📚 Acceleration Caused by Gravity | 重力加速度
In the study of mechanics, one of the most fundamental concepts is the acceleration experienced by objects due to the gravitational pull of the Earth. This acceleration, commonly denoted by the symbol g, is approximately 9.81 m s⁻² near the Earth's surface. Understanding g is essential for solving problems involving free fall, projectile motion, and the measurement of gravitational field strength. This article explores the definition, value, variation, and experimental determination of the acceleration caused by gravity, aligned with the CIE A-Level Physics syllabus.
在力学研究中，物体因地球引力而产生的加速度是最基本的概念之一。这个加速度通常用符号 g 表示，在地球表面附近约为 9.81 m s⁻²。理解 g 对于解决自由落体、抛体运动以及测量引力场强度的问题至关重要。本文依据 CIE A-Level 物理考纲，探讨重力加速度的定义、数值、变化规律以及实验测定方法。
1. Definition of Acceleration due to Gravity | 重力加速度的定义
The acceleration due to gravity, g, is the acceleration experienced by a body when it is allowed to fall freely under the influence of the Earth's gravitational field, with air resistance considered negligible. It represents the rate of change of velocity of a freely falling object. The direction of this acceleration is always vertically downwards towards the centre of the Earth. In SI units, g is expressed in metres per second squared (m s⁻²). At any point on or near the Earth's surface, the magnitude of g is numerically equal to the gravitational field strength at that location, which has units of N kg⁻¹.
重力加速度 g 是物体在地球引力场中自由下落（忽略空气阻力）时所经历的加速度。它表示自由落体速度的变化率。加速度的方向始终竖直向下，指向地心。在国际单位制中，g 的单位是米每二次方秒（m s⁻²）。在地球表面或附近任意一点，g 的大小在数值上等于该点的引力场强度，引力场强度的单位是牛顿每千克（N kg⁻¹）。
2. Free Fall and Constant Acceleration Equations | 自由落体与匀加速运动方程
When an object falls freely near the Earth's surface, it moves with constant acceleration g, provided that air resistance can be ignored. The standard equations of uniformly accelerated motion (SUVAT) can be applied directly, replacing a with g and considering the downward direction as positive (or negative, depending on the chosen sign convention). The relevant equations include:
- v = u + g t
- s = u t + ½ g t²
- v² = u² + 2 g s
- s = (u + v) t / 2
). These relationships are widely used in both theoretical problems and laboratory measurements of g.
当物体在地球表面附近自由下落时，如果忽略空气阻力，它将做加速度为 g 的匀加速运动。可以直接应用匀变速直线运动方程（SUVAT 方程），用 g 代替 a，并规定向下为正方向（或负方向，取决于所选的符号约定）。相关方程包括：
- v = u + g t
- s = u t + ½ g t²
- v² = u² + 2 g s
- s = (u + v) t / 2
若物体从静止开始下落（u = 0），那么经过时间 t 的位移简化为 s = ½ g t²，下落距离 s 后的速度为 v = √(2 g s)。这些关系广泛应用于理论题目和 g 的实验室测量中。
3. Standard Value of g | g 的标准值
On the Earth' problems. In examinations, you may be instructed to use g = 9.8 m s⁻² or 10 m s⁻² for simpler calculations. It is important to remember that g is not a universal constant; it varies slightly from place to place due to factors such as altitude, latitude, and local geological structures.
在地球表面，国际公认的重力加速度标准值为 9.80665 m s⁻²，在大多数 A-Level 题目中常取 9.81 m s⁻²。考试中可能要求使用 g = 9.8 m s⁻² 或为
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