Work Done and Power | 功与功率

📚 Work Done and Power | 功与功率

In IGCSE Edexcel Science, the concepts of work done and power are fundamental to understanding how energy is transferred when forces act over distances. Whether you are lifting a book or an engine driving a car, the same physical principles apply. This article unpacks these key ideas, links them to energy transfer, and provides plenty of worked examples so you can tackle exam questions with confidence.

在 IGCSE Edexcel 科学中，功和功率是理解力通过位移传递能量时的两个基本概念。无论你是举起一本书，还是发动机驱动汽车，物理原理都是相通的。本文将剖析这些核心思想，把它们与能量传递联系起来，并提供大量计算示例，帮助你自信地应对考试题目。

1. What is Work Done? | 什么是功？

In physics, ‘work’ has a very specific meaning. Work is done whenever a force makes something move. If you push a trolley and it travels a distance, you have done work on the trolley. Energy is transferred mechanically from your body to the trolley. The greater the force and the greater the distance moved in the direction of the force, the more work is done.

在物理学中，“功”有非常明确的含义。只要一个力让物体发生了移动，就做了功。如果你推动一辆购物手推车，它前进了一段距离，那么你就对手推车做了功，能量以机械的方式从你的身体传递到了手推车上。力越大，沿力的方向移动的距离越大，做的功就越多。

2. The Formula for Work Done | 功的计算公式

The equation that links work, force and distance is one of the most important in mechanics. It is written as:

W = F × d

where W stands for work done in joules (J), F is the force applied in newtons (N) and d is the distance moved in the direction of the force in metres (m). It is essential to remember that the distance must be measured along the same line as the force. If you lift a weight vertically upwards, the distance is the vertical height gained.

联系功、力和距离的方程是力学中最重要的公式之一，写作：

W = F × d

其中 W 代表功，单位为焦耳（J）；F 是施加的力，单位为牛顿（N）；d 是沿力的方向移动的距离，单位为米（m）。务必记住，距离必须沿着力的作用线测量。如果你竖直向上举起一个重物，距离就是它上升的垂直高度。

3. Units of Work and Energy | 功与能量的单位

Work and energy have the same SI unit: the joule (J). 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. You will also encounter kilojoules (kJ), where 1 kJ = 1000 J, and megajoules (MJ) for larger quantities. In the context of mechanics, it is often helpful to think of work as ‘energy on the move’ because doing work always results in an energy transfer.

功和能量具有相同的国际单位：焦耳（J）。1 焦耳的定义是：1 牛顿的力使物体沿力的方向移动 1 米所做的功。你还会遇到千焦（kJ），1 kJ = 1000 J，以及更大的兆焦（MJ）。在力学的语境下，把功看作“正在转移的能量”通常会很有帮助，因为做功总是导致能量传递。

4. Work Done and Energy Transfer | 功与能量传递

Whenever work is done, energy is transferred from one store to another. For example, when you lift a box onto a shelf, you do work against gravity. The energy from your muscles is transferred to the gravitational potential energy store of the box. When a car brakes, friction does work on the moving parts; kinetic energy is transferred to the thermal energy store of the brakes and surroundings. The formula W = Fd can be used to calculate the amount of energy transferred, which is a direct demonstration of the principle of conservation of energy.

每当做功时，能量就从一种储存形式转移到另一种储存形式。例如，你把箱子举到架子上，就克服重力做了功，你肌肉中的能量转移到了箱子的重力势能储存中。当汽车刹车时，摩擦力对运动部件做功，动能转移到刹车和周围环境的热能储存中。可用公式 W = Fd 计算出转移了多少能量，这直接体现了能量守恒原理。

5. Calculating Work Done: Examples | 功的计算示例

Let us look at a typical IGCSE question. A student pushes a desk with a constant force of 80 N across the floor for a distance of 3.0 m. Calculate the work done.

Using W = F × d, we have W = 80 N × 3.0 m = 240 J. So 240 joules of work are done on the desk. Another common scenario involves lifting objects vertically. If a weightlifter raises a 200 N barbell through a height of 2.5 m, the work done against gravity is W = 200 N × 2.5 m = 500 J. Notice how we only use the vertical distance, as the force acts upwards.

我们来看一道典型的 IGCSE 题目。一名学生用 80 N 的恒力将课桌沿地板推动了 3.0 m。计算所做的功。

使用 W = F × d，得到 W = 80 N × 3.0 m = 240 J。因此，对课桌做了 240 焦耳的功。另一种常见情况是竖直举起物体。如果一位举重运动员将 200 N 的杠铃举高了 2.5 m，克服重力所做的功为 W = 200 N × 2.5 m = 500 J。注意，我们只用了垂直距离，因为力的方向向上。

6. Introduction to Power | 功率简介

Power is a measure of how quickly work is done or how rapidly energy is transferred. Two machines can do the same amount of work, but the one that completes the task in a shorter time has a higher power rating. In everyday language, we describe a powerful car as one that can accelerate quickly or climb hills with ease. In physics, power places energy transfer on a timescale.

功率是衡量做功快慢或者能量传递快慢的物理量。两台机器可以做同样多的功，但用时更短的一台机器功率更大。在日常语言中，我们说一辆汽车动力强劲，是指它能迅速加速或轻松爬坡。在物理学中，功率将能量传递放到了时间尺度上。

7. Power Formula and Units | 功率公式与单位

The power equation is:

P = W / t

where P is power in watts (W), W is work done or energy transferred in joules (J), and t is the time taken in seconds (s). One watt is equivalent to one joule per second. Since work is energy transferred, you will also see this written as P = E / t. For larger outputs, kilowatts (kW) and megawatts (MW) are used. Remember that 1 kW = 1000 W.

功率的方程是：

P = W / t

其中 P 是功率，单位瓦特（W）；W 是做的功或转移的能量，单位焦耳（J）；t 是所用时间，单位秒（s）。1 瓦特等于每秒 1 焦耳。因为功即转移的能量，你也常看到写成 P = E / t。对于更大的功率输出，还会用到千瓦（kW）和兆瓦（MW）。记住 1 kW = 1000 W。

8. Relationship between Work, Energy and Power | 功、能量与功率的关系

Work, energy and power are deeply interconnected. The work–energy theorem tells us that the total work done on an object equals its change in kinetic energy, assuming no other energy transfers. Power then tells us how fast that change occurs. For instance, if an electric motor does 600 J of work in 5 seconds, its power output is P = 600 J / 5 s = 120 W. This is a typical way to link the three concepts: force does work, work changes energy, and power quantifies the rate of this process.

功、能量和功率紧密相连。功—能定理告诉我们，假设没有其他能量传递，作用在一个物体上的总功等于其动能的变化量。功率则反映了这一变化发生的速率。例如，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 J / 5 s = 120 W。这是联系这三个概念的典型方式：力做功，功改变能量，功率则量化这个过程发生的快慢。

9. Practical Applications of Work and Power | 功和功率的实际应用

You can find these principles everywhere. Climbing stairs is an excellent practical demonstration: the work you do against gravity is your weight multiplied by the vertical height of the stairs. By timing how quickly you climb, you can calculate your leg power. Engineers use work and power to design elevators, cars and cranes. A crane lifting a load does work against gravity, and its motor must supply enough power to lift the load within a given time. The same logic applies to escalators, conveyor belts and even heart muscles pumping blood.

这些原理随处可见。上楼梯就是一个很好的实际演示：你克服重力所做的功等于你的体重乘以楼梯的垂直高度。测出你快速爬楼所用的时间，就可以算出你腿部的功率。工程师们在设计电梯、汽车和起重机时都会用到功与功率。起重机吊起重物时要克服重力做功，其电动机必须提供足够的功率才能在给定时间内举起负载。同样的逻辑也适用于自动扶梯、传送带，甚至心脏肌肉泵送血液的过程。

10. Converting Between Joules and Other Energy Units | 焦耳与其他能量单位之间的换算

In exam questions, you may need to convert between joules and kilowatt-hours (kW h) or between watts and horsepower. The key conversion for IGCSE is 1 kW h = 3.6 × 10⁶ J. This arises because 1 kW = 1000 J/s and one hour is 3600 seconds, so 1000 × 3600 = 3 600 000 J. Remembering this allows you to calculate the energy consumed by an electrical appliance. A 2 kW heater running for 1.5 hours uses E = P × t = 2 kW × 1.5 h = 3.0 kW h, which equals 3.0 × 3.6 × 10⁶ J = 1.08 × 10⁷ J.

在考试题目中，你可能需要将焦耳与千瓦时（kW h）进行换算，或在瓦特与马力之间换算。IGCSE 必须掌握的关键换算是：1 kW h = 3.6 × 10⁶ J。这是因为 1 kW = 1000 J/s，而 1 小时为 3600 秒，因此 1000 × 3600 = 3 600 000 J。记住这一点，你就能计算电器的耗能。一台 2 kW 的取暖器工作 1.5 小时，消耗的能量为 E = P × t = 2 kW × 1.5 h = 3.0 kW h，等于 3.0 × 3.6 × 10⁶ J = 1.08 × 10⁷ J。

11. Common Mistakes and Exam Tips | 常见错误与考试技巧

A classic error is forgetting to use distance in the direction of the force. If a person pulls a suitcase at an angle, only the horizontal component of the force does work on the suitcase. For IGCSE, however, most problem sets restrict forces to acting along the line of movement. Another common pitfall is mixing up units: always convert distance into metres and time into seconds before substituting into formulas. Also, students sometimes confuse power with energy; remember that power is a rate. When interpreting ‘work done’ questions, underline the force and the distance in the text and check they are parallel.

一个典型错误是忘记使用沿力方向的距离。如果有人斜着拉行李箱，只有力的水平分量对箱子做功。不过，IGCSE 的题目大多将力限制在运动方向上。另一个常见错误是单位混淆：代入公式前，一定要把距离换算成米，时间换算成秒。此外，学生有时分不清功率和能量；记住功率是一种速率。在解答“功”的问题时，将题中的力和距离画上重点线，并检查它们是否平行。

12. Summary and Key Equations | 总结与关键方程

To recap, work done measures the energy transferred when a force moves an object: W = F × d. Power is the rate of doing work or transferring energy: P = W / t (or P = E / t). Both concepts are linked through the joule and the watt. Always keep units consistent and think about the direction of the force. These equations will also reappear in gravitational potential energy calculations (GPE = mgh) and kinetic energy (KE = ½mv²), where the work done against gravity or by a resultant force is the link.

总结一下，功衡量的是力使物体移动时所传递的能量：W = F × d。功率是做功或能量传递的速率：P = W / t（或 P = E / t）。两个概念通过焦耳和瓦特联系在一起。务必保持单位一致，并考虑力的方向。这些方程还会在重力势能（GPE = mgh）和动能（KE = ½mv²）的计算中反复出现，其中克服重力做的功或合力做的功正是联系它们的纽带。

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Work Done and Power | 功与功率