CIE A Level Physics Coursebook: Experimental Investigations | CIE A Level物理教材实验探究

📚 CIE A Level Physics Coursebook: Experimental Investigations | CIE A Level物理教材实验探究

Experimental investigations are the backbone of the CIE A Level Physics course, providing students with the opportunity to develop practical skills, analyse data, and understand the scientific method. The Coursebook emphasises a range of core experiments that not only reinforce theoretical concepts but also prepare students for the practical assessment components (Paper 3 and Paper 5). This article explores key experiments, common techniques, uncertainty analysis, and evaluation strategies, mirroring the approach in the official CIE Coursebook.

实验探究是 CIE A Level 物理课程的基石，为学生提供了发展实践技能、分析数据和理解科学方法的机会。课程教材重点介绍一系列核心实验，不仅强化理论概念，也为实践考核部分（第3卷和第5卷）做好准备。本文探索关键实验、常用技术、不确定度分析和评估策略，反映官方CIE教材的方法。

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1. Understanding Experimental Design | 理解实验设计

Every well-planned experiment begins with a clear identification of the independent variable (the quantity you change), the dependent variable (the quantity you measure) and the control variables (quantities kept constant). For example, in investigating the period of a pendulum, the length is the independent variable, the period is the dependent variable, and the mass of the bob and amplitude (if small) are controlled. A fair test requires that only the independent variable influences the dependent variable, so all other factors must be held steady.

每个精心设计的实验都始于清晰识别自变量（你改变的量）、因变量（你测量的量）和控制变量（保持恒定的量）。例如，在探究单摆的周期时，摆长为自变量，周期为因变量，摆球质量和振幅（若保持小角度）为控制变量。公平测试要求只有自变量影响因变量，因此所有其他因素必须保持稳定。

Reliability is improved by repeating measurements and calculating a mean. The number of significant figures quoted in a result should reflect the precision of the instrument; for instance, a metre rule typically reads to the nearest 1 mm, giving lengths such as 0.452 m (three significant figures). Before collecting data, a preliminary experiment often helps to establish a suitable range and interval for the independent variable.

通过重复测量并计算平均值可以提高可靠性。结果中所引用的有效数字位数应反映仪器的精确度；例如，米尺通常可读到最接近的 1 mm，因此长度记录为 0.452 m（三位有效数字）这类格式。收集数据之前，进行预实验通常有助于为自变量确定合适的范围和间隔。

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2. Key Measurements and Instruments | 关键测量与仪器

Selecting the right measuring instrument is crucial for minimising uncertainty. The table below summarises common instruments used in A Level physics experiments, along with their typical resolutions and associated absolute uncertainties (where half the smallest division is usually taken as the reading uncertainty, unless digital).

选择合适的测量仪器对减小不确定度至关重要。下表总结了A Level物理实验中常用的仪器，以及它们的典型分辨率和相关的绝对不确定度（通常取最小刻度的一半作为读数不确定度，数字仪器除外）。

Instrument / 仪器	Quantity / 测量量	Typical resolution / 典型分辨率	Reading uncertainty / 读数不确定度
Metre rule / 米尺	Length / 长度	1 mm	±0.5 mm
Vernier callipers / 游标卡尺	Small length/diameter / 小长度/直径	0.1 mm or 0.02 mm	±0.05 mm
Micrometer screw gauge / 千分尺	Very small lengths / 极短长度	0.01 mm	±0.005 mm
Digital stopwatch / 数字秒表	Time / 时间	0.01 s	±0.01 s (plus reaction time)
Analogue ammeter / 模拟电流表	Current / 电流	0.01 A or 0.1 A	± half smallest division

When using instruments, remember to check for zero errors. For example, a micrometer must be closed fully and the reading checked; if it does not read exactly zero, a zero correction must be applied to all subsequent measurements. Parallax error is another common systematic error, especially when reading analogue scales.

使用仪器时，记得检查零点误差。例如，千分尺必须完全闭合并检查读数；如果读数不恰好为零，则需对所有后续测量进行零点校正。视差误差是另一种常见的系统误差，尤其当读取模拟刻度时需要注意。

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3. Uncertainties and Errors | 不确定度与误差

No measurement is perfect; uncertainty arises from the instrument' ution itself for digital ones. The absolute uncertainty Δx has the same units as the measurement. The fractional uncertainty is Δx / x, and the percentage uncertainty is (Δx / x) × 100%.

任何测量都不是完美的；不确定度来自仪器的分辨率以及随机变化。读数不确定度通常取模拟仪器最小刻度的一半，或数字仪器分辨率本身。绝对不确定度 Δx 与测量值的单位相同。相对不确定度为 Δx / x，百分不确定度为 (Δx / x) × 100%。

When quantities are combined, uncertainties propagate. The rules used at A Level are:

If Q = A ± B, then ΔQ = ΔA + ΔB

当物理量组合时，不确定度会传播。A Level中使用的规则如下：

若 Q = A ± B，则 ΔQ = ΔA + ΔB

If Q = AB or Q = A/B, then ΔQ/Q = ΔA/A + ΔB/B

若 Q = AB 或 Q = A/B，则 ΔQ/Q = ΔA/A + ΔB/B

For powers, if Q = Aⁿ, then ΔQ/Q = |n| certainty when the number of repeats is small, and the standard deviation for larger sets.

对于乘方，如果 Q = Aⁿ，则 ΔQ/Q = |n| × ΔA/A。重复读数有助于估计随机不确定度；当重复次数较少时，可用数据的分散度（极差的一半）作为绝对不确定度，数据集较大时用标准差。

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4. Data Presentation and Graphing | 数据呈现与作图

Experimental data must be recorded in clear tables with headings that include units, e.g. ‘Length L / m’ and ‘Time t / s’. Each column should show raw readings and, if necessary, calculated means. Graphs are powerful tools: plotting the dependent variable on the y‑axis and the independent variable on the x‑axis often yields a straight line if the relationship is linear.

实验数据必须记录在清晰的表格中，表头含单位，例如“长度 L / m”和“时间 t / s”。每列应显示原始读数，如有必要，还应展示计算的平均值。图线是强有力的工具：若关系是线性的，将因变量绘于 y 轴、自变量绘于 x 轴通常会得到一条直线。

nce, if time has an uncertainty of ±0.2 s, the error bar extends 0.2 s above and below the point. To find the uncertainty in a gradient, draw the steepest and shallowest reasonable lines through the error bars, calculate their gradients m_max and m_min, then the uncertainty is (m_max – m_min)/2.

最佳拟合线应尽可能穿过误差棒。误差棒表示每个数据点的绝对不确定度；例如，若时间的不确定度为 ±0.2 s，误差棒从该点上下各延伸 0.2 s。为求出斜率的不确定度，可穿过误差棒画出可能的“最陡线”和“最浅线”，计算其斜率 m_max 和 m_min，则不确定度为 (m_max – m_min)/2。

The intercept on the y‑axis often gives a physical constant. For example, in a voltage‑current graph, the y‑ mx + c; always compare this with the linearised form of the physical law to extract constants.

y 轴上的截距常常给出物理常数。例如，在电压-电流图中，y 轴截距即为电池的电动势。直线方程为 y = mx + c；务必将其与物理定律的线性化形式进行比较，以提取常数。

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5. Determining 'g' by Free Fall | 通过自由落体测定重力加速度 g

A classic experiment measures the acceleration of free fall, g, using an electromagnet to release a steel ball and a trapdoor or light gate to measure the time of fall t over a known distance s. The equation of motion from rest is:

s = ½ g t²

经典实验通过电磁铁释放钢球，并用捕捉器或光闸测量钢球落下已知距离 s 的时间 t，从而测定自由落体加速度 g。由静止出发的运动方程为：

s = ½ g t²

To linearise the relationship, plot s on the y‑axis against t² on the x‑ e mean, minimising the effect of reaction time. The metre rule measures s with an uncertainty of ±0.5 mm, while the stopwatch adds a reaction‑time uncertainty, often around ±0.1 s.

为将关系线性化，将 s 绘于 y 轴，t² 绘于 x 轴。所得直线的斜率等于 ½ g，因此 g = 2 × 斜率。必须对每个高度多次测量时间并取平均值，以减小反应时间的影响。米尺测量 s 的不确定度为 ±0.5 mm，而秒表会引入反应时间不确定度，通常约 ±0.1 s。

In the Coursebook, students are encouraged to evaluate sources of error: air resistance is negligible for a dense steel ball falling a short distance; however, a larger distance increases timing uncertainty relative to the time of fall. The experiment can also be performed with a light gate connected to a data logger, which greatly reduces reaction‑time errors.

教材鼓励学生评估误差来源：致密钢球下落短距离时空气阻力可忽略；然而，下落距离增大会使计时不确定度相对于下落时间变大。该实验也可用连接数据采集器的光闸进行，这将大幅减少反应时间误差。

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6. Investigating Newton's Second Law | 探究牛顿第二定律

Newton' ing a linear air track. A glider of mass M is attached to a light string that passes over a pulley and supports a small mass m. The accelerating force is the weight of m, provided friction is compensated by tilting the track slightly. The acceleration a is measured using a light gate and a double‑interrupt card, or two light gates to measure the time to travel a distance.

牛顿第二定律 F = ma 可用线性气垫导轨进行验证。质量为 M 的滑行器连接一根轻绳，轻绳绕过滑轮悬挂小质量 m。加速力为 m 的重量，前提是通过微微倾斜导轨补偿摩擦力。加速度 a 用光闸和双遮光卡，或用两个光闸测量通过一定距离的时间来测定。

A graph of acceleration a (y‑axis) versus the accelerating force F = mg (x‑ ng m while transferring masses from the glider to the hanger keeps the total mass constant—a key design feature highlighted in the Coursebook.

若保持总质量 (M + m) 不变，加速度 a（y 轴）对加速力 F = mg（x 轴）作图应为一条过原点的直线。直线的斜率为 1/(M + m)。改变 m 的同时将质量从滑行器转移到吊钩上，以保持总质量恒定，这是教材重点强调的设计要点。

Alternatively, keeping F constant and varying the total mass yields a verification that a ∝ 1/mass. A graph of a against 1/(M + m) should be linear. This experiment requires careful elimination of systematic errors, such as ensuring the string is horizontal and the pulley is frictionless.

或者，保持 F 不变，改变总质量，可验证 a ∝ 1/质量。a 对 1/(M + m) 作图应为线性。该实验需要仔细消除系统误差，例如确保绳子水平且滑轮无摩擦。

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7. Resistivity of a Wire | 金属丝的电阻率

s connected in a circuit with an ammeter, voltmeter and a variable power supply or a metre‑ h L of the wire is varied, and the corresponding resistance R = V/I is recorded. The cross‑ by measuring the diameter d with a micrometer at several positions, calculating A = πd²/4.

金属丝的电阻率 ρ 利用关系式 R = ρL/A 测定。将待测金属丝接入带有电流表、电压表和可变电源或米桥的电路中。改变金属丝的长度 L，记录对应的电阻 R = V/I。横截面积 A 则通过使用千分尺在多个位置测量直径 d，然后计算 A = πd²/4 得出。

Since R = (ρ/A) × L, a graph of R (y‑axis) against L (x‑ is determined by combining the uncertainties in the gradient and in the area measurement.

由于 R = (ρ/A) × L，R（y 轴）对 L（x 轴）作图得到一条过原点的直线，斜率为 ρ/A。因此，电阻率可计算为 ρ = 斜率 × A。ρ 的不确定度由斜率的不确定度和面积测量的不确定度合成得到。

Common errors include heating of the wire (which increases resistance) and a non‑uniform diameter. The Coursebook advises keeping the current low and using a micrometer carefully, taking a zero reading before use.

常见误差包括导线发热（导致电阻增大）以及直径不均匀。教材建议保持低电流，仔细使用千分尺，并在使用前读取零点。

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8. Young's Modulus of a Wire | 金属丝的杨氏模量

Young's modulus E is a measure of the stiffness of a material. For a wire of original length L₀ and cross‑sectional area A, subjected to a force F, the extension ΔL follows:

E = (F/A) / (ΔL/L₀) = F L₀ / A ΔL

杨氏模量 E 是衡量材料刚度的量。对于原长为 L₀、横截面积为 A 的金属丝，在拉力 F 作用下产生的伸长量 ΔL 符合：

E = (F/A) / (ΔL/L₀) = F L₀ / A ΔL

The experiment is usually carried out using a long wire (about 2 m) clamped at one end, running over a pulley, with a mass hanger attached. A small marker on the wire and a travelling microscope or vernier scale allow measurement of the extension as masses are added. It is crucial to load and unload gradually to detect any plastic deformation and to use a reference wire to compensate for thermal expansion.

该实验通常采用一根长金属丝（约 2 m），一端固定，绕过滑轮，末端悬挂砝码。金属丝上装有小标记，用移测显微镜或游标尺测量加载砝码后的伸长量。务必逐渐加载和卸载，以检测任何塑性形变，并使用参考丝补偿热膨胀的影响。

A graph of force F (y‑axis) against extension ΔL (x‑axis) yields a straight line in the Hooke' icrometer is again used to measure the diameter of the wire in several places, and the mean diameter is used to calculate A.

在胡克定律区域内，力 F（y 轴）对伸长量 ΔL（x 轴）作图可得一条直线。该直线的斜率为 EA/L₀，因此 E = 斜率 × L₀ / A。再次使用千分尺在多个位置测量金属丝直径，取平均直径以计算 A。

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9. Oscillations: Simple Pendulum and Mass‑Spring System | 摆动：单摆与弹簧振子

The simple pendulum offers a straightforward method for determining g. The period T for small oscillations is:

T = 2π √L/g

单摆提供了测量 g 的简便方法。小角度摆动时的周期 T 为：

T = 2π √L/g

/gradient. The length L is measured to the centre of the bob, and the time for 20 oscillations is recorded to reduce timing uncertainty.

两边平方得 T² = (4π²/g) L。因此，T² 对 L 作图是一条过原点的直线，斜率为 4π²/g，从而 g = 4π²/斜率。长度 L 测量到摆球中心，记录 20 次全摆动的时间以减小计时不确定度。

A mass‑spring system also undergoes simple harmonic motion with period:

T = 2π √m/k

弹簧-质量系统也做简谐运动，周期为：

T = 2π √m/k

Plotting T² against the effective mass m (including a fraction of the spring mass) gives a line whose gradient is 4π²/k. The investigation reinforces the concept of energy changes and damping, all covered in the Coursebook. Care must be taken to keep oscillations small and to measure m using an electronic balance.

将 T² 对有效质量 m（包括弹簧质量的一部分）作图，得到的直线斜率为 4π²/k。该探究强化了能量变化和阻尼的概念，这些都在教材中有所涵盖。需注意保持摆动幅度小，并使用电子天平测量质量 m。

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10. Electrical Circuits and Internal Resistance | 电路与内电阻

A battery or cell has an electromotive force (e.m.f.) ε and an internal resistance r. The terminal potential difference V across the cell is given by:

V = ε – I r

电池或电源具有电动势 (e.m.f.) ε 和内电阻 r。电池两端的路端电压 V 由下式给出：

V = ε – I r

istor is used to alter the current I, and the corresponding V is recorded. A graph of V (y‑axis) against I (x‑axis) yields a straight line with a y‑intercept equal to ε and gradient = –r. The negative sign is often ignored, so r = |gradient|.

为求出 ε 和 r，使用可变电阻改变电流 I，并记录相应的 V。V（y 轴）对 I（x 轴）作图得到一条直线，y 轴截距等于 ε，斜率为 –r。负号通常忽略，因此 r = |斜率|。

ce box and an ammeter. The circuit equation is ε = I(R + r). Rearranging gives R = (ε / I) – r. A graph of R against 1/I is a straight line with gradient ε and intercept – he variable resistor and the proper use of digital multimeters for more accurate readings.

另一种方法使用电阻箱和电流表。电路方程为 ε = I(R + r)。整理得 R = (ε / I) – r。将 R 对 1/I 作图，得到斜率为 ε、截距为 –r 的直线。学生必须注意可变电阻中的接触电阻影响，并正确使用数字万用表以获得更准确的读数。

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11. Waves: Speed of Sound and Standing Waves | 波动：声速与驻波

The speed of sound in air can be measured using a resonance tube. A tuning fork of known frequency f is sounded above a tube whose effective length can be varied by adjusting the water level. Resonance occurs when the length of the air column L corresponds to λ/4, 3λ/4, etc., where λ is the wavelength.

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