AS Physics Unit 1 Mark Scheme Jun19: Experimental Investigation of Young's Modulus | AS物理第一单元2019年6月评分方案：杨氏模量实验探究解析

📚 AS Physics Unit 1 Mark Scheme Jun19: Experimental Investigation of Young’s Modulus | AS物理第一单元2019年6月评分方案：杨氏模量实验探究解析

In AS Physics Unit 1, the experimental investigation question is a reliable differentiator, and the June 2019 mark scheme provides a blueprint for exactly what examiners expect. By unpacking this mark scheme, students can see how marks are allocated for measurement techniques, data handling, graph work and uncertainty analysis. This article breaks down the Young’s modulus experiment featured in that exam, translating examiner shorthand into actionable revision.

在AS物理第一单元中，实验探究题是区分度很高的一道题，而2019年6月的评分方案恰好为考官期望提供了清晰的蓝图。拆解这份评分方案，学生就能看明白测量技术、数据处理、作图与不确定度分析的得分点。本文逐层剖析该卷中的杨氏模量实验，把考官的简略评语转化为可用考前复习的行动指南。

1. Experiment Overview and the Mark Scheme’s Mindset | 实验概览与评分方案的思维

The June 2019 Unit 1 required candidates to determine the Young modulus of a metal wire using a simple setup: a wire fixed at one end, a marker attached, a metre rule behind the marker, and a hanger for adding masses. The mark scheme rewards a logical sequence of practical steps, not just the final number. Every detail from zeroing instruments to plotting a best-fit line is assessed.

2019年6月第一单元试题要求利用一套简单装置测定金属丝的杨氏模量：一端固定的金属丝、附着的标记物、标记后的米尺以及一个加载砝码的挂钩。评分方案奖励的是一套有逻辑的实操步骤，而不是仅仅得出最终数字。从仪器调零到绘制最佳拟合线，每个细节都会被评估。

Examiners look for evidence that you understand why a particular tool is chosen, how to minimise random and systematic errors, and how uncertainties propagate. The mark scheme explicitly links each mark to a specific skill: using a micrometer, reading a metre rule without parallax, tabulating repeated readings, calculating a gradient, and combining percentage uncertainties.

考官希望看到你有证据证明你理解为何选择某种工具、如何减少随机和系统误差以及不确定度如何传递。评分方案将每一分都对应到明确的技能：使用千分尺、无视察地读取米尺、将重复读数列表、计算斜率以及合成百分不确定度。

2. Measuring the Diameter with a Micrometer | 用千分尺测量直径

The mark scheme insists that the diameter must be measured with a micrometer screw gauge, not a ruler or vernier callipers. This is because the wire is typically less than 0.5 mm thick, so a micrometer with a resolution of 0.01 mm is required. A candidate who chooses a vernier calliper (resolution 0.1 mm) will lose the method mark immediately.

评分方案强调，直径必须用千分尺测量，而不是用直尺或游标卡尺。这是因为金属丝直径通常小于0.5 mm，因此需要分辨率为0.01 mm的千分尺。若考生选用游标卡尺（分辨率0.1 mm），方法分将直接扣掉。

You must also check for a zero error by closing the jaws before taking readings. The mark scheme often gives a mark for ‘check zero error and subtract/add correction’. Take at least three diameter readings at different points along the wire and in perpendicular directions to average out any non-uniformity. In June 2019, the raw data showed readings of 0.28 mm and 0.27 mm; the mean diameter was 0.275 mm. The cross-sectional area A is then calculated using A = πd²/4.

你还必须在测量前将测砧闭合以检查零误差。评分方案常为“检查零误差并减去/加上修正值”留出1分。沿着金属丝的不同位置、在相互垂直的方向上至少取三次直径读数，以消除粗细不均的影响。2019年6月的原始数据显示两个读数为0.28 mm和0.27 mm，平均直径为0.275 mm。接着用公式 A = πd²/4 计算截面积。

Use a micrometer with 0.01 mm resolution; check zero error before use and record the correction. — 使用分辨率为0.01 mm的千分尺；使用前检查零误差并记录修正值。
Take readings at several positions and in two perpendicular directions; record the mean diameter. — 在几个位置和两个正交方向上测量直径；记录平均直径。
Calculate cross-sectional area using A = πd²/4 and keep the value in m². — 用 A = πd²/4 计算截面积，并保留平方米单位。

3. Determining the Original Length and Avoiding Parallax | 测定原长与避免视察

The original length L of the wire should be measured with a metre rule, since the length is typically around 1–2 m and does not need micrometre precision. However, an examiner will award a mark for stating that you must clamp the rule vertically, align the zero mark carefully, and read the scale at eye level to avoid parallax error. The mark scheme in June 2019 rewarded ‘use a set square to align the marker with the rule’ or ‘use a travelling microscope’ as an alternative method for measuring extension, but for original length the rule is sufficient.

金属丝的原长 L 通常用米尺测量，因为长度一般在1到2米左右，无需微米级精度。不过，考官会为“将米尺竖直固定、小心对齐零刻线并在眼睛水平位置读数以避免视差”给出得分。2019年6月的评分方案对“使用三角板将标记物与直尺对齐”或“改用移动显微镜测量伸长量”都给予认可，但对于原长来说，米尺即可满足要求。

Always record the original length with its absolute uncertainty, usually ±1 mm for a metre rule, unless a more precise instrument is used. The mark scheme demands that you state this uncertainty explicitly in a table or in the data section. If you fail to provide an uncertainty, the mark for ‘appreciation of uncertainty’ may be lost.

一定要记录原长及其绝对不确定度，米尺通常为 ±1 mm，除非使用了更精密的仪器。评分方案要求你在表格或数据部分明确写出这个不确定度。如果缺失这一项，评估不确定度的得分就可能丢掉。

4. Measuring Extension Accurately | 精确测量伸长量

In the June 2019 setup, extension is measured by recording the new position of the marker on the metre rule after each mass is added. The mark scheme highlights two essential precautions: first, wait for the wire to stop stretching before taking a reading (to avoid dynamic effects); second, always subtract the initial marker reading from each subsequent reading to obtain extension. Do not simply record the new scale reading as extension.

2019年6月的装置中，伸长量是通过每次增加砝码后记录标记物在米尺上的新位置来测定的。评分方案强调两个必要预防措施：其一，待金属丝停止伸长后再读数（避免动态效应）；其二，始终用每次读数减去初始标记读数来得到伸长量，绝不能直接把新刻度当作伸长量。

Where the extension is very small, candidates can suggest using a travelling microscope or a digital indicator to improve precision. The mark scheme treats these as valid improvements for an extra mark in planning questions, but in this particular assessed task the metre rule method was fixed. Still, showing awareness of parallax correction by placing the eye level with the marker and using an outstretched ruler could earn a ‘detail’ mark.

如果伸长量非常小，考生可以建议改用移动显微镜或数显指示表来提高精度。评分方案在计划类题目中把这些视为有效改进并给分，但在这道具体评估题中，米尺方法已固定。不过，写出通过眼睛平视标记物和用延伸直尺来消除视差的意识，仍可能获得细节分。

5. Recording and Tabulating Data | 记录与表格数据

The mark scheme insists that all raw data be presented in a clear table with headings and units. In the June 2019 paper, the table required columns for mass, weight (force), marker reading, extension, and possibly the calculated extension. The unit for extension must be mm or m, but be consistent. The force is calculated as mass × 9.81 N kg⁻¹, and the mark scheme expects ‘weight = mg’ to be used, with m in kg.

评分方案坚持所有原始数据都要在清晰的表格中呈现，包含表头与单位。2019年6月的试题中，表格需要的列包括质量、重量（力）、标记物读数、伸长量，以及可能再列一列计算出的伸长量。伸长量的单位必须使用mm或m，并保持一致。力由质量乘以9.81 N kg⁻¹算出，评分方案要求使用“重量=mg”，且质量以kg为单位。

Significant figures matter. The mark scheme penalises over-quoting or under-quoting. Normally, raw data should reflect the precision of the instrument: if the metre rule reads to the nearest mm, then the reading should be given as 235 mm, not 235.0 mm. Calculated extensions may be given to one extra decimal place to avoid rounding errors.

有效数字很重要。评分方案会对过度保留或不足保留的数字扣分。通常原始数据应反映仪器精度：如果米尺读数精确到毫米，则应表示为235 mm，而不是235.0 mm。计算出的伸长量可以多保留一位小数，以避免舍入误差。

6. Plotting the Force-Extension Graph | 绘制力-伸长图

A force-extension graph must be plotted with force (weight) on the y-axis and extension on the x-axis. The June 2019 mark scheme allocated marks for appropriate scales, accurately plotted points, and a best-fit straight line. The axes must be labelled with quantities and units, e.g. ‘Weight / N’ and ‘Extension / mm’.

必须绘制力-伸长图，其中力（重量）为y轴，伸长量为x轴。2019年6月的评分方案为合适的坐标尺度、准确描点以及一条最佳拟合直线分配了分数。坐标轴务必标注物理量与单位，例如“Weight / N”和“Extension / mm”。

The line of best fit does not have to pass through the origin unless the data strongly suggest it. The mark scheme accepts a line that passes through the error bars of all points. If a point is clearly anomalous, it should be circled and ignored in the trend line. A mark is often available for identifying an anomalous point.

最佳拟合线不必强制通过原点，除非数据强烈表明如此。评分方案接受通过所有数据点误差棒的直线。如果存在明显异常点，应圈出并在画趋势线时忽略。指出异常点通常也能得到1分。

Choose a scale that uses at least half the graph paper in each direction. — 选取能使图线在各方向至少占据格子一半范围的坐标尺度。
Label axes with ‘Weight / N’ and ‘Extension / mm’ (or m). — 用“Weight / N”和“Extension / mm”（或m）标注坐标轴。
Plot points as small crosses or dots with circles; draw error bars if uncertainties are known. — 用细叉或加点套圈的方式描点；如果已知不确定度则画误差棒。
Draw one smooth best-fit line, not joining point to point. — 画一条平滑的最佳拟合线，而不要逐点连接。

7. Calculating the Gradient and Its Uncertainty | 计算斜率及其不确定度

The gradient k of the force-extension graph is needed because Young modulus E = (L/A) × k, provided L and A are in consistent SI units. The mark scheme expects the gradient to be calculated from a large triangle covering at least half the line, with the coordinates clearly read from the best-fit line, not data points. Show the values used, e.g., ΔF/Δx = (8.0 N) / (6.5 mm).

需要力-伸长图的斜率 k，因为杨氏模量 E = (L/A) × k，前提是 L 和 A 采用一致的国际单位。评分方案期望你用覆盖至少半条线的大三角形求斜率，坐标应从最佳拟合线上读取，而非数据点。列出所用数值，例如 ΔF/Δx = (8.0 N) / (6.5 mm)。

To find the uncertainty in the gradient, draw a ‘worst acceptable line’ – either the steepest or shallowest line that still fits the error bars. The mark scheme awards a separate mark for calculating the difference between best and worst gradients, then the half-range gives the absolute uncertainty in k. This mirrors the typical ‘uncertainty from graph’ mark.

要得到斜率的不确定度，可画一条“最差可接受线”——即仍通过误差棒的最陡或最平线。评分方案单独给1分用于计算最佳与最差斜率之差，再用半区间作为 k 的绝对不确定度。这对应于常见的“从图中求不确定度”得分点。

8. Computing Young’s Modulus Step by Step | 逐步计算杨氏模量

E = FL / (A ΔL)

Since the gradient k = F/ΔL, the expression becomes E = (L/A) × k. The mark scheme gives clear step marks: first calculate k from graph, then multiply by L/A. For example, if L = 2.500 m (±0.001 m) and A = 5.94 × 10⁻⁸ m² (from d = 0.275 mm), then L/A = 4.21 × 10⁷ m⁻¹. Multiplying by k (e.g., 1.23 × 10³ N m⁻¹) gives E ≈ 5.2 × 10¹⁰ Pa.

因为斜率 k = F/ΔL，表达式变为 E = (L/A) × k。评分方案给出了清晰的步骤分：先由图求出 k，再乘以 L/A。例如，若 L = 2.500 m (±0.001 m)，A = 5.94 × 10⁻⁸ m²（d = 0.275 mm 得到），则 L/A = 4.21 × 10⁷ m⁻¹。乘以 k（如 1.23 × 10³ N m⁻¹）得到 E ≈ 5.2 × 10¹⁰ Pa。

Always convert all units to SI before substituting: length in m, area in m², force in N. A mark is frequently reserved for the correct unit of Young modulus (Pa or N m⁻²) and a sensible answer, typically in the range of 10¹¹ Pa for steel. The mark scheme also credits comparing the calculated E with known values and calculating percentage difference when required.

代入前务必将所有单位化为国际单位：长度为m，面积为m²，力为N。通常会有1分属于杨氏模量的正确单位（Pa或N m⁻²）以及一个合理范围的值，例如钢材的杨氏模量通常约10¹¹ Pa。评分方案也会对将计算值同已知值比较并在要求时计算百分差的回答给分。

9. Uncertainty Analysis for Young’s Modulus | 杨氏模量的不确定度分析

The total percentage uncertainty in E is the sum of the percentage uncertainties of L/A and k. Since A depends on d², the percentage uncertainty in A is twice that of d. The June 2019 mark scheme expected candidates to handle this propagation: %U(E) = %U(k) + %U(L) + 2 × %U(d). L is measured with a metre rule, so %U(L) is usually very small (e.g., 0.04% for 2.5 m ± 1 mm). d is measured with a micrometer, so %U(d) = (0.01 mm / 0.275 mm) × 100% ≈ 3.6%; thus 2 × %U(d) ≈ 7.2%. The gradient uncertainty %U(k) comes from the worst acceptable line method.

E 的总百分不确定度是 L/A 和 k 的百分不确定度之和。由于 A 取决于 d²，A 的百分不确定度是 d 的两倍。2019年6月的评分方案期望考生能处理这种传递关系：%U(E) = %U(k) + %U(L) + 2 × %U(d)。L 用米尺测量，因此 %U(L) 通常非常小（例如，对 2.5 m ± 1 mm 约为 0.04%）。d 用千分尺测量，因此 %U(d) = (0.01 mm / 0.275 mm) × 100% ≈ 3.6%；2 × %U(d) ≈ 7.2%。斜率不确定度 %U(k) 来自最差可接受线法。

The mark scheme explicitly penalises missing the factor of 2 for diameter uncertainty. It also expects a statement of the final E value together with its absolute uncertainty or percentage uncertainty, written as E = (5.2 ± 0.6) × 10¹⁰ Pa or E = 5.2 × 10¹⁰ Pa ± 12%. Showing the combination of uncertainties in clear steps is the key to securing full marks.

评分方案明确会对漏掉直径不确定度的因子2进行扣分。它还期望学生写出最终的 E 值及其绝对不确定度或百分不确定度，表达为 E = (5.2 ± 0.6) × 10¹⁰ Pa 或 E = 5.2 × 10¹⁰ Pa ± 12%。将不确定度合成过程以清晰步骤展示，是拿到满分的关键。

%U(d) = (resolution / mean d) × 100%; then multiply by 2 for area. — %U(d) = (分辨率 / 平均直径) × 100%；然后将其乘以2得到面积的不确定度。
%U(k) = (|best gradient – worst gradient| / best gradient) × 100%. — %U(k) = (|最佳斜率 – 最差斜率| / 最佳斜率) × 100%。
Add all %U contributions; never subtract or cancel them. — 将所有的百分不确定度相加，切勿相减或抵消。

10. Common Mistakes and Examiner Tips from the Mark Scheme | 评分方案中的常见错误与考官提示

One recurring error is forgetting to subtract the initial marker reading. Candidates sometimes plot the scale reading directly, resulting in a curved or offset graph that does not earn the best-fit line mark. Another is using the raw diameter instead of dividing by 2 to get radius; the area formula A = πr² must be used, or equivalently A = πd²/4.

一个常见错误是忘记减去初始标记读数。考生有时直接把刻度读数来画图，结果得到一条曲线或平移的直线，拿不到最佳拟合线的分数。另一个错误是直接用直径代替半径，面积公式必须使用 A = πr² 或等价的 A = πd²/4。

Unit confusion is heavily penalised. The mark scheme shows that candidates who kept extension in mm but force in N often forgot to convert gradient to m when calculating E. The easiest route is to convert extension to metres as soon as possible. Additionally, some students draw a ‘line of worst fit’ that is parallel to the best fit; this is mathematically incorrect as the worst acceptable line should pivot around the centroid of the data to capture the maximum plausible gradient variation.

单位混淆会被严厉扣分。评分方案显示，那些将伸长量保留为mm、力用N的考生，在计算E时常常忘记把斜率换算为m。最简单的方法是将伸长量尽早换算为米。此外，有些学生画的“最差拟合线”与最佳线平行，这在数学上是不对的，因为最差可接受线应该绕数据中心点转动，以捕捉到斜率可能的最大变化范围。

Finally, when asked to comment on accuracy, the mark scheme expects candidates to compare their answer with a reference value (e.g., 2.0 × 10¹¹ Pa for steel). A simple ‘my value is close’ is insufficient; you must calculate a percentage difference and relate it to the experimental uncertainty. If the percentage difference lies within the total percentage uncertainty, the result is considered accurate within experimental limits.

最后，当被要求评论准确度时，评分方案期望考生将自己的答案与参考值（例如钢的 2.0 × 10¹¹ Pa）进行比较。简单一句“我的值很接近”是不够的；必须计算百分差，并将其与实验不确定度联系起来。如果百分差落在总百分不确定度范围之内，则结果在实验误差范围内被认为是准确的。

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AS Physics Unit 1 Mark Scheme Jun19: Experimental Investigation of Young’s Modulus | AS物理第一单元2019年6月评分方案：杨氏模量实验探究解析