AS Physics Insert 2 (Jan 22): Experimental Investigation of Newton’s Second Law | AS物理实验探究：牛顿第二定律(2022年1月卷二)

📚 AS Physics Insert 2 (Jan 22): Experimental Investigation of Newton’s Second Law | AS物理实验探究：牛顿第二定律(2022年1月卷二)

This article unpacks the classic AS Physics investigation typically presented in exam board inserts, focusing on how the acceleration of a trolley varies with the applied force when total mass is kept constant. We will break down the apparatus, procedure, data handling and error considerations to help you prepare for Paper 2 experimental questions.

本文针对考试局常设在试卷插页中的经典AS物理实验进行解析，重点探讨在小车总质量不变时加速度如何随作用力变化。我们将拆解实验装置、步骤、数据处理及误差分析，助你备战卷二实验类题目。

1. Aims & Context | 实验目标与背景

This investigation is designed to verify Newton’s second law of motion: the resultant force on an object is directly proportional to the acceleration produced, provided the mass stays constant. By varying the driving force on a trolley and measuring its acceleration, a linear relationship between F and a should emerge.

该实验旨在验证牛顿第二运动定律：在质量不变时，物体所受的合力与产生的加速度成正比。通过改变小车受到的驱动力并测量加速度，预期会观察到 F 与 a 之间的线性关系。

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2. Apparatus & Setup | 实验装置与搭建

You need a low‑friction linear air track or a dynamics trolley on a smooth ramp, a pulley clamped to the edge, light inextensible string, a set of slotted masses, two light gates connected to a data logger, and a metre rule. A diagram typically shows the trolley attached via the string over the pulley to a hanging mass providing the force.

你需要使用低阻力的线性气垫导轨或光滑斜面上的动力学小车、一个固定在边缘的滑轮、轻质不可伸长的细绳、一套槽码、两个连接数据采集器的光门以及一把米尺。插页中的示意图通常展示小车通过绕过滑轮的细绳与悬挂的砝码相连，由砝码重量提供驱动力。

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3. Underlying Physics | 核心物理原理

Newton’s second law is expressed as F = m a, where F is the net force, m is the total mass of the system, and a is the acceleration. In this experiment, the force is supplied by the weight of the hanging mass W = mₕ g. To keep the total mass constant, any mass transferred from the trolley to the hanger changes the force while leaving the combined mass unchanged.

牛顿第二定律表达为 F = m a，其中 F 是净力，m 是系统的总质量，a 是加速度。在本实验中，力由悬挂砝码的重量 W = mₕ g 提供。为了保持总质量不变，每次从车上移动一个砝码到悬挂端，既改变了拉力又使系统总质量始终一致。

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4. Procedure Step by Step | 操作步骤

Begin with a fixed total mass, e.g. 0.600 kg, by placing five 20 g masses on the trolley and one 20 g mass on the hanger. Record the time intervals t₁ and t₂ from the light gates and the distance s between them. Transfer one mass from the trolley to the hanger, increasing the force, and repeat until all masses are on the hanger. Always release the trolley from rest.

从固定的总质量开始，例如 0.600 kg，将五个 20 g 砝码放在小车上，一个 20 g 砝码挂在钩子上。记录光门测得的时间间隔 t₁、t₂ 以及光门间的距离 s。然后从小车上移动一个砝码到悬挂端以增大力，重复操作直到所有砝码都挂上。每次都必须从静止释放小车。

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5. Data Collection & Table | 数据记录与表格

A typical data table records the hanging mass, applied force, time intervals, calculated velocity at each gate and the acceleration. Here is an example with a total system mass of 0.600 kg:

典型的数据表会记录悬挂质量、施加力、时间间隔、计算出的各门处速度以及加速度。以下是系统总质量 0.600 kg 时的示例：

Hanging mass / kg	Force F / N	t₁ / s	t₂ / s	v₁ / m s⁻¹	v₂ / m s⁻¹	Acceleration a / m s⁻²
0.020	0.196	0.042	0.030	0.48	0.67	0.32
0.040	0.392	0.030	0.021	0.67	0.95	0.63
0.060	0.588	0.024	0.017	0.83	1.18	0.95

Note: Acceleration is calculated using a = (v₂² − v₁²) / (2s), where s is the distance between the gates (here 0.500 m).

注意：加速度使用公式 a = (v₂² − v₁²) / (2s) 计算，其中 s 是光门间距（本例中为 0.500 m）。

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6. Data Analysis & Graph | 数据分析与作图

Plot a graph of force F (y-axis) against acceleration a (x-axis). According to F = m a, the graph should be a straight line passing through the origin, with gradient equal to the total mass of the system. In practice, the line may not be perfectly straight due to friction, and the intercept may deviate slightly from zero.

绘制力 F（纵轴）对加速度 a（横轴）的图线。根据 F = m a，图像应为一条过原点的直线，斜率等于系统的总质量。实际由于摩擦，图线可能并非完全直线，截距也可能略微偏离零点。

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7. Uncertainty & Random Errors | 不确定度与随机误差

Random errors arise from reaction time when releasing the trolley, slight variations in the release mechanism, and fluctuations in the light gate timers. The uncertainty in a can be estimated using the spread of repeated readings or by propagating the absolute uncertainties in t₁, t₂ and s. A typical procedure produces an uncertainty of about 5–8% in the acceleration value.

随机误差来源于释放小车的反应时间、释放机构的微小变化以及光门计时器的波动。加速度的不确定度可通过重复测量的散布范围来估算，或通过传播 t₁、t₂ 和 s 的绝对不确定度获得。典型流程下加速度值的不确定度约为 5–8%。

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8. Systematic Errors & Compensation | 系统误差与修正

The main systematic error is friction in the pulley and between the trolley and the track. If the track is not level, a component of gravity adds to the force. Friction can be compensated by tilting the track slightly so that the trolley moves at constant velocity when given a gentle push—this is called friction compensation.

主要的系统误差来自滑轮摩擦以及小车与轨道间的摩擦力。若轨道未调平，重力分量会叠加到作用力上。摩擦可通过稍稍倾斜轨道进行补偿，使得轻推小车后它能匀速运动——这称为摩擦补偿。

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9. Improving Accuracy | 提高实验准确度

Using a linear air track eliminates contact friction entirely. Employing digital light gates with a resolution of 0.1 ms improves timing precision. Keeping the hanging masses small relative to the total mass ensures the string tension is closer to the weight, and repeating each measurement five times allows for outlier rejection. Always check the pulley is free to rotate and the string is horizontal.

使用线性气垫导轨可彻底消除接触摩擦。采用分辨率为 0.1 ms 的数字光门能提升计时精度。让悬挂质量远小于系统总质量可确保细绳张力更接近砝码重量，每项测量重复五次则便于剔除异常值。务必检查滑轮转动灵活且细绳保持水平。

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10. Sample Graph & Evaluation | 示例图线与评估

When the data from Section 5 is plotted, the gradient yields 0.61 kg, close to the actual total mass of 0.600 kg. The small discrepancy can be attributed to residual friction and the fact that the string’s tension is slightly less than mₕ g due to the acceleration of the hanger itself. A y-intercept of +0.02 N suggests a tiny uncorrected frictional force.

将第5节的数据作图，斜率得出 0.61 kg，与 0.600 kg 的实际总质量接近。微小的偏差可归因于残留摩擦，以及由于砝码自身也在加速，细绳张力略小于 mₕ g。+0.02 N 的截距表明存在极小的未补偿摩擦力。

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11. Common Exam Questions | 常见考题

Questions often ask you to state the independent variable (force, by moving masses), explain why the total mass is kept constant (to ensure a is directly proportional to F), or deduce the total mass from the gradient. You may also be asked to suggest why the graph might not pass through the origin or how to improve measurements.

考题常要求你指出自变量（通过移动砝码改变的力），解释为什么总质量保持不变（确保 a 与 F 成正比），或从斜率推导出系统总质量。还可能要求你说明图像为何可能不经过原点，或如何改进测量。

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12. Linking to the Jan22 Insert | 结合2022年1月插页

In the actual AS Physics Insert 2 (Jan 2022), you would have seen a similar setup with a trolley, mass hanger and curved mask on the trolley to break the light beams. The insert typically provides a data table and asks you to complete calculations, plot a graph and discuss limitations. By understanding this classic investigation, you can confidently tackle any variation presented.

在实际的2022年1月AS物理卷二插页中，你会看到类似的小车、砝码钩以及车上用于遮断光线的弧形遮光片装置。插页通常提供数据表，要求你完成计算、绘制图线并讨论局限性。掌握了这个经典实验后，你就能从容应对卷中出现的任何变体。

Published by TutorHao | Physics Revision Series | aleveler.com

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