📚 IGCSE WJEC Physics: Work and Energy – Key Points | IGCSE WJEC 物理：功与能量 考点精讲
Welcome to this focused revision guide on Work and Energy for the WJEC IGCSE Physics specification. Understanding work, energy, and their relationship is fundamental to explaining how forces cause motion and how energy is transferred in systems.
欢迎阅读这篇针对 WJEC IGCSE 物理考纲的功与能量精讲。理解功、能量及其相互关系，是解释力如何引起运动以及能量如何在系统中转移的基础。
1. Work: Definition and Concept | 功：定义与概念
Work is done when a force causes an object to move through a distance in the direction of the force. It is a scalar quantity, meaning it has magnitude but no direction, and is measured in joules (J).
当一个力使物体沿力的方向移动一段距离时，力就做了功。功是标量，只有大小没有方向，单位为焦耳（J）。
For work to be done, two conditions must be met: a force must act on the object, and the object must move. Moreover, the movement must have a component in the same direction as the force. If you push a wall and it doesn’t move, no work is done on the wall, despite the force applied.
要做功，必须满足两个条件：物体受力的作用，并且物体发生运动。此外，运动方向必须在力的方向上有分量。如果你用力推一堵墙而墙保持静止，尽管你施加了力，但你并没有对墙做功。
Everyday examples of work include lifting a book onto a shelf (work against gravity), pushing a trolley along a supermarket aisle (work against friction), and a car engine doing work to accelerate the vehicle.
日常做功的例子包括把书搬到书架上（克服重力做功）、在超市过道推购物车（克服摩擦做功）、以及汽车发动机做功使车辆加速。
2. The Formula for Work | 功的计算公式
When the force is constant and acts in the same direction as the displacement, work done is the product of the force and the distance moved.
当力恒定且方向与位移方向相同时，所做的功等于力与移动距离的乘积。
Work done (W) = Force (F) × distance moved in the direction of force (d)
W = F d
The unit of work, the joule, is equivalent to a newton–metre (N m). 1 joule of work is done when a force of 1 newton moves an object 1 metre along the line of action of the force.
功的单位焦耳等于牛顿·米（N m）。当一个1牛顿的力使物体沿力的方向移动1米时，所做的功就是1焦耳。
If the force is applied at an angle to the displacement, only the component of the force parallel to the displacement does work. In WJEC IGCSE calculations, questions usually involve forces and motion in the same straight line, so W = Fd can be used directly.
如果力与位移成一定角度，只有沿位移方向的分力做功。在WJEC IGCSE的计算中，题目通常涉及力和运动在同一直线上，因此可以直接使用W = Fd。
3. Energy: The Capacity to Do Work | 能量：做功的本领
Energy is defined as the ability to do work. It is also a scalar quantity measured in joules. Objects or systems that possess energy can exert forces over distances, thus performing work.
能量被定义为做功的本领。它也是一个标量，单位为焦耳。拥有能量的物体或系统可以在距离上施加力，从而做功。
Energy exists in many different forms, all of which can be converted from one to another. The common forms include kinetic energy (energy of motion), gravitational potential energy (energy stored due to an object’s height), elastic potential energy (stored in stretched or compressed materials), thermal energy, chemical energy, nuclear energy, and electromagnetic energy.
能量以多种不同形式存在，它们之间都可以相互转化。常见的形式包括动能（运动的能量）、重力势能（因物体高度而储存的能量）、弹性势能（储存在拉伸或压缩的材料中）、内能、化学能、核能和电磁能。
In any process, energy is transferred or transformed, but never created or destroyed. This is the bedrock of all calculations involving work and energy.
在任何过程中，能量只会转移或转化，而不会凭空产生或消失。这是所有涉及功和能量计算的基础。
4. Kinetic Energy | 动能
Kinetic energy (KE) is the energy an object possesses due to its motion. The amount of kinetic energy depends on the object’s mass and its speed squared.
动能（KE）是物体因运动而具有的能量。动能的大小取决于物体的质量及其速度的平方。
Kinetic energy = ½ × mass × speed²
KE = ½ m v²
Mass (m) is in kilograms (kg), speed (v) is in metres per second (m/s), and kinetic energy is in joules. Because speed is squared, doubling the speed quadruples the kinetic energy for the same mass. This explains why high-speed collisions cause proportionally more damage.
质量（m）的单位是千克（kg），速度（v）的单位是米/秒（m/s），动能的单位是焦耳。由于速度被平方，质量相同时，速度加倍会使动能变为原来的四倍。这解释了为什么高速碰撞造成的破坏成比例增大。
When a net force accelerates an object from rest, the work done by the force is converted into the object’s kinetic energy (assuming no energy losses).
当一个净力使物体从静止加速，力所做的功（若没有能量损失）转化为物体的动能。
5. Gravitational Potential Energy | 重力势能
Gravitational potential energy (GPE) is the energy stored in an object because of its position above the Earth’s surface. It depends on the object’s mass, the gravitational field strength, and the vertical height.
重力势能（GPE）是物体由于位于地球表面上方而储存的能量。它取决于物体的质量、重力场强度和垂直高度。
Gravitational potential energy = mass × gravitational field strength × height
GPE = m g h
Here, m is mass in kg, g is gravitational field strength (on Earth, 9.8 N/kg, often taken as 10 N/kg in exam questions), and h is the change in vertical height in metres. GPE is also measured in joules.
这里，m是质量（kg），g是重力场强度（地球表面约为9.8 N/kg，考题中常取10 N/kg），h是垂直高度的变化（m）。GPE的单位也是焦耳。
When an object is raised at constant speed, the work done against gravity equals the gain in GPE. If the object falls, its GPE decreases and is converted into kinetic energy, provided air resistance is negligible.
当物体匀速升高时，克服重力所做的功等于其增加的重力势能。如果物体下落，其重力势能减少并转化为动能（前提是空气阻力可忽略不计）。
6. The Principle of Conservation of Energy | 能量守恒定律
The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred from one form to another, or from one object to another. The total energy of an isolated system remains constant.
能量守恒定律指出，能量既不会凭空产生，也不会凭空消失，它只能从一种形式转化为另一种形式，或从一个物体转移到另一个物体。孤立系统的总能量保持不变。
A swinging pendulum is a classic illustration: at the highest points, energy is all gravitational potential; at the lowest point, it is all kinetic. Energy continuously transforms between GPE and KE, but the sum (ignoring air resistance) stays the same.
摆动的摆锤就是一个经典的例子：在最高点，能量全部为重力势能；在最低点，能量全部为动能。能量不断地在重力势能和动能之间转换，但它们的总和（忽略空气阻力）保持不变。
This principle is used to solve many energy problems: for example, when an object falls, the loss in GPE equals the gain in KE, allowing you to find the speed just before impact.
该原理可用于解决许多能量问题：例如，当物体下落时，减少的重力势能等于增加的动能，从而可以求出物体即将撞击前的速度。
7. Work–Energy Principle | 功与能的关系
The work–energy principle states that the net work done on an object is equal to its change in kinetic energy. This is a powerful tool for linking forces and motion without detailed kinematics.
功-能原理指出，对物体所做的净功等于其动能的变化量。这是在不使用详细运动学的情况下，将力与运动联系起来的强大工具。
Net work done = change in kinetic energy = ½ m v² – ½ m u²
In practice, you may also account for work done against friction or gravity. When a car accelerates, the engine does work; some of this work increases the car’s KE, while the rest is done against friction and air resistance, converted into thermal energy.
在实际中，你可能还需要考虑克服摩擦或重力所做的功。当汽车加速时，发动机做功；一部分功增加汽车的动能，其余的则用于克服摩擦和空气阻力，转化为内能。
For vertical motion, the work done by a lifting force minus work against gravity equals the gain in KE. Understanding how work translates into different energy stores is crucial for tackling IGCSE problems.
对于竖直运动，提升力所做的功减去克服重力做的功，等于动能的增加量。理解功如何转化为不同能量储存，对于解决IGCSE题目至关重要。
8. Power | 功率
Power is the rate at which work is done or the rate at which energy is transferred. It is a scalar quantity and its SI unit is the watt (W), which is equivalent to one joule per second (J/s).
功率是做功的速率或能量转移的速率。它是一个标量，国际单位是瓦特（W），相当于1焦耳/秒（J/s）。
Power = work done / time taken
P = W / t
Alternatively, since energy transferred is equal to work done, we can also write P = E / t. A more powerful engine can do the same amount of work in less time, or more work in the same time.
或者，由于转移的能量等于所做的功，我们也可以写成 P = E / t。一台更强大的发动机能在更短时间内完成同样的功，或在相同时间内做更多的功。
Exam questions often ask you to calculate the power developed when lifting an object or climbing stairs. You first calculate the work done (GPE gained) and then divide by time. Remember to use consistent units.
考题中常常要求计算提升物体或爬楼梯时产生的功率。你首先需计算所做的功（增加的重力势能），然后除以时间。务必要使用一致的单位。
9. Efficiency | 效率
Efficiency measures how well a device converts input energy into useful output energy. It is expressed as a percentage and can never exceed 100% due to energy dissipation, usually as thermal energy.
效率衡量一个设备将输入能量转化为有用输出能量的程度。它用百分数表示，由于能量耗散（通常为内能），效率永远不会超过100%。
Efficiency = (useful energy output / total energy input) × 100%
Efficiency = (useful power output / total power input) × 100%
For example, an electric motor that delivers 80 J of useful mechanical work while consuming 100 J of electrical energy has an efficiency of (80/100) × 100% = 80%. The remaining 20 J is wasted, primarily as heat.
例如，一台电动机消耗100焦耳电能，输出80焦耳有用机械功，其效率为 (80/100) × 100% = 80%。剩下的20焦耳被浪费，主要是以热能的形式散失。
When asked to improve efficiency in a system, think about reducing friction (lubrication), reducing air resistance (streamlining), or minimizing electrical resistance in circuits. Energy ‘loss’ simply means energy has been transferred to a store that is not useful.
当被问及如何提高系统效率时，可以思考减少摩擦（润滑）、降低空气阻力（流线型设计）或减小电路中的电阻。能量的“损失”仅仅意味着能量转移到了无用的能量库中。
10. Common Examples and Exam Tips | 常见例题与考试技巧
A typical exam question might ask: “A student of mass 50 kg climbs a staircase of vertical height 12 m in 15 s. Calculate the work done and the power developed. (g = 10 N/kg)”
典型的考题可能是：“一名质量50千克的学生在15秒内爬上一段垂直高度为12米的楼梯。计算所做的功和产生的功率。（g = 10 N/kg）”
Solution: Work done against gravity = mgh = 50 × 10 × 12 = 6000 J. Power = work / time = 6000 / 15 = 400 W.
解答：克服重力做功 = mgh = 50×10×12 = 6000 J。功率 = 功 / 时间 = 6000 / 15 = 400 W。
A falling object problem: “A stone of mass 0.5 kg falls from a height of 20 m. Assuming g = 10 N/kg and no air resistance, find its speed just before hitting the ground.” Use conservation of energy: loss in GPE = gain in KE; mgh = ½ mv². Cancel m: 10×20 = ½ v² => v² = 400 => v = 20 m/s.
落体问题：“一块质量0.5千克的石头从20米高处落下。设g = 10 N/kg，不计空气阻力，求它刚要撞击地面前的速度。”利用能量守恒：重力势能减少量 = 动能增加量；mgh = ½ mv²。约去m：10×20 = ½ v² => v² = 400 => v = 20 m/s。
Common mistakes: forgetting that distance in W = Fd must be in the direction of the force; using horizontal distance for vertical work; confusing mass and weight; forgetting to square speed in KE; and adding incorrect units. Always read the question carefully and state the formula before substituting values.
常见错误：忘记W = Fd中的距离必须是沿力的方向；竖直做功时误用水平距离；混淆质量和重量；动能计算中忘记给速度平方；以及单位使用错误。务必仔细读题，先列公式再代入数值。
When dealing with efficiency, clearly identify “useful” output and total input. For a sloping surface, break down forces into components only if required; however, most IGCSE WD/energy problems involve linear motion along the line of the force.
处理效率问题时，要清楚识别“有用”输出和总输入。对于斜面，必要时才分解力；不过，多数IGCSE的功和能量问题涉及的是沿力的方向的直线运动。
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