📚 Common Mistakes in IB & CCEA Physics | IB 与 CCEA 物理易错题精讲
Physics exams often test not only knowledge but also the ability to avoid common pitfalls. This article highlights frequent mistakes made by students in IB and CCEA Physics, providing clear explanations to help you achieve higher marks. Each section addresses a specific misconception and shows the correct approach.
物理考试不仅考查知识，更考验学生避开常见陷阱的能力。本文精选了 IB 与 CCEA 物理课程中学生最常犯的错误，并给出清晰的正确解析，助你稳步提升成绩。
1. Mass vs Weight | 质量与重力的区别
Many students mistakenly treat mass and weight as the same quantity. Mass is a measure of the amount of matter in an object, measured in kilograms (kg) and remains constant everywhere. Weight is the gravitational force acting on that mass, given by W = m × g, measured in newtons (N). On the Moon, an object’s mass does not change, but its weight becomes about one-sixth of its Earth value.
许多学生错误地认为质量与重量是同一个量。质量衡量物体所含物质的多少，单位是千克（kg），且在任何地方保持不变。重量则是作用在该质量上的引力，公式为 W = m × g，单位是牛顿（N）。在月球上，物体的质量不变，但重量大约只有地球上的六分之一。
In practical problems, using a balance measures mass, whereas a spring scale measures weight. When drawing free-body diagrams, always label weight as ‘W’ or ‘mg’, never simply as ‘mass’.
在实际问题中，天平测量的是质量，而弹簧秤测量的是重量。画受力示意图时，一定要将重力标注为 ‘W’ 或 ‘mg’，绝不可只写 ‘质量’。
2. Average Speed vs Instantaneous Speed | 平均速率与瞬时速率
A common error is to use the formula for average speed when the question asks for instantaneous speed. Average speed = total distance / total time, vₐᵥ = Δs / Δt, while instantaneous speed is the speed at a specific moment, found from the gradient of a distance–time graph. Do not simply divide total distance by time if the speed is not constant.
一个常见错误是当题目求瞬时速率时却使用了平均速率公式。平均速率 = 总路程 / 总时间，vₐᵥ = Δs / Δt；而瞬时速率是某一特定时刻的速率，需要从距离–时间图的切线斜率求得。如果速度不恒定，就不能简单用总路程除以时间。
In IB and CCEA questions, you may be given a curved s–t graph and asked for the speed at t = 3 s. Always draw a tangent and calculate its gradient, not rise/run over a large interval.
在 IB 和 CCEA 试题中，经常会给出弯曲的 s–t 图并要求计算 t = 3 s 时的速率。务必画出切线并用切线斜率计算，而不是在大时间间隔上取上升量/水平量。
3. Newton’s Third Law Misapplication | 牛顿第三定律的误用
Many students think that if a book rests on a table, the weight of the book and the normal force from the table form an action–reaction pair. This is incorrect. The two forces in Newton’s third law must act on different objects. The weight is the Earth pulling the book down, so its reaction is the book pulling the Earth up. The normal force is the table pushing the book up, and its reaction is the book pushing the table down.
许多学生认为静止在桌面上的书所受的重力与桌面对书的支持力是一对作用力与反作用力，这是错误的。牛顿第三定律中的两个力必须作用在不同物体上。重力是地球吸引书向下的力，其反作用力是书吸引地球向上的力；支持力是桌面向上推书的力，其反作用力是书向下压桌面的力。
Use the notation F₁₂ = -F₂₁ to keep the pairing clear. Always ask: ‘What object exerts this force, and on what object?’ Only if the two answers swap do you have a third-law pair.
可用标记 F₁₂ = -F₂₁ 来明确配对。遇到力的题目时，先问自己：“这个力是谁施加给谁的？”只有当两个答案互换了施力物体和受力物体时，才构成第三定律的力对。
4. Work and Energy: Including Friction | 功与能：不可忽略的摩擦力
When applying conservation of energy, students often forget to include work done against friction, which converts mechanical energy into thermal energy. The complete statement is Wₙₑₜ = ΔEₖ + ΔEₚ + W_friction. If you ignore the friction term, you will overestimate the final speed or height.
在应用能量守恒时，学生常忘记计入克服摩擦力所做的功，这部分功使机械能转化为内能。完整的表达式为 Wₙₑₜ = ΔEₖ + ΔEₚ + W_friction。如果忽略摩擦项，就会高估末速度或上升高度。
A typical mistake appears when a block slides down a rough incline. Some candidates set mgh = ½mv², forgetting the energy dissipated as heat. The correct equation is mgh – f × d = ½mv², where f is the frictional force and d the distance along the slope.
一个典型错误出现在粗糙斜面下滑的问题中。常有考生列出 mgh = ½mv²，却忘记了以热能形式耗散的能量。正确的方程应为 mgh – f × d = ½mv²，其中 f 是摩擦力，d 是沿斜面的距离。
5. Elastic vs Inelastic Collisions | 弹性与非弹性碰撞的动量问题
Momentum is conserved in all collisions, but kinetic energy is conserved only in perfectly elastic collisions. A classic mistake is to assume that kinetic energy is always conserved. In inelastic collisions, some kinetic energy is converted to other forms, so you cannot equate total kinetic energy before and after the collision unless the problem states it is elastic.
动量在所有碰撞中均守恒，但动能只有在完全弹性碰撞中才守恒。一个经典错误就是总是假设动能守恒。在非弹性碰撞中，部分动能被转化为其他形式的能量，因此除非题目说明是弹性碰撞，否则不能令碰撞前后的总动能相等。
For an inelastic collision, use m₁u₁ + m₂u₂ = (m₁+m₂)v for perfectly inelastic cases, and calculate the loss in kinetic energy separately. For elastic collisions, you may also use u₁ – u₂ = v₂ – v₁ together with momentum conservation.
对于完全非弹性碰撞，使用 m₁u₁ + m₂u₂ = (m₁+m₂)v，并单独计算动能的损失。对于弹性碰撞，除了动量守恒外，还可以结合 u₁ – u₂ = v₂ – v₁ 来求解。
6. Centripetal Force Direction | 向心力方向误区
Centripetal force is not a new type of force but the net force directed towards the centre of circular motion. Many students incorrectly draw a centrifugal force acting outward or label the tension as the ‘centripetal force’ without considering other contributions. For an object in uniform circular motion, the resultant of all real forces (tension, gravity, normal) must provide F = m v² / r towards the centre.
向心力并非是一种新的作用力，而是指向圆心的合力。很多学生错误地在受力图中画出向外的离心力，或者将绳的张力直接标为“向心力”而不考虑其他力的贡献。对于做匀速圆周运动的物体，所有真实力（张力、重力、支持力）的合力必须提供指向圆心的 F = m v² / r。
In vertical circular motion, the speed changes, so the centripetal force requirement varies. At the top, mg + T_top = m v² / r; at the bottom, T_bottom – mg = m v² / r. Always draw a clear free-body diagram and resolve forces towards the centre.
在竖直面内的圆周运动中，速率是变化的，因此向心力需求也随之改变。在最高点：mg + T_top = m v² / r；在最低点：T_bottom – mg = m v² / r。务必画出清晰的受力图，并将力沿着向心方向分解。
7. Internal Resistance in Circuits | 电路中的内阻计算错误
A frequent error is to treat a battery as an ideal source with zero internal resistance. In reality, the terminal voltage V = ε – I r, where ε is the emf and r the internal resistance. When the external load R is connected, the current is I = ε / (R + r), not simply ε / R. Ignoring r leads to overestimation of current and terminal voltage.
一个常见错误是把电池当成内阻为零的理想电源。实际上，路端电压 V = ε – I r，其中 ε 为电动势，r 为内阻。当外接负载 R 时，电路中的电流为 I = ε / (R + r)，而不是 ε / R。忽略内阻会导致高估电流和路端电压。
In experiments measuring internal resistance, a graph of V against I gives a straight line with gradient = -r and intercept = ε. Students sometimes misinterpret the gradient or forget that the circuit must include a variable resistor to obtain multiple data points.
在测量内阻的实验中，V–I 图是一条直线，其斜率为 -r，截距为 ε。有时学生误解斜率的含义，或者忘记电路必须包含可变电阻以获得多组数据点。
8. Wave Interference Conditions | 波的干涉条件混淆
For stable interference patterns, the sources must be coherent – that is, they must emit waves with a constant phase difference and the same frequency. A typical mistake is to use two separate light bulbs or non-synchronised speakers, which produce changing phase differences resulting in no clear interference pattern. Always ensure the sources are derived from the same original wave, e.g. by passing light through a double slit.
要产生稳定的干涉图样，波源必须相干——即具有恒定的相位差和相同的频率。典型错误是使用两个独立的灯泡或未经同步的扬声器，它们产生的相位差不断变化，无法形成清晰的干涉图样。一定要确保波源来自同一原始波，例如通过双缝的光。
Constructive interference occurs when the path difference is n λ (n = 0, 1, 2…), and destructive interference when it is (n + ½) λ. Memorising the conditions without understanding coherence leads to incorrect predictions in exam questions.
当路程差为 n λ（n = 0, 1, 2…）时发生相长干涉，路程差为 (n + ½) λ 时发生相消干涉。若只记条件而不理解相干性的要求，在考试中极易做出错误推断。
9. Photoelectric Effect: Intensity vs Frequency | 光电效应：光强与频率
The photoelectric effect shows that electrons are emitted only if the incident photon energy h f exceeds the work function Φ of the metal. A widespread error is to think that increasing the intensity of light will inevitably cause emission. If the frequency is below the threshold f₀ = Φ / h, no electrons are emitted no matter how intense the light is. Intensity increases the number of photons, thus the number of emitted electrons, but only if f > f₀.
光电效应表明，只有入射光子能量 h f 大于金属的逸出功 Φ 时，电子才会逸出。一个普遍错误是认为增强光的强度就一定能引发电子发射。若频率低于截止频率 f₀ = Φ / h，再强的光照也无法打出电子。光强只增加光子数目，从而增加逸出电子的数量，但前提是 f > f₀。
Einstein’s equation is Eₖ max = h f – Φ. The stopping potential Vₛ is related to the maximum kinetic energy by e Vₛ = Eₖ max. Graphs of Eₖ max against f show a straight line of gradient h; confusing the gradient with Φ is another common slip.
爱因斯坦方程为 Eₖ max = h f – Φ。遏止电压 Vₛ 与最大动能的关系为 e Vₛ = Eₖ max。Eₖ max 对 f 的图线是一条斜率为 h 的直线；将斜率误认为是 Φ 是又一常见失误。
10. Radioactive Decay and Half-Life | 放射性衰变与半衰期
Students frequently mishandle half-life calculations by applying linear reasoning instead of exponential decay. The number of undecayed nuclei after n half-lives is N = N₀ (½)ⁿ, where n = t / T½. A typical error is to say that after two half-lives, all nuclei have decayed, which is false because each half-life halves the remaining amount, not the original amount sequentially subtracted.
学生在半衰期计算中常犯的错误是用线性思维代替指数衰减。经过 n 个半衰期后，未衰变的原子核数为 N = N₀ (½)ⁿ，其中 n = t / T½。典型错误是认为经过两个半衰期后原子核就全部衰变完，这是错误的，因为每个半衰期都是将剩余的数量减半，而不是每次减去初始量的一半。
When plotting decay curves, always use an exponential decrease, and do not join points with straight lines from one half-life to the next. To find the half-life from a graph, determine the time taken for the activity or number count to fall by half, and verify it is constant.
绘制衰变曲线时，一定要使用指数下降的曲线，不要用直线连接一个半衰期至下一个半衰期的数据点。从图中求半衰期时，应取活度或计数降至一半所需的时间，并验证该时间是否恒定。
Published by TutorHao | Physics Revision Series | aleveler.com
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