A-Level Physics Insert Unit 2 Jan21: Investigating Free Fall | A-Level 物理插入材料 Unit 2 2021年1月：自由落体实验探究

📚 A-Level Physics Insert Unit 2 Jan21: Investigating Free Fall | A-Level 物理插入材料 Unit 2 2021年1月：自由落体实验探究

This article explores the experimental investigation presented in the A-Level Physics Insert for Unit 2 (January 2021), which focuses on determining the acceleration due to gravity, g, using a free fall method. The insert provides apparatus details, a data table, and guidance for analysis. We will break down the key concepts, measurement techniques, data processing, and error evaluation to help students excel in their practical assessments.

本文探究 A-Level 物理 Unit 2（2021 年 1 月）插入材料中展示的实验研究，该实验旨在通过自由落体法测定重力加速度 g。插入材料中包含仪器细节、数据表格及分析指引。我们将拆解核心概念、测量技巧、数据处理和误差评估，助力学生在实验考核中脱颖而出。

1. Introduction to the Insert | 插入材料简介

The AQA A-Level Physics Unit 2 insert for January 2021 presented a practical scenario where a steel ball is dropped from various heights to measure g. The insert included a labeled diagram of an electromagnet release mechanism and a light gate connected to a digital timer. Students were expected to use the supplied data to calculate g, plot a graph, and evaluate uncertainties. Understanding this insert is vital because similar free‑fall investigations are frequently assessed in written papers and practical endorsements.

AQA A-Level 物理 2021 年 1 月 Unit 2 插入材料给出了一个通过从不同高度释放钢球来测量 g 的实验情景。该材料附有一幅带标注的电磁铁释放装置及连接数字计时器的光门示意图。要求学生利用提供的数据计算 g、绘制图线并评估不确定度。理解这份插入材料至关重要，因为类似的自由落体探究在笔试和实验认证中经常出现。

2. Apparatus and Setup | 仪器与装置

The core apparatus includes a claw‑attached electromagnet powered by a low‑voltage DC supply, a steel ball bearing, a light gate or optical switch positioned directly below, and an electronic timer that starts when the circuit to the electromagnet is broken and stops when the ball interrupts the light beam. A metre rule with millimetre graduations is clamped securely to measure the distance s from the bottom of the ball to the top of the light gate. The insert emphasised that the electromagnet must release cleanly to avoid introducing an initial downward push, and that the light gate must be precisely aligned so the ball cuts the beam at the same point every time.

核心仪器包括一个由低压直流电源供电的铁爪式电磁铁、一个钢球、一个置于正下方的光门（或光开关），以及一个在电磁铁电路断开时启动、当球遮挡光束时停止的电子计时器。一把带有毫米刻度的米尺被牢固夹持，用于测量从球底部到光门顶部的距离 s。插入材料强调，电磁铁必须干脆地释放，避免引入向下的初推力；光门必须精确对准，以便球每次都在同一点切断光束。

Additional equipment included a spirit level to ensure the light gate is horizontal and a plumb line to confirm the electromagnet is directly above the detection zone. The insert diagram showed a scale drawing with typical working heights between 0.200 m and 1.000 m. Students were reminded that connecting leads should be kept tidy to prevent tripping and that the ball must be caught in a sand tray after passing the gate to avoid damage.

其他设备还包括一个用于确保光门水平的气泡水平仪和一个用于验证电磁铁在探测区域正上方的铅垂线。插入材料中的示意图为一幅标注尺寸的图示，典型工作高度在 0.200 m 到 1.000 m 之间。提醒学生连接导线需保持整洁以防绊倒，并且球通过光门后必须落入沙盘以避免损坏。

3. Experimental Principle and Theory | 实验原理与理论

When a body falls freely from rest and air resistance is negligible, its motion is governed by the kinematic equation s = ½ g t², where s is the vertical displacement, g is the acceleration due to gravity, and t is the time of fall. This relationship assumes initial velocity u = 0 and constant acceleration. Since the equation is linear in t², a graph of s against t² yields a straight line passing through the origin with gradient equal to ½ g. Consequently, the value of g can be found by doubling the gradient.

当物体从静止开始自由下落且空气阻力可忽略时，其运动遵循运动学方程 s = ½ g t²，其中 s 为竖直位移，g 为重力加速度，t 为下落时间。该关系假设初速度 u = 0 且加速度恒定。由于方程对 t² 呈线性，作 s 对 t² 的图线会得到一条通过原点的直线，其斜率等于 ½ g。因此，g 的值可由斜率的两倍求得。

The insert highlighted that students must recognise the significance of the origin: if there is a systematic time delay, the best‑fit line may not pass through the origin, indicating a systematic error in the release mechanism or timer triggering. Derivation of the relationship from the full equation s = ut + ½ at² with u = 0 was expected as part of data analysis. Understanding the proportionality s ∝ t² is fundamental for interpreting the shape of the graph.

插入材料强调学生必须认识到原点的意义：若存在系统性的时间延迟，最佳拟合线可能不通过原点，这表明释放机构或计时器触发存在系统误差。从完整方程 s = ut + ½ at² 出发并令 u = 0 推导出该关系是数据分析要求的一部分。理解 s ∝ t² 的正比关系是解读图线形状的基础。

4. Measurement Procedure | 测量步骤

The electromagnet was adjusted to a series of predetermined heights s, starting from 0.200 m and increasing in steps of 0.200 m up to 1.000 m. At each height, the ball was carefully attached to the electromagnet, and the timer was reset to zero. The circuit was then broken using a switch; the ball released and fell, triggering the timer to stop as it passed through the light gate. Three repeat readings of time t were recorded to allow calculation of a mean, reducing random errors from timing fluctuations. The insert reminded students to avoid parallax error when reading the metre rule by aligning eye level with the ball’s bottom edge.

电磁铁被调节至一系列预设高度 s，从 0.200 m 开始，以 0.200 m 为步长增至 1.000 m。在每个高度，球被小心吸附到电磁铁上，计时器归零。然后用开关断开电路；球释放并下落，通过光门时触发计时器停止。每次记录三个时间 t 的重复读数，以计算平均值，减少计时波动带来的随机误差。插入材料提醒学生在读取米尺时应将视线与球底边缘对齐，以避免视差误差。

To ensure consistency, the experimenter checked that the ball was stationary before release and that the electromagnet did not impart an initial velocity. The insert advised using a set square to verify that the metre rule was vertical and that the distance s was measured to the nearest millimetre. After collecting all raw data, the mean t was calculated to at least three significant figures, and any anomalous readings (e.g., those caused by the ball missing the light gate) were repeated.

为确保一致性，实验者确认球在释放前保持静止，并且电磁铁未施加初速度。插入材料建议使用三角尺检验米尺是否垂直，且距离 s 需精确到毫米。在收集所有原始数据后，计算平均 t 至少保留三位有效数字；任何异常读数（例如因球未经过光门导致）均须重测。

5. Data Recording | 数据记录

The insert supplied a partially completed table; candidates were required to fill in missing values and calculate additional columns. A typical example of the data recorded might appear as follows:

插入材料给出了一张部分完成的表格，要求考生填写缺失数值并计算额外的列。以下是一组典型的记录数据示例：

From the table, note that the raw times increase non‑linearly with height, while t² increases proportionally. Correctly calculating the mean time and t² to the appropriate number of significant figures is essential; the insert expected t² to be quoted to 3 s.f. where possible, consistent with the precision of s and t. Any miscalculation would propagate through graphical analysis and affect the final g value.

从表中可注意到，原始时间随高度呈非线性增加，而 t² 则成正比增加。正确计算平均时间和 t² 并保留适当的有效数字至关重要；插入材料要求 t² 尽量保留三位有效数字，与 s 和 t 的精度一致。任何计算失误都会传递到图线分析中，影响最终 g 值。

6. Processing Raw Data | 原始数据处理

For each height, the mean t was squared to obtain t². The insert required students to complete a table with these derived values and to check that the ratio s / t²

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