📚 IB Physics: Common Mistake Questions Explained | IB 物理：易错题精讲
IB Physics examiners consistently report that many marks are lost not due to a lack of understanding, but because of avoidable errors in applying concepts, handling data, and managing unit conversions. This walkthrough unpacks ten of the most frequent pitfalls, explaining why students trip up and how to sidestep these traps with clarity and precision. Each section targets a specific blunder, provides a real-exam-style scenario, and models the correct reasoning so you can build error-free habits.
IB 物理阅卷老师反复指出，许多失分并非因为概念完全不懂，而是源于在应用概念、处理数据和单位换算时出现本可避免的错误。本文逐一剖析十个最高频的易错点，解释学生为何会掉进陷阱，并清晰准确地展示如何避开它们。每一节都聚焦一个具体的常见错误，给出真实考试风格的场景，并示范正确推理，帮助你养成零失误的答题习惯。
1. Significant Figures and Unit Conversion Errors | 有效数字与单位换算的误区
A typical blunder occurs when students multiply 6.0 cm by 5.00 cm to calculate area and present the answer as 30.0 cm² or 30.00 cm², wrongly preserving decimal digits. Since 6.0 has two significant figures, the product must be rounded to two significant figures: 30 cm². Another frequent slip involves converting squared or cubic units: many candidates treat 5 mm² as 5 × 10⁻³ m², forgetting that the conversion factor must be squared as well. Because 1 mm = 10⁻³ m, 1 mm² = (10⁻³ m)² = 10⁻⁶ m², so 5 mm² equals 5 × 10⁻⁶ m². Always check whether an answer’s precision is justified by the given data, and square or cube conversion factors together with their units.
经典错误：学生用 6.0 cm 乘以 5.00 cm 计算面积，结果写成 30.0 cm² 或 30.00 cm²，误把小数位数当成有效数字。实际上 6.0 只有两位有效数字，乘积也应保留两位有效数字，即 30 cm²。另一个常见失误出现在面积或体积单位换算上：很多人直接把 5 mm² 写成 5 × 10⁻³ m²，忘记了换算系数也要平方。因为 1 mm = 10⁻³ m，所以 1 mm² = (10⁻³ m)² = 10⁻⁶ m²，因此 5 mm² = 5 × 10⁻⁶ m²。一定要根据给定数据的精度决定答案的有效位数，并且在换算时对单位整体进行乘方。
2. Misusing Vector Components in Equilibrium | 平衡问题中矢量分量的混淆
When resolving a force of magnitude F into horizontal and vertical components, students often mislabel the adjacent and opposite sides of the right triangle. A force inclined at angle θ to the horizontal has a horizontal component F cosθ and a vertical component F sinθ. Errors arise when the angle is measured from the vertical – then the components swap. In equilibrium problems, treating the vertical equilibrium equation as F sinθ = weight can be correct only if θ is measured from the horizontal. Always draw a large, clear diagram and label the angle relative to the axis you are resolving along. A second mistake is forgetting that the normal reaction is not always equal to mg; on an incline, N = mg cosθ, and using mg sinθ in the friction inequality requires careful separation of parallel and perpendicular directions.
在将大小为 F 的力分解为水平和竖直分量时，学生经常标错直角三角形的邻边与对边。与水平方向夹 θ 角的力，其水平分量为 F cosθ，竖直分量为 F sinθ。若题目给出的角度是力与竖直方向的夹角，则分量关系恰好对调。在平衡问题中，把竖直方向方程直接写成 F sinθ = mg 只有在 θ 是从水平线量起时才成立。一定要画出大而清晰的示意图，并标出角度相对于分解轴的位置。另一个易错点是忘记支持力并不总等于 mg；在斜面上，N = mg cosθ，而运用 mg sinθ 进行摩擦不等式分析时，必须严格区分平行和垂直斜面的方向。
3. Misapplying Newton’s Third Law | 牛顿第三定律的常见误用
A classic exam trap asks students to identify the Newton’s third law pair of a force. If a book rests on a table, many answer that the upward normal force from the table and the downward weight of the book are an action–reaction pair. This is incorrect because both forces act on the same object – the book – whereas Third Law pairs act on different bodies. The correct pair to the weight (Earth pulling book) is the gravitational pull of the book on the Earth. The pair to the normal force (table pushing book) is the book pushing down on the table. Getting this wrong undermines free-body diagrams. Check: if two forces are nominated as a Third Law pair, they must be of the same type (e.g., both gravitational or both contact), equal in magnitude, opposite in direction, and must act on different objects.
考试中一个经典陷阱是让学生找出某个力的牛顿第三定律反作用力。比如一本书静止在桌面上，很多人会答：桌面向上的支持力与书的重力是一对作用力与反作用力。这是错误的，因为这两个力都作用在同一物体——书上，而第三定律的配对力必须作用在不同物体上。重力的正确反作用力是书对地球的引力；支持力的反作用力是书对桌面向下的压力。混淆这一点会让受力分析彻底出错。判断两个力是否为第三定律配对力的方法是：它们必须属于同种性质的力（同为引力或同为接触力）、大小相等、方向相反，并且分别作用在两个不同的物体上。
4. Energy Conservation Oversights | 能量守恒中的疏忽
Students frequently apply the mechanical energy conservation equation ½mv² + mgh = constant without checking whether non-conservative forces do work. If a block slides down a rough incline, friction dissipates energy as heat; writing ½mv² = mgh neglects the work done against friction and leads to an overestimated final speed. In spring systems, the presence of an external force or a hand slowly releasing the spring can alter the energy balance: if a mass is lowered gently onto a vertical spring, the gravitational potential energy lost does not equal the spring’s elastic potential energy gained because some energy is taken away by the hand. Always start with the work–energy theorem: W_net = ΔKE, and track all non-conservative work.
学生常常不经检查非保守力是否做功就直接套用机械能守恒方程 ½mv² + mgh = 常数。例如一个物块沿粗糙斜面下滑，摩擦力将一部分能量转化为内能；若只写 ½mv² = mgh 就会忽略克服摩擦力做的功，导致末速度被高估。在弹簧系统中，若用手缓慢释放物体，手的支持力也会带走一部分能量：物体轻轻落在竖直弹簧上时，重力势能的减少并不等于弹簧弹性势能的增加。解题时应从功能定理 W_net = ΔKE 出发，完整记录所有非保守力做功。
5. Electric Circuit Analysis – Internal Resistance Blunders | 电路分析——内阻相关错误
When a cell has internal resistance r, the terminal potential difference is V = ε – Ir. A common error is writing V = ε + Ir when the current direction is mislabelled, or forgetting that the power delivered to the external load is P = I²R, not I²(R + r). In experiments to determine emf and r from a V–I graph, students sometimes misinterpret the y-intercept as r rather than ε, or the negative gradient as 1/r. The equation V = –r I + ε shows that gradient = –r, so r = |gradient|. Another nuance: when connecting identical cells in parallel, the combined emf remains ε but the internal resistance becomes r/n, which changes the maximum power transfer condition (R_load = r/n) and can catch candidates off guard.
当电源存在内阻 r 时，端电压 V = ε – Ir。常见错误有：由于电流方向标注混乱而误写成 V = ε + Ir，或是在计算负载获得的功率时写成 P = I²(R + r)，正确的应该是 P = I²R。在用 V–I 图像测量电动势和内阻的实验中，学生有时会把纵轴截距当作 r（实际是 ε），或者把负斜率的倒数误认为 r。根据方程 V = –r I + ε，斜率为 –r，因此 r 等于斜率的绝对值。另一个易错点是：相同电池并联时，总电动势仍为 ε，但总内阻变为 r/n；这将改变最大功率传输条件（R_load = r/n），很容易在选择题中让人措手不及。
6. Thermal Physics: Interpreting p–V Diagrams | 热学：p-V 图解读误区
On a pressure–volume diagram, isothermal curves are hyperbolas (p ∝ 1/V), whereas adiabatic curves are steeper. Students often mislabel them or misread the area under the curve: the work done on the gas during compression is the area under the p–V curve, but sign conventions matter. If the volume increases, work is done by the gas; if it decreases, work is done on the gas. In thermodynamic cycles, confusion arises when calculating net work as the area enclosed by the cycle: clockwise cycle → net work done by gas; anticlockwise → net work done on gas. Also, when using ΔU = Q – W (IB Physics data booklet convention W = work done by gas), mixing up the sign can flip the entire energy flow analysis. Always state the first law convention you are using before substituting numbers.
在压强–体积图中，等温线是双曲线（p ∝ 1/V），绝热线则更陡。学生经常混淆这两种曲线，或误读曲线下的面积：压缩过程中外界对气体做的功等于 p-V 曲线下方的面积，但正负号非常关键。气体体积增大时，气体对外做功；体积减小时，外界对气体做功。在热循环问题中，容易错在把循环包围的面积当作净功，但忘记了正负：顺时针循环 → 气体对外做净功；逆时针循环 → 外界对气体做净功。此外，IB 物理数据手册使用 ΔU = Q – W（W 为气体对外做的功），一旦符号用反，整个能量流向分析就会全盘出错。代入数据前，务必先明确你所采用的第一定律符号约定。
7. Simple Harmonic Motion: Phase and Sign Gremlins | 简谐运动中的相位与符号陷阱
In SHM, displacement, velocity and acceleration are out of phase: x = x₀ sin(ωt), v = ωx₀ cos(ωt), a = –ω²x. A common slip is forgetting the negative sign in the acceleration equation, or writing v = –ωx₀ sin(ωt) when the displacement started from zero at t=0. The sign depends on the chosen form – sine or cosine – and the initial conditions. When a pendulum is released from its amplitude, starting conditions fit a cosine function. Another high-frequency mistake arises when calculating maximum speed: students might write v_max = ω²x₀, whereas it is v_max = ωx₀. Similarly, linking angular frequency to spring constant and mass (ω = √(k/m)) and to pendulum length (ω = √(g/L)) often gets swapped. Practise writing down the position-time function explicitly before differentiation, and check units: rad s⁻¹ for ω.
在简谐运动中，位移、速度和加速度之间存在相位差：x = x₀ sin(ωt)，v = ωx₀ cos(ωt)，a = –ω²x。常见的失误包括：漏掉加速度方程中的负号，或当 t=0 时物体从平衡位置出发却错误地写出 v = –ωx₀ sin(ωt)。符号取决于选用正弦还是余弦形式以及初始条件。例如单摆从振幅处释放，位移更适合用余弦函数。另一个高频错误在计算最大速度时出现：学生常写成 v_max = ω²x₀，而实际上 v_max = ωx₀。弹簧振子的角频率 ω = √(k/m) 与单摆角频率 ω = √(g/L) 也经常被混淆。建议在求导前明确写出位置随时间变化的函数表达式，并养成检查单位的习惯：ω 的单位为 rad s⁻¹。
8. Wave Interference and Path Difference Pitfalls | 波的干涉与波程差陷阱
Two-source interference problems require calculating the path difference s₁P – s₂P in terms of wavelength. Destructive interference occurs when path difference = (n + ½)λ, but many students forget the half-integer condition for minima and use nλ instead. Another error is neglecting the π phase change upon reflection at a fixed boundary: if one of two sound waves reflects off a wall, an extra ½λ path difference must be added even if the geometrical path difference seems to satisfy a condition. In double-slit light interference, moving from bright fringe to dark fringe involves a shift of ½λ in path difference, and mixing up the formulas Δy = λD/d (fringe spacing) with y_n = nλD/d (position of nth bright fringe) can cost marks. Always draw a diagram and explicitly state the interference condition being applied.
双源干涉问题需要计算波程差 s₁P – s₂P 与波长的关系。相消干涉的条件是波程差 = (n + ½)λ，但很多同学遗忘了半整数条件，在计算极小值时误用 nλ。另一个常见错误是忽略在固定端界面上反射时的 π 相位突变：若声波经过墙壁反射，即便几何波程差看似满足某一条件，仍需额外加上 ½λ 的等效波程差。在光的双缝干涉中，从亮纹移到暗纹对应波程差变化 ½λ，而把条纹间距 Δy = λD/d 与第 n 级亮纹位置 y_n = nλD/d 混用的现象也屡见不鲜。解题时务必画出示意图，并明确写出所依据的干涉条件。
9. Nuclear Physics: Activity and Decay Constant Confusions | 核物理：活度与衰变常数的混淆
The activity A of a radioactive sample is A = λN, where λ is the decay constant and N is the number of undecayed nuclei. A standard blunder is using the total number of atoms initially present in a compound without isolating the radioactive isotope fraction. For instance, when only a certain fraction of nuclei in a sample are radioactive, N must reflect that fraction. Another pitfall lies in the exponential decay equation N = N₀ e^(–λt). Students sometimes misapply logarithms: to find λ from a half-life graph, the gradient of a ln(N) vs. t graph is –λ, not λ. The relationship between half-life and decay constant t₁/₂ = ln2 / λ is often reversed, leading to λ = t₁/₂ / ln2. Always test logic: if t₁/₂ is large, λ should be small. Also, be aware that activity and count rate are proportional under identical detection conditions, but the corrected count rate must account for background radiation.
放射性样品的活度 A = λN，其中 λ 为衰变常数，N 为尚未衰变的原子核数目。典型错误在于直接使用样品中全部原子初始数目，而没有从中分离出具有放射性的同位素比例。例如，只有部分原子核具有放射性时，N 必须乘以这一比例。另一陷阱出现在指数衰变公式 N = N₀ e^(–λt) 的应用中：学生在用对数法求 λ 时，绘制 ln(N)–t 图后，经常把斜率误认作 λ，实际上斜率为 –λ。半衰期与衰变常数的关系 t₁/₂ = ln2 / λ 也常被倒置为 λ = t₁/₂ / ln2。应养成逻辑检验的习惯：半衰期越长，λ 应当越小。此外，在探测条件相同的前提下活度与计数率成正比，但最终计数率必须扣除本底辐射后方可使用。
10. Data-Based Questions: Linearisation Missteps | 数据处理题中的线性化失误
IB Paper 3 or the data-analysis component often demands transforming a non-linear equation into the form y = mx + c. A power-law relationship such as T = k L^p requires taking logs: ln T = ln k + p ln L, so plotting ln T against ln L yields a straight line with gradient p. Errors peak when students haphazardly take logs without isolating the variable, or when they assign the plotted axes incorrectly, for example plotting T vs. L^p instead of the linearised form. For an exponential decay, the transformation y = ln(voltage) against t gives slope –λ. Many candidates forget to propagate uncertainties correctly in log scales; the absolute uncertainty in ln(x) is approximately Δx/x. Practise identifying what should be plotted on each axis to extract the desired quantity from the gradient or intercept, and always include units, even in logarithmic plots, by labelling as ln(T/s) or ln(T) but with T in seconds.
IB 物理试卷三或数据分析部分经常要求将非线性方程转化为 y = mx + c 的直线形式。如幂律关系 T = k L^p，需两边取对数：ln T = ln k + p ln L，于是画出 ln T 对 ln L 的图可得一条斜率为 p 的直线。学生最容易犯错的地方在于随意取对数而不先分离变量，或者错误地选择坐标轴，比如直接画 T 对 L^p 图，而非线性化后的图。对于指数衰减，正确的线性化是绘制 ln(电压) 对 t 图，其斜率为 –λ。很多考生忘记了在对数坐标下正确传递不确定度：ln(x) 的绝对不确定度近似为 Δx/x。考试中务必刻意练习如何选取横纵坐标变量才能从斜率或截距中提取目标物理量，并且即使在取对数的情况下也要写明单位，例如用 ln(T/s) 来标示，表明 T 以秒为单位。
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