📚 A-Level Physics: Mastering Application Questions with the Unit 2 Insert (Jan 21) | A-Level 物理：利用 Unit 2 插页 (2021年1月) 破解应用题技巧
Many students treat the formula and data insert as an afterthought, but in A-Level Physics Unit 2, the Jan 21 insert is a carefully designed tool that holds the key to unlocking application questions. This guide shows you how to read, interpret, and apply every section of that insert, from SUVAT equations to wave constants, so you can turn what looks like a daunting problem into a straightforward calculation.
许多同学把公式与数据插页视为可有可无的附件，但 A-Level 物理 Unit 2 2021 年 1 月的插页实际上是一个精心设计的工具，掌握它就等于拿到了应用题的钥匙。本文教你如何读懂、解读并运用插页中的每一个部分——从运动学方程到波动常数——让看似复杂的题目变成清晰的计算。
1. Understanding the Insert Layout | 了解插页结构
The Jan 21 insert is divided into clear sections: a table of fundamental constants, kinematic formulas, material property equations, wave relationships, and quantum principles. Before you even read the question, spend 30 seconds scanning the insert. Identify which block of equations will be relevant. For example, if a question mentions ‘tensile stress’ you should immediately spot the Young modulus section with E = σ / ε and the values for common materials.
2021 年 1 月的插页由几个清晰的板块组成：基本常数表、运动学公式、材料性质方程、波动关系和量子原理。在下笔答题之前，花 30 秒快速浏览插页。先判断哪一组公式可能用到。比如题目提到“拉伸应力”，你应立刻定位到杨氏模量区域，那里有 E = σ / ε 以及常见材料的数值。
The insert also includes data such as the density of aluminium, the speed of sound in air, and Planck’s constant. These are not random; they are there because at least one question will require them. Treat the insert as a checklist of the concepts being tested.
插页中还给出了铝的密度、空气中的声速、普朗克常数等数据。它们不是随便放上去的，一定有至少一道题需要用到。把整份插页看成一份考点清单，对照它梳理知识。
2. Mechanics: Selecting the Right SUVAT Equation | 力学：选择合适的运动学方程
The insert lists the standard SUVAT equations: v = u + at, s = ½(u+v)t, s = ut + ½at², v² = u² + 2as. Application questions often omit one quantity deliberately. Start by listing the five variables (s, u, v, a, t) and ticking those given in the problem. Then scan the insert to pick the equation that contains only the knowns and the one unknown you need. If a question gives u, a, t and asks for s, you will immediately select s = ut + ½at².
插页列出了标准的运动学方程：v = u + at、s = ½(u+v)t、s = ut + ½at²、v² = u² + 2as。应用题常故意缺省一个物理量。解题时先把五个变量 (s, u, v, a, t) 列出来，在已知量上打勾。然后对照插页，挑选只包含已知量和所求未知量的那个方程。一旦题目给出 u、a、t 求 s，立刻选 s = ut + ½at²。
A common trap is using an equation with acceleration when the motion is actually uniform. Always check the phrase ‘constant velocity’ or ‘uniform acceleration’ in the question. The insert provides equations for uniformly accelerated motion only; for constant velocity simply use s = vt.
一个常见陷阱是明明物体做匀速运动，却用含有加速度的公式。一定要仔细审题，看清“匀速”还是“匀加速”。插页只给出了匀加速运动的公式，匀速直线运动直接使用 s = vt。
3. Working with Force–Extension Graphs | 处理力-伸长图
The insert does not draw graphs for you, but it supplies the key relationships: F = kΔL and the energy stored E = ½FΔL = ½k(ΔL)². When an application question provides a force–extension graph, your job is to extract data from the linear region. Use the gradient to find k, but make sure you convert extension to metres. Many marks are lost by leaving ΔL in mm or cm.
插页不会替你画图，但它给出了核心关系：F = kΔL 以及储存的能量 E = ½FΔL = ½k(ΔL)²。当应用题提供一根力-伸长图线时，你要从线性区域提取数据。用斜率求 k，但务必把伸长量换算成米。很多同学因为 ΔL 仍用毫米或厘米而丢分。
For energy stored, do not simply use ½F_max × ΔL_max if the graph has curved beyond the elastic limit. The formula only applies in the linear, elastic region. The insert reminds you of this implicitly by listing Hooke’s law; application questions test whether you know its limits.
求储存的能量时，如果图线在弹性极限后弯曲，不能直接用 ½F_max × ΔL_max。公式只在弹性范围内适用。插页虽然只列出了胡克定律，但这恰恰暗示你要注意其适用条件——应用题就是考你有没有这个概念。
4. Young Modulus & Material Properties | 杨氏模量与材料性质
The Jan 21 insert includes the Young modulus equation E = σ / ε = (F/A) / (ΔL/L), along with values for aluminium (7.0 × 10¹⁰ Pa) and copper (1.3 × 10¹¹ Pa). When a problem gives a stress–strain graph, use the initial gradient to compute E. Remember that area A is often given in mm²; convert to m² by multiplying by 10⁻⁶.
2021 年 1 月的插页包含杨氏模量公式 E = σ / ε = (F/A) / (ΔL/L)，并附有铝 (7.0 × 10¹⁰ Pa) 和铜 (1.3 × 10¹¹ Pa) 的数值。若题目给出应力-应变图，用初始斜率求 E。特别注意截面积 A 常以 mm² 给出，要换算成 m² (乘以 10⁻⁶)。
Application questions often ask you to identify a material by comparing calculated E with the insert table. Show your working clearly, and quote the table value explicitly. Conclude whether the material is likely aluminium or copper, and comment on any discrepancy due to experimental error.
应用题常让你通过计算 E 并与插页表格对比来鉴别材料。写出清晰的计算过程，明确引用表格数值。最后推断材料是铝还是铜，并说明误差可能造成的不一致。
5. Wave Basics: v = f λ | 波的基础：波速公式
The insert gives the fundamental wave equation v = f λ. Use it methodically: identify whether the wave is transverse (e.g. on a string) or longitudinal (sound). Then note the given frequency and wavelength, ensuring units are hertz and metres. If a question provides a time period T, remember f = 1/T. The insert does not list that directly, so you must recall it.
插页给出了基础波动方程 v = f λ。解题时要分清是横波（如弦上波）还是纵波（声波）。写出已知的频率和波长，确保单位是赫兹和米。如果题目给的是周期 T，记住 f = 1/T，这一点插页上没有，需要自己回忆。
A favourite application combines v = f λ with the wave speed on a string, v = √(T/μ), which is also on the insert. You may need to equate the two expressions to solve for frequency in a standing wave setup. Always check that μ (mass per unit length) is in kg m⁻¹.
一类经典应用题是把 v = f λ 与弦上波速公式 v = √(T/μ) 结合起来（后者同样在插页上）。你可能需要将两个式子联立，求解驻波问题里的频率。务必检查 μ（单位长度质量）单位为 kg m⁻¹。
6. Refractive Index & Snell’s Law | 折射率与斯涅尔定律
The insert provides Snell’s law: n₁ sin θ₁ = n₂ sin θ₂. It also gives the refractive index formula n = c / v and the critical angle relation sin θ_c = 1/n (for light going into air). When working application questions, start by labelling the two media clearly. Often the core difficulty is geometry – drawing a clear diagram and correctly identifying the angle of incidence and refraction with respect to the normal.
插页给出了斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂，还有折射率公式 n = c / v 以及临界角关系 sin θ_c = 1/n（光射向空气时）。做应用题时，先清晰标出两种介质。很多时候难点在于几何——画出清晰的示意图，正确找出入射角、折射角（均相对于法线）。
Use the critical angle from the insert if it’s provided for a specific material. If not, calculate it. Application questions frequently involve an optical fibre or a semi-circular block, testing whether total internal reflection occurs. Check that sin θ > sin θ_c simply by comparing the incident angle with the critical value you read or compute.
如果插页直接给出了某种材料的临界角，直接使用；否则自己计算。应用题常出现光纤或半圆形玻璃砖，考察全反射是否发生。只需将入射角与查得或算出的临界角比较，检验 sin θ 是否大于 sin θ_c。
7. Interference & Path Difference | 干涉与光程差
The double-slit equation Δx = λD / s is on the insert, along with the diffraction grating formula d sin θ = nλ. When you see an interference pattern, immediately note whether it is produced by a double slit or a grating. For a grating, the insert gives d = 1/N, where N is the number of lines per metre; if they give lines per mm, multiply by 10³.
插页上列出了双缝干涉公式 Δx = λD / s 以及衍射光栅方程 d sin θ = nλ。看到干涉图样时，立即判断是双缝还是光栅产生的。对于光栅，插页有 d = 1/N，其中 N 是每米的刻线数；如果题目给的是每毫米刻线数，要乘以 10³。
Application questions often require you to find the wavelength of an unknown laser. Use the measured fringe spacing and the known slit separation. Remember that D must be in metres and all quantities in SI. The insert also prompts you to think about fringe separation Δx, which you might need to measure from a diagram or a given scale.
应用题常要求计算未知激光的波长。用测得的条纹间距和已知的双缝间距计算。注意 D 必须用米，所有量均用国际单位制。插页提示你关注条纹间距 Δx，你可能需要从示意图或给定的标尺上测量。
8. Stationary Waves on Strings | 弦上的驻波
Alongside v = √(T/μ), the insert reminds you of the relationship for harmonic frequencies: f = (1/2L) √(T/μ) for the fundamental, and for the nth harmonic, f_n = n × (1/2L) √(T/μ) under fixed ends. In application questions, you might be asked to predict the tension needed to produce a certain frequency. Rearrange carefully: square both sides, multiply by 4L² μ, and substitute numbers.
除了 v = √(T/μ)，插页还提醒你基频公式 f = (1/2L) √(T/μ)，两端固定的弦上第 n 次谐波满足 f_n = n × (1/2L) √(T/μ)。应用题可能让你预测产生某一频率所需的张力。仔细移项：两边平方，乘以 4L² μ，再代入数据。
Be alert to units: L in metres, T in newtons, μ in kg m⁻¹. If μ is given in g cm⁻¹, convert to kg m⁻¹ by multiplying by 0.001 / 0.01, i.e. 0.1. The insert does not do unit conversions for you; it expects sound numerical hygiene.
单位务必留意：L 用米，T 用牛，μ 用 kg m⁻¹。假如 μ 给的是 g cm⁻¹，要转换成 kg m⁻¹（乘以 0.1）。插页不会帮你做单位换算，它默认你有扎实的数字处理习惯。
9. Photoelectric Effect & Planck Constant | 光电效应与普朗克常数
The insert includes E = hf and the photoelectric equation hf = Φ + ½mv²_max. It also provides Planck’s constant h = 6.63 × 10⁻³⁴ J s. Application questions often give a table of stopping voltage against frequency; your task is to use eV = ½mv²_max and plot a graph where gradient equals h/e. Extract the gradient, multiply by e (1.60 × 10⁻¹⁹ C) and compare with the given h.
插页包含 E = hf 和光电方程 hf = Φ + ½mv²_max，并提供了普朗克常数 h = 6.63 × 10⁻³⁴ J s。应用题常给出一组遏止电压与频率的数据，你需要利用 eV_stop = ½mv²_max，画图后斜率等于 h/e。求出斜率，乘以基本电荷 e (1.60 × 10⁻¹⁹ C)，再与给定的 h 比较。
Another typical task is calculating the work function Φ. Use the intercept on the frequency axis (threshold frequency f₀) and Φ = hf₀. The insert’s h makes calculations straightforward. Always express Φ in joules or electronvolts as requested, using the conversion 1 eV = 1.60 × 10⁻¹⁹ J.
另一类常见题是求功函数 Φ。利用频率轴截距（截止频率 f₀）和 Φ = hf₀ 即可求得。插页上的 h 让计算变得直接。最后根据题目要求，将 Φ 用焦耳或电子伏特表示，记住转换关系 1 eV = 1.60 × 10⁻¹⁹ J。
10. Using Provided Constants and Units | 使用提供的常数与单位
The Jan 21 insert supplies density of aluminium (2700 kg m⁻³), speed of sound in air (340 m s⁻¹), acceleration of free fall (9.81 m s⁻²), and others. Application questions weave these into larger problems: e.g. calculating the mass of an aluminium wire given its dimensions, then using that mass in a wave speed calculation. Always cross-check units when a constant appears; the density is in kg m⁻³, so volume must be in m³.
2021 年 1 月的插页提供了铝的密度 (2700 kg m⁻³)、空气中的声速 (340 m s⁻¹)、自由落体加速度 (9.81 m s⁻²) 等。应用题会把这些常数融入复杂情景，比如先根据铝线的尺寸求质量，再把质量代入波速计算。每次用到常数都要核对单位是否匹配：密度是 kg m⁻³，那么体积就必须用 m³。
Write down every quantity with its units before substituting. If the question gives a length in cm, convert to m first. Use the insert as a prompt – if you see ‘speed of sound’, consider whether the question involves echoes, resonance tubes, or Doppler shifts. The insert is a nudge to recall associated phenomena.
代入公式前，每个量都要写出带单位的数值。如果题目给的长度是 cm，先转换成 m。把插页当成提示——一看到“空气中的声速”，就要联想到可能涉及回声、共鸣管或多普勒效应。插页在悄悄帮你回忆相关现象。
11. Common Pitfalls & How to Avoid Them | 常见陷阱与规避方法
One major pitfall is using the sine of the angle in degrees when the equation requires radians. In Unit 2, most angle measurements in waves and optics are in degrees (sin θ works fine), but if a question gives angular measurements for, say, oscillations, be careful with the calculator mode. The insert does not specify radians, but always check the context.
一大陷阱是公式需要弧度时却把角度当作度来算正弦。在 Unit 2 中，波动和光学里 sin θ 用度没有问题，但如果涉及简谐运动的角频率，要小心计算器模式。插页虽未明示，但要根据上下文判断。
Another is ignoring significant figures. Constants like h = 6.63 × 10⁻³⁴ have three significant figures; your final answer should typically match. Also, watch out for ‘show that’ questions – they require you to work backwards using the given answer to find a missing datum, often by rearranging an equation from the insert.
另外，有效数字常被忽略。像 h = 6.63 × 10⁻³⁴ 这样的常数有三位有效数字，最终答案一般也应保留三位。还要小心“证明题”（show that），这类题需要你利用给出的答案反过来推导缺失的数据，往往只需重新排列插页上的某个公式。
12. Exam Strategy: Reading the Insert Before the Question | 考试策略：答题前先读插页
A practical tip: when you open the exam paper, first locate the Jan 21 insert. Spend a minute categorising each formula – mechanics, materials, waves, quantum. Note any numerical data that will be needed. Then, as you read a question, the relevant section of the insert will already feel familiar, reducing anxiety and sloppy mistakes.
一条实用建议：打开试卷后，先用一分钟把 Jan 21 插页浏览一遍，将公式归类——力学、材料、波动、量子。留意哪些数据一定会用到。这样在读题时，对应的插页板块已经印在脑海里，能有效减少紧张和粗心错误。
During the exam, keep the insert next to your question paper. Whenever you feel stuck, scan it again – sometimes seeing E = σ / ε will remind you to check whether the question is about stress or strain. Trust the insert as a safety net, but also trust your training: the insert is a tool, not a substitute for understanding.
考试过程中把插页放在试题旁。一旦卡壳就再扫一眼——有时看到 E = σ / ε 就能提醒自己题目可能考的是应力还是应变。把插页当作安全网，但同时也要相信自己的训练：插页是工具，不是理解的替代品。
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