📚 Work & Power | 功与功率
Work and power are fundamental concepts in physics that describe how forces cause energy transfer over time. Understanding these ideas is essential for analyzing mechanical systems and real-world applications, from lifting objects to driving vehicles. In IGCSE Physics, work is defined as the transfer of energy when a force moves an object, while power measures the rate at which work is done. This article covers the key definitions, equations, examples, and common pitfalls related to work and power.
功和功率是物理学中描述力如何随时间引起能量传递的基本概念。理解这些概念对于分析机械系统和实际应用至关重要，从提起物体到驱动车辆。在IGCSE物理中，功定义为当一个力使物体移动时的能量传递，而功率衡量做功的速率。本文涵盖与功和功率相关的关键定义、公式、示例以及常见误区。
1. What is Work? | 什么是功？
In physics, work is done when a force causes an object to move in the direction of the force. The amount of work depends on two quantities: the magnitude of the force and the distance moved in the direction of the force. If the force is applied but there is no movement (e.g., pushing against a rigid wall), no work is done in the physical sense, even though the person may feel tired. Similarly, if a force acts perpendicular to the direction of motion, such as the upward force when carrying a box horizontally at constant speed, no work is done on the box in the direction of motion.
在物理学中，当一个力使物体沿力的方向移动时，就做了功。功的大小取决于两个量：力的大小和沿力的方向移动的距离。如果施加了力但没有产生移动（例如推一堵坚固的墙），则没有做物理意义上的功，尽管人可能会感到疲劳。同样，如果力垂直于运动方向，例如匀速水平搬运箱子时的向上力，则在运动方向上没有对箱子做功。
Work is a scalar quantity, measured in joules (J). One joule is equal to the work done when a force of one newton moves an object one metre in the direction of the force.
功是一个标量，以焦耳（J）为单位。1焦耳等于1牛顿的力使物体沿力的方向移动1米所做的功。
2. The Work Equation | 功的公式
W = F × d
where W is work (J), F is the applied force (N), and d is the distance moved in the direction of the force (m). This formula applies only when the force and displacement are in the same line. When the force and displacement are in opposite directions – for example, friction decelerating a sliding box – the work done is negative, meaning energy is transferred away from the object.
其中W是功（J），F是作用力（N），d是沿力的方向移动的距离（m）。该公式仅适用于力与位移沿同一直线的情况。当力与位移方向相反时——例如摩擦力使滑动中的箱子减速——所做的功为负值，意味着能量从物体中转移出去。
pushes a box 5 m along a smooth floor, the work done on the box is W = 10 N × 5 m = 50 J.
例如，如果10 N的恒力推一个箱子沿光滑地板移动5 m，则对箱子做的功为 W = 10 N × 5 m = 50 J。
3. Work Done Against Gravity | 克服重力所做的功
e work done is W = m × g × h. This work is stored as gravitational potential energy (GPE).
提起物体时，你要克服重力做功。匀速提起所需的力等于物体的重量 mg。如果将其提升竖直高度 h，做功为 W = m × g × h。这些功以重力势能的形式储存。
W = mgh
r the object, work is done by gravity (often considered negative work done on the object).
例如，在地球上（g≈10 m/s²）将2 kg的物体提升1.5 m，需要做功 W = 2 × 10 × 1.5 = 30 J。注意，如果要降低物体，重力做正功（通常看作对物体做负功）。
4. Work and Energy Transfer | 功与能量转移
Work is a means of transferring energy. When work is done on an object, energy is transferred to that object, often increasing its kinetic energy, potential energy or internal energy. Conversely, when work is done by an object, it transfers energy away. The amount of work done equals the amount of energy transferred. This principle is crucial: if a car engine does 500 J of work on the car, the car's energy increases by 500 J (ignoring losses).
功是传递能量的一种方式。对物体做功时，能量传递给该物体，通常增加其动能、势能或内能。反之，当物体做功时，它将能量传递出去。做功的量等于转移的能量。这一原则至关重要：如果汽车发动机对汽车做了500 J的功，汽车的能量就增加500 J（忽略损耗）。
In problems, we often equate the work done by a force to a change in energy. For example, the kinetic energy gained by an object moving from rest is equal to the net work done on it. This link to the work–energy principle (see Section 8) underpins many calculations.
在解题中，我们经常将力所做的功等同于能量的变化。例如，物体从静止开始运动所获得的动能就等于作用于它的净功。这种与功能原理（见第8节）的联系为许多计算提供了基础。
5. What is Power? | 什么是功率？
uantity, measured in watts (W). One watt is defined as one joule per second (1 W = 1 J/s).
功率是做功的速率，或能量传递的速率。一个强大的机器能在短时间内做大量的功。功率是标量，以瓦特（W）为单位。1瓦特定义为每秒1焦耳（1 W = 1 J/s）。
a motor that does 200 J of work in 4 seconds has a power output of P = 200 J / 4 s = 50 W.
例如，一个额定功率为60 W的灯泡每秒将60焦耳的电能转化为光能和热能。相比之下，一个电动机在4秒内做200 J的功，其输出功率为 P = 200 J / 4 s = 50 W。
6. The Power Equation | 功率的公式
P = W / t
, a 2 kW electric heater used for 30 seconds transfers 2000 W × 30 s = 60 000 J of energy.
其中P为功率（W），W为做功（J）或转移的能量（J），t为时间（s）。此式可变形为 W = P × t。因此，一台功率为2 kW的电热器使用30秒，传递的能量为 2000 W × 30 s = 60 000 J。
o be calculated using P = F × v. This is derived from W = Fd and v = d/t: P = (Fd)/t = Fv.
当恒力 F 使物体以恒定速度 v 移动时，功率也可用 P = F × v 计算。这可由 W = Fd 和 v = d/t 推导，P = (Fd)/t = Fv。
P = F × v
/s = 10 000 W. This formula is useful when you know the propulsive force and steady speed.
例如，汽车发动机施加500 N的力并以20 m/s行驶，产生的功率是 P = 500 N × 20 m/s = 10 000 W。当已知驱动力和恒定速度时，这一公式很有用。
7. Efficiency and Work | 效率与功
In any system, not all the work done or energy input is converted to useful output; some is wasted, usually as heat. Efficiency measures how well a system converts input energy into useful work.
在任何系统中，并非所有做的
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