📚 IGCSE AQA Physics: Work and Energy | IGCSE AQA 物理：功与能量考点精讲
In IGCSE AQA Physics, the concepts of work and energy are fundamental to understanding how forces cause changes in motion and how energy is transferred and conserved. This revision guide covers the key definitions, formulas, units, and common exam applications, from work done by a force to kinetic and gravitational potential energy, power, and efficiency.
在 IGCSE AQA 物理中，功和能量的概念是理解力如何引起运动变化以及能量如何转化和守恒的基础。这份考点精讲涵盖了关键定义、公式、单位以及常见考试应用，包括力做功、动能、重力势能、功率和效率等。
1. What is Work? | 什么是功？
Work is done whenever a force causes an object to move through a distance. For work to be done, the force must have a component in the direction of the displacement. If the force is perpendicular to the movement, no work is done – for example, when holding a heavy bag still, you may feel tired but no mechanical work is done on the bag because there is no movement in the direction of the force.
只要力使物体移动一段距离，就做了功。要产生功，力在位移方向上必须有分量。如果力与运动方向垂直，则没有做功——例如静止提着沉重的包，你会感到疲劳，但对包并没有做机械功，因为包没有在力的方向上移动。
2. Work Done Formula | 功的公式
The amount of work done is calculated using the equation: work done = force × distance moved in the direction of the force. This can be written as W = F d, where W is work done in joules (J), F is the force in newtons (N), and d is the distance in metres (m).
做功的大小用以下公式计算：功 = 力 × 沿力方向移动的距离。写作 W = F d，其中 W 是功，单位为焦耳 (J)；F 是力，单位为牛顿 (N)；d 是距离，单位为米 (m)。
W = F d
One joule is defined as the work done when a force of one newton moves an object one metre in the direction of the force.
一焦耳定义为：一牛顿的力使物体沿力的方向移动一米所做的功。
3. Units of Work and Energy | 功和能量的单位
Work and all forms of energy are measured in joules (J). This is the SI unit for energy. Sometimes kilojoules (kJ) are used, where 1 kJ = 1000 J. The joule is named after James Prescott Joule, who demonstrated the equivalence of mechanical work and heat energy.
功和所有形式的能量都以焦耳 (J) 为单位。这是能量的国际单位。有时使用千焦 (kJ)，1 kJ = 1000 J。焦耳以詹姆斯·普雷斯科特·焦耳命名，他证明了机械功与热能的等价性。
4. Gravitational Potential Energy | 重力势能
Gravitational potential energy (GPE) is the energy an object possesses due to its height above the ground. The change in GPE when an object is lifted is equal to the work done against gravity. The formula is ΔEₚ = m g h, where m is mass (kg), g is gravitational field strength (9.8 N/kg on Earth, often rounded to 10 N/kg in IGCSE problems), and h is the change in height (m).
重力势能 (GPE) 是物体因离地高度而具有的能量。物体被抬高时重力势能的变化等于克服重力所做的功。公式为 ΔEₚ = m g h，其中 m 为质量 (kg)，g 为重力场强度（地球表面为 9.8 N/kg，IGCSE 题目中通常取 10 N/kg），h 为高度变化 (m)。
ΔEₚ = m g h
When an object falls, it loses GPE and gains kinetic energy, assuming no air resistance. The equation also assumes the gravitational field is uniform.
物体下落时，若无空气阻力，重力势能减少，动能增加。此公式也假设重力场是均匀的。
5. Kinetic Energy | 动能
Kinetic energy is the energy of a moving object. Any object with mass m and speed v has kinetic energy given by the equation Eₖ = ½ m v². The unit is joules (J). Doubling the mass doubles the kinetic energy; doubling the speed quadruples the kinetic energy because it depends on v².
动能是运动物体的能量。任何质量为 m、速度为 v 的物体都具有动能，公式为 Eₖ = ½ m v²，单位为焦耳 (J)。质量加倍，动能加倍；速度加倍，动能变为原来的四倍，因为它取决于 v²。
Eₖ = ½ m v²
This relationship is frequently tested: if the speed of a car increases from 10 m/s to 20 m/s, its kinetic energy increases by a factor of 4, provided mass stays the same.
这个关系经常被考查：如果汽车速度从 10 m/s 增加到 20 m/s，在质量不变的情况下，其动能增加为原来的 4 倍。
6. Conservation of Energy | 能量守恒
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 moved from one place to another. In a closed system, the total energy is constant. For a falling object (ignoring air resistance), the decrease in GPE equals the increase in kinetic energy.
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。在封闭系统中，总能量保持不变。对于自由下落的物体（忽略空气阻力），重力势能的减少等于动能的增加。
m g h = ½ m v² (for a fall from rest)
In real situations, some energy is always transferred as heat due to friction or air resistance, but the total energy is still conserved.
在实际情况下，由于摩擦或空气阻力，总有一部分能量转化为热能，但总能量仍然守恒。
7. Work-Energy Principle | 功能原理
The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy. If a resultant force does work on an object, it speeds up; if the object does work against a force (e.g., braking), it slows down. This links the concepts of force, distance, and energy change directly.
功能原理指出：作用在物体上的净功等于其动能的变化量。如果合外力对物体做功，物体会加速；如果物体克服外力做功（如刹车），物体会减速。这直接将力、距离和能量变化联系起来。
W_net = ΔEₖ
For example, to find the braking force needed to stop a car, you can calculate the car’s initial kinetic energy and set work done = force × braking distance.
例如，要计算使汽车停止所需的制动力，可以先求出汽车的初始动能，然后令做功 = 制动力 × 刹车距离。
8. Power | 功率
Power is the rate at which work is done or energy is transferred. The formula is P = W / t or P = ΔE / t, where P is power in watts (W), W is work done or energy transferred in joules (J), and t is time in seconds (s). One watt is one joule per second.
功率是做功或能量转化的速率。公式为 P = W / t 或 P = ΔE / t，其中 P 是功率，单位为瓦特 (W)；W 是功或能量转化量，单位为焦耳 (J)；t 是时间，单位为秒 (s)。一瓦特等于每秒一焦耳。
P = W / t
Another useful form combines force and velocity: when a constant force moves an object at a steady speed, power can be calculated as P = F v, where v is the velocity in m/s. This is derived from P = (F d) / t = F v.
另一个实用形式结合了力和速度：当恒定力使物体匀速运动时，功率可以用 P = F v 计算，其中 v 是速度 (m/s)。这是由 P = (F d) / t = F v 推导而来的。
9. Efficiency | 效率
Efficiency measures how much of the energy input is converted into useful output energy. It is given by the ratio: efficiency = (useful energy output ÷ total energy input) × 100%. Efficiency can also be expressed in terms of power: efficiency = (useful power output ÷ total power input) × 100%.
效率衡量有多少输入能量转化为有用的输出能量。公式为：效率 = (有用能量输出 ÷ 总能量输入) × 100%。效率也可以用功率表示：效率 = (有用功率输出 ÷ 总功率输入) × 100%。
η = (E_useful / E_input) × 100%
No real machine is 100% efficient; some energy is always wasted, usually as heat due to friction. IGCSE problems may ask you to identify wasted energy and calculate efficiency from given data.
没有机器的效率能达到 100%；总有一些能量被浪费，通常因摩擦以热的形式散失。IGCSE 题目可能会要求识别浪费的能量并根据给定数据计算效率。
10. Work Done Against Friction | 克服摩擦力做功
When an object slides across a surface, work is done against friction. This work converts kinetic energy (or some input energy) into thermal energy, raising the temperature of the surfaces. The work done against friction is equal to the frictional force multiplied by the distance moved: W_friction = F_friction × d.
当物体在表面上滑动时，需克服摩擦力做功。这个功将动能（或某种输入能量）转化为热能，使接触面温度升高。克服摩擦力所做的功等于摩擦力乘以移动距离：W_friction = F_friction × d。
Understanding this is important for braking distance and energy dissipation questions. The kinetic energy lost is transferred to heat in the brakes and tyres.
理解这一点对于刹车距离和能量耗散问题非常重要。损失的动能转化为刹车和轮胎中的热量。
11. Summary and Common Mistakes | 总结与常见错误
Key points to remember: work requires both force and movement in the same direction; energy is always conserved; GPE = mgh, KE = ½mv²; power is rate of energy transfer. Common mistakes include forgetting to square the velocity in the KE equation, confusing mass and weight, using cm or km instead of metres, and forgetting to convert to joules. In efficiency calculations, always check whether you need a decimal or a percentage, and ensure the useful output never exceeds the input.
需要牢记的重点：功需要力和位移在同一方向；能量总是守恒的；GPE = mgh，KE = ½mv²；功率是能量传递的速率。常见错误包括：动能方程中忘记将速度平方，混淆质量和重量，使用厘米或千米而不是米，忘记换算为焦耳。在效率计算中，务必确认题目要求的是小数还是百分比，并确保有用输出不会超过输入。
Practising rearranging these formulas and applying them to real-world contexts will build confidence for the exam.
练习这些公式的变形并将它们应用到实际场景中，将为考试建立信心。
Published by TutorHao | Physics Revision Series | aleveler.com
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