A2 Physics: Practical Skills and Experiment Guide | A2 物理：实验操作指南

📚 A2 Physics: Practical Skills and Experiment Guide | A2 物理：实验操作指南

Mastering A2 Physics requires not only theoretical understanding but also strong experimental skills. This guide walks you through the essential planning, data collection, analysis, and evaluation methods you will need for Paper 3 or practical assessments. From determining g to investigating radioactive decay, each section provides clear steps and key equations to help you prepare.

掌握 A2 物理不仅需要理论理解，更需要扎实的实验技能。本指南将带你梳理必需的实验规划、数据收集、分析和评估方法，适用于试卷 3 或实践考查。从测定重力加速度 g 到探究放射性衰变，每个小节都给出清晰的步骤和关键方程，助你全力备考。

1. Planning and Safety in Experiments | 实验规划与安全

Before any A2 Physics experiment, you must identify the independent, dependent and control variables. A step‑by‑step method should be written to reduce both systematic and random errors. Always carry out a risk assessment and use appropriate safety equipment such as goggles, gloves or a fume cupboard when handling hazardous materials.

在任何 A2 物理实验开始前，你必须确定自变量、因变量和控制变量。应写出逐步操作的方法，以减小系统误差和随机误差。始终进行风险评估，处理危险材料时使用护目镜、手套或通风橱等安全装备。

Preliminary trials allow you to check that your ranges and intervals are suitable. For example, if you are adding masses in a Young modulus experiment, you should first test whether the wire stretches without exceeding its elastic limit. Adapt your plan based on these trial results.

预实验可以帮你检查测量范围和间隔是否合适。例如在杨氏模量实验中增加砝码时，应首先测试金属丝是否在弹性极限内伸展。根据这些试验结果调整你的计划。

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2. Measuring Instruments and Uncertainty | 测量仪器与不确定度

Use a micrometer screw gauge (resolution ±0.01 mm) for small diameters like wire thickness, and vernier calipers (resolution ±0.1 mm) for lengths up to a few centimetres. For longer lengths a metre rule (±1 mm) is suitable. Digital multimeters and data loggers can reduce reading errors when measuring voltage or current.

使用千分尺（分度值 ±0.01 mm）测量导线直径等小尺寸，使用游标卡尺（分度值 ±0.1 mm）测量几厘米的长度。更长的距离可用米尺（±1 mm）。数字万用表和数据记录仪在测量电压或电流时可减少读数误差。

Every measurement has an absolute uncertainty, often taken as half the resolution. The percentage uncertainty of a quantity is (absolute uncertainty / measured value) × 100%. When quantities are combined, you add percentage uncertainties for multiplication or division, and add absolute uncertainties for addition or subtraction.

每个测量值都有绝对不确定度，通常取仪器分度值的一半。百分比不确定度为（绝对不确定度 / 测量值）× 100%。当物理量进行乘除运算时，将各自的百分比不确定度相加；进行加减运算时，将绝对不确定度相加。

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3. Data Collection and Tabulation | 数据收集与表格

Record all data in a table with clear headings that include both the quantity and its unit. Maintain a consistent number of decimal places for each column, matching the resolution of the instrument. For example, if you measure length to 1 mm, write 0.500 m rather than 0.5 m. Always include a column for repeat readings and calculate a mean.

将所有数据记录在表格中，表头需清晰注明物理量及其单位。每列应保持一致的小数位数，与仪器分度值相匹配。例如，若以毫米精度测量长度，应写为 0.500 m 而非 0.5 m。务必包含重复读数栏并计算平均值。

When measuring time repeatedly with a stopwatch, your reaction time introduces a random error. Taking at least three readings and averaging helps. Record the range of repeats and use (range ÷ 2) to estimate the absolute uncertainty in the average.

用秒表多次测量时间时，反应时间会引入随机误差。至少读取三个数值并取平均有助于减小影响。记录重复读数的范围，使用（范围 ÷ 2）估算平均值的绝对不确定度。

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4. Graphical Analysis and Linearising Equations | 图像分析与方程线性化

Plot the independent variable on the x‑axis and the dependent variable on the y‑axis. Choose scales that use more than half the graph paper in both directions. Draw a best‑fit straight line or smooth curve through the points, ignoring obvious outliers. For a straight line, calculate the gradient using a large triangle and the y‑intercept from the graph.

将自变量标在 x 轴，因变量标在 y 轴。选择能使两个方向均占据一半以上图纸的刻度。绘制一条穿过数据点的最佳拟合直线或平滑曲线，忽略明显异常点。对于直线，利用大三角形计算斜率，并从图上读取 y 轴截距。

Many A2 relationships are non‑linear. You can linearise them by changing what you plot. For instance, if the theory predicts y = ax² + b, plotting y against x² gives a straight line with gradient a and intercept b. Similarly, for T² ∝ l in a pendulum, plot T² vs l.

很多 A2 物理关系是非线性的，但可通过变换坐标将其线性化。例如若理论给出 y = ax² + b，将 y 对 x² 作图则得到斜率为 a、截距为 b 的直线。类似地，对于单摆 T² ∝ l，可绘制 T²–l 图。

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5. Mechanics: Determining the Acceleration of Free Fall g | 力学：测定自由落体加速度 g

Drop a steel ball from rest through a known height h measured using a metre rule. Use two light gates connected to a timer to measure the time t taken to fall. Since initial velocity u = 0, the equation h = ½ gt² applies. Plot h on the y‑axis against t² on the x‑axis. The gradient equals ½ g, so g = 2 × gradient.

从静止释放一个钢球，通过已知高度 h 自由下落，用米尺测量高度。使用两个连接计时器的光门测量下落时间 t。由于初速度 u = 0，适用公式 h = ½ gt²。将 h 作为 y 轴，t² 作为 x 轴作图。斜率等于 ½ g，故 g = 2 × 斜率。

Alternatively, use a single light gate to measure the instantaneous speed v at the bottom. By timing the ball’s diameter you find v. Then using v² = 2gh, plot v² against h; the gradient is 2g. This avoids measuring time from rest and reduces reaction‑time uncertainty.

另一种方法是使用单个光门测量底端的瞬时速度 v。通过测量钢球直径通过光门的时间得到 v。利用 v² = 2gh，绘制 v²–h 图，斜率为 2g。这避免测量从静止开始的掉落时间，减小了反应时间带来的不确定度。

h = ½ g t²

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6. Materials: Measuring the Young Modulus | 材料：测量杨氏模量

Clamp a long, thin copper or steel wire vertically. Add known masses to the hanger and measure the extension ΔL using a vernier scale or a travelling microscope. The original length L is measured with a metre rule, and the diameter d of the wire is found with a micrometer. The cross‑sectional area A = π d² / 4. Young modulus E = (F L) / (A ΔL).

将一根细长铜丝或钢丝垂直夹紧。往吊架添加已知质量，用游标尺或移测显微镜测量伸长量 ΔL。原始长度 L 用米尺测量，导线直径 d 用千分尺测量。横截面积 A = π d² / 4。杨氏模量 E = (F L) / (A ΔL)。

Plot stress (F/A) against strain (ΔL/L) to obtain a stress–strain curve. Alternatively, plot F (weight) against ΔL. The gradient of the straight‑line portion is EA/L, allowing you to calculate E. Avoid exceeding the elastic limit during loading.

绘制应力（F/A）– 应变（ΔL/L）曲线得到应力‑应变图。也可绘制载重 F 对 ΔL 的图。直线部分的梯度等于 EA/L，由此可计算 E。加载过程中切勿超过弹性极限。

E = (F L) / (A ΔL)

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7. Electricity: Resistivity of a Wire | 电学：导线电阻率

Set up a circuit with a power supply, ammeter and voltmeter to measure the resistance R = V/I of a nichrome or constantan wire. Vary the length L of the wire between the crocodile clips and record the voltage and current for each length. Measure the diameter d of the wire with a micrometer to find area A. Resistivity ρ = RA / L.

搭建含有电源、电流表和电压表的电路，测量镍铬或康铜丝的电阻 R = V/I。改变鳄鱼夹之间导线的长度 L，记录每个长度下的电压和电流。用千分尺测量导线直径 d 以求得截面积 A。电阻率 ρ = RA / L。

Plot R on the y‑axis against L on the x‑axis. The gradient of the straight line equals ρ / A. Multiply the gradient by the cross‑sectional area to obtain ρ. Keep the current small to avoid heating the wire, as resistance increases with temperature.

将 R 作为 y 轴，L 作为 x 轴作图。直线的斜率等于 ρ / A。将斜率乘以横截面积即可得到 ρ。保持电流较小以避免导线发热，因为电阻随温度升高而增大。

ρ = R A / L

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8. Capacitor Charge and Discharge | 电容器充放电

Connect a capacitor C in series with a resistor R, a switch, a voltmeter and a DC supply. While charging, record the voltmeter reading V at regular time intervals. During discharge, remove the supply and record V as the capacitor discharges through the resistor. The discharge equation is V = V₀ exp(–t / RC), where RC is the time constant.

将电容器 C 与电阻 R、开关、电压表和直流电源串联。充电时，每隔一定时间记录电压表读数 V。放电时移除电源，记录电容器经电阻放电时的 V。放电方程为 V = V₀ exp(–t / RC)，其中 RC 为时间常数。

To linearise, take the natural logarithm: ln V = ln V₀ – t / RC. Plot ln V against t; the graph is a straight line with gradient –1 / RC and intercept ln V₀. Use this to calculate C if R is known, or compare with the nominal value.

为线性化，取自然对数：ln V = ln V₀ – t / RC。绘制 ln V–t 图，得到斜率为 –1 / RC、截距为 ln V₀ 的直线。若已知 R 便可计算 C，或与标称值进行比较。

V = V₀ exp(–t / RC)

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9. Waves: Double Slit and Diffraction Grating | 波动：双缝干涉与衍射光栅

Shine a laser of known wavelength λ onto a double slit with slit separation a. Observe the interference fringes on a screen at distance D. Measure the fringe spacing Δx between several bright fringes and divide by the number of gaps. The relation λ = a Δx / D holds for small angles. For a diffraction grating with line spacing d, use nλ = d sin θ, measuring the angle θ for order n.

用已知波长 λ 的激光照射狭缝间距为 a 的双缝。在距离为 D 的屏幕上观察干涉条纹。测量若干条亮纹之间的条纹间距 Δx，并除以间隔数。对于小角度，有 λ = a Δx / D。对于刻线间距为 d 的衍射光栅，使用 nλ = d sin θ，测量第 n 级的衍射角 θ。

For the grating, measure the distance between the zero order and the first order spot on a screen, and the distance from grating to screen. Then tan θ = distance / D. Use a protractor or geometry to find sin θ. Multiple orders improve accuracy. Do not look directly at the laser beam.

对于光栅，测量屏幕上零级与一级亮点之间的距离，以及光栅到屏幕的距离。利用 tan θ = 距离 / D，用量角器或几何关系求出 sin θ。测量多级条纹可提升精度。切勿直视激光束。

nλ = d sin θ

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10. Radioactivity: Inverse-Square Law for Gamma Radiation | 放射性：γ 射线的平方反比定律

Place a gamma source (e.g., Co‑60) in front of a Geiger‑Müller tube connected to a counter. First, measure the background count rate over several minutes. Then record the count rate C at different distances d from the source, using the same time interval for each. Subtract the background rate from each reading to obtain the corrected count rate C’.

将 γ 源（如 Co‑60）放置在连接计数器的盖革‑米勒管前。首先测量几分钟的本底计数率。然后在不同距离 d 处记录计数率 C，每次测量时间相同。从每个读数中减去本底计数率，得到修正计数率 C’。

According to the inverse‑square law, C’ ∝ 1/d². Plot corrected count rate against 1/d²; the graph should be a straight line through the origin. Alternatively, plot ln C’ against ln d; the gradient should be –2. Consider safety: use tongs and minimise exposure time.

根据平方反比定律，C’ ∝ 1/d²。将修正计数率对 1/d² 作图，应为一条过原点的直线。也可绘制 ln C’–ln d 图，斜率应为 –2。注意安全：使用夹具并尽量减少暴露时间。

C’ ∝ 1 / d²

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11. Error Analysis and Practical Improvements | 误差分析与实验改进

Systematic errors arise from faulty equipment or experimental design, such as a zero error on a micrometer or a consistently low voltmeter reading. These can be reduced by calibrating instruments, checking zero before use, or including a control experiment. Random errors, caused by unpredictable fluctuations, are reduced by taking repeat readings and averaging.

系统误差源于仪器故障或实验设计不当，例如千分尺的零误差或电压表读数持续偏低。可通过校准仪器、使用前检查零点或设置对照实验来减少。随机误差由不可预测的波动引起，通过重复读数取平均值来减小。

Identify the largest source of percentage uncertainty in your experiment. Often it is the measurement with the smallest magnitude, such as extension in the Young modulus experiment. Suggest practical improvements: use a longer wire to increase extension, or employ a data logger to reduce timing uncertainty. Always state why the change improves the result.

找出实验中百分比不确定度最大的来源。往往是量值最小的那个测量量，例如杨氏模量实验中的伸长量。提出实际改进建议：使用更长的导线以增大伸长量，或采用数据记录仪来降低计时不确定度。务必说明改进为何能改善结果。

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12. Writing a Concise Evaluation | 撰写简明的评估

An effective evaluation comments on the reliability and accuracy of your data. Discuss whether repeats were consistent and whether the graph was a straight line as predicted by theory. Mention any anomalies and explain how they might have occurred. Your conclusion should state the final experimental value with its overall uncertainty, and compare it with an accepted value using percentage difference.

一份有效的评估需评价数据的可靠性和准确性。讨论重复读数是否一致，以及图像是否如理论预期呈直线。提及任何异常点并解释其可能成因。结论应给出最终的实验值及其总不确定度，并用百分比差异与公认值进行比较。

Suggest specific improvements that would directly reduce the largest uncertainty. For example, ‘using a longer wire gave a larger extension, making the percentage uncertainty in ΔL smaller.’ Finish by rating the overall confidence in your results, e.g., ‘The experiment is reliable because the percentage difference from the accepted value is within 5%.’

提出具体改进措施，直接降低最大的不确定度。例如，“使用更长的导线可获得更大的伸长量，使 ΔL 的百分比不确定度减小。”最后评估对结果的总体可信度，如“实验结果可信，因为与公认值的百分比差异在 5% 以内。”

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