📚 8.02 Work Done and Energy Transfer | 8.02 功与能量转移
F × d, and how energy is never created or destroyed but simply transferred from one store to another when work is done. By the end, you will be confident in calculating work done and applying the principle of energy conservation to real‑world situations.
在物理学中，功和能量的概念是理解物体为何以及如何运动的基础。本文重点讨论功与能量转移之间的关系，这是 Edexcel IGCSE 科学学生必须掌握的核心主题。我们将探讨功的定义、基本方程 W = F × d，以及做功时能量如何从一种储存形式转移到另一种，而不是凭空产生或消失。通过阅读本文，你将能够熟练计算做功的大小，并将能量守恒原理应用于实际情境中。
1. What Is Work in Physics? | 物理学中的功是什么？
In everyday language, ‘work’ might mean studying for an exam or lifting a heavy box. In physics, however, work has a very specific meaning: work is done whenever a force causes an object to move through a distance. The force must act in the direction of the movement for work to be done. If you push against a wall and it does not move, no work is done on the wall in the scientific sense, even though you may feel tired.
在日常用语中，“做功”可能指备考学习或搬重物。但在物理学中，功有非常精确的定义：只要一个力使物体沿力的方向移动一段距离，就说力做了功。如果推一堵墙而墙纹丝不动，从科学意义上说，没有对墙做功，尽管你感到很累。
Energy is the ability to do work. When work is done, energy is transferred from one object to another or converted from one form to another. For example, when you lift a book, chemical energy stored in your muscles is transferred to the book as gravitational potential energy. The amount of energy transferred equals the amount of work done.
能量是做功的本领。当做功发生，能量会从一个物体转移到另一个物体，或从一种形式转换为另一种形式。例如，当你举起一本书，肌肉中的化学能转化为书的重力势能。转移的能量大小等于所做的功。
2. The Definition of Work Done | 功的定义
Work done is defined as the product of the force applied and the distance moved in the direction of the force. This relationship is captured in the equation:
功的大小定义为施加的力与物体在力的方向上移动距离的乘积。这个关系由以下方程表示：
work done = force × distance moved in the direction of the force
功 = 力 × 沿力方向移动的距离
In symbols, we write this as:
用符号表示为：
W = F × d
Where W is work done in joules (J), F is force in newtons (N), and d is distance in metres (m). It is crucial that the distance is measured along the line of the force. If the force is applied at an angle, only the component of the force parallel to the displacement does work.
其中 W 表示功，单位焦耳 (J)；F 表示力，单位牛顿 (N)；d 表示距离，单位米 (m)。必须注意，距离是沿着力的作用线测量的。如果力与位移方向成一定角度，那么只有平行于位移的分力才做功。
3. Units of Work and Energy | 功和能量的单位
. Because energy is the capacity to do work, it makes sense that they share the same unit.
功和能量都使用同一个单位：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。换句话说，1 J = 1 N·m。由于能量是做功的本领，它们使用相同单位是合理的。
| Quantity 物理量 | Symbol 符号 | Unit 单位 |
|---|---|---|
| Work 功 | W | joule (J) 焦耳 |
| Energy 能量 | E | joule (J) 焦耳 |
| Force 力 | F | newton (N) 牛顿 |
| Distance 距离 | d | metre (m) 米 |
It is important to convert all distances to metres and forces to newtons before using the formula to obtain work in joules.
在力学中，你常会遇到千焦 (kJ)，1 kJ = 1000 J。在使用公式之前，必须将所有距离转换为米，力转换为牛顿，以得到以焦耳为单位的功。
4. Work Done and Energy Transfers | 功与能量转移
Doing work is a mechanism for transferring energy. Whenever work is done on an object, energy is transferred to that object. Conversely, when an object does work, it transfers energy away from itself. This is a direct application of the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred between stores.
做功是能量转移的一种机制。每当对一个物体做功，能量就转移到该物体。反之，当一个物体对外做功，它自身能量就会减少。这是能量守恒原理的直接应用，该原理指出：能量既不能凭空产生，也不能凭空消失，只能在不同储存形式之间转移。
- Lifting a box ainst gravity; chemical energy from your food → gravitational potential energy of the box.
- Braking a bicycle on : friction does work on the wheel; kinetic energy → thermal energy of the brakes and surroundings.
- Stretching a spring : the applied force does work; chemical energy → elastic potential energy stored in the spring.
- 举起箱子：你对重力做功；食物中的化学能 → 箱子的重力势能。
- 刹车减速：摩擦力对车轮做功；动能 → 刹车和周围环境的内能。
- 拉伸弹簧：施加的力做功；化学能 → 弹簧储存的弹性势能。
Understanding this link helps explain why machines get hot after prolonged use: some of the energy transferred ends up as thermal energy due to friction.
理解这种联系有助于解释为什么机器长时间使用后会发热：由于摩擦，部分转移的能量最终以热的形式耗散。
5. Calculating Work Done – Step‑by‑Step | 功的计算——分步解析
To solve any work done problem, follow these steps:
要解决任何关于功的问题，请遵循以下步骤：
- Identify the force that is doing work. It could be a push, pull, lift, or frictional force.
- Determine the distance the object moves while the force is applied, measured parallel to the force.
- Check the units: force in N, distance in m.
- Apply W = F × d.
- State the answer in joules.
- 确认做功的力：可以是推力、拉力、举力或摩擦力。
- 确定在力作用下物体移动的距离，沿力方向测量。
- 检查单位：力用牛顿，距离用米。
- 使用 W = F × d 计算。
- 答案以焦耳给出。
Example: A box is pushed with a constant force of 40 N across a floor for a distance of 5 m. Calculate the work done.
W = F × d = 40 N × 5 m = 200 J. Therefore, 200 J of work is done by the pushing force.
示例：一个箱子在 40 N 的恒力推动下在地板上移动了 5 m。求所做的功。
W = F × d = 40 N × 5 m = 200 J。因此，推力做功 200 焦耳。
6. When Is Work Done Equal to Zero? | 什么情况下功为零？
There are three common situations where the work done is zero even though forces are present:
在三种常见情况下，即使有力的存在，功也等于零：
- No displacement g stationary does zero work on the bag, although your muscles are using energy internally.
- Force perpendicular to displacement: If the force is at a right angle to the direction of motion, no work is done by that force. For instance, the centripetal force on a planet moving in a circular orbit does zero work because the force is always perpendicular to the velocity.
- No force in the direction of motion: If an object moves at constant velocity with no net force acting (Newton’s first law), the net work done is zero.
- 没有位移：如果物体没有移动 (d = 0)，则 W = 0。静止地提着重物没有对物体做功，尽管肌肉内部在消耗能量。
- 力垂直于位移：如果力与运动方向成直角，这个力不做功。例如，沿圆形轨道运动的行星所受的向心力做功为零，因为力始终垂直于速度。
- 在运动方向没有分力：如果物体以匀速运动且不受净力作用（牛顿第一定律），则净功为零。
It is important to distinguish between physical work and the effort you feel. In physics, only the combination of force and movement in the same direction counts as work.
区分物理上的功和主观感受到的“费力”很重要。在物理中，只有力和同向移动同时存在才算做功。
7. Gravitational Potential Energy and Work | 重力势能与功
When an object is lifted vertically, work is done against gravity. The gravitational potential energy (GPE) gained by the object is equal to the work done in lifting it, assuming no energy is lost. The change in GPE can be calculated using:
当物体被竖直举起时，外力克服重力做功。物体获得的重力势能 (GPE) 等于举高过程中所做的功，前提是无能量损失。重力势能的变化可用下式计算：
ΔGPE = m × g × Δh
mg), and the distance lifted is Δh. So work done against gravity = weight × height gained.
其中 m 为质量 (kg)，g 为引力场强（地球上约 10 N/kg），Δh 为高度变化 (m)。该式实际源于 W = F × d，因为匀速提起物体所需的力等于其重量 (mg)，距离就是上升的高度 Δh。因此克服重力做功 = 重量 × 升高的高度。
done = mgΔh = 2 × 10 × 1.5 = 30 J. The book gains 30 J of gravitational potential energy.
示例：一本 2 kg 的书被举高 1.5 m 放到书架上。做功 = mgΔh = 2 × 10 × 1.5 = 30 J。书获得了 30 J 的重力势能。
8. Kinetic Energy and Work | 动能与功
Work done on an object can also change its speed, and therefore its kinetic energy (KE). The kinetic energy of a moving object is given by:
对物体做功还可以改变其速度，从而改变其动能 (KE)。运动物体的动能为：
KE = ½ × m × v²
Where v is the speed in m/s. The work‑energy principle states that the net work done on an object is equal to its change in kinetic energy:
其中 v 是速率 (m/s)。动能定理指出，对一个物体所做的净功等于其动能的变化量：
Wnet = ΔKE = KE_final – KE_initial
If a force accelerates an object from rest to a speed v, then the work done is exactly ½mv². This shows the direct equivalence between work and energy transfer.
如果一个力使物体从静止加速到速度 v，那么所做的功正好等于 ½mv²。这直接展示了功与能量转移的等价关系。
9. Power: The Rate of Doing Work | 功率：做功的快慢
Power is defined as the rate at which work is done, or the rate of energy transfer. The equation for power is:
功率定义为单位时间内做功的多少，或能量转移的速率。功率的方程是：
power = work done / time taken
P = W / t
cond (1 W = 1 J/s). A more powerful engine does the same amount of work in a shorter time.
其中 P 为功率，单位瓦特 (W)；W 为功 (J)；t 为时间 (s)。1 瓦等于每秒 1 焦耳 (1 W = 1 J/s)。功率更大的发动机能在更短的时间内做同样多的功。
n electric motor does 600 J of work in 5 seconds, its power output is P = 600 / 5 = 120 W.
示例：如果一台电动机在 5 秒内做了 600 J 的功，其输出功率为 P = 600 / 5 = 120 W。
10. Efficiency of Energy Transfers | 能量转移的效率
In real systems, not all the energy input is converted into useful work. Some energy is always dissipated, typically as heat due to friction or air resistance. Efficiency describes how much of the input energy is usefully transferred:
在真实系统中，并非所有输入能量都转化为有用功。总有一部分能量以热的形式耗散，通常是由于摩擦或空气阻力。效率描述了输入能量中有多大比例被有用转移：
efficiency = (useful output energy / total input energy) × 100%
效率 = (有用输出能量 / 总输入能量) × 100%
Or, since work and energy are equivalent, efficiency can also be expressed in terms of power:
由于功与能量等价，效率也可用功率表示：
efficiency = (useful power output / total power input) × 100%
No machine can be 100% efficient because some energy is always lost to the surroundings. Understanding efficiency helps engineers design better systems where most input work is converted into the desired form.
没有任何机器能达到 100% 的效率，因为总会有部分能量散失到环境中。理解效率有助于工程师设计出更好的系统，使大部分输入功转化为所需的形式。
11. Common Misconceptions about Work | 关于功的常见误区
Many students confuse the physics definition of work with everyday notions of effort. Here are some clarifications:
许多学生容易将物理学中功的定义与日常概念中的“费力”混淆。以下是一些澄清：
- Holding a heavy object motionless . Your muscles are doing internal biological work, but no mechanical work is done on the object.
- Walking on a level surface at constant speed does no net work against gravity because the vertical height does not change. However, you do work against friction and air resistance.
- If force and distance are both doubled, the work done becomes four times larger, because W = F × d.
- 静止提着很重的物体没有对物体做功，因为 d = 0。你的肌肉做了内部生物功，但未对物体做机械功。
- 在水平面上匀速行走，没有克服重力做净功，因为高度没有变化。但你会克服摩擦和空气阻力做功。
- 如果力和距离都加倍，做的功将变为原来的四倍，因为 W = F × d。
Another common error is mixing up weight and mass. Weight is a force (N), while mass is in kg. Always use weight in the work equation when dealing with lifting against gravity.
另一个常见错误是混淆重量和质量。重量是力（N），而质量用 kg。在涉及克服重力做功时，务必在公式中使用重量而不是质量。
12. Practical Applications and Exam Tips | 实际应用与考试技巧
When tackling exam questions on work and energy, keep these points in mind:
在处理有关功和能量的考试题目时，请记住以下几点：
- Always read the question carefully to identify whether you need to find work done, energy transferred, or power.
- Show the formula in symbols and then substitute the numbers, including units. This helps avoid simple arithmetic errors.
- Check that the distance used is in the direction of the force. If a force is applied at an angle, you may need to resolve it (though IGCSE usually keeps forces parallel to motion).
- Remember that work and energy are scalar quantities – they do not have a direction. The sign (positive or negative) only indicates whether energy is transferred to or from the object.
- Use g = 10 N/kg unless told otherwise. In Edexcel IGCSE exams, Earth’s gravitational field strength is usually taken as 10 N/kg.
- 仔细阅读题目，确定需要求的是功、转移的能量还是功率。
- 先用符号列出公式，再代入数值和单位，这有助于避免简单的计算错误。
- 确认所用的距离是沿力方向的。如果力与运动有夹角，可能需要分解力（不过 IGCSE 通常保持力与运动平行）。
- 记住功和能量都是标量――它们没有方向。正负号仅表示能量是转移到物体还是从物体转移出去。
- 除非题目另有说明，使用 g = 10 N/kg。在 Edexcel IGCSE 考试中，地球的引力场强通常取 10 N/kg。
Applying these strategies will help you master work and energy problems and approach related topics—such as conservation of energy and power—with confidence.
运用这些策略，你定能掌握功与能量问题，并自信地处理能量守恒、功率等相关主题。
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