📚 AS Physics Practical Investigation: Unpacking the Unit 5 Insert June 2019 | AS 物理实验探究：解读 2019 年 6 月单元 5 插页
In the AS Physics practical assessment, the Insert booklet provides the essential scenario, apparatus diagrams, raw data tables and instructions that underpin your investigation. The June 2019 Unit 5 Insert is a classic example: it guided candidates through an experiment to determine the spring constant and investigate energy transfers in a mass‑spring system. Mastering this Insert not only prepares you for the exam but also builds the analytical and evaluative skills that define a confident physicist.
在 AS 物理实验考核中，插页（Insert）小册子会提供实验场景、装置图、原始数据表格以及关键操作指南。2019 年 6 月单元 5 的插页就是一个经典案例：它引领考生通过实验测定弹簧的劲度系数，并探究弹簧–重物系统中的能量转化。吃透这份插页不仅能帮助你应对考试，更能培养一名自信的物理学者所需的分析与评估能力。
1. What Is the Unit 5 Practical Insert? | 什么是单元 5 实验插页？
The Insert is a printed booklet that accompanies the question paper for externally assessed practical units in AS Physics. It supplies the background to an investigation, labelled photographs or line diagrams of the apparatus, tables for recording measurements, and sometimes guidance on how to use unfamiliar sensors. For the June 2019 sitting, the Insert focused on a dynamics‑energy investigation using a vertically‑mounted spring and a known mass.
插页是 AS 物理外部考核实验单元随试卷一同下发的小册子。它提供研究背景、标注好的实验装置照片或简图、记录测量数据的表格，有时还会指导如何使用陌生的传感器。2019 年 6 月的这场考试中，插页围绕一个动力学与能量探究展开，使用了一根竖直悬挂的弹簧和一个已知质量的重物。
The key idea is that every practical judgement – from drawing a line of best fit to calculating uncertainty – must be anchored in the information provided. You are not expected to have performed the exact experiment beforehand; instead, you use the Insert to visualise the setup and apply standard practical physics principles.
其核心理念在于，每一个实验判断——从画出一条最佳拟合线到计算不确定度——都必须依据插页给出的信息。你不一定要事先做过完全相同的实验；相反，你要利用插页来想象装置，并运用标准的实验物理原理。
2. Aim and Underlying Theory | 实验目标与理论依据
The Insert set out two linked objectives: first, to determine the spring constant k of a helical spring using Hooke’s Law and a force‑extension graph; second, to verify the conservation of energy principle by comparing the loss of gravitational potential energy of the falling mass with the elastic potential energy stored in the spring.
插页提出了两个相互关联的目标：第一，利用胡克定律和力–伸长量图测定螺旋弹簧的劲度系数 k；第二，通过比较下落物体减少的重力势能与弹簧中储存的弹性势能，验证能量守恒原理。
Hooke’s Law states that the force F applied to a spring is directly proportional to its extension x, as long as the elastic limit is not exceeded: F = kx. The elastic potential energy stored is Eₑ = ½ kx². For a mass m falling from rest, the loss in gravitational potential energy is ΔEₚ = mgΔh, where Δh is the vertical distance the mass falls from its unloaded position to its lowest point.
胡克定律指出，只要不超过弹性限度，施加在弹簧上的力 F 与其伸长量 x 成正比：F = kx。弹簧储存的弹性势能为 Eₑ = ½ kx²。对于一个从静止开始下落的质量 m，减少的重力势能为 ΔEₚ = mgΔh，其中 Δh 是重物从未悬挂位置到最低点的竖直距离。
By measuring the extension for a range of loads, you can plot a graph of F against x; the gradient equals k. Then, using a motion sensor or light gates (as suggested in the Insert), you can measure the speed v of the mass at the instant it passes the equilibrium position, allowing a direct energy comparison between ½ mv² + ½ kx₀² and mgΔh, where x₀ is the equilibrium extension.
通过测量不同负载下的伸长量，你可以画出 F 对 x 的图像，其斜率就是 k。接着，借助运动传感器或光门（插页中有暗示），你可以测出重物经过平衡位置瞬间的速度 v，从而对 ½ mv² + ½ kx₀² 与 mgΔh 进行直接的能量比较，其中 x₀ 是平衡伸长量。
3. Apparatus and Setup Depicted | 仪器与装置展示
The Insert featured a labelled diagram of a retort stand holding a long spring, with a metre rule clamped parallel to the spring. A 100 g mass hanger was attached to the lower end of the spring, and a set of slotted masses was shown beside it. A data logger with a light gate was positioned to detect the passing of the mass, and a pointer on the hanger served as a reference for reading the extension.
插页中有一幅标注好的示意图：铁架台夹持着一根长弹簧，一根米尺用夹具固定在弹簧旁边。弹簧下端挂着一个 100 g 的挂钩砝码，旁边画有一套槽码。一个带有光门的数据采集器被安装在可以探测重物经过的位置，挂钩上的指针则作为读取伸长量的参考。
Key features to note are the set‑square used to ensure the metre rule was vertical, the digital balance for measuring additional masses, and the clamping of the light gate at the equilibrium position. The Insert also included a close‑up of the Vernier scale on the rule – though in practice a millimetre scale was used – to highlight reading precision.
需要注意的关键细节是：用三角尺来保证米尺竖直；用电子天平称量附加质量；光门被夹固在平衡位置。插页中还有一张游标尺的放大图（尽管实际操作中使用的是毫米刻度），以此强调读数精度。
4. Step‑by‑Step Procedure from the Insert | 来自插页的实验步骤
The procedure was broken into two parts. Part A dealt with the static method for determining k. Students were instructed to suspend the mass hanger, measure the initial length of the spring l₀, add loads in 50 g increments up to 400 g, and at each stage measure the new length l. The extension x was then calculated as l − l₀.
实验步骤分为两部分。A 部分处理测定 k 的静态方法。指导考生悬挂挂钩砝码，测量弹簧原长 l₀，以 50 g 为一个增量增加负载，直到 400 g，每增加一次便测量弹簧新的长度 l。伸长量 x 则通过 l − l₀ 计算得到。
Part B moved to the energy investigation. The mass was pulled down a measured distance y from the equilibrium position and released. A light gate recorded the time Δt for a card of width w to cut the beam as the mass rose through the equilibrium point, giving the speed v = w / Δt. Several values of y were used, and the corresponding speeds at equilibrium were recorded.
B 部分进入能量探究。重物被从平衡位置向下拉开一段测好的距离 y，然后释放。当重物向上经过平衡点时，一块宽度为 w 的挡光片会遮断光束，光门记录下遮光时间 Δt，从而得出速度 v = w / Δt。实验使用了几个不同的 y 值，并记录了相应的平衡点速度。
To minimise timing errors, the Insert recommended repeating each release three times and calculating the mean Δt. It also stressed that the spring must not be stretched beyond its elastic limit, and that oscillations should remain purely vertical.
为了减少计时误差，插页建议每次释放重复三次，并计算平均 Δt。它还强调，弹簧的伸长量不能超出弹性限度，且振荡必须保持纯竖直方向。
5. Raw Data and Systematic Tabulation | 原始数据与系统表格
An empty results table was printed in the Insert for Part A, with columns: mass m / kg, weight W / N, length l / mm, and extension x / mm. The inclusion of the weight column reinforced the need to convert mass into force using g = 9.81 m s⁻². A sample of hypothetical data might look like this:
插页上印有 A 部分的空数据表格，包含下列各列：质量 m / kg、重量 W / N、长度 l / mm、伸长量 x / mm。表中有重量一栏，强调了需要利用 g = 9.81 m s⁻²将质量转化为力。一组假设的实验数据可能如下表所示：
| m / kg | W / N | l / mm | x / mm |
|---|---|---|---|
| 0.100 | 0.981 | 315 | 15 |
| 0.150 | 1.472 | 330 | 30 |
| 0.200 | 1.962 | 346 | 46 |
| 0.250 | 2.453 | 362 | 62 |
| 0.300 | 2.943 | 378 | 78 |
For Part B, a separate table recorded the initial displacement y, the time Δt for the card to pass through the light gate, and the calculated instantaneous speed v. It is vital to include units in the headings, as required by the Insert, and to record all raw readings to the same number of decimal places.
B 部分另有一个表格记录初始位移 y、挡光片通过光门的时间 Δt 以及计算出的瞬时速度 v。按照插页的要求，表头中必须带单位，并且所有原始读数都应保留相同的小数位数。
6. Graph Plotting and Determination of k | 绘图与 k 的测定
Using the data from Part A, you must plot a graph of W on the vertical axis against x on the horizontal axis. The Insert typically provides a grid with sensible scales. The points should form a straight line through the origin, confirming Hooke’s Law. The gradient of the best‑fit line equals the spring constant k.
利用 A 部分的数据，你需要画一张 W（纵轴）对 x（横轴）的图。插页通常会给出坐标纸，标度合适。数据点应该形成一条过原点的直线，从而验证胡克定律。最佳拟合线的斜率就等于弹簧的劲度系数 k。
When drawing the best‑fit line, ignore obvious anomalous points and ensure the line balances points above and below it. To calculate the gradient, choose two widely separated points on the line – not data points – and use:
k = ΔW / Δx = (W₂ − W₁) / (x₂ − x₁)
绘制最佳拟合线时，应忽略明显异常的数据点，并确保直线上下两侧的点大致均等。计算斜率时，选取直线上相距较远的两个点（而非实测数据点），使用公式：
k = ΔW / Δx = (W₂ − W₁) / (x₂ − x₁)
The graph also allows you to estimate the uncertainty in k. Draw two further lines: the steepest and the shallowest possible straight lines that still reasonably fit the data points. The absolute uncertainty Δk is then given by half the difference between the gradients of these two extreme lines: Δk = (k_max − k_min) / 2.
此图还能够估算 k 的不确定度。再画两直线：一条尽可能陡峭，一条尽可能平缓，但仍能合理地逼近数据点。这两条极值线的斜率之差的一半，就是 k 的绝对不确定度：Δk = (k_max − k_min) / 2。
7. Energy Investigation: Analysis of Part B Data | 能量探究：B 部分数据分析
In Part B, for each displacement y, the gravitational potential energy lost relative to the equilibrium position is mg(y + x₀) approximately, but the Insert guided candidates to consider the energy just as the mass passes equilibrium, where the elastic potential energy is ½ kx₀² and the kinetic energy is ½ mv². The energy transferred from the extra GPE stored by pulling the mass down a distance y becomes kinetic and additional elastic energy as the spring stretches further.
在 B 部分中，对于每一个位移 y，相对于平衡位置损失的重力势能约等于 mg(y + x₀)，但插页引导考生考虑重物恰好经过平衡位置瞬间的能量状态，此时弹性势能为 ½ kx₀²，动能为 ½ mv²。把质量往下拉一段距离 y 所储存的额外重力势能，会转化为动能以及弹簧进一步拉伸所需的额外弹性势能。
A straightforward approach is to plot a graph of v² against y². If energy is conserved, the relationship should be linear, as the kinetic energy gain is proportional to the square of the displacement from equilibrium. The Insert hinted that the gradient of this second graph could be compared with 2g or used to find the effective acceleration.
一个直接的做法是画出 v² 对 y² 的图像。若能量守恒，此关系就是线性的，因为动能的增加量正比于离开平衡位置的位移的平方。插页暗示，这张图的斜率可以和 2g 相比较，或者用于求解有效加速度。
Any discrepancy between the predicted and measured gradient indicates energy losses – primarily due to air resistance and internal friction in the spring. The discussion of such discrepancies is typically worth several marks on the question paper, and the Insert’s guidance on systematic errors helps you formulate a physics‑grounded evaluation.
预测斜率与由实验测得的斜率之间的任何偏差，都表明存在着能量损耗——主要来自空气阻力和弹簧内部摩擦。在试卷上，对此类偏差的讨论通常值好几分。插页中关于系统误差的提示，能帮助你有理有据地进行评价。
8. Uncertainty Calculations and Propagation | 不确定度计算与传播
Understanding uncertainty is central to the Unit 5 Insert. The metre rule used for x had a resolution of ±1 mm, so the absolute uncertainty in a single length reading was ±0.5 mm, but because x came from two readings (l − l₀), the absolute uncertainty in x was propagated as ±1 mm. For the light gate timing, the resolution was ±0.001 s, but the dominant uncertainty often came from reaction time or alignment.
理解不确定度是单元 5 插页的核心。测量 x 所用的米尺分辨率为 ±1 mm，因此单次长度读数的绝对不确定度为 ±0.5 mm。但由于 x 是由两次读数相减得到（l − l₀），x 的绝对不确定度便传播为 ±1 mm。光门计时的分辨率是 ±0.001 s，但主要的不确定度往往来自人的反应时间或装置的对齐问题。
The Insert expected you to calculate percentage uncertainty in each quantity and to combine them appropriately. For example, percentage uncertainty in k:
%U(k) = %U(ΔW) + %U(Δx)
where %U(Δx) = (Δx不确定性 / Δx) × 100% and an equivalent calculation for ΔW. The largest contributor to uncertainty usually comes from the measurement of small extensions at low loads.
插页期望你计算每个量的百分不确定度，并恰当地加以合成。例如 k 的不确定度：
%U(k) = %U(ΔW) + %U(Δx)
其中 %U(Δx) = (Δx的不确定度 / Δx) × 100%，对 ΔW 的计算类似。最大的不确定度来源通常是低负荷下对小伸长量的测量。
For the speed measurement, the uncertainty in v arose from uncertainties in w and Δt: %U(v) = %U(w) + %U(Δt). The Insert’s sample calculations demonstrated that sharp, precise values of w and taking the mean of several readings were crucial in keeping the overall uncertainty below 5%.
在速度测量中，v 的不确定度来自 w 和 Δt 的不确定度：%U(v) = %U(w) + %U(Δt)。插页中的计算示例表明，精确测定 w 值并对多次读数取平均值，是将总不确定度控制在 5% 以下的关键。
9. Common Sources of Error and Refinements | 常见误差来源与改进
Several systematic errors were baked into the Insert scenario. The metre rule might not be perfectly vertical, causing a parallax error in reading lengths. The spring could develop a ‘set’ if extended beyond its elastic limit, invalidating Hooke’s Law. Additionally, oscillations often became slightly elliptic rather than pure linear motion, leading to an underestimate of the equilibrium speed.
插页场景中本身就设置了若干系统误差：米尺可能不是完全竖直，导致在读取长度时出现视差；弹簧若被拉伸超过弹性限度，就会产生‘永久形变’，使胡克定律无效；此外，振荡往往略带椭圆，而非纯粹的直线运动，这会低估平衡点的速度。
To minimise parallax, a set square and a digital height gauge could replace the metre rule. A low‑friction pulley or better clamping of the spring can prevent sideways wobbling. Using a stiffer spring with a higher k reduces the relative extension error. The Insert also mentioned that repeating the experiment with a different spring could test the robustness of the energy conservation claim.
为减少视差，可用三角尺和数字式高度计取代普通米尺。使用低摩擦滑轮或更牢靠地固定弹簧，可以防止横向摆动。换用一根 k 值较大的硬弹簧，能降低相对伸长误差。插页中还提到，用另一根弹簧重复实验，可以检验能量守恒这一结论的稳健性。
10. Tackling Exam‑Style Questions Based on the Insert | 应对基于插页的考试题型
Typical questions that follow the Unit 5 Insert ask you to state one improvement to the procedure, explain why two readings are taken instead of one, calculate the spring constant from given data, or evaluate the significance of an anomaly. A powerful technique is to always reference the specific apparatus shown in the Insert when suggesting an improvement.
紧接单元 5 插页的典型问题包括：指出实验步骤中一项可改进之处；解释为何要读数两次而非一次；根据给定数据计算弹簧的劲度系数；或者评估一个异常点的显著程度。一个很有用的技巧是，在提出改进建议时，务必结合插页中所展示的具体装置来说明。
For instance, if asked to reduce the uncertainty in k, do not just say ‘use more precise instruments’. Instead, connect it to the Insert: ‘Use the light gate to measure the extension dynamically, or replace the metre rule with a Vernier scale having a resolution of ±0.1 mm, while keeping the spring clamped identically as shown.’ This level of detail shows that you have truly engaged with the Insert.
例如，若题目要求降低 k 的不确定度，不要只说‘使用更精密的仪器’。而要结合插页内容回答：‘利用光门动态测量伸长，或者将米尺替换为分辨率为 ±0.1 mm 的游标卡尺，同时保持弹簧如插页所示那样被夹持。’这种细节程度表明你真正吃透了插页。
Another common question expects you to use energy ideas to predict the maximum speed for a given y. The Insert supplies the value of k and the mass, so you can equate: ½ mv² = ½ ky² (if ignoring x₀ shift) and solve for v. Always show clear substitution, e.g., v = √(k/m) × y, and state the assumption of no air resistance.
另一类常见试题期望你利用能量概念，预测某个给定 y 下的最大速度。插页会提供 k 和质量数值，因此你可以列式：½ mv² = ½ ky²（若忽略 x₀ 偏移）并求解 v。务必清晰地写出代入步骤，例如 v = √(k/m) × y，并声明忽略了空气阻力的假设。
11. Evaluation and Extended Thinking | 评估与拓展思维
An excellent evaluation does
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