📚 Work, Energy and Power | 功、能量与功率
Energy is one of the most fundamental concepts in IGCSE Science. From the food we eat to the electricity that powers our homes, energy is constantly being transferred and transformed. In physics, understanding how energy is measured, stored, and how efficiently it is used allows us to explain everything from a moving car to a glowing light bulb. This revision guide covers the key topics of work, energy and power, as outlined in the Edexcel IGCSE Science specification.
能量是IGCSE科学中最基本的概念之一。从我们吃的食物到点亮家中的电，能量无时无刻不在转移与转化。在物理学中，理解能量的测量、储存及使用效率，使我们能够解释从行驶的汽车到发光的灯泡等各种现象。这篇复习指南涵盖了Edexcel IGCSE科学大纲中功、能量与功率的核心内容。
1. What is Energy? | 什么是能量？
Energy is a scalar quantity that describes the ability of a system to do work. It is measured in joules (J), named after the physicist James Prescott Joule. One joule is the amount of energy transferred when a force of one newton moves an object through a distance of one metre in the direction of the force.
能量是一个标量，描述系统做功的能力。它以焦耳（J）为单位，以物理学家詹姆斯·普雷斯科特·焦耳的名字命名。一焦耳是当一牛顿的力使物体沿力的方向移动一米距离时所转移的能量。
There are many different ways of storing energy, often referred to as 'energy stores'. These include kinetic, gravitational potential, chemical, elastic, thermal, nuclear, electrostatic and magnetic energy. In any process, energy is transferred from one store to another, but the total amount of energy in a closed system remains constant – this is the principle of conservation of energy.
能量有许多不同的储存方式，通常称为“能量储存”。这包括动能、重力势能、化学能、弹性势能、热能、核能、静电势能和磁能。在任何过程中，能量会从一个储存转移到另一个储存，但在封闭系统内总能量保持不变——这就是能量守恒原理。
2. Work Done – The Link Between Force and Energy | 做功——力与能量的纽带
Work is done whenever a force causes an object to move. For work to be done in the scientific sense, the force must be applied and the object must move in the direction of that force. If you push against a wall and it does not move, no work is done on the wall in physics, even though you might feel tired.
只要力使物体移动，就做了功。在科学意义上，要做功，必须施加力并且物体必须沿力的方向移动。如果你推一堵墙而墙没有移动，尽管你可能感觉疲惫，但在物理学中你对墙没有做功。
The amount of work done is calculated using the equation:
W = F × d
where W is work done in joules (J), F is the force in newtons (N) and d equires work done against gravity: W = mg × d = (2 × 10) × 1.5 = 30 J (using g ≈ 10 m/s²).
做功量的计算公式为：
W = F × d
其中 W 是功，单位为焦耳（J），F 是力，单位为牛顿（N），d 是物体沿力方向移动的距离，单位为米（m）。例如，将一个2 kg的箱子垂直提升1.5 m，克服重力所做的功为：W = mg × d = (2 × 10) × 1.5 = 30 J（取g ≈ 10 m/s²）。
If the force is applied at an angle to the movement, only the component of the force in the direction of the motion counts towards work done. This is an important distinction that often appears in higher-level questions.
如果力的方向与运动方向成一定角度，则只有沿运动方向的分力才计入做功。这是一个重要的区分，常见于更高层级的问题中。
3. Calculating Power | 计算功率
Power is the rate at which work is done or the rate at which energy is transferred. A more powerful engine, for instance, can do the same amount of work in a shorter time. Power is measured in watts (W), where one watt is equal to one joule per second.
功率是做功的速率或能量转移的速率。例如，一台功率更大的发动机能在更短的时间内完成相同的功。功率的单位是瓦特（W），一瓦特等于一焦耳每秒。
The two most common forms of the power equation are:
P = W ÷ t and P = E ÷ t
where P is power in watts (W), W is work done in joules (J), E is energy transferred in joules (J) and t 5 m in 4 seconds does work W = 10 × 5 = 50 J, so its power output is P = 50 ÷ 4 = 12.5 W.
功率公式的两种最常见形式为：
P = W ÷ t 和 P = E ÷ t
其中 P 是功率，单位瓦特（W），W 是功，单位焦耳（J），E 是转移的能量，单位焦耳（J），t 是时间，单位秒（s）。例如，一台电机在4秒内将一个10 N的重物提升5 m，做功W = 10 × 5 = 50 J，因此其输出功率为P = 50 ÷ 4 = 12.5 W。
4. Energy Stores and Transfer Pathways | 能量储存与转移途径
Modern GCSE physics emphasises the idea of energy stores rather than 'forms of energy'. The main energy stores you need to know are:
现代GCSE物理强调能量储存的概念，而非“能量形式”。你需要知道的主要能量储存包括：
Kinetic energy – energy stored in moving objects. The faster an object moves, the larger its kinetic store.
动能——储存在运动物体中的能量。物体移动得越快，其动能储存越大。
Gravitational potential energy – energy stored due to an object's height above the ground. Lifting an object increases this store.
重力势能——因物体距离地面有一定高度而储存的能量。提升物体会增加这一能量储存。
Chemical energy – energy stored in fuels, food and batteries. This energy is transferred by chemical reactions.
化学能——储存在燃料、食物和电池中的能量。这种能量通过化学反应被转移。
Elastic potential energy – energy stored in stretched or compressed springs and elastically deformed objects.
弹性势能——储存在被拉伸或压缩的弹簧及发生弹性形变的物体中的能量。
Thermal energy (internal energy) – the total kinetic and potential energy of particles inside a substance. Heating increases this store.
热能（内能）——物质内部分子的动能和势能总和。加热会增加这一储存。
Nuclear energy – energy stored in the nucleus of an atom, released during nuclear fission, fusion or radioactive decay.
核能——储存在原子核中的能量，在核裂变、核聚变或放射性衰变过程中释放。
Electrostatic and magnetic energy – energy stored between charged objects or magnetic poles.
静电势能和磁能——带电物体或磁极之间储存的能量。
Energy can be transferred between these stores via four main pathways: mechanically (by a force doing work), electrically (by an electric current), by heating (due to a temperature difference) and by radiation (such as light and sound waves).
能量可以通过四种主要途径在这些储存之间转移：机械做功（通过力做功）、电流做功（通过电流）、加热（因温度差引起）以及辐射（如光波和声波）。
5. Kinetic and Gravitational Potential Energy | 动能与重力势能
Two of the most frequently calculated energy stores are kinetic energy (Ek) and gravitational potential energy (Ep).
两种最常计算的能量储存是动能（Ek）和重力势能（Ep）。
The kinetic energy of a moving object is given by:
Ek = ½ m v²
where m is the mass in kilograms and v is the speed in metres per second. Notice that doubling the speed quadruples the kinetic energy, which is why braking distances increase dramatically at higher speeds.
运动物体的动能公式为：
Ek = ½ m v²
其中m为质量，单位千克，v为速度，单位米/秒。请注意，速度加倍会使动能变为四倍，这就是为什么高速下制动距离会大幅增加。
Gravitational potential energy depends on an object's mass, height and the gravitational field strength:
Ep = m g h
where g is the gravitational field strength (9.8 N/kg on Earth, often rounded to 10 N/kg in IGCSE problems) and h is the height above the reference point in metres.
重力势能取决于物体的质量、高度和重力场强度：
Ep = m g h
其中g是重力场强度（地球为9.8 N/kg，IGCSE问题中常取10 N/kg），h是相对于参考点的高度，单位米。
In many problems, such as a roller coaster descending a hill, gravitational potential energy is converted into kinetic energy, assuming air resistance and friction are negligible.
在许多问题中，例如过山车下坡时，若忽略空气阻力和摩擦力，重力势能会转化为动能。
6. Conservation of Energy | 能量守恒定律
The law of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one energy store to another. This means that the total energy in a closed system always stays the same.
能量守恒定律指出，能量既不能被创造也不能被消灭；它只能从一个能量储存转移到另一个能量储存。这意味着在一个封闭系统中，总能量始终保持不变。
Consider a pendulum swinging. At the highest points, the bob has maximum gravitational potential energy and zero kinetic energy. At the lowest point, all that potential energy has been transferred to kinetic energy, and the bob moves at its fastest. As it rises again, kinetic energy is transferred back to gravitational potential energy. Throughout the motion, the sum of Ek and Ep stays constant if we ignore air resistance.
以一个摆动的摆锤为例。在最高点，摆锤具有最大的重力势能和零动能。在最低点，所有势能都转化为动能，摆锤移动速度最快。当它再次升高时，动能又转回重力势能。在整个运动过程中，如果忽略空气阻力，Ek与Ep之和保持不变。
In real systems, however, some energy is always dissipated – usually as thermal energy due to friction or air resistance. This dissipated energy is not 'lost' but spreads out into the surroundings, making it less useful for doing work. This is why no machine can be 100% efficient.
然而在真实系统中，总有一部分能量会被耗散——通常是由于摩擦或空气阻力而以热能形式耗散。这些耗散的能量并非“消失”，而是散布到周围环境中，使其不再适合做功。这就是为什么没有任何机器是100%有效的原因。
7. Efficiency of Energy Transfers | 能量转移的效率
Efficiency measures how much of the total input energy is converted into useful output energy. It can be expressed as a percentage using the equation:
Efficiency = (useful output energy ÷ total input energy) × 100%
效率用于衡量总输入能量中有多少转化为有用的输出能量。可以用以下公式以百分比表示：
效率 = (有用的输出能量 ÷ 总输入能量) × 100%
be written in terms of power: efficiency = (useful power output ÷ total power input) × 100%. Efficiency can never exceed 100% ficient than an incandescent bulb because a larger proportion of electrical energy is converted into light rather than heat.
同样的比率也可以用功率表示：效率 = (有用输出功率 ÷ 总输入功率) × 100%。由于能量耗散，效率永远不可能超过100%。在IGCSE考试中，你可能会被要求计算效率或比较设备，例如LED灯泡比白炽灯高效得多，因为它将更大比例的电能转化为光而非热。
Improving efficiency reduces energy waste and has both economic and environmental benefits. Engineers aim to minimise friction, air resistance and electrical resistance to increase the useful output of machines.
提高效率可减少能量浪费，具有经济和环境的双重效益。工程师们致力于减小摩擦、空气阻力和电阻，以提高机器的有用输出。
8. Sankey Diagrams | 桑基图
A Sankey diagram is a visual representation of energy transfers into and out of a device. The width of each arrow is proportional to the amount of energy it represents. The input energy is shown by an arrow on the left, while useful and wasted energy outputs branch off to the right.
桑基图是一种直观表示设备能量输入与输出转移的图表。每个箭头的宽度与其所代表的能量大小成正比。输入能量由左侧箭头表示，而有用和浪费的能量输出则从分支箭头指向右侧。
For example, a filament lamp may convert only 10% of the electrical energy input into light
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