📚 Edexcel IGCSE Science 804: Work, Energy and Power | Edexcel IGCSE 科学804：功、能量与功率
In everyday language we talk about 'work' being almost any activity, but in physics the term has a very precise meaning. This article covers the key ideas of work, energy and power that you need to master for Edexcel IGCSE Science (Double Award or separate Physics). You will learn how to calculate work done by a force, understand the link between work and energy transferred, and use the power equation to compare how quickly energy is converted.
在日常语言中，“工作”几乎可以指任何活动，但在物理学中这个术语有着非常精确的含义。本文将介绍你在 Edexcel IGCSE 科学（双奖或独立物理）中必须掌握的功、能量和功率的关键概念。你将学会如何计算力所做的功，理解功与能量转移之间的联系，并运用功率公式来比较能量转换的快慢。
1. Definition of Work | 功的定义
Work is done whenever a force makes something move. The simplest definition is that work is the energy transferred when a force acts over a distance. If the object does not move, no work is done – no matter how large the force applied.
当一个力使物体发生移动时，就做了功。最简单的定义是，功就是力作用一段距离所转移的能量。如果物体没有移动，无论施加的力有多大，都没有做功。
and it stays still, the force is there but the distance moved is zero, so work done = 0 J.
必须认识到，移动必须是在力的方向上。如果你推一堵墙而墙纹丝不动，力是存在的，但移动距离为零，因此做功为 0 焦耳。
2. The Work Equation | 功的公式
The amount of work done can be calculated using the straightforward relationship:
功的大小可以用一个简单的关系式计算：
W = F × d
Where W is work done in joules (J), F is the force in newtons (N) and d is the distance moved in the direction of the force in metres (m).
其中 W 为做功，单位是焦耳 (J)；F 是力，单位是牛顿 (N)；d 是在力的方向上移动的距离，单位是米 (m)。
teel beam vertically by 6 m, the work done on the beam is W = 500 N × 6 m = 3000 J (3 kJ).
例如，如果一台起重机用 500 N 的力将一根钢梁垂直吊起 6 m，则对钢梁做的功为 W = 500 N × 6 m = 3000 J (3 kJ)。
3. Work and Energy Transfer | 功与能量的转移
Work is a measure of energy transfer. When work is done by a force, energy is moved from one store to another or from one object to another. The amount of work done equals the amount of energy transferred.
功是能量转移的量度。当一个力做功时，能量会从一个储存库转移到另一个储存库，或从一个物体转移到另一个物体。做功的多少等于转移的能量大小。
If you lift a book, the chemical energy in your muscles is transferred to the gravitational potential store of the book. The work done on the book equals the increase in its gravitational potential energy, assuming no energy is wasted.
如果你举起一本书，你肌肉中的化学能就转移到了书的引力势能储存库中。对书做的功等于它引力势能的增加量，前提是没有能量被浪费。
4. Power: Rate of Doing Work | 功率：做功的快慢
Power tells us how quickly work is done or how fast energy is transferred. Two machines may do the same amount of work, but the one that finishes the task in a shorter time has a greater power.
功率告诉我们做功的快慢，或者说能量转移的速率。两台机器可能做同样多的功，但在更短时间内完成任务的机器功率更大。
The equation for power is:
功率的公式为：
P = W ÷ t
P is power in watts (W), W is work done in joules (J) and t is time taken in seconds (s). One watt means one joule per second.
P 是功率，单位是瓦特 (W)；W 是功，单位是焦耳 (J)；t 是所需时间，单位是秒 (s)。1 瓦特等于每秒 1 焦耳。
5. Power from Energy Transferred | 通过能量转移求功率
Since work done equals energy transferred, we can also write the power equation using energy E:
由于做功等于能量转移，我们也可以使用能量 E 来表示功率公式：
P = E ÷ t
This is especially useful when dealing with electrical appliances or motors that convert energy from one form to another over time.
在处理随时间将能量从一种形式转换为另一种形式的电器或电动机时，这一公式尤其有用。
rical energy to thermal energy in 90 s, its power is P = 180 000 J ÷ 90 s = 2000 W (2 kW).
例如，一个电热水壶在 90 秒内将 180 000 J 的电能转化为热能，那么它的功率为 P = 180 000 J ÷ 90 s = 2000 W (2 kW)。
6. Efficiency and Wasted Energy | 效率与浪费的能量
No device transfers energy perfectly – some energy is always transferred to less useful stores, such as thermal energy in the surroundings. Efficiency describes the proportion of the total input energy that is converted into useful output.
没有任何设备能做到完美地转移能量——总有一部分能量会转移到不太有用的储存库中，例如周围环境中的热能。效率描述的是总输入能量中被转化为有用输出能量的比例。
Efficiency can be calculated using:
效率可用下式计算：
Efficiency = (useful output energy ÷ total input energy) × 100%
Because energy cannot be created or destroyed, the wasted energy plus the useful output energy always equal the total input energy. Efficiency is therefore a number between 0% and 100%.
由于能量不能凭空产生或消失，浪费的能量加上有用输出能量总是等于总输入能量。因此效率是一个介于 0% 到 100% 之间的数值。
7. Efficiency in Terms of Power | 用功率表示的效率
Efficiency can also be expressed using power rather than total energy, as long as the time period is the same:
只要时间相同，效率也可以用功率而不是总能量来表示：
Efficiency = (useful power output ÷ total power input) × 100%
This form is handy when you are given information about power ratings, for instance with motors or light bulbs.
当你拿到有关功率额定值的信息时（例如电动机或灯泡），这种形式就显得很方便。
8. Gravitational Potential Energy and Work | 引力势能与功
When an object is lifted at a steady speed, the work done against gravity is equal to the gravitational potential energy (GPE) gained. The GPE equation is:
当一个物体被匀速举起时，克服重力所做的功等于所获得的引力势能 (GPE)。引力势能的公式为：
ΔGPE = m × g × Δh
Here m is mass (kg), g is gravitational field strength (about 9.8 N/kg on Earth, usually rounded to 10 N/kg for IGCSE) and Δh is the change in height (m).
其中 m 为质量 (kg)，g 为引力场强度（地球表面约 9.8 N/kg，IGCSE 中常取 10 N/kg），Δh 为高度的变化 (m)。
5 m, GPE gained = 2 × 10 × 5 = 100 J. The work done by the lifting force is at least 100 J – more if there is friction or other losses.
如果一个 2 kg 的物体被举高 5 m，获得的 GPE = 2 × 10 × 5 = 100 J。提升力所做的功至少为 100 J——如果有摩擦或其他损耗，则会更多。
9. Kinetic Energy and Work | 动能与功
When a resultant force causes an object to accelerate, work is done to increase the object's kinetic energy (KE). The kinetic energy depends on mass and speed:
当合力使物体加速时，做功增加了物体的动能 (KE)。动能取决于质量和速度：
KE = ½ × m × v²
m is mass (kg), v is speed (m/s). The work done by the accelerating force equals the change in kinetic energy, assuming no energy is transferred to other stores.
m 为质量 (kg)，v 为速度 (m/s)。在没有能量转移到其他储存库的理想情况下，加速力所做的功等于动能的变化量。
to a speed of 8 m/s, the work done on the ball is KE = 0.5 × 0.5 × 8² = 0.25 × 64 = 16 J.
例如，一个 0.5 kg 的足球被从静止踢至 8 m/s 的速度，则对球做的功为 KE = 0.5 × 0.5 × 8² = 0.25 × 64 = 16 J。
10. Units and Conversions | 单位与换算
It is vital to use standard SI units when applying these equations. Common IGCSE requirements are:
在应用这些公式时，必须使用标准国际单位。IGCSE 中常见的单位要求有：
| Quantity 物理量 | Unit 单位 | Symbol 符号 |
|---|---|---|
| Work / Energy | joule | J |
| Force | newton | N |
| Distance | metre | m |
| Time | second | s |
| Power | watt | W |
| Mass | kilogram | kg |
| Speed / velocity | metre per second | m/s |
100) when converting values before substituting into a formula. Always make sure mass is in kg, not grams.
在代入公式前换算数值时要留意前缀，例如千 (×1000)、兆 (×10⁶) 和厘 (÷100)。务必确保质量的单位是千克，而不是克。
11. Linking Work, Energy and Power in Problems | 在实际问题中联系功、能和功率
ulate work done against gravity (W = m g Δh), then use P = W ÷ t to find the power needed.
许多 IGCSE 题目要求你综合运用概念。一个典型的问题可能是：一台电动机在一定时间内将重物提升了一段距离。你需要先计算克服重力所做的功 (W = m g Δh)，再用 P = W ÷ t 求出所需的功率。
If the motor is not 100% l electrical energy input: total input = useful output energy ÷ efficiency (as a decimal).
如果电动机的效率不是 100%，你可能还需要计算总的电能输入：总输入 = 有用输出能量 ÷ 效率（以小数表示）。
12. Common Misconceptions and Exam Tips | 常见误区与考试技巧
Students often confuse force with work, or think that holding a heavy object stationary does work. Remember: without movement in the direction of the force, work done is zero. Another mistake is forgetting to square the speed in the KE formula. Mark schemes will check for the correct use of v².
学生们经常混淆力与功，或者认为静止地托住一个重物就是在做功。请记住：如果没有沿力方向的移动，做功为零。另一个常见错误是在动能公式中忘记对速度取平方。考试评分标准会检查 v² 的使用是否正确。
When giving efficiency as a percentage, ensure you multiply by 100. In multi-step calculations, show all working clearly - you can often earn marks even if the final answer is wrong. Finally, always check that your final answer has the correct unit, as missing or wrong units cost straightforward marks.
当用百分比表示效率时，一定要记得乘以 100。在多步运算中，清楚地展示所有演算过程——即使最终答案错误，你往往也能得到一些分数。最后，务必检查最终答案的单位是否正确，因为单位缺失或错误会白白丢分。
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