A-Level Edexcel Physics: Work, Energy and Power Key Points | A-Level Edexcel 物理：功与能量考点精讲

📚 A-Level Edexcel Physics: Work, Energy and Power Key Points | A-Level Edexcel 物理：功与能量考点精讲

Understanding work, energy, and power is fundamental to A-Level Physics. This guide covers the essential concepts for Edexcel Physics, including definitions, equations, and common applications. Mastering these topics will help you solve problems involving mechanical energy conservation, power calculations, and graphical analysis.

理解功、能量和功率是 A-Level 物理的基础。本指南涵盖 Edexcel 物理的核心概念，包括定义、方程和常见应用。掌握这些主题将帮助你解决涉及机械能守恒、功率计算和图形分析的问题。

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1. Work Done by a Constant Force | 恒力做功

For a constant force, the work done is defined as the product of the force and the displacement in the direction of the force:

W = F s cosθ

where F is the magnitude of the force, s is the displacement, and θ is the angle between the force and displacement vectors. Work is a scalar quantity measured in joules (J). When the force and displacement are parallel (θ = 0°), work is positive and maximum. If θ = 90°, no work is done. Negative work occurs when θ > 90°, indicating energy is transferred away from the object.

对于恒力，所做的功定义为力的大小与沿力方向位移的乘积：

W = F s cosθ

其中 F 是力的大小，s 是位移，θ 是力矢量与位移矢量之间的夹角。功是一个标量，单位为焦耳 (J)。当力与位移平行 (θ = 0°) 时，功为正且最大。若 θ = 90°，不做功。当 θ > 90° 时产生负功，表示能量从物体转移走。

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2. Work Done by a Variable Force | 变力做功

When a force is not constant, work is determined by the area under a force-displacement graph. For a spring obeying Hooke’s law, the force is directly proportional to extension: F = kx. The work done to stretch the spring from 0 to x is equal to the area of the triangle under the graph:

W = ½ F_max × x = ½ kx²

This energy is stored as elastic potential energy. The graph of force against extension is a straight line through the origin; any area under the curve represents the work done.

当力不恒定时，功由力-位移图下的面积决定。对于遵守胡克定律的弹簧，力与伸长量成正比：F = kx。将弹簧从 0 拉伸至 x 所做的功等于图像下三角形的面积：

W = ½ F_max × x = ½ kx²

该能量以弹性势能的形式储存。力对伸长量的图像是一条经过原点的直线；曲线下的任何面积都代表所做的功。

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3. Kinetic Energy and the Work-Energy Theorem | 动能与动能定理

Kinetic energy (KE) is the energy an object possesses due to its motion and is given by:

KE = ½ mv²

where m is mass and v is speed. The work-energy theorem is one of the most powerful tools in mechanics: the net work done on an object equals its change in kinetic energy.

W_net = ΔKE = ½ mv² − ½ mu²

Here u is the initial speed. This principle applies for both constant and variable net forces, enabling you to solve problems without calculating acceleration or time.

动能 (KE) 是物体由于运动而具有的能量，由下式给出：

KE = ½ mv²

其中 m 是质量，v 是速率。动能定理是力学中最强大的工具之一：对物体所做的净功等于其动能的变化量。

W_net = ΔKE = ½ mv² − ½ mu²

这里 u 是初速率。该原理适用于恒净力和变净力，使你无需计算加速度或时间即可解题。

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4. Gravitational Potential Energy | 重力势能

Gravitational potential energy (GPE) is the energy stored due to an object’s position in a gravitational field. Near the Earth’s surface, the change in GPE when an object changes height is:

ΔE_p = mgΔh

with m being mass, g the gravitational field strength (9.81 ms⁻²), and Δh the vertical height change. The zero of GPE can be chosen arbitrarily; only differences in GPE have physical significance. The work done against gravity when lifting an object equals the gain in GPE, provided no other energy transfers occur.

重力势能 (GPE) 是因物体在引力场中的位置而储存的能量。在地球表面附近，物体高度变化时 GPE 的变化量为：

ΔE_p = mgΔh

其中 m 为质量，g 为引力场强度 (9.81 ms⁻²)，Δh 为垂直高度变化。零势能面的选择是任意的，只有势能差值才有物理意义。在无其他能量转移的情况下，提起物体克服重力所做的功等于 GPE 的增量。

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5. Elastic Potential Energy | 弹性势能

When a spring (or any elastic object) is stretched or compressed, energy is stored as elastic potential energy (EPE). For an ideal spring obeying Hooke’s law, the energy stored when the extension is x is:

E_e = ½ kx²

where k is the spring constant. This formula is derived directly from the area under the F-x graph. In exam questions, it is usually assumed that the spring is ideal, although in practice some energy may be dissipated as thermal energy. Remember that x represents the extension or compression from the natural length, not the total length of the spring.

当弹簧（或任何弹性物体）被拉伸或压缩时，能量以弹性势能 (EPE) 的形式储存。对于遵守胡克定律的理想弹簧，当伸长量为 x 时储存的能量为：

E_e = ½ kx²

其中 k 是劲度系数。该公式直接由 F-x 图下的面积导出。考试题目中通常假定弹簧是理想的，尽管实际中部分能量可能以热能耗散。请记住，x 代表相对于原长的伸长量或压缩量，而不是弹簧的总长度。

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6. Conservation of Mechanical Energy | 机械能守恒

In a system where only conservative forces do work (e.g. gravity and elastic spring forces), the total mechanical energy remains constant. This is expressed as:

KE + GPE + EPE = constant

For a falling object without air resistance, GPE is converted into KE. For a pendulum or mass-spring system, energy oscillates between KE and potential energy. If non-conservative forces (such as friction or air resistance) are present, mechanical energy is not conserved; some energy is dissipated to thermal energy, but total energy of the universe is still conserved.

在仅保守力（如重力和弹力）做功的系统中，总机械能保持不变。这可以表示为：

动能 + 重力势能 + 弹性势能 = 常数

对于无空气阻力的自由落体，重力势能转化为动能。对于摆或弹簧振子，能量

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