AS Physics: Force and Extension Experiment – June 2019 Unit 1 Insert | AS物理：力与伸长量实验探究 – 2019年6月单元一插页真题

📚 AS Physics: Force and Extension Experiment – June 2019 Unit 1 Insert | AS物理：力与伸长量实验探究 – 2019年6月单元一插页真题

The June 2019 Edexcel AS Physics Unit 1 (WPH11/01) paper featured an experimental insert requiring students to interpret data from a spring investigation. This classic Hooke’s law experiment assesses your ability to process raw measurements, plot accurate force–extension graphs, determine the spring constant, and evaluate uncertainties. Mastering the insert-based question is essential for securing top marks in the practical and data-handling components of the examination.

2019年6月Edexcel AS物理单元一（WPH11/01）试卷中，实验插页要求学生分析弹簧实验的数据。这个经典的胡克定律实验考查你处理原始数据、绘制精确的力–伸长图、求弹簧劲度系数以及评估不确定度的能力。彻底掌握这类插页题型，是你在考试中拿下实践与数据处理部分高分的关键。

1. Experiment Overview | 实验概述

The aim of this investigation is to explore the relationship between the force applied to a helical spring and its resulting extension. The experiment verifies Hooke’s law, which states that the extension is directly proportional to the applied force up to the elastic limit. From the collected data, the spring constant k can be calculated as the gradient of the force–extension graph.

本实验旨在探究施加于螺旋弹簧的力与其伸长量之间的关系。实验验证了胡克定律，即在弹性限度内，伸长量与作用力成正比。通过采集的数据，可根据力–伸长图线的斜率求出弹簧的劲度系数 k。

2. Apparatus and Setup | 装置与搭建

A typical setup includes a sturdy clamp and stand, a helical spring with a pointer, a metre rule, a set of slotted masses (e.g., 100 g each), and a mass hanger. The metre rule is positioned vertically alongside the spring, with the pointer indicating the extension. It is crucial to avoid parallax error by ensuring the eye is level with the pointer, and to check that the rule’s zero coincides with the initial position of the pointer.

典型装置包括稳固的铁架台和夹子、带有指针的螺旋弹簧、一把米尺、一套槽码（例如每个100 g）以及一个挂码盘。米尺紧贴弹簧竖直放置，由指针指示伸长量。关键是眼睛要平视指针以消除视差，并确保米尺的零刻度与指针的初始位置对齐。

3. The Insert Data Table | 插页数据表

The June 2019 insert provided the following measurements of mass and extension for a spring. The masses are added incrementally, and the corresponding pointer readings are recorded. A portion of the tabulated data is shown here:

2019年6月的插页提供了弹簧的质量与伸长量测量值如下。质量逐渐增加，对应指针读数被记录。以下展示部分数据表：

Mass m / g	Extension x / mm
100	23
200	46
300	69
400	92
500	117
600	145

Notice that the extension values are given to the nearest millimetre. In the exam, you are expected to record readings to the precision of the measuring instrument and then convert them to SI units for plotting.

请注意，伸长值精确至毫米。在考试中，你需要按测量仪器的精度记录读数，然后将其转换为国际单位制以便绘图。

4. Data Processing | 数据处理

Before plotting, the mass data must be converted to force using F = mg, where g = 9.81 N kg⁻¹. Extensions in millimetres are converted to metres by dividing by 1000. For example, a mass of 100 g (0.100 kg) gives F = 0.100 × 9.81 = 0.981 N, and an extension of 23 mm becomes 0.023 m. The processed data table should include columns for Force / N and Extension / m.

在绘图前，必须利用 F = mg（g = 9.81 N kg⁻¹）将质量数据转换为力。伸长量以毫米为单位转化为米，需除以1000。例如，质量100 g（0.100 kg）产生的力为 F = 0.100 × 9.81 = 0.981 N，23 mm的伸长量即为0.023 m。处理后的数据表格应包含力 / N 和伸长量 / m 两栏。

F = 0.100 × 9.81 = 0.981 N  x = 23 / 1000 = 0.023 m

Always use consistent significant figures according to the precision of the original measurements. Typically, the force is given to three significant figures, and the extension to two or three significant figures.

务必根据原始测量精度使用一致的有效数字。通常，力保留三位有效数字，伸长量保留两位或三位有效数字。

5. Plotting the Force–Extension Graph | 绘制力–伸长图

With the processed data, plot a graph of Force (F) on the y-axis against Extension (x) on the x-axis. The points should appear to lie on a straight line passing through the origin. Draw a single, best‑fit straight line through the data points. Avoid simply ‘joining the dots’; instead, use a transparent ruler to achieve an even spread of points above and below the line.

利用处理后的数据，以力（F）为y轴、伸长量（x）为x轴描点作图。这些数据点应大致落在一条通过原点的直线上。穿过数据点绘制一条最佳拟合直线。切勿只是“连点成线”；要用透明直尺使直线两侧点分布均匀。

If the graph is a straight line through the origin, Hooke’s law is obeyed: F = kx. The spring constant k is the gradient of this line. To find k, select two widely spaced points on the line (not from the data table) and use:

若图线为通过原点的直线，则满足胡克定律：F = kx。弹簧劲度系数 k 即为该直线的斜率。求 k 时，选取最佳拟合线上的两个间距较远的点（非原始数据点），并计算：

k = ΔF / Δx = (F₂ − F₁) / (x₂ − x₁)

For instance, choosing points (0.020 m, 0.88 N) and (0.140 m, 6.18 N) gives k ≈ (6.18 − 0.88) / (0.140 − 0.020) = 5.30 / 0.120 ≈ 44.2 N m⁻¹. The units are newtons per metre.

例如，选取点 (0.020 m, 0.88 N) 和 (0.140 m, 6.18 N)，可得 k ≈ (6.18 − 0.88) / (0.140 − 0.020) = 5.30 / 0.120 ≈ 44.2 N m⁻¹。单位是牛顿每米。

6. Uncertainty Determination | 不确定度计算

The main source of uncertainty is the measurement of extension. If a metre rule has a precision of ±1 mm, the absolute uncertainty in each extension reading is ±0.001 m. When the extension is small, the percentage uncertainty is larger, which is why the worst fit lines might be used to find the uncertainty in the gradient. Draw two more lines – the steepest and the shallowest that are still reasonably consistent with the error bars – and calculate their gradients k_max and k_min.

主要的不确定度来源于伸长量的测量。若米尺精度为±1 mm，则每个伸长量读数的绝对不确定度为±0.001 m。较小伸长量对应的百分比不确定度更大，因此常采用最劣拟合线求梯度不确定度。再画两条线——一条最陡和一条最平缓，但都合理地落在误差棒范围内，并计算其斜率 k_max 和 k_min。

Δk = (k_max − k_min) / 2

The final value can then be expressed as k ± Δk. In exam insert questions, you might also be asked to estimate the percentage uncertainty in k, which is (Δk / k) × 100%.

最终结果可表示为 k ± Δk。在考试插页题中，也可能要求估算 k 的百分比不确定度，即 (Δk / k) × 100%。

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

Common systematic errors include a zero error when the spring is already slightly stretched before adding mass, or the metre rule not being vertically aligned. This can be minimised by carefully setting the pointer to zero at the start and using a spirit level to align the rule. Parallax error is another issue when the pointer is at a distance from the scale; using a mirror behind the pointer or a set‑square can help.

常见的系统误差包括零点误差（弹簧在未加质量时已略微伸长）或米尺未垂直放置。通过开始时细心将指针对零，并使用水平尺调准米尺，可使其最小化。视差也是问题之一，指针与刻度尺距离较大时尤为明显；在指针后方使用镜面或直角规有助于消除视差。

Additionally, the mass of the spring itself can cause a slight initial extension. While this is often negligible, you may correct for it by adding a small pre‑load to straighten the coils before taking the reference zero reading. During the experiment, vibrations and oscillations should be allowed to settle before reading the pointer position.

此外，弹簧自身质量也可能引起轻微的初始伸长。虽然通常可以忽略，但也可通过预加一小质量使线圈拉直，然后再定零位读数来校正。实验过程中，读数前应让振动与振荡完全静止。

8. Application to Exam-Style Questions | 考试题型应用

In the June 2019 Unit 1 paper, follow‑up questions often required students to calculate k from the gradient, comment on the linearity of the graph, determine the elastic limit from deviation of the graph, and estimate uncertainties using worst‑fit lines. Always label axes with quantity and unit (e.g., Force / N), use sensible scales that occupy more than half the graph grid, and show clearly how the gradient was calculated using a large triangle.

在2019年6月的单元一试卷中，后续题目通常要求学生从斜率求 k、评述图线的线性、根据偏离点判断弹性极限，以及利用最劣拟合线估算不确定度。作答时务必标明坐标轴为量及其单位（如 Force / N），选用合理尺度使其占图面一半以上，并清晰画出用于计算斜率的大三角形。

If the insert provided raw pointer positions instead of extensions, remember to subtract the initial pointer reading to find the true extension. Also check if the mass given includes the hanger; if not, you must add its mass to the applied load.

如果插页提供的是指针原始读数而非伸长量，记住要减去初始指针读数方能得到实际伸长量。同时检查给出的质量是否已包含挂码盘；若未包含，则须将盘质量计入施加载荷。

9. Key Takeaways for AS Physics Revision | AS物理复习要点

The force–extension insert experiment reinforces core practical skills: recording data with correct precision, converting units to SI, plotting and interpreting graphs, calculating gradients, and quantifying uncertainties. It also deepens understanding of Hooke’s law and the concept of the elastic limit. Practising with past papers and insert data will build confidence in handling this type of question under timed conditions.

力–伸长实验插页强化了核心实验技能：以正确精度记录数据、将单位转化为国际单位制、绘制并解读图形、计算斜率以及量化不确定度。同时加深了对胡克定律及弹性极限概念的理解。利用历年真题和插页数据进行练习，可帮助你在限时条件下从容应对此类题型。

Remember, clear presentation of worked calculations and graphical analysis can earn method marks even if the final numerical answer is slightly off. Always show the steps of substituting values into the gradient formula, and never forget the unit for k, N m⁻¹.

请记住，即便最终数值略有偏差，清晰展示计算过程与图像分析也可获得方法分。务必展现代入斜率公式的步骤，且永远不要忘记 k 的单位 N m⁻¹。

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