📚 Work and Energy: CIE A-Level Physics Key Concepts | 功与能量考点精讲
In CIE A-Level Physics, work and energy are central topics that bridge force and motion. They allow us to analyse systems without having to track every detail of the motion, using energy conservation and work-energy principles. This article covers the essential concepts, formulas and exam tips you need to master.
在 CIE A-Level 物理中，功和能量是连接力与运动的核心主题。它们使我们能够利用能量守恒和功能原理来分析系统，而无需追踪运动的每一个细节。本文涵盖你需要掌握的基本概念、公式和应试技巧。
1. Definition of Work | 功的定义
Work is done when a force moves an object through a displacement in the direction of the force. It is a scalar quantity, meaning it has magnitude but no direction.
当力使物体在力的方向上发生位移时，就说力做了功。功是标量，这意味着它有大小但没有方向。
If the force and displacement are in the same direction, the work done W is the product of the force magnitude F and the displacement magnitude s.
如果力与位移方向相同，所做的功 W 就是力的大小 F 与位移大小 s 的乘积。
W = F s
When the force acts at an angle θ to the displacement, only the component of the force in the direction of the displacement does work.
当力与位移成角度 θ 时，只有力在位移方向上的分量才做功。
W = F s cosθ
The unit of work is the joule (J). 1 J = 1 N m.
功的单位是焦耳 (J)。1 J = 1 N m。
2. Work Done by a Constant Force | 恒力做功
For a constant force acting along a straight line, the work done can be positive, negative or zero. Positive work is done when the force has a component in the direction of motion, transferring energy to the object. Negative work is done when the force opposes the motion, removing energy from the object.
对于沿直线作用的恒力，所做的功可以是正的、负的或零。当力在运动方向上有分量时，做正功，将能量传递给物体。当力与运动方向相反时，做负功，从物体中带走能量。
Work is zero if the force is perpendicular to the displacement (cos90° = 0), such as the normal reaction force when an object moves horizontally.
如果力垂直于位移（cos90° = 0），则功为零，例如物体水平运动时法向反作用力不做功。
When multiple forces act, the total work done is the sum of the work done by each force, which is equivalent to the work done by the resultant force.
当多个力作用时，总功等于每个力所做功的代数和，这也等于合力所做的功。
3. Kinetic Energy | 动能
Kinetic energy (Eₖ) is the energy an object possesses due to its motion. It is defined as:
动能 (Eₖ) 是物体由于运动而具有的能量。其定义为：
Eₖ = ½ m v²
where m is the mass and v is the speed. Kinetic energy is always positive or zero and is measured in joules.
其中 m 是质量，v 是速率。动能总是正值或零，并以焦耳为单位。
The work-energy theorem (discussed later) links the change in kinetic energy directly to the net work done on the object.
功能定理（稍后讨论）将动能的变化与对该物体所做的净功直接联系起来。
4. Gravitational Potential Energy | 重力势能
Gravitational potential energy (Eₚ) is the energy stored in an object due to its position in a gravitational field. Near the Earth’s surface, it is given by:
重力势能 (Eₚ) 是由于物体在重力场中的位置而储存的能量。在地球表面附近，其公式为：
Eₚ = m g h
where h is the vertical height above a chosen reference level. The choice of reference level is arbitrary; what matters is the change in potential energy, ΔEₚ = mg Δh.
其中 h 是相对于所选参考平面的竖直高度。参考平面的选择是任意的；重要的是势能的变化量，ΔEₚ = mg Δh。
Gravitational force is conservative, meaning the work done by gravity is independent of the path taken and depends only on the change in height.
重力是保守力，这意味着重力所做的功与路径无关，只取决于高度的变化。
5. Elastic Potential Energy | 弹性势能
Elastic potential energy is the energy stored in an object when it is deformed elastically, such as a stretched spring. For a spring obeying Hooke’s law (F = k x, where k is the spring constant and x is the extension or compression), the elastic potential energy Eₑ is:
弹性势能是物体发生弹性形变（例如拉伸的弹簧）时储存的能量。对于遵守胡克定律（F = k x，其中 k 是劲度系数，x 是伸长量或压缩量）的弹簧，弹性势能 Eₑ 为：
Eₑ = ½ k x²
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