📚 A-Level Physics: Mastering Experimental Investigations from Jun 18 Paper 4 | A-Level 物理：2018年6月试卷4实验探究深度解析
Experimental investigation questions in A-Level Physics Paper 4 test your ability to design, carry out, and analyse practical work. This article uses a classic investigation from the June 2018 Paper 4 — determining the acceleration of free fall g using a freely falling body — to illustrate key skills. We will explore the apparatus, procedure, data handling, and common pitfalls to help you score full marks in such structured questions.
A-Level 物理试卷4中的实验探究题考查你设计、实施和分析实际实验的能力。本文以2018年6月试卷4中的一道经典探究——用自由落体测定重力加速度 g ——为例，讲解关键技能。我们将探讨设备、步骤、数据处理和常见陷阱，帮助你在结构化问题中拿到满分。
1. Understanding the Experimental Objective | 理解实验目标
The aim is to determine an accurate value for the acceleration of free fall, g, near the Earth’ s surface. The underlying physical principle is that a body falling freely from rest under constant gravitational acceleration obeys the equation s = ½ g t², where s is the vertical distance fallen and t is the time taken. By measuring s and t for multiple heights, g can be found from a suitable graph.
目标是准确测定地球表面附近自由落体的加速度 g。其基础物理原理是，物体从静止开始仅在恒定重力加速度作用下下落，满足方程 s = ½ g t²，其中 s 为下落距离，t 为所需时间。测量不同高度下的 s 和 t，可通过合适的图像求出 g。
2. Designing the Apparatus | 设计实验装置
The typical setup includes an electromagnet to hold and release a steel ball, a vertical scale or metre rule, and an electronic timer connected to two sensors. A switch simultaneously breaks the magnet circuit and starts the timer when the ball is released. A second sensor, placed at a known distance below, stops the timer when the ball passes it. This eliminates reaction-time errors in starting and stopping the clock.
典型装置包括一个用于吸附并释放钢球的电磁铁、一把竖直标尺或米尺，以及连接两个传感器的电子计时器。开关在释放小球的同时断开电磁铁电路并启动计时器。在下方已知距离处放置第二个传感器，当小球经过时停止计时。这消除了启动和停表的反应时间误差。
- Key components: Electromagnet, steel ball, two light gates or impact sensors, digital timer, metre rule, plumb line.
- 关键部件：电磁铁、钢球、两个光门或触发传感器、数字计时器、米尺、铅垂线。
3. Controlling Variables and Ensuring a Fair Test | 控制变量与保证公平测试
The independent variable is the vertical distance s between the release point and the lower sensor. The dependent variable is the square of the time interval t². To keep the experiment fair, the ball must be released from rest each time, and air resistance should be minimised by using a dense, spherical steel ball. The release height is varied systematically, for example from 0.200 m to 1.200 m, while ensuring the electromagnet holds the ball consistently at the same position.
自变量是释放点与下方传感器之间的垂直距离 s。因变量是时间间隔的平方 t²。为保证实验公平，小球每次必须从静止释放，并应使用密度大的球形钢球以最小化空气阻力。释放高度系统变化，例如从 0.200 m 到 1.200 m，同时确保电磁铁每次将小球固定在相同位置。
Control variables: the shape and mass of the ball, the release mechanism, the ambient conditions. The plumb line ensures the line of fall is vertical and the sensors are aligned.
控制变量：小球的形状和质量、释放机构、环境条件。铅垂线确保下落路径竖直且传感器对齐。
4. Detailed Data-Collection Procedure | 详细数据采集步骤
1. Set up the electromagnet and upper sensor so that the ball breaks the circuit the instant it is released. 2. Position the lower sensor a measured distance s directly below, using the metre rule and plumb line to measure accurately. 3. Release the ball and record the time t displayed on the timer. 4. Repeat the timing three times for each value of s to obtain an average t, reducing random error. 5. Increase s by lowering the sensor, and repeat the process for at least six different heights.
1. 安装电磁铁和上传感器，使小球释放瞬间断开电路。2. 将下传感器置于正下方测量好的距离 s 处，用米尺和铅垂线准确测量。3. 释放小球并记录计时器显示的时间 t。4. 对每个 s 值重复计时三次取平均 t，以减小随机误差。5. 通过向下移动传感器增大 s，并对至少六个不同高度重复以上过程。
Record all raw data in a table with columns for s (m), t₁ (s), t₂ (s), t₃ (s), mean t (s), and t² (s²).
将所有原始数据记录在表格中，包括 s (m)、t₁ (s)、t₂ (s)、t₃ (s)、平均 t (s) 和 t² (s²) 列。
5. Safety Precautions | 安全注意事项
Although this is a low-risk experiment, a falling steel ball can cause injury. Place a soft landing pad or a box of sand below to catch the ball. Keep feet and hands clear of the fall zone. If using an electromagnet with a power supply, check cables for damage to avoid electrical shock. The apparatus should be stable and securely clamped to prevent toppling.
尽管这是一个低风险实验，但下落的钢球可能造成伤害。在下方放置软着陆垫或沙盒接住小球。保持手、脚远离下落区域。如果使用连接电源的电磁铁，检查导线是否损坏以避免触电。装置必须稳定并牢固夹紧，防止倾倒。
6. Data Processing and Graph Plotting | 数据处理与作图
Calculate t² for each s. From s = ½ g t², a graph of s on the vertical axis against t² on the horizontal axis should yield a straight line passing through the origin. The gradient of the line equals ½ g, so g = 2 × gradient. Use a sharp pencil to plot points and draw the line of best fit. Do not force the line through the origin unless the data strongly suggest it; instead, determine the y-intercept and comment on systematic error if it is not zero.
对每个 s 计算 t²。根据 s = ½ g t²，以 s 为纵轴，t² 为横轴作图应得到一条过原点的直线。直线斜率等于 ½ g，因此 g = 2 × 斜率。用削尖的铅笔描点并画最佳拟合线。不要强迫直线过原点，除非数据强烈表明这一点；应确定 y 轴截距，若不为零则评论系统误差。
The uncertainty in the gradient can be found by drawing the steepest and shallowest worst-fit lines and using: percentage uncertainty = (max gradient − min gradient) / (2 × best gradient) × 100%.
梯度的不确定度可通过画最陡和最缓的最差拟合线求得：百分不确定度 = (最大斜率 − 最小斜率) / (2 × 最佳斜率) × 100%。
7. Common Sources of Error and How to Reduce Them | 常见误差来源与减小方法
Systematic error: If the distance s is measured from the bottom of the ball at release to the top of the sensor, but the centre of mass falls a slightly different distance, all values are offset. Use the centre of mass as the reference point. Also, a zero error in the timer or metre rule will shift the graph line but not change its gradient. Random timing variations are reduced by repeat readings.
系统误差：如果距离 s 测量的是从释放时球的底部到传感器顶部，但质心下落的距离略有不同，所有值都会偏移。应以质心为参考点。此外，计时器或米尺的零点误差会使图像平移但不改变斜率。通过重复读数可减小计时的随机变化。
| Type of Error 误差类型 | Example 示例 | Improvement 改进方法 |
|---|---|---|
| Systematic 系统 | Parallax in measuring s 测量 s 时的视差 | Use a set-square or pointer at eye level 用三角尺或指针，与眼同高 |
| Random 随机 | Variation in timer triggering 计时触发波动 | Repeat several times and calculate mean 重复多次求平均 |
8. Calculating g and Comparing with Standard Value | 计算 g 并与标准值比较
Using the best-fit gradient m, g = 2m. Express g in m s⁻² to three significant figures. If the standard value is 9.81 m s⁻², compute the percentage difference: |experimental g − 9.81| / 9.81 × 100%. A difference within 2% is considered good for a school laboratory. If the difference is larger, evaluate whether a systematic error, such as a delayed start of timing, is present.
利用最佳拟合斜率 m，得 g = 2m。以 m s⁻² 为单位，保留三位有效数字表述 g。如果标准值为 9.81 m s⁻²，计算百分差：|实验 g − 9.81| / 9.81 × 100%。学生实验室内差异在 2% 以内算良好。若差异较大，评估是否存在系统误差，例如计时启动延迟。
g = 2 × (Δs / Δt²)
9. Understanding the Physics Behind the Method | 理解方法背后的物理
The equation s = ½ g t² assumes initial velocity u = 0 and constant acceleration. It also ignores air resistance. In reality, air drag causes the acceleration to decrease slightly, especially for longer falls, which could produce a curve in the s–t² graph. Choosing small release heights and a dense ball minimises this effect. The linearity of the plotted points checks the validity of the constant-acceleration assumption.
方程 s = ½ g t² 假设初速度 u = 0 且加速度恒定，同时忽略了空气阻力。实际上空气阻力会使加速度略微减小，尤其对长距离下落，可能导致 s–t² 图像弯曲。选择较小的释放高度及密度大的小球可将该效应降到最低。描点的线性关系检验了加速度恒定假设的有效性。
10. Modifying the Experiment to Improve Accuracy | 改进实验以提高精度
Use a laser distance sensor and data-logger to record the position of the ball at very short time intervals directly, producing an s–t graph. The velocity-time graph can then be derived, whose gradient gives g more directly. Alternatively, use a trapdoor and dual-beam light gates to start and stop the timer more precisely. Measure the diameter of the ball and use it to correct for the time taken to pass through the light beam.
可使用激光距离传感器和数据记录仪，以极短时间间隔直接记录小球位置，得到 s–t 图。进而推得速度-时间图，其斜率可直接给出 g。或使用翻板式装置和双光束光门更精确地启停计时器。测量小球直径，并用于修正通过光束的时间。
11. Linking to Exam Questions: Jun 18 Paper 4 | 联系考题：2018年6月试卷4
In the June 2018 Paper 4 structured question, you were likely asked to describe how to determine g, list precautions, identify sources of error, and calculate g from data, including an uncertainty treatment. You needed to explain why a graph of s against t² is better than calculating g from a single pair of readings — because it averages out random errors and allows identification of anomalous points. The mark scheme rewarded clear, step-by-step descriptions and valid safety points.
在2018年6月试卷4的结构题中，很可能要求你描述如何测定 g，列出注意事项，识别误差来源，并从包含不确定度处理的的数据中计算 g。你需要解释为什么用 s–t² 图比用单组读数计算 g 更好——因为它平均了随机误差并能识别异常点。评分标准奖励清晰的分步描述和有效的安全要点。
Graph advantage: Reduces random error and checks equation validity.
图像优点：减小随机误差并检验方程有效性。
12. Final Exam Tips for Experimental Investigation Questions | 实验探究题应考总结
- Always read the stem carefully to understand the independent, dependent, and control variables. 仔细阅读题干，理解自变量、因变量和控制变量。
- When describing a procedure, use numbered steps and include precise instructions, like ‘measure the distance using a metre rule with the eye level to avoid parallax’. 描述步骤时用编号，并包含精确指示，如“用米尺测量距离，视线与尺面垂直以消除视差”。
- Mention at least two safety precautions relevant to the specific apparatus. 至少提及两条与具体装置相关的安全注意事项。
- Show all graph work clearly, label axes with quantities and units, and write the gradient calculation in full. 清晰展示所有图像处理，轴上标出物理量和单位，完整写出斜率计算。
- Use the phrase ‘repeat and calculate mean’ to address random errors. 用“重复并求平均”应对随机误差。
- Distinguish between systematic and random errors in your evaluation. 评估时区分系统误差与随机误差。
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