📚 IGCSE Physics: Work and Energy – Key Revision Points | 功与能量考点精讲
Work and energy are fundamental concepts in IGCSE Physics. Understanding how forces do work, the different forms of energy, and the principles of energy transfer and conservation is essential for solving physics problems and achieving high marks in exams. This article summarises all the key points you need to know, with clear explanations and dual-language support to strengthen your grasp of the topic.
功和能量是IGCSE物理的基础概念。理解力如何做功、能量的不同形式以及能量转移和守恒原理，对于解决物理问题和在考试中取得高分至关重要。本文总结了你需要掌握的所有要点，并通过清晰的双语讲解来帮助你扎实掌握这一主题。
1. What is Work Done? | 什么是功？
In everyday language, ‘work’ can mean many different things, but in physics it has a very precise definition. Work is done when a force causes an object to move in the direction of the force. If there is no motion, no work is done – regardless of how much effort you put in. For example, holding a heavy book still above your head does no work on the book because its displacement is zero, even though your muscles may feel tired.
在日常语言中，“功”可以指许多不同的事情，但在物理学中它有一个非常精确的定义。当一个力使物体沿力的方向发生移动时，力就对物体做了功。如果没有移动，无论你花了多大的力气，都没有做功。例如，把一本重书静止地举过头顶，书的位移为零，因此没有对书做功，尽管你的肌肉可能感到疲劳。
The amount of work done is calculated using the equation:
功的大小由以下公式计算：
W = F × d
where W is the work done in joules (J), F is the magnitude of the force applied in newtons (N), and d is the distance moved by the object in the direction of the force in metres (m). Remember that the force and displacement must be along the same line; if the force is applied at an angle to the motion, only the component of the force in the direction of motion does work. In IGCSE problems, however, we mostly consider forces acting parallel or antiparallel to the displacement.
其中 W 是所做的功，单位为焦耳（J），F 是所施力的大小，单位为牛顿（N），d 是物体沿力的方向移动的距离，单位为米（m）。要记住，力和位移必须在同一直线上；如果力与运动方向成一定角度，只有沿运动方向的分力做功。不过，在IGCSE的问题中，我们通常只考虑力与位移平行或反向的情况。
2. The Joule: Unit of Work and Energy | 焦耳：功与能量的单位
The SI unit of both work and energy is the joule (J). One joule is defined as the work done when a force of 1 newton moves an object through a distance of 1 metre in the direction of the force. Thus, 1 J = 1 N·m. Because energy is the capacity to do work, it is measured in the same unit. To give you a sense of scale, the energy needed to lift a small apple from the ground to a height of 1 metre is approximately 1 J.
功和能量的国际单位都是焦耳（J）。1焦耳定义为1牛顿的力使物体沿力的方向移动1米所做的功。因此，1 J = 1 N·m。由于能量是做功的本领，它的单位与功相同。为了给你一个数量级的概念，将一个约100克的小苹果从地面举到1米高所需的能量约为1 J。
3. Kinetic Energy | 动能
Any moving object possesses kinetic energy. The amount of kinetic energy depends on the object’s mass and the square of its speed. A heavier object or a faster-moving object has greater kinetic energy.
任何运动的物体都具有动能。动能的大小取决于物体的质量和速度的平方。质量越大、速度越快，动能就越大。
The kinetic energy is given by the formula:
动能由以下公式给出：
Eₖ = ½ m v²
where m is the mass in kilograms (kg) and v is the speed in metres per second (m/s). Notice that if the speed doubles, the kinetic energy becomes four times greater because of the v² term. Always use SI units when substituting into this equation to obtain the energy in joules.
式中 m 是质量，单位为千克（kg），v 是速度，单位为米每秒（m/s）。注意，由于含有 v² 项，速度变为原来的两倍时，动能将变为原来的四倍。在代入公式时，务必使用国际单位制，这样才能得到以焦耳为单位的能量值。
4. Gravitational Potential Energy | 重力势能
Gravitational potential energy (GPE) is the energy stored in an object because of its position in a gravitational field. When an object is lifted vertically, work is done against gravity, and this energy becomes stored as GPE. The change in gravitational potential energy is calculated by:
重力势能（GPE）是物体由于在重力场中的位置而储存的能量。当物体被竖直提升时，外力克服重力做功，这部分能量就以重力势能的形式储存起来。重力势能的变化量由下式计算：
Eₚ = m g h
Here, m is the mass (kg), g is the gravitational field strength (on Earth, about 9.8 m/s², often approximated as 10 m/s² for IGCSE), and h is the vertical height gained (m). It is crucial to use the vertical distance only; any horizontal movement does not change the GPE. When an object falls, its GPE decreases and is usually converted into kinetic energy, assuming air resistance is negligible.
这里 m 是质量（kg），g 是重力场强（在地球上约为 9.8 m/s²，IGCSE考试中常取 10 m/s²），h 是获得的垂直高度（m）。关键是只使用垂直距离；水平方向的移动不会改变重力势能。当物体下落时，其重力势能减少，并且在忽略空气阻力的情况下，通常转化为动能。
5. Elastic Potential Energy | 弹性势能
Elastic potential energy is the energy stored in objects that are stretched, compressed or bent, such as springs, rubber bands and bowstrings. This energy is stored as long as the object is deformed within its elastic limit – beyond this limit, the material may be permanently deformed or break.
弹性势能是储存在被拉伸、压缩或弯曲的物体（如弹簧、橡皮筋和弓弦）中的能量。只要物体在弹性限度内发生形变，能量就会被储存起来；超过这一限度，材料可能发生永久变形或断裂。
For a spring obeying Hooke’s law, the elastic potential energy can be calculated using:
对于遵守胡克定律的弹簧，弹性势能可以通过以下公式计算：
Eₑ = ½ k x² or Eₑ = ½ F x
where k is the spring constant (N/m), x is the extension or compression (m), and F is the applied force. Remember that the force increases linearly with extension, so the average force is half the maximum force, which explains the factor of ½.
其中 k 是弹簧常数（N/m），x 是伸长量或压缩量（m），F 是施加的力。要记住，力随伸长量线性增加，因此平均力是最大力的一半，这就解释了系数 ½ 的由来。
6. Work-Energy Relationship | 功与能的关系
The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy. This can be written as:
功能原理指出，对物体做的总功等于其动能的变化量。这可以写作：
Wnet = ΔEₖ
If the net work is positive, the object speeds up; if it is negative (e.g., work done by friction), the object slows down. This principle helps us connect the idea of doing work with changes in motion without directly using forces and acceleration in every problem.
如果总功为正，物体加速；如果总功为负（例如摩擦力做了负功），物体减速。这一原理帮助我们将做功与运动变化联系起来，无需在每个问题中都直接使用力和加速度。
7. Conservation of Energy | 能量守恒
The law of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one form to another or moved from one place to another. The total energy of an isolated system remains constant. This is one of the most powerful ideas in physics and allows us to predict outcomes in many situations without tracking every detail of the forces involved.
能量守恒定律指出，能量既不能被创造也不能被消灭；它只能从一种形式转化为另一种形式，或从一个地方转移到另一个地方。孤立系统的总能量保持不变。这是物理学中最强大的思想之一，使我们能够在不追踪每一个力的细节的情况下预测许多情况下的结果。
A classic IGCSE example is a pendulum: at its highest point, the bob has maximum GPE and zero kinetic energy; at the lowest point, GPE is minimum and kinetic energy is maximum. Ignoring air resistance and friction, the sum of GPE and KE at any point is constant.
IGCSE中一个经典的例子是单摆：在最高点，摆球的重力势能最大，动能为零；在最低点，重力势能最小，动能最大。忽略空气阻力和摩擦，在任何一点重力势能与动能之和都是恒定的。
8. Power | 功率
Power is the rate at which work is done or energy is transferred. A machine that does the same amount of work in a shorter time has greater power. The formula for power is:
功率是做功或能量转移的速率。在更短时间内做相同
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