📚 IGCSE CCEA Physics: Work and Energy – Key Points | IGCSE CCEA 物理：功与能量 考点精讲
In IGCSE CCEA Physics, work and energy form the foundation for understanding how forces cause changes and how energy is transferred and conserved. Mastering these concepts is essential for tackling mechanics problems and energy calculations, from kinetic energy to efficiency. This guide breaks down the key ideas, formulas, and typical exam applications step by step.
在 IGCSE CCEA 物理中，功与能量是理解力如何引起变化以及能量如何传递和守恒的基础。掌握这些概念对于解决力学问题和能量计算（从动能到效率）至关重要。本指南将逐步拆解关键概念、公式和典型考试应用。
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. If there is no movement, or the force is perpendicular to the displacement, no physical work is done – even if you feel tired! Work is a scalar quantity measured in joules (J).
在物理学中，当一个力使物体沿力的方向移动时，就做了功。如果没有移动，或者力与位移方向垂直，则没有做物理功——即使你感到累！功是标量，单位为焦耳 (J)。
The key condition is that the force must have a component along the displacement. For example, lifting a book vertically does work against gravity, but holding a heavy bag still does zero work on the bag.
关键条件是力必须沿位移方向有分量。例如，竖直提起一本书克服重力做功，但提着重物静止不动则对物体做功为零。
2. Calculating Work Done | 计算做功
When the force is constant and acts in the same direction as the displacement, work done W is given by:
当力恒定且与位移同向时，所做的功 W 由下式给出：
W = F × d
a becomes W = F d cos θ. For CCEA IGCSE, the most common case is force parallel to motion, such as pushing a box, or lifting an object vertically where F equals weight mg.
其中 W 为功 (J)，F 为力 (N)，d 为沿力方向移动的距离 (m)。若力与位移夹角为 θ，则公式变为 W = F d cos θ。CCEA IGCSE 中最常见的情况是力与运动方向平行，例如推箱子，或竖直提升物体，其中 F 等于重力 mg。
3. Energy: Forms and Units | 能量：形式与单位
Energy is the ability to do work. Like work, energy is a scalar and is measured in joules (J). Energy exists in various forms: kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, and more. In mechanics, we are mainly concerned with kinetic energy and potential energy.
能量是做功的能力。与功一样，能量是标量，单位为焦耳 (J)。能量以多种形式存在：动能、重力势能、弹性势能、热能、化学能、核能等。在力学中，我们主要关注动能和势能。
Energy can be transferred from one form to another or from one object to another, but the total energy in a closed system remains constant – this is the principle of conservation of energy, a central idea in CCEA exams.
能量可以从一种形式转化为另一种形式，或从一个物体传递到另一个物体，但封闭系统中的总能量保持不变——这是能量守恒原理，是 CCEA 考试的核心概念。
4. Kinetic Energy | 动能
Kinetic energy (KE) is the energy an object possesses due to its motion. The kinetic energy of an object of mass m moving at speed v is:
动能 (KE) 是物体因运动而具有的能量。质量为 m、速度为 v 的物体的动能为：
KE = ½ m v²
Here m is in kg, v in m/s, and KE comes out in joules. Note that KE depends on the square of the speed, so doubling the speed quadruples the kinetic energy. This explains why high‑speed collisions are far more destructive.
此处 m 单位为 kg，v 为 m/s，算出的 KE 单位为焦耳。注意动能与速度的平方成正比，因此速度加倍则动能变为四倍。这解释了为什么高速碰撞的破坏力大得多。
In CCEA questions, you are often asked to calculate final speed from KE gained, or to compare KE before and after an event.
在 CCEA 考题中，常要求根据获得的动能计算末速度，或比较事件前后的动能。
5. Gravitational Potential Energy | 重力势能
Gravitational potential energy (GPE) is the energy stored in an object due to its height above a reference level. Near Earth's surface, it is calculated as:
重力势能 (GPE) 是物体由于高于参考面而储存的能量。在地球表面附近，计算公式为：
GPE = m g h
, often taken as 10 N/kg in exam problems), and h is height (m). GPE is also measured in joules.
其中 m 为质量 (kg)，g 为重力场强度（地球约为 9.8 N/kg，考题中常取 10 N/kg），h 为高度 (m)。GPE 的单位也是焦耳。
The choice of reference level (e.g., ground, floor) is arbitrary; only changes in GPE are physically meaningful. Lifting an object increases its GPE; lowering it decreases GPE.
参考面（例如地面、地板）的选择是任意的；只有 GPE 的变化才有物理意义。提升物体增加其 GPE；降低物体减少 GPE。
6. Elastic Potential Energy (Springs) | 弹性势能（弹簧）
When a spring or any elastic object is stretched or compressed, work is done to deform it, and energy is stored as elastic potential energy. For a spring obeying Hooke's law, the energy stored is:
当弹簧或任何弹性物体被拉伸或压缩时，形变过程中做了功，能量以弹性势能形式储存。对于遵循胡克定律的弹簧，储存的能量为：
Eₑ = ½ k x²
k is the spring constant (N/m) and x is the extension or compression (m). Note the similarity to the kinetic energy formula – it’s again proportional to the square of x.
k 为劲度系数 (N/m)，x 为伸长量或压缩量 (m)。注意与动能公式的相似性——同样与 x 的平方成正比。
While the full derivation is not always required, you may need to calculate energy stored from a force‑extension graph as the area under the line, which for a straight line gives ½ F x.
虽然不总要求完整推导，但可能需要从力–伸长图像中计算储存的能量，即图线下的面积，对直线给出 ½ F x。
7. Conservation of Energy | 能量守恒
The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. In any process, total energy before equals total energy after, provided no energy enters or leaves the system.
能量守恒定律指出，能量不能被创造或消灭，只能从一种形式转化为另一种形式。在任何过程中，只要没有能量进入或离开系统，之前的总能量等于之后的总能量。
the top is converted to KE at the bottom, so mgh = ½ m v², allowing you to find speed v = √2gh. This neglects air resistance; if air resistance is significant, some energy is transferred to thermal energy.
经典的 CCEA 题目涉及落体：顶部的 GPE 转化为底部的 KE，所以 mgh = ½ m v²，可求速度 v = √2gh。这忽略了空气阻力；若空气阻力显著，部分能量转化为热能。
Energy flow diagrams (Sankey diagrams) are often used to show energy transfers and highlight useful vs wasted energy.
能量流程图（桑基图）常用于展示能量转移并突出有用能量与浪费能量。
8. Power: Rate of Doing Work | 功率：做功的速率
energy is transferred. It is a scalar quantity with the unit watt (W), where 1 W = 1 J/s.
功率是做功的快慢，或能量转移的速率。它是标量，单位为瓦特 (W)，1 W = 1 J/s。
The average power P is given by:
平均功率 P 由下式给出：
P = W / t or P = ΔE / t
where W is work done or ΔE is energy transferred, and t is time (s). High power means a large amount of work is done in a short time – for example, a powerful motor can lift a heavy load quickly.
其中 W 为做的功或 ΔE 为转移的能量，t 为时间 (s)。高功率意味着在短时间内完成大量功——例如，大功率电机能快速提起重物。
ect moving at constant speed v against a constant force F (e.g., a car overcoming friction).
另一个有用的形式是 P = F v，适用于物体以恒定速度 v 运动克服恒力 F 的情况（例如汽车克服摩擦力）。
9. Efficiency | 效率
No machine is perfect; some input energy is always converted to unwanted forms (usually heat). Efficiency measures how much of the input energy is transferred to useful output energy.
没有机器是完美的；总有一部分输入能量转化为不需要的形式（通常是热）。效率衡量输入能量中有多少转化为有用的输出能量。
Efficiency = (Useful energy output / Total energy input) × 100%
Or using power: Efficiency = (Useful power output / Total power input) × 100%. Efficiency has no unit and is always less than 100% for real devices.
或用功率表示：效率 = (有用输出功率 / 总输入功率) × 100%。效率无单位，对于实际设备总是小于 100%。
CCEA exam questions often ask you to calculate efficiency from given energy values, or to explain why a device (e.g., light bulb, electric motor) cannot be 100% efficient due to friction, resistance, or heat loss.
CCEA 考题常要求根据给出的能量值计算效率，或解释为何设备（如灯泡、电动机）因摩擦、电阻或热损失而不能达到 100% 效率。
10. Work–Energy Principle & Practical Examples | 功-能原理与实际例子
The work–energy principle states that the net work done on an object equals its change in kinetic energy: Wnet = ΔKE. This links the concepts of force, displacement, and speed.
功-能原理指出，作用在物体上的净功等于其动能的变化：Wnet = ΔKE。这联系了力、位移和速度的概念。
For example, when a car brakes, the friction force does negative work, reducing the car’s KE. When you throw a ball upwards, your hand does work to give it KE, which then converts to GPE as it rises. At the highest point, KE is momentarily zero and GPE is maximum.
例如，汽车刹车时，摩擦力做负功，减小汽车的动能。向上抛球时，手对球做功赋予其动能，上升过程中动能转化为重力势能。在最高点，动能瞬时为零，重力势能最大。
os: a sliding block on a slope (GPE → KE + work against friction), a pendulum swinging (KE ⇌ th losses). Always identify the energy changes and apply conservation of energy carefully.
典型考题场景：斜坡上的滑块（GPE → KE + 克服摩擦做功）、摆动的单摆（KE ⇌ GPE）、过山车（有损耗的能量转换）。始终明确能量变化，并谨慎应用能量守恒。
Remember to show all working, use the correct units, and convert mass to kg, distance to metres, and time to seconds where necessary. CCEA mark schemes reward clear formula statements and substitution.
记得展示所有步骤，使用正确单位，必要时将质量转换为 kg、距离转换为米、时间转换为秒。CCEA 评分标准奖励清晰的公式陈述和代入过程。
Published by TutorHao | Physics Revision Series | aleveler.com
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