📚 Edexcel A-Level Combined Science Topic 1.29: Power, Work Done and Efficiency | 爱德思 A-Level 综合科学 1.29：功率、做功与效率
In Edexcel A-Level Combined Science, Topic 1.29 brings together three closely related ideas: work done, power and efficiency. These ideas explain how energy is transferred by forces, how quickly that transfer happens, and how much of the input energy is converted into useful output. This article covers the essential definitions, equations, experimental methods, common errors and exam-style applications.
在爱德思 A-Level 综合科学中，主题 1.29 将三个密切相关的概念联系在一起：做功、功率和效率。这些概念解释了力如何转移能量、能量转移得有多快，以及有多少输入能量转化为有用输出。本文涵盖核心定义、公式、实验方法、常见错误和考试应用。
1. Work Done and the Joule | 做功与焦耳
Work is done when a force moves an object in the direction of the force. The amount of work done is calculated by multiplying the force by the distance moved in the direction of the force. This simple equation is one of the most important tools in energy calculations.
当力使物体沿力的方向移动时，就做了功。做功的大小等于力乘以物体沿力的方向移动的距离。这个简单的公式是能量计算中最重要的工具之一。
W = F × d
In this equation, W is work done in joules (J), F is force in newtons (N), and d is distance moved in metres (m). One joule is defined as the work done when a force of 1 newton moves an object 1 metre in the direction of the force.
在这个公式中，W 表示做功（单位为焦耳，J），F 表示力（单位为牛顿，N），d 表示移动距离（单位为米，m）。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。
- If the distance moved is zero, no work is done, even if a large force is applied.
- 如果移动距离为零，即使施加了很大的力，也不做功。
- If the force and distance are in opposite directions, the work done is negative.
- 如果力与移动距离方向相反，则做负功。
- Work done is a scalar quantity, even though force and displacement are vectors.
- 做功是标量，虽然力和位移都是矢量。
2. Force, Direction and Zero Work | 力、方向与不做功
Work is only done by the component of the force that acts in the direction of motion. If the force is perpendicular to the displacement, that force does no work. This principle often surprises students, but it is essential for understanding circular motion and carrying forces.
只有沿运动方向的分力才做功。如果力与位移方向垂直，则该力不做功。这一原理常常让学生感到意外，但它是理解圆周运动和搬运物体的关键。
W = F × d × cos θ
This general form is useful for forces applied at an angle to a ramp or pulling a sledge.
其中 θ 是力矢量与位移矢量之间的夹角。当 θ = 0° 时，cos θ = 1，因此 W = F × d。当 θ = 90° 时，cos θ = 0，因此不做功。这个通用形式适用于力与斜面成一定角度或拉雪橇等情况。
3. Power as Rate of Energy Transfer | 功率是能量转移的速率
Power is defined as the rate at which work is done or the rate at which energy is transferred. A machine that does the same amount of work in a shorter time has greater power. Power is measured in watts, where one watt is equal to one joule per second.
功率定义为单位时间内做功的多少或能量转移的速率。一台机器如果在更短时间内做相同的功，它的功率就更大。功率的单位是瓦特，1 瓦特等于每秒 1 焦耳。
P = W / t
In this equation, P is power in watts (W), W is work done in joules (J), and t is time in seconds (s). Since power is a rate, the unit watt is equivalent to J/s. In everyday situations, power may be given in kil
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