📚 Acceleration Caused by Gravity | 重力加速度
In CIE A-Level Physics, the acceleration caused by gravity, denoted by g, is a fundamental idea linking force, motion, and gravitational fields. It explains why a dropped stone and a dropped coin hit the ground together in a vacuum, why your weight changes in a lift, and why a satellite can orbit the Earth forever. This article explains its meaning, its link with gravitational field strength, its measurement in the laboratory, its use in kinematics, and the common exam pitfalls that cost marks.
在 CIE A-Level 物理中，重力加速度 g 是联系力、运动和引力场的基本概念。它解释了为什么在真空中石子和硬币会同时落地，为什么你在电梯里的"体重"会变化，以及为什么卫星可以永远绕地球运行。本文解释其含义、与引力场强度的联系、实验室测量方法、在运动学中的应用，以及那些最容易丢分的常见考试误区。
1. What is Acceleration due to Gravity? | 什么是重力加速度？
Acceleration due to gravity is the acceleration experienced by a body when the only force acting on it is gravity. Near Earth's surface its magnitude is about 9.81 m s⁻² and its direction is vertically downward, towards the centre of the Earth.
重力加速度是物体仅在重力作用下所获得的加速度。在地球表面附近其大小约为 9.81 m s⁻²，方向竖直向下，指向地心。
Because g is an acceleration, its SI unit is m s⁻². It is a vector quantity: stating "g = 9.81 m s⁻²" which direction is positive and keep that choice consistent throughout the whole solution.
由于 g 是加速度，其 SI 单位是 m s⁻²。它是矢量：只说"g = 9.81 m s⁻²"而不说明方向是不完整的，因此在计算中必须选定正方向，并在整道题中保持一致。
In the absence of air resistance, all objects fall with the same acceleration g, regardless of their mass. In CIE numerical problems, g is usually taken as 9.81 m s⁻² unless the question gives a different value such as 9.8 m s⁻² or 10 m s⁻². Always read the front of the paper or the question itself before choosing a value.
在没有空气阻力时，所有物体无论质量大小都以相同的加速度 g 下落。在 CIE 数值题中，除非题目给出 9.8 m s⁻² 或 10 m s⁻² 等不同值，通常将 g 取为 9.81 m s⁻²。作答前务必查看试卷卷首或题干所给数值。
g = 9.81 m s⁻² ≈ 9.8 m s⁻² (vertically downward)
2. Gravitational Field Strength and g | 引力场强度与 g
In CIE A-Level Physics, g can also be described as the gravitational field strength, defined as the gravitational force per unit mass on a small test mass placed at that point in the field.
在 CIE A-Level 物理中，g 也可描述为引力场强度，其定义为放置在引力场中某点的小检验质量所受到的引力与该质量的比值。
g = F / m
, the units N kg⁻¹ and m s⁻² are identical, which is why the same symbol g can be quoted as 9.81 m s⁻² or 9.81 N kg⁻¹.
变形可得 F = mg，即物体的重量。这使 g 具有等效单位 N kg⁻¹。由于 1 N = 1 kg m s⁻²，单位 N kg⁻¹ 与 m s⁻² 完全相同，这正是同一个 g 既可以写作 9.81 m s⁻² 又可以写作 9.81 N kg⁻¹ 的原因。
| Quantity 物理量 | Symbol 符号 | SI unit 单位 |
| Acceleration due to gravity 重力加速度 | g | m s⁻² |
| Gravitational field strength 引力场强度 | g | N kg⁻¹ |
| Weight 重量 | W | N |
| Mass 质量 | m | kg |
Because the field strength is defined per unit mass, g does not depend on the mass of the object placed in the field. Two objects of different mass at the same point in the field experience the same field strength, and therefore the same acceleration.
由于场强度是按单位质量定义的，g 与放入场中物体的质量无关。位于场中同一点的两个不同质量的物体感受到相同的场强度，因此也具有相同的加速度。
3. g and Newton's Second Law | g 与牛顿第二定律
The link between force and acceleration is Newton' orce is its weight W = mg, so substituting into F = ma gives mg = ma, and therefore a = g.
力与加速度的联系由牛顿第二定律 F = ma 给出。对于自由落体，唯一的作用力是其重量 W = mg，代入 F = ma 得 mg = ma，因此 a = g。
W = mg → mg = ma → a = g
This is an important piece of reasoning in CIE mark schemes: the mass cancels, so the acceleration of free fall is independent of mass. Notice that m appears on both sides of the equation, which is why the result holds for a feather and for a hammer alike, provided air resistance is negligible.
这是 CIE 评分标准中重要的推理步骤：质量被约去，因此自由落体加速度与质量无关。注意 m 出现在方程两边，这正是为什么只要空气阻力可忽略，羽毛和铁锤的结果就完全相同。
an g and decreases as the object speeds up, eventually becoming zero at terminal velocity.
当空气阻力不可忽略时，合力为 W − R，其中 R 为阻力。此时加速度 a = (mg − R)/m，小于 g，并随物体速度增大而减小，最终在收尾速度时变为零。
4. Free Fall and the Independence of Mass | 自由落体与质量无关性
Free fall means motion under gravity alone, with no other forces such as air resistance, upthrust or tension acting. In a vacuum, a coin and a feather released together from the same height land at the same instant because both have acceleration g.
自由落体指仅在重力作用下的运动，不受空气阻力、浮力或张力等其他力作用。在真空中，从同一高度同时释放的硬币和羽毛会同时落地，因为两者的加速度都是 g。
In everyday air, the feather falls more slowly because the drag force is large compared with its weight. The difference is caused by air resistance, not by gravity, and examiners frequently ask you to explain this distinction in words.
在普通空气中，羽毛下落更慢，因为其阻力相对重量很大。这一差异由空气阻力造成，而非重力，考官经常会要求你用文字解释这一区别。
Galileo's famous conclusion, that all bodies fall with the same acceleration in the absence of air resistance, can be tested with a vacuum tube experiment. A ball of mass m and a ball of mass 2m fall with identical acceleration even though the heavier one has twice the weight, because it also has twice the inertia.
伽利略的著名结论——在没有空气阻力时所有物体下落加速度相同——可以用真空管实验验证。质量为 m 与 2m 的两个小球加速度完全相同，尽管较重的球重量翻倍，但它的惯性同样翻倍。
5. Using g in Kinematics | 在运动学中使用 g
n convention). The five quantities are s, u, v, a and t, and each of the four kinematic equations links four of them.
对于竖直方向的抛体运动，标准 SUVAT 方程适用，只需取 a = g（或 a = −g，取决于符号约定）。五个量是 s、u、v、a、t，四个运动学方程各联系其中四个。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
These equations may only be used when the acceleration is uniform, which is true for motion under gravity when air resistance is negligible. For projectile motion, the horizontal and vertical components are treated separately: the horizontal acceleration is zero, while the vertical acceleration is g.
只有在加速度恒定时才能使用这些方程，而当空气阻力可忽略时，重力作用下的运动恰好满足这一条件。对于抛体运动，水平与竖直分量分开处理：水平加速度为零，竖直加速度为 g。
Dropped from rest: u = 0, so h = ½gt² and v = gt.
从静止下落：u = 0，因此 h = ½gt²、v = gt。
highest point v = 0, and the time to rise equals the time to fall back to the same level.
竖直上抛：在最高点 v = 0，上升时间等于落回同一高度所用的时间。
Displacement is a vector: a stone thrown up and caught again has zero displacement but non-zero distance travelled.
位移是矢量：上抛并接回的石头位移为零，但路程不为零。
6. Sign Conventions and the Vector Nature of g | 符号约定与 g 的矢量性
Most CIE errors in gravity questions come from inconsistent signs rather than from the physics. Choose one direction as positive before you start, state it clearly, and never change it halfway through a calculation.
CIE 重力题中的多数错误来自符号不一致，而非物理理解。开始计算前先选定一个正方向，清楚说明，并且中途绝不更改。
a body thrown upward has u = −20 m s⁻¹. Both choices give the same physical answers, but mixing them gives nonsense.
若取向上为正，则 g = −9.81 m s⁻²，下落物体的速度为负。若取向下为正，则 g = +9.81 m s⁻²，被竖直上抛的物体初速度 u = −20 m s⁻¹。两种选择给出相同的物理答案，但混用就会得到错误结果。
ergy gained when rising by height h is ΔEₚ = mgh, and it converts back to kinetic energy on the way down, which gives an alternative route to many kinematics answers.
记住速率是速度的大小，因此负速度只是表示物体沿着你定义的反方向运动。上升高度 h 所获得的势能为 ΔEₚ = mgh，下落时又转回动能，这为许多运动学问题提供了另一条解题途径。
7. Measuring g in the Laboratory | 实验室测量 g
s/t². Repeating for several heights and plotting 2s against t² produces a straight line through the origin whose gradient is g.
经典的 CIE 实验用电磁铁释放钢球，并用光门与落板计时。由 u = 0 的 s = ½gt² 可得 g = 2s/t²。改变多个高度重复测量，作 2s 对 t² 的图像，得到一条过原点的直线，其斜率即为 g。
g = 2s / t²
cceleration from v² = u² + 2as. A third uses a ticker-tape timer, where the spacing between successive dots increases by equal amounts each tick, and the acceleration is found from the dot spacing.
第二种方法使用相距已知距离的两个光门，测量小球通过两门的时间，得到初末速度，再由 v² = u² + 2as 求加速度。第三种方法使用打点计时器，纸带上相邻点间距每次增加相同的量，由点距可求出加速度。
Use a heavy, small ball to reduce the relative effect of air resistance.
使用重而小的球以减小空气阻力的相对影响。
Repeat each height at least three times and average, to reduce random error.
每个高度至少重复三次并取平均，以减小随机误差。
Measure the height from the bottom of the ball to the trapdoor, and remember to include reaction-time or instrument-delay errors in your evaluation.
高度应从球底部量到落板，并在误差分析中考虑人的反应时间或仪器延迟。
Do not use a stopwatch for a single short fall if a light gate is available; human reaction time is about 0.2 s, which is huge compared with a 0.4 s fall.
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8. Mass, Weight and Apparent Weight | 质量、重量与视重
nal force on that mass, W = mg, measured in newtons and dependent on the local value of g.
质量是物质的多少，是惯性的量度，单位为千克，在宇宙任何地方都不变。重量是作用在该质量上的引力，W = mg，单位为牛顿，取决于当地的 g 值。
contact force N rather than mg. In a lift accelerating upward with acceleration a, Newton' + a) and you feel heavier. Accelerating downward gives N = m(g − a) and you feel lighter.
视重是秤的读数，等于支持力 N 而非 mg。在向上以加速度 a 加速的电梯中，由牛顿第二定律 N − mg = ma，得 N = m(g + a)，人会感觉变重。向下加速时 N = m(g − a)，人会感觉变轻。
N = m(g + a) or N = m(g − a)
apparently weightless even though the real weight mg has not changed. This is exactly the condition of an astronaut in orbit, which is why orbiting is often described as continuous free fall.
若缆绳断裂，a = g 向下，N = 0：乘客处于自由落体状态，看上去失重，尽管其真实重量 mg 并未改变。这正是轨道上宇航员的状态，也是人们把环绕运动称为"持续自由落体"的原因。
9. g in a Gravitational Field | 引力场中的 g
Outside a spherical mass, the field strength is given by Newton' e gravitational constant, M is the mass producing the field and r is the distance from its centre.
在球对称质量外部，场强度由万有引力定律除以检验质量得到：g = GM/r²，其中 G 为引力常量，M 为产生场的质量，r 为到球心的距离。
g = GM / r²
with the square of the distance from the centre, which agrees with the inverse-square law shown by the spacing of gravitational field lines. At the Earth' at twice that distance from the centre g falls to about one quarter of its surface value.
该式表明 g 随到球心距离的平方减小，这与引力场线间距所体现的平方反比规律一致。在地球表面 r = 6.37 × 10⁶ m；在离球心两倍距离处，g 降至表面值约四分之一。
GM/r², the acceleration due to gravity on the Moon, whose mass is about 1/81 of the Earth's and whose radius is about 0.27 of the Earth' h of the terrestrial value. Mass stays the same on the Moon, but weight drops by a factor of six.
由 g = GM/r²，月球质量约为地球的 1/81、半径约为地球的 0.27 倍，因此其重力加速度约为 1.6 m s⁻²，约为地球的六分之一。在月球上质量不变，但重量降为六分之一。
10. Common Exam Pitfalls | 常见考试误区
Most lost marks in this topic come from a small number of repeated mistakes. Read the following list carefully and check your own working against it before every mock exam.
本主题的失分大多来自少数几个反复出现的错误。请仔细阅读下面清单，并在每次模考前对照检查自己的作答。
Confusing mass and weight: an answer of "the weight is 5 kg" gains no marks. Mass in kg, weight in N.
混淆质量与重量：写出"重量是 5 kg"不得分。质量单位 kg，重量单位 N。
Forgetting the direction of g, or changing the positive direction halfway through a calculation.
忽略 g 的方向，或在计算中途改变正方向。
ance is stated to be significant; the acceleration then varies and SUVAT no longer applies.
题目说明空气阻力不可忽略时仍用 a = g 套用 v = u + at；此时加速度在变化，SUVAT 不再适用。
Mixing components in projectile questions, such as using the vertical acceleration for the horizontal motion.
抛体问题中混用分量，例如把竖直加速度用到水平运动上。
Quoting g to more significant figures than the data allows, or ignoring the value of g stated at the top of the paper.
保留的有效数字超过数据所能支持，或忽略试卷卷首给出的 g 值。
Writing "g is constant" without qualification: g varies with altitude, latitude, local rock density and distance from the Earth's centre.
不加限定地写"g 是常数"：g 随海拔、纬度、当地岩石密度以及到地心的距离而变化。
11. Worked Examples | 例题精讲
9.8 m s⁻² and downward as positive, find the height of the cliff and the speed on impact.
例题 1：一块石头从悬崖顶由静止落下，经 3.0 s 到达海面。取 g = 9.8 m s⁻²、向下为正，求悬崖高度与落水速度。
h = ½gt² = ½ × 9.8 × 3.0² = 44.1 m
v = gt = 9.8 × 3.0 = 29.4 m s⁻¹ ≈ 29 m s⁻¹ downward
s⁻², find the maximum height and the total time of flight before it returns to the thrower's hand.
例题 2：以 20 m s⁻¹ 竖直上抛一小球。取向上为正、g = 9.8 m s⁻²，求最大高度及球回到抛出点所需的总时间。
h = u²/(2g) = 20² / (2 × 9.8) = 20.4 m
t = 2u/g = 2 × 20 / 9.8 = 4.1 s
in a lift accelerating upward at 2.0 m s⁻². Take g = 9.8 m s⁻² and find the scale reading.
例题 3：质量为 70 kg 的学生站在以 2.0 m s⁻² 向上加速的电梯内的秤上。取 g = 9.8 m s⁻²，求秤的读数。
N = m(g + a) = 70 × (9.8 + 2.0) = 826 N ≈ 830 N
Notice that in each example the first step is to choose and state a positive direction, and the last step is to check the unit and the number of significant figures. Examiners award method marks for these intermediate steps, so always show them.
注意每道例题的第一步都是选定并说明正方向，最后一步是检查单位与有效数字。考官会为这些中间步骤给出方法分，因此务必写出过程。
12. Quick Revision Checklist | 快速复习清单
Use this checklist the night before the paper. If you can explain every line in your own words, both in English and in Chinese, you are ready for the gravity questions.
考前一夜使用本清单。如果每一条你都能用自己的话（中英皆可）解释清楚，那么重力相关题目你已准备就绪。
Define acceleration due to gravity and give its magnitude, unit and direction.
定义重力加速度并给出大小、单位与方向。
State that g equals gravitational field strength and prove that N kg⁻¹ and m s⁻² are equivalent.
说明 g 等于引力场强度，并证明 N kg⁻¹ 与 m s⁻² 等价。
Derive a = g from F = ma and W = mg, and explain why mass cancels.
由 F = ma 与 W = mg 推出 a = g，并解释质量为何被约去。
Describe two laboratory methods for measuring g and the graph used to find it.
描述两种实验室测量 g 的方法及用于求 g 的图像。
Apply SUVAT with a = ±g, keeping the sign convention consistent.
在 a = ±g 下应用 SUVAT，并保持符号约定一致。
Explain apparent weight in a lift using N = m(g ± a).
用 N = m(g ± a) 解释电梯中的视重。
Use g = GM/r² to compare field strength on different planets and at different altitudes.
用 g = GM/r² 比较不同行星及不同高度的场强度。
With these ideas in place, gravity becomes one of the most reliable sources of marks in the whole CIE A-Level Physics paper, because the physics is simple and the equations are few. Practise the sign convention until it is automatic, and always quote g to the precision the question allows.
掌握这些要点后，重力将成为整个 CIE A-Level 物理试卷中最稳定的得分点之一，因为物理原理简单、公式数量少。把符号约定练到自动化，并始终按题目允许的精度给出 g 值。
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