Step 3 – Substitute the numbers carefully, including units. Perform the calculation and show the working.
步骤 3 – 小心代入数字，包括单位。进行计算并展示过程。
Step 4 – State your answer clearly and compare it with a given limit or standard, if required. Add a concluding sentence that refers back to the scenario.
步骤 4 – 清晰地陈述答案，如有需要则与给定限值或标准进行比较。添加一句回顾情境的总结句。
Step 5 – Check that units are consistent (e.g., convert km/h to m/s if needed) and that your answer is physically reasonable.
步骤 5 – 检查单位是否一致（例如，如有需要将 km/h 转换为 m/s），以及你的答案在物理上是否合理。
8. Practice Exercises with Hints | 练习与提示
| Practice problem | Hint |
|---|---|
| A cyclist travels 900 m in 2 minutes. Calculate the speed in m/s and km/h. Is it above 25 km/h? | Convert time to seconds: 2 min = 120 s. Use v = s / t, then multiply m/s by 3.6. |
| A 1500 W microwave heats 0.2 kg of soup from 15 °C to 75 °C in 50 seconds. The specific heat capacity is 3800 J/(kg °C). Find the efficiency. | rgy (E = P × t) and the heat gained by the soup (Q = m × c × Δθ). Efficiency = Q / E × 100%. |
| A metal block has a mass of 500 g and a volume of 80 cm³. Will it float in water? (Density of water = 1 g/cm³) | Find density in g/cm³: 500 / 80 = 6.25 g/cm³. Compare with 1 g/cm³; if higher, it sinks. |
| A speaker produces a sound of 90 dB at a concert. The safe exposure time at this level is only 30 minutes. Explain why the sound level is dangerous and suggest a hearing protection method. | Use the decibel scale and link high intensity to damage of hair cells in the ear. Earplugs reduce intensity reaching the eardrum. |
Working through these exercises will build your confidence in applying physics to real situations. Always remember to show full working and relate your answer back to the context provided.
完成这些练习将建立你在真实情境中应用物理学的信心。始终记得展示完整过程，并将答案联系回所提供的语境。
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