📚 Typical Example Problems in IB WJEC Physics | IB WJEC 物理：典型例题详解
Physics is not learned by reading alone. In both the IB Diploma Programme and the WJEC A-level specification, the marks that separate a grade 6 from a grade 7, or a B from an A, are almost always earned in numerical questions: a projectile launched at an angle, two masses joined by a string over a pulley, a cell with internal resistance, a photon striking a metal surface. This article collects the problem types that examiners return to year after year and works through each one in full, step by step, explaining the physics rather than only the arithmetic.
物理不是靠阅读就能学会的。无论是 IB 文凭课程还是 WJEC A-level 大纲，区分 6 分与 7 分、B 与 A 的分数几乎都出现在计算题中：以某个角度抛出的物体、用细绳跨过滑轮连接的两个物体、带内阻的电池、打在金属表面的光子。本文汇集了考官年年重复考核的题型，并逐步完整解答，重点解释物理思路，而不只是算术过程。
Each example is written in the style of a model answer: the physical principle is named first, then the general equation is written in symbols, then the numbers are substituted, and finally the result is checked for plausibility. If you copy this routine into your own answers, the structure alone will protect a large number of method marks.
每道例题都按"标准答案"的风格书写：先点明物理原理，再用符号写出通式，然后代入数值，最后检验结果是否合理。如果你把这套流程搬进自己的答卷，单是结构本身就能守住大量方法分。
1. How to Approach These Problems | 解题通用策略
Every worked example below follows the same five-step routine. First, read the question twice and decide which branch of physics it belongs to. Second, draw a large labelled diagram - most lost marks in mechanics and electricity come from a missing or careless diagram. Third, write the general equation in symbols before substituting any numbers. Fourth, substitute with units and keep three significant figures. Fifth, ask whether the answer is physically sensible: a car travelling at 500 m/s is a red flag.
下文每道例题都遵循同样的五步流程。第一步，读题两遍，判断它属于物理的哪个分支。第二步，画一幅清晰的大标注图——力学和电学中丢分，多半源于图缺失或画得草率。第三步，先用符号写出通式，再代入数字。第四步，带单位代入并保留三位有效数字。第五步，检查答案是否符合物理常识：汽车速度算出 500 m/s 就是明显的警报。
Method marks matter a great deal. In IB Paper 2 and in the WJEC unit papers, a correctly written algebraic statement such as T = m₁a or E = hc/λ earns credit even if the final number is wrong. Writing the general equation first therefore costs you five seconds and can gain you two marks.
方法分非常重要。在 IB 第二卷和 WJEC 各单元试卷中，只要写出 T = m₁a 或 E = hc/λ 这样的正确代数式就能得分，即使最后算错。先写通式只花你五秒钟，却可能拿到两分。
Constants used throughout this article, taken from the data booklet: gravitational field strength g = 9.8 m/s²; speed of light c = 3.0 × 10⁸ m/s; Planck constant h = 6.63 × 10⁻³⁴ J s; elementary charge e = 1.6 × 10⁻¹⁹ C; specific heat capacity of water 4200 J kg⁻¹ K⁻¹; molar gas constant R = 8.31 J mol⁻¹ K⁻¹.
本文全程使用的常量（取自数据手册）：重力场强度 g = 9.8 m/s²；光速 c = 3.0 × 10⁸ m/s；普朗克常量 h = 6.63 × 10⁻³⁴ J s；元电荷 e = 1.6 × 10⁻¹⁹ C；水的比热容 4200 J kg⁻¹ K⁻¹；摩尔气体常量 R = 8.31 J mol⁻¹ K⁻¹。
2. Projectile Motion | 抛体运动
A ball is kicked from the ground with an initial speed of 20 m/s at 30° to the horizontal. Calculate (a) the maximum height reached, (b) the total time of flight, and (c) the horizontal range. Take g = 9.8 m/s² and ignore air resistance.
一球以 20 m/s 的初速度、与水平面成 30° 角从地面踢出。求：(a) 达到的最大高度，(b) 总飞行时间，(c) 水平射程。取 g = 9.8 m/s²，忽略空气阻力。
Step 1 - resolve the initial velocity. The key idea is that horizontal and vertical motions are independent: the horizontal component is constant because there is no horizontal force, while the vertical component changes uniformly under gravity.
步骤 1——分解初速度。核心思想是水平方向与竖直方向的运动相互独立：水平方向没有力，所以速度恒定；竖直方向只受重力，速度均匀变化。
ux = u cos θ = 20 × cos 30° ≈ 17.32 m/s uy = u sin θ = 20 × sin 30° = 10 m/s
(a) At the highest point the vertical velocity is momentarily zero, so we use vy² = uy² − 2gH with vy = 0.
(a) 在最高点，竖直分速度瞬时为零，因此用 vy² = uy² − 2gH，并令 vy = 0。
H = uy² / (2g) = 10² / (2 × 9.8) = 100 / 19.6 ≈ 5.10 m
(b) The time to rise to the peak is tup = uy/g, and by symmetry the total flight time is twice this value for a launch and landing at the same height.
(b) 上升到最高点所用时间为 tup = uy/g；由于起落高度相同，运动具有对称性，总飞行时间是它的两倍。
tup = 10 / 9.8 ≈ 1.02 s T = 2tup ≈ 2.04 s
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