a-level-physics-mark-scheme-unit-1-jan21 Experimental Investigation | A-Level 物理 Unit 1 2021年1月评分标准 实验探究

📚 a-level-physics-mark-scheme-unit-1-jan21 Experimental Investigation | A-Level 物理 Unit 1 2021年1月评分标准 实验探究

This article unpacks the experimental investigation question from the Edexcel International Advanced Level Physics Unit 1 (WPH11/01) January 2021 examination and its corresponding mark scheme. By understanding the examiner’s expectations, students can master the structure of practical-based questions, secure high marks on data analysis, uncertainty evaluation, and experimental improvement suggestions.

本文深入剖析 Edexcel 国际 A-Level 物理 Unit 1（WPH11/01）2021 年 1 月考试中的实验探究题及其评分标准。通过理解考官的期望，学生可以掌握实验类题目的答题结构，在数据分析、不确定度评估和实验改进建议等环节稳拿高分。

1. The Core Task: Determining g and k | 核心任务：测定重力加速度 g 与弹簧劲度系数 k

The January 2021 paper required candidates to design and evaluate an experiment to determine the acceleration of free fall, g, using a spring of unknown stiffness and a set of slotted masses. The spring constant k had to be found first via Hooke’s law, and then the same spring was used in a dynamic energy transfer setup to extract g from measurements of extension and speed.

2021 年 1 月的试卷要求考生设计并评估一个实验，利用一根未知劲度系数的弹簧和一组槽码来测定自由落体加速度 g。首先需要通过胡克定律求出弹簧劲度系数 k，然后让同一根弹簧在动态能量转换装置中工作，通过测量伸长量和速度来提取 g 值。

The mark scheme rewarded a logical sequence: measure mass and extension for static loading, plot force–extension graph to find k, then attach a mass to the unstretched spring, release it and record the lowest point speed using a light gate, and finally apply energy conservation to calculate g.

评分标准鼓励逻辑清晰的步骤：先测量静态加载时的质量和伸长量，绘制力–伸长图求出 k，然后将质量块挂在未拉伸的弹簧上释放，用光门记录最低点的速度，最后应用能量守恒计算 g。

2. Apparatus and Measurements | 仪器与测量量

Candidates needed to list essential apparatus: a helical spring, a metre rule with millimetre scale, a set of 50 g slotted masses and hanger, a stand and clamp, a light gate connected to a data logger, and a card of known length attached to the mass. The mark scheme accepted any workable arrangement but insisted on specifying how each instrument was used.

考生需列出必要仪器：螺旋弹簧、毫米刻度米尺、一组 50 g 槽码及挂架、铁架台和夹具、连接数据记录器的光门，以及固定在质量块上的已知长度挡光片。评分标准接受任何可行装置，但坚持要求说明每种仪器的使用方式。

Key measurements included the original length of the spring, the loaded length for 5–6 different masses, the mass of the hanger, the length of the interrupt card, and the time for the card to pass through the light gate. The mark scheme emphasized recording raw data with appropriate precision, typically to 1 mm for lengths and 0.01 s for time.

关键测量量包括弹簧原长、5–6 组不同质量下的负载长度、挂架质量、挡光片长度以及挡光片通过光门的时间。评分标准强调以适当精度记录原始数据，长度通常精确到 1 mm，时间精确到 0.01 s。

3. Static Method for k | 测定 k 的静态方法

The spring constant k is obtained by adding masses to the hanger and measuring the extension x = loaded length − original length. The weight Mg provides the stretching force F. A table of M, F, loaded length, and x should be prepared. The mark scheme awarded marks for column headings with units and for calculating x correctly.

弹簧劲度系数 k 通过在挂架上增加质量并测量伸长量 x = 负载长度 − 原长来获得。重量 Mg 提供拉伸力 F。应准备一个包含 M、F、负载长度和 x 的表格。评分标准对带单位的列标题以及正确计算 x 给予分数。

Mass M / kg	Weight F / N	Loaded length / m	Extension x / m
0.050	0.49	0.215	0.035
0.100	0.98	0.250	0.070

The mark scheme expected a force–extension graph with F on the y‑axis and x on the x‑axis. A line of best fit should pass through the origin, and its gradient equals k. Candidates could be asked to determine k from the graph or to comment on whether the spring obeys Hooke’s law.

评分标准要求绘制力–伸长图，y 轴为 F，x 轴为 x。最佳拟合线应通过原点，其梯度等于 k。考生可能被要求从图中确定 k，或评论弹簧是否遵守胡克定律。

4. Dynamic Determination of g | 动态测定 g

To find g, the spring is clamped at the top and a mass M is hung from the unstretched lower end. The mass is released from rest at the point where the spring just becomes taut, so initial extension = 0. As the mass falls, the spring stretches and the mass reaches a maximum speed at the equilibrium position. The light gate placed at this point measures the time t for the interrupt card of length L to pass, giving speed v = L ÷ t.

为测定 g，将弹簧顶部夹紧，质量块 M 悬挂于未拉伸的下端。质量块从弹簧刚好绷紧的位置静止释放，因此初始伸长 = 0。质量块下落过程中弹簧拉伸，质量块在平衡位置达到最大速度。安置在该点的光门测量长度为 L 的挡光片通过的时间 t，从而得到速度 v = L ÷ t。

The energy conservation equation between release point and equilibrium is: mgx₀ = ½ kx₀² + ½ mv², where x₀ is the equilibrium extension. Rearranging yields g = (kx₀² + mv²) / (2mx₀). The mark scheme accepted this expression and awarded marks for correct substitution of k, m, x₀ and v.

释放点与平衡位置之间的能量守恒方程为：mgx₀ = ½ kx₀² + ½ mv²，其中 x₀ 为平衡伸长量。整理得 g = (kx₀² + mv²) / (2mx₀)。评分标准接受该表达式，并对正确代入 k、m、x₀ 和 v 给予分数。

5. Graph Plotting and Gradient Analysis | 绘图与梯度分析

An alternative approach rewarded by the mark scheme was to measure the maximum speed v for different release extensions. By varying the starting position, one can plot v² against x² or apply a linearised equation. The examiner often provides a relationship such as v² = (2g) x − (k/m) x², and a graph of v² against x yields a straight line with intercept zero and gradient 2g.

评分标准奖励的另一种方法是对不同的释放伸长量测量最大速度 v。通过改变起始位置，可以绘制 v²–x² 图或应用线性化方程。考官通常给出关系式如 v² = (2g) x – (k/m) x²，并且 v²–x 图是一条过原点、梯度为 2g 的直线。

Students must label axes with quantity, unit and scale, and draw a best‑fit line. The mark scheme penalises incorrectly plotted points or lines forced through the origin if the data do not support it. The gradient is taken from a large triangle on the line, and the final value of g is calculated with appropriate significant figures.

学生必须用物理量、单位和标度标注坐标轴，并画出最佳拟合线。若数据不支持过原点而强行画线，或描点错误，评分标准会扣分。梯度取目标线上一个大三角形的值，最终 g 值以适当有效数字算出。

6. Uncertainty Estimation | 不确定度估计

The mark scheme expected candidates to estimate percentage uncertainties in extension and time, and to combine them to find the percentage uncertainty in g. For extension, repeated measurements at a single load give a range ± half‑range, which is converted to percentage. Alternatively, the uncertainty in a metre‑rule reading is ±1 mm, and two readings are taken for extension, giving an absolute uncertainty of ±2 mm.

评分标准期望考生估计伸长量和时间的百分不确定度，并合成求 g 的百分不确定度。对于伸长量，在单一负载下重复测量可得范围 ±半范围，转换为百分数。或者，米尺读数的绝对不确定度为 ±1 mm，而伸长量需要两次读数，故绝对不确定度为 ±2 mm。

For time, the data logger may show a resolution of 0.001 s, but the mark scheme often gives a realistic uncertainty such as ±0.005 s due to reaction time or card twisting. The percentage uncertainty in v is the sum of percentage uncertainties in L and t. Finally, the uncertainty in g is found by combining those in k, x₀ and v using the rules for multiplication and powers.

对于时间，数据记录器可能显示分辨力为 0.001 s，但评分标准通常给出 ±0.005 s, 因为存在反应时间或挡光片扭曲等现实因素。v 的百分不确定度是 L 和 t 的百分不确定度之和。最后，使用乘方运算法则合并 k、x₀ 和 v 的不确定度以求得 g 的不确定度。

7. Sources of Error and Improvements | 误差来源与改进

The mark scheme listed several systematic and random errors. A significant systematic error arises from the spring’s own mass; the effective mass of the spring should be added to the suspended mass when using energy conservation. An improvement is to suspend a range of masses and use the intercept analysis, or to measure the period of oscillation instead, though that technique lies outside Unit 1.

评分标准列出了若干系统误差和随机误差。弹簧自身的质量是一个重要的系统误差来源；应用能量守恒时应将弹簧的有效质量附加到悬挂质量上。改进措施是悬挂一系列质量并利用截距分析，或改为测量振荡周期，不过该方法超出了 Unit 1 范围。

Other errors include parallax when reading the metre rule, the card not passing perpendicularly through the light gate, and energy loss due to air resistance. Improvements: use a set‑square to align the rule, ensure the light gate is level and the card rigid, and use a vacuum chamber (not practical but credited). The mark scheme also rewarded taking multiple readings and using a fiducial marker for consistent release height.

其他误差包括读取米尺时的视差、挡光片未垂直通过光门以及空气阻力导致的能量损失。改进方法：用三角板校准米尺，确保光门水平且挡光片刚性，并使用真空室（虽不实用但给分）。评分标准还对多次读数以及使用基准标记确保一致的释放高度给予奖励。

8. Safety Considerations | 安全注意事项

Although the experiment appears low‑risk, the mark scheme awarded marks for mentioning that heavy masses should be placed over a soft surface to protect feet, and that the stand must be stable to prevent toppling. Eye protection is not usually required, but mentioning securing loose clothing and tying back long hair was accepted.

虽然实验看似低风险，但评分标准对提及将重物放置于软垫上以保护脚部、支架必须稳固防倒等给出分数。通常不需要护目镜，但提到固定宽松衣物和束起长发亦可接受。

9. Data Recording and Presentation | 数据记录与呈现

The mark scheme insisted on recording all data in a clear table with correct units and consistent decimal places. Derived quantities must be shown with a sample calculation. Graphs must occupy at least half the grid and have correctly labelled axes. The examiner penalises missing units, inconsistent significant figures, and rough, non‑linear scales.

评分标准坚持将所有数据记录在清晰的表格中，注明正确单位和一致的小数位数。导出量须展示计算样例。图线必须占据至少一半的网格纸并有正确标注的坐标轴。考官对缺失单位、有效数字不一致以及粗略的非线性标度会加以扣分。

10. Linking Mark Scheme to Exam Technique | 评分标准与应试技巧结合

By studying the January 2021 Unit 1 mark scheme, students learn that experimental questions are marked in a highly structured way: apparatus (1‑2 marks), method description (2‑3 marks), measurements and table (3‑4 marks), graph and analysis (3‑4 marks), uncertainty (2‑3 marks), and evaluation (2‑3 marks). Copying the style from the mark scheme, such as bullet‑point steps and explicit use of “measure…”, “record…”, “repeat…”, maximises marks.

通过研究 2021 年 1 月 Unit 1 评分标准，学生们发现实验题按高度结构化的方式评分：仪器（1–2 分）、方法描述（2–3 分）、测量量与表格（3–4 分）、绘图与分析（3–4 分）、不确定度（2–3 分）以及评估（2–3 分）。模仿评分标准的风格，例如使用分步列表和明确写出“测量…”“记录…”“重复…”，即可实现分数最大化。

Practising with past paper mark schemes helps internalise generic phrases like “use a metre rule with mm scale to measure the original length and the loaded length, ensuring the eye is at right angles to the scale to avoid parallax error”. These earn marks across similar topics.

利用历年真题评分标准进行练习，有助于内化通用句式，如“使用毫米刻度米尺测量原长和负载长度，确保视线与刻度垂直以避免视差误差”。这些表达在类似主题中均能得分。

11. Examiner’s Common Pitfalls | 考官常见的失分点

The mark scheme revealed that many candidates lost marks by not stating that the spring must be loaded gently to avoid overshoot, or by using the total hanging mass without including the hanger. Others confused extension with loaded length, failed to convert grams to kilograms, or attempted to plot force in grams. The scheme also highlighted that “repeat measurements and take mean” must be paired with a justification, such as “to reduce random error”.

评分标准揭示了许多考生的失分点：未说明必须轻缓加载弹簧以避免过冲，或使用总悬挂质量时未计入挂架质量。还有人混淆了伸长量与负载长度，忘记将克换算为千克，或试图以克为单位绘制力的图线。评分标准还强调“重复测量并取平均值”必须附上理由，如“以减小随机误差”。

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