Essential Physics for Cambridge IGCSE: Experimental Investigations | IGCSE 物理核心实验探究

📚 Essential Physics for Cambridge IGCSE: Experimental Investigations | IGCSE 物理核心实验探究

Physics is an experimental science; many of the fundamental principles can be explored and understood through hands-on investigations. In the Cambridge IGCSE curriculum, practical work not only reinforces theoretical concepts but also develops skills in measurement, data analysis, and evaluation. This article revisits eight classic experiments that are central to the IGCSE Physics syllabus, explaining the setup, procedure, key equations, and common pitfalls. Each section pairs English and Chinese explanations so that you can master both the scientific language and the underlying physical ideas.

物理是一门实验科学，许多基本原理都可以通过动手探究来领悟和理解。在剑桥 IGCSE 课程中，实验操作不仅巩固理论知识，还培养测量、数据分析和评价能力。本文重温了 IGCSE 物理教学大纲中八个核心实验，详细说明装置、步骤、关键公式以及常见误区。每个小节都配有中英文对照，帮助你同时掌握科学语言和背后的物理思想。

1. Measuring Speed and Acceleration | 测量速度和加速度

One of the first quantitative experiments in kinematics uses a ticker timer, a device that prints dots on a paper tape at a constant frequency (often 50 Hz, meaning one dot every 0.02 s). A trolley is released down a gently sloping runway, pulling the tape through the timer. After the run, the tape is marked off into equal time intervals – every 5 dots represents 0.10 s. By measuring the distance between these marks, students can calculate the average speed for each interval and then plot a velocity–time graph. The gradient of this graph gives the acceleration, while the area under the line represents the total distance travelled. The key equations are:

运动学中最早的定量实验之一是使用打点计时器，该装置以恒定频率（通常为 50 Hz，即每 0.02 秒打一个点）在纸带上打点。将一辆小车从略微倾斜的跑道上释放，纸带穿过计时器。实验后，在纸带上标记出相等的时间间隔——每 5 个点代表 0.10 秒。测量这些标记之间的距离，即可计算每个间隔内的平均速度，然后绘制速度–时间图像。该图像的斜率代表加速度，而图线下的面积代表总位移。关键方程为：

v = s / t

a = (v – u) / t

In the typical investigation, students vary the angle of the slope to see how acceleration changes, keeping the mass of the trolley constant. A common mistake is to forget to account for the initial distance before timing, so starting the tape when the trolley is already moving gives more reliable data. This experiment highlights the difference between instantaneous and average speed and illustrates the concept of uniform acceleration.

在典型的探究中，学生改变斜面角度以观察加速度如何变化，同时保持小车质量不变。一个常见错误是忘记在计时前留出初始距离，因此在小车已经开始运动时再启动纸带可获得更可靠的数据。该实验突显了瞬时速度和平均速度的区别，并展示了匀加速运动的概念。

2. Hooke’s Law Investigation | 胡克定律探究

The relationship between the extension of a spring and the applied force is investigated by hanging different masses on a metal spring and measuring the resulting length. A ruler or a set of optical pins measures the extension (elongation) from the spring’s original length. The force is calculated from F = mg, where m is the total suspended mass and g ≈ 9.8 m s⁻². Plotting force against extension produces a straight line through the origin up to the elastic limit; its gradient is the spring constant k. Hooke’s Law is stated as:

通过在金属弹簧上悬挂不同质量的砝码并测量其长度变化，探究弹簧伸长量与作用力之间的关系。用直尺或光学针测量弹簧相对原长的伸长量。力由 F = mg 计算，其中 m 是悬挂的总质量，g ≈ 9.8 m s⁻²。绘制力–伸长量图，在弹性限度内，得到一条过原点的直线；其斜率即为弹簧常数 k。胡克定律表述为：

F = kx

Students can also investigate two springs in series and in parallel. For series, the same force extends both, so the total extension adds up (1/k_total = 1/k₁ + 1/k₂). For parallel, the extension is the same but the force is shared. This practical reinforces concepts of elastic potential energy (area under the F–x graph) and the distinction between elastic and plastic deformation. Care must be taken to avoid over-stretching the spring beyond its elastic limit, as hysteresis effects then prevent accurate repeatability.

学生还可以探究两个弹簧串联和并联的情况。串联时，相同的力使两者伸长，总伸长量相加（1/k_total = 1/k₁ + 1/k₂）。并联时，伸长量相同但力被分担。该实验强化了弹性势能（F–x 图下的面积）以及弹性形变与塑性形变的区别。必须注意避免将弹簧过度拉伸至弹性限度之外，否则磁滞效应会影响准确重复。

3. Density of Solids and Liquids | 固体和液体的密度测定

Density (ρ) is mass per unit volume. For a regular solid, such as a rectangular block, the volume is found by measuring length, width, and height with a ruler or vernier calipers. The mass is measured on a digital balance. For an irregularly shaped object, the volume is determined by the displacement method: water is poured into a measuring cylinder, the object is submerged, and the difference in water levels gives the volume. To avoid parallax error, the cylinder is read at eye level with the bottom of the meniscus. The density is then calculated using:

密度（ρ）是单位体积的质量。对于规则固体，如长方体，用直尺或游标卡尺测量长、宽、高即可得到体积。质量用电子天平测量。对于形状不规则的物体，采用排水法测定体积：将水倒入量筒，浸没物体后水面示数之差即为体积。为避免视差错误，应在与液面凹面最低处水平的位置读取量筒示数。然后利用下式计算密度：

ρ = m / V

Liquids are simpler: the mass of an empty container is measured, then the container is filled with the liquid and reweighed; the difference is the mass of the liquid. Volume is read directly from the measuring cylinder. Common errors include air bubbles trapped on the solid (reducing apparent volume), not fully drying the solid when re-used, and using a balance that has not been zeroed. Students can extend the investigation to determine the density of substances like cork that float, by using a sinker to hold the object underwater.

液体更为简单：先称量空容器的质量，再装入液体后称量，两次示数之差即为液体质量。体积可直接从量筒读出。常见错误包括固体表面附着气泡（使表观体积减小），重新使用时未将固体完全擦干，以及未调零天平。学生可扩展探究，例如测量浮在水面的软木密度，此时可用一个坠体将待测物压入水中。

4. Factors Affecting the Period of a Simple Pendulum | 影响单摆周期的因素

A simple pendulum consists of a small bob attached to a light, inextensible string. The bob is displaced by a small angle (less than about 10°) and released. The time for a number of complete oscillations is measured with a stopwatch, and the period T is found by dividing the total time by the number of swings. By varying the length L of the pendulum while keeping the mass and amplitude constant, students discover that T is proportional to √L, but does not depend on the mass of the bob. The relationship is:

单摆由悬挂在一根轻质且不可伸长的细线上的小摆球构成。将摆球拉离平衡位置一个较小的角度（小于约 10°）然后释放。用秒表测量多次全振动的时间，将总时间除以摆动次数即得周期 T。通过改变摆长 L 而保持摆球质量和摆幅不变，学生发现 T 与 √L 成正比，但与摆球质量无关。其关系式为：

T = 2π√(L / g)

To test the dependence on L, a graph of T² against L gives a straight line through the origin, with gradient 4π²/g, allowing g to be calculated. It is essential to count oscillations from the centre of the swing to avoid the reaction-time error at the ends. Also, the length should be measured from the point of suspension to the centre of the bob. This investigation elegantly introduces the concept of simple harmonic motion and the independence of period from amplitude for small oscillations.

为检验周期对摆长的依赖关系，绘制 T² 与 L 的图像，应得到一条过原点的直线，其斜率为 4π²/g，由此可计算重力加速度 g。关键在于从摆动的中心位置开始计数，以避免在端点处的反应时间误差。此外，摆长应从悬点量至摆球中心。该实验优雅地引入了简谐运动概念，以及小振幅下周期与振幅无关的特性。

5. Refraction of Light through a Glass Block | 光通过玻璃块的折射

When a ray of light passes from air into a denser medium like glass, it bends towards the normal. In this standard practical, a rectangular glass block is placed on a sheet of paper and its outline is drawn. Pins are used to trace the path of a light ray entering and leaving the block. The incident ray and the emergent ray are marked, and the angles of incidence (i) and refraction (r) are measured with a protractor. Snell’s law states:

当光线从空气进入玻璃等光密介质时，会向法线偏折。在这个标准实验中，将一矩形玻璃砖放在一张纸上，画出其轮廓。用大头针标示光线射入和射出玻璃砖的路径。标记出入射光线和出射光线，用量角器测量入射角（i）和折射角（r）。斯涅尔定律给出：

n = sin i / sin r

By measuring several pairs of i and r and plotting sin i against sin r, a straight line through the origin is obtained, with gradient equal to the refractive index n. Students also observe that the emergent ray is parallel to the incident ray but laterally displaced. Additionally, when light passes from glass into air at a sufficiently large angle, total internal reflection occurs; this can be shown with a semicircular block. The critical angle c satisfies sin c = 1/n. Common refinements include using a fibre-optic light source for narrow rays and marking the ray paths precisely on paper to reduce random errors.

通过测量若干组 i 和 r 并绘制 sin i – sin r 图像，可得到一条过原点的直线，其斜率等于折射率 n。学生还会观察到出射光线与入射光线平行但存在侧向位移。此外，当光线从玻璃射向空气且入射角足够大时，会发生全内反射；这可用半圆形玻璃砖演示。临界角 c 满足 sin c = 1/n。常见的改进包括使用光纤光源获得细窄光线，并在纸上精确标记光路以减小偶然误差。

6. Ohm’s Law and the Resistance of a Wire | 欧姆定律与导线电阻

The relationship between the current through a conductor and the potential difference (voltage) across it is investigated with a simple circuit. A fixed resistor or a length of resistance wire is connected to a power supply, an ammeter (in series), and a voltmeter (in parallel). The voltage is varied using a variable power supply or a rheostat as a potential divider. For an ohmic resistor, the current is directly proportional to the voltage, and a graph of I against V is a straight line through the origin. Ohm’s Law is:

通过一个简单的电路可以探究通过导体的电流与其两端电势差（电压）之间的关系。将一个固定电阻或一段电阻丝与电源、安培表（串联）和电压表（并联）连接。使用可调电源或将变阻器作为分压器来改变电压。对于欧姆导体，电流与电压成正比，I–V 图像是一条过原点的直线。欧姆定律为：

R = V / I

When investigating the factors affecting the resistance of a wire, students alter the length L of a uniform wire and measure the corresponding voltage and current to find R. The relationship R ∝ L is verified. Furthermore, using wires of different thickness (cross-sectional area A) shows that R ∝ 1/A. The resistivity ρ can then be determined from R = ρL/A. The experiment also teaches about contact resistance, heating effects (temperature rise can cause resistance increase), and the use of a metre bridge for more accurate measurements.

当探究影响导线电阻的因素时，学生改变一段均匀导线的长度 L，测量相应的电压和电流以求出 R。可验证 R ∝ L 的关系。此外，使用不同粗细（横截面积 A）的导线表明 R ∝ 1/A。随后可由 R = ρL/A 求出电阻率 ρ。该实验还使学生了解到接触电阻、热效应（温度升高会导致电阻增大）以及为更精确测量而使用的米桥。

7. Series and Parallel Circuits | 串联和并联电路

Circuits with two or more resistors (or bulbs) are wired in series and in parallel to compare the distribution of current and voltage. In a series circuit, the current is the same at every point, but the total voltage from the supply is shared between the components. The equivalent resistance is simply the sum: R_total = R₁ + R₂. In a parallel circuit, the voltage across each branch is equal to the supply voltage, but the total current is the sum of the branch currents. The equivalent resistance for two resistors is given by:

用两个或多个电阻（或灯泡）分别组成串联和并联电路，比较电流和电压的分配规律。在串联电路中，各处电流相同，但电源总电压在元件间分配。等效电阻即为各电阻之和：R_total = R₁ + R₂。在并联电路中，各支路两端电压相等且等于电源电压，但总电流等于各支路电流之和。对于两个电阻，等效电阻由下式给出：

1/R_total = 1/R₁ + 1/R₂

A practical challenge is to build a combination circuit and predict the ammeter and voltmeter readings. Students typically use multimeters to measure voltage across each component and current through them. They can investigate how the brightness of a bulb changes when more bulbs are added, either in series (dimmer) or in parallel (brightness unchanged, but total power increases). This experiment emphasises the conservation of charge (current) and energy (voltage) and provides a foundation for understanding domestic wiring, where appliances are connected in parallel so that they each receive the full mains voltage.

一个具有挑战性的实践是搭建混联电路并预测安培表和电压表的读数。学生通常使用万用表测量每个元件两端的电压和流过它们的电流。他们可以探究当增加更多灯泡时亮度如何变化：串联时灯泡变暗，并联时亮度不变但总功率增加。该实验强调了电荷守恒（电流）和能量守恒（电压），并为理解家庭电路（电器采用并联以便每个都能获得完整的电源电压）打下基础。

8. Magnetic Field Patterns | 磁场分布

The shape of magnetic fields around permanent magnets and current-carrying conductors is mapped using iron filings and plotting compasses. For a bar magnet, filings are sprinkled on a piece of paper placed over the magnet; tapping the paper gently allows the filings to align along the field lines. The pattern reveals field lines that run from the north to the south pole outside the magnet, and form closed loops. Using a small plotting compass, the direction of the field (north to south) is marked. Two like poles repel, producing a neutral point where the fields cancel; unlike poles attract, giving a uniform field region.

使用铁屑和描图罗盘可以描绘永磁体和载流导体周围的磁场形状。对于条形磁铁，将铁屑撒在覆盖于磁铁上的纸面上，轻轻敲击纸张使铁屑沿磁感线排列。图案显示磁感线在磁体外由 N 极指向 S 极，形成闭合回路。用小描图罗盘标出磁场的方向（N 至 S）。同名磁极相斥，产生一个磁场抵消的中性点；异名磁极相吸，出现一个匀强磁场区域。

For electromagnetism, a long straight wire or a solenoid can be investigated. A current-carrying straight wire produces concentric circular field lines, whose direction can be determined by the right-hand grip rule. A solenoid produces a field very similar to that of a bar magnet, with a uniform interior field. Students can increase the number of turns or insert a soft iron core to observe the increase in magnetic strength, as seen by the density of the filings. This investigation connects directly to the principles of electromagnets, motors, and generators.

在电磁学方面，可以研究长直导线或螺线管。载流直导线产生以导线为圆心的同心圆形磁感线，其方向由右手定则判断。螺线管产生的磁场与条形磁铁非常相似，内部为匀强磁场。学生可增加线圈匝数或插入软铁芯，观察磁场强度（通过铁屑的密集程度反映）的增加。该探究直接关联电磁铁、电动机和发电机的原理。

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Essential Physics for Cambridge IGCSE: Experimental Investigations | IGCSE 物理核心实验探究