Year 8 CIE Engineering: Formula and Theorem Quick Reference Guide | Year 8 CIE 工程：公式定理速查手册

📚 Year 8 CIE Engineering: Formula and Theorem Quick Reference Guide | Year 8 CIE 工程：公式定理速查手册

Welcome to your essential quick reference guide for Year 8 CIE Engineering. This handbook collects the key formulae and theorems you will encounter, with clear explanations to help you revise, solve problems, and build your confidence. Use it alongside your class notes and past paper questions.

欢迎使用你的 Year 8 CIE 工程核心公式定理速查手册。本手册汇集了你将遇到的关键公式与定理，并配有清晰的解释，帮助你复习、解题并建立信心。请结合课堂笔记和历年真题一起使用。

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1. Force, Mass, and Acceleration | 力、质量与加速度

Newton’s Second Law is central to engineering: the net force acting on an object equals its mass multiplied by its acceleration. This relationship allows engineers to predict how objects will move when forces are applied.

牛顿第二定律是工程学的核心：作用在物体上的净力等于其质量乘以加速度。这一关系使工程师能够预测物体受力时将如何运动。

F = m × a

In this formula, F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²). One newton is the force needed to accelerate 1 kg at 1 m/s².

在此公式中，F 是力（牛顿，N），m 是质量（千克，kg），a 是加速度（米每二次方秒，m/s²）。一牛顿是使 1 kg 物体产生 1 m/s² 加速度所需的力。

Weight is a specific type of force caused by gravity. On Earth, the gravitational field strength g is approximately 9.8 N/kg, so weight W = m × g. This is why a 1 kg mass weighs about 9.8 N.

重量是由重力引起的一种特殊力。在地球上，重力场强度 g 约为 9.8 N/kg，因此重量 W = m × g。这就是为什么 1 kg 质量的物体重约 9.8 N。

W = m × g

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2. Pressure in Solids and Fluids | 固体与流体中的压力

Pressure describes how concentrated a force is. For a solid resting on a surface, pressure P (in pascals, Pa) is the force divided by the area over which the force acts.

压力描述了力的集中程度。对于放置在表面上的固体，压力 P（帕斯卡，Pa）等于力除以力作用的面積。

P = F / A

A sharp knife cuts easily because the force is concentrated on a tiny area, producing high pressure. The same force spread over a large area gives low pressure – think of snowshoes preventing you from sinking.

锋利的刀容易切割是因为力集中在极小的面积上，产生了高压。同样的力分散在大面积上则产生低压——想象一下雪鞋防止你陷入雪中。

In a liquid, pressure increases with depth. The pressure at a particular depth is given by p = ρ × g × h, where ρ (rho) is the density of the liquid, g is gravitational field strength, and h is the depth below the surface.

在液体中，压力随深度增加。某一深度处的压力由 p = ρ × g × h 给出，其中 ρ (rho) 是液体的密度，g 是重力场强度，h 是液面下的深度。

p = ρ × g × h

This is why dams are thicker at the bottom and why deep-sea vessels must withstand enormous pressures.

这就是为什么大坝底部更厚，以及深海船只必须承受巨大压力的原因。

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3. Work and Mechanical Energy | 功与机械能

Work is done when a force moves an object. If the force and the movement are in the same direction, the work done W equals the force multiplied by the distance moved.

当力使物体移动时就做了功。如果力与移动方向相同，做功 W 等于力乘以移动的距离。

W = F × d

Work is measured in joules (J). One joule is the work done when a force of 1 newton moves an object 1 metre in the direction of the force.

功的单位是焦耳 (J)。一焦耳是 1 牛顿的力使物体沿力的方向移动 1 米所做的功。

Kinetic energy (Ek) is the energy an object possesses due to its motion. It depends on mass and speed squared.

动能 (Ek) 是物体因运动而具有的能量。它取决于质量和速度的平方。

Ek = ½ m v²

Gravitational potential energy (Ep) is stored energy due to an object’s height above a reference level. It is given by Ep = m g h, where h is the height in metres.

重力势能 (Ep) 是由于物体高于参考面而储存的能量。公式为 Ep = m g h，其中 h 是高度，单位为米。

Ep = m g h

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4. Power and Efficiency | 功率与效率

Power measures how quickly work is done or energy is transferred. The fundamental formula is power equals work done divided by time taken.

功率衡量做功或能量传递的快慢。基本公式为功率等于所做的功除以所用时间。

P = W / t

Alternatively, if you know the energy change E, you can use P = E / t. Power is measured in watts (W); 1 W =

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