📚 Year 7 Edexcel Engineering Formula Quick Reference Handbook | 工程公式定理速查手册
Welcome to the Year 7 Engineering Formula Quick Reference Handbook. This guide collects the essential formulas, principles and theorems you will meet in the Edexcel engineering curriculum. Mastering these relationships will help you analyse forces, motion, electrical circuits and energy transfers. Use this handbook to support your revision and build a solid foundation in engineering science.
欢迎使用七年级工程公式速查手册。本指南汇集了Edexcel工程课程中你会遇到的核心公式、原理与定理。掌握这些关系式有助于你分析力、运动、电路和能量转移。请用这本手册辅助复习，打下坚实的工程科学基础。
1. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is one of the most fundamental in engineering. Speed is the distance travelled per unit time.
速度、距离和时间之间的关系是工程中最基本的关系之一。速度是单位时间内经过的距离。
The formula is written as: v = d / t, where v stands for speed, d for distance and t for time. In SI units, distance is measured in metres (m) and time in seconds (s), giving speed in metres per second (m/s).
其公式为：v = d / t，其中 v 代表速度，d 代表距离，t 代表时间。在国际单位制中，距离用米(m)测量，时间用秒(s)测量，因此速度的单位是米每秒(m/s)。
Engineers use this equation when designing transport systems, calculating journey times or estimating the velocity of moving components in a machine.
工程师在设计交通系统、计算行程时间或估算机器中运动部件的速度时，都会用到这个方程。
2. Force, Mass and Acceleration | 力、质量与加速度
Newton’s second law of motion explains how an object behaves when a net force acts upon it. The law states that the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass.
牛顿第二运动定律解释了物体在受到净力作用时的行为。该定律指出，物体的加速度与所受到的合力成正比，与物体的质量成反比。
The formula is: F = m × a. Force F is measured in newtons (N), mass m in kilograms (kg) and acceleration a in metres per second squared (m/s²). One newton is defined as the force needed to accelerate a 1 kg mass by 1 m/s².
公式为：F = m × a。力 F 的单位是牛顿(N)，质量 m 的单位是千克(kg)，加速度 a 的单位是米每二次方秒(m/s²)。一牛顿定义为使1千克质量产生1 m/s²加速度所需的力。
In an engineering context, this law is used to calculate the forces required in lifting systems, vehicle acceleration and the design of structures that must withstand dynamic loads.
在工程背景下，该定律用于计算起重系统、车辆加速和承受动载荷的结构设计中所需的作用力。
3. Work Done | 做功
Work is done whenever a force moves an object through a distance in the direction of the force. Work is a measure of energy transfer and is closely linked to the concept of mechanical effort.
只要力使物体沿力的方向移动一段距离，力就做了功。功是能量转移的量度，与机械作用的概念密切相关。
The equation for work is: W = F × d, where W is work in joules (J), F is the applied force in newtons (N) and d is the distance moved in the direction of the force in metres (m). One joule equals one newton metre.
功的公式为：W = F × d，其中 W 表示功，单位焦耳(J)；F 为施加的力，单位牛顿(N)；d 为沿力方向移动的距离，单位米(m)。一焦耳等于一牛顿·米。
If the force and the movement are in opposite directions, the work done is negative, which often represents energy being taken out of the system, such as by friction.
如果力与运动方向相反，则所做的功为负值，这通常代表能量从系统中被带走，例如由摩擦引起的能量损失。
4. Power | 功率
Power describes how quickly work is done or how fast energy is transferred from one form to another. High-power machines perform the same amount of work in less time than low-power ones.
功率描述做功的快慢程度，或能量从一种形式转化为另一种形式的速率。高功率机器比低功率机器在更短的时间内完成相同的功。
The power equation can be expressed as: P = W / t or P = E / t, where P is power in watts (W), W is work in joules (J), E is energy transferred in joules and t is time in seconds (s). One watt is equivalent to one joule per second.
功率公式可表示为：P = W / t 或 P = E / t，其中 P 为功率，单位瓦特(W)；W 为功，单位焦耳(J)；E 为转移的能量(J)；t 为时间(s)。一瓦特等于每秒一焦耳。
In mechanical engineering, power ratings of motors and engines are critical. They tell the designer whether a machine can lift a certain load or drive a vehicle at a required speed.
在机械工程中，电动机和发动机的额定功率至关重要。它们告诉设计师机器是否能够提升特定负载或使车辆达到所需速度。
5. Mechanical Advantage | 机械效益
Simple machines such as levers, pulleys and gears are used to make work easier. Mechanical advantage (MA) indicates how many times a machine multiplies the effort force applied to it.
杠杆、滑轮和齿轮等简单机械用于使工作更省力。机械效益(MA)表示机器将施加的力放大了多少倍。
The basic formula is: MA = load / effort. The load is the force that the machine overcomes, and the effort is the force you apply. A machine with an MA greater than 1 allows you to lift a heavy load with less effort.
基本公式为：MA = 负载 / 施力。负载是机器要克服的力，施力是你施加的力。机械效益大于1的机器可以让你用较小的力抬起重物。
For a lever, MA can also be found from the distances from the fulcrum: MA = effort arm / load arm. A longer effort arm gives a higher mechanical advantage.
对于杠杆，机械效益也可通过距支点的距离求得：MA = 施力臂 / 负载臂。较长的施力臂能产生更大的机械效益。
6. Efficiency | 效率
No real machine converts all the input energy into useful output work; some energy is always lost, typically as heat due to friction. Efficiency measures how well a machine uses the energy supplied to it.
现实中的机器不可能将全部输入能量转化为有用的输出功；总会损失部分能量，通常是因摩擦产生的热量。效率衡量了机器利用所供能量的程度。
Efficiency is calculated using: η = (useful output energy / total input energy) × 100%, where η (Greek letter eta) is expressed as a percentage. The same formula can use useful power output and total power input.
效率的计算公式为：η = (有用输出能量 / 总输入能量) × 100%，其中 η（希腊字母eta）以百分比表示。该公式也可使用有用输出功率和总输入功率。
An efficiency of 75% means that three-quarters of the input energy is turned into useful work, while 25% is wasted. Engineers constantly work to reduce waste and increase efficiency through better lubrication, design and materials.
效率为75%意味着四分之三的输入能量转化为有用功，而25%被浪费。工程师不断通过改善润滑、优化设计和选用更佳材料来减少浪费、提高效率。
7. Ohm’s Law | 欧姆定律
In electrical and electronic engineering, Ohm’s Law is the foundation for understanding how circuits behave. It links voltage, current and resistance in a simple linear relationship.
在电气与电子工程中，欧姆定律是理解电路行为的基础。它用一个简单的线性关系将电压、电流和电阻联系起来。
The law is written as: V = I × R. Voltage V is measured in volts (V), current I in amperes (A) and resistance R in ohms (Ω). If you know any two of these quantities, you can calculate the third.
定律可写成：V = I × R。电压 V 的单位是伏特(V)，电流 I 的单位是安培(A)，电阻 R 的单位是欧姆(Ω)。只要知道其中任意两个量，就能求出第三个量。
Ohm’s Law is used every day by engineers to design circuit protection, select the right resistors and ensure that components receive the correct operating voltage.
工程师每天都运用欧姆定律来设计电路保护、选择正确的电阻器，并确保元器件获得正确的工作电压。
8. Density | 密度
Density tells us how much mass is packed into a given volume. Materials with high density, like steel, contain a lot of mass in a small space, while low-density materials, like foam, are light for their size.
密度告诉我们单位体积内包含多少质量。高密度材料（如钢）在较小空间内蕴含大量质量，而低密度材料（如泡沫）相对其体积来说较轻。
The density formula is: ρ = m / V, where ρ (rho) stands for density, m for mass and V for volume. Common units are kilograms per cubic metre (kg/m³) and grams per cubic centimetre (g/cm³).
密度公式为：ρ = m / V，其中 ρ (rho) 代表密度，m 代表质量，V 代表体积。常用单位是千克每立方米(kg/m³)和克每立方厘米(g/cm³)。
Engineers use density data to select materials for structures, vehicles and products. Choosing a material with the right density can make a product lighter, stronger and more fuel-efficient.
工程师利用密度数据为建筑、车辆和产品选择材料。选择密度合适的材料可使产品更轻、更强且更省油。
9. Pressure | 压强
Pressure describes how concentrated a force is on a surface. The same force applied over a smaller area produces a larger pressure.
压强描述力在表面上的集中程度。相同的力作用在更小的面积上会产生更大的压强。
The pressure equation is: p = F / A, where p is pressure in pascals (Pa), F is the perpendicular force in newtons (N) and A is the area in square metres (m²). One pascal is equivalent to one newton per square metre.
压强公式为：p = F / A，其中 p 表示压强，单位帕斯卡(Pa)；F 为垂直作用力(N)；A 为受力面积(m²)。一帕斯卡等于一牛顿每平方米。
Pressure is a key concept in hydraulic systems, where a small force applied to a small piston creates a high pressure that can be used to generate a large force on a bigger piston. This is the principle behind car brakes and hydraulic presses.
压强是液压系统中的关键概念：在小活塞上施加较小的力可以产生较高的压强，进而用于在较大活塞上产生很大的力。这就是汽车制动器和液压机背后的原理。
10. Moments | 力矩
A moment, also called a torque, measures the turning effect produced by a force acting at a distance from a pivot or fulcrum. Moments are responsible for the rotation of wheels, levers and shafts.
力矩（也称扭矩）衡量力在距支点或转轴一定距离处所产生的转动效应。力矩是车轮、杠杆和转轴转动的原因。
The moment of a force is found using: M = F × d, where M is the moment in newton metres (N m), F is the force in newtons and d is the perpendicular distance from the pivot to the line of action of the force.
力矩的计算公式为：M = F × d，其中 M 为力矩，单位牛顿·米(N m)；F 为力(N)；d 为从支点到力作用线的垂直距离。
For a system to be in equilibrium, the principle of moments states that the sum of clockwise moments must equal the sum of anticlockwise moments. This principle helps engineers balance cranes, bridges and seesaws.
当系统处于平衡时，力矩原理指出顺时针力矩之和必须等于逆时针力矩之和。这一原理帮助工程师平衡起重机、桥梁和跷跷板。
11. Hooke’s Law | 胡克定律
Hooke’s Law describes how many elastic materials, especially metal springs, behave when they are stretched or compressed. Within the elastic limit, the extension is directly proportional to the applied force.
胡克定律描述了许多弹性材料（特别是金属弹簧）在拉伸或压缩时的行为。在弹性限度内，伸长量与施加的力成正比。
The law is written as: F = k × x, where F is the force applied, k is the spring constant (a measure of stiffness) and x is the extension (or compression) from the original length. The unit of the spring constant is newtons per metre (N/m).
该定律写作：F = k × x，其中 F 为施加的力，k 为弹簧常数（衡量刚度的大小），x 为相对于原长的伸长量（或压缩量）。弹簧常数的单位是牛顿每米(N/m)。
If the spring is stretched beyond its elastic limit, it will be permanently deformed and Hooke’s Law no longer applies. Engineers must stay within the safe working range when designing suspension systems or measurement devices that rely on springs.
如果弹簧被拉伸超过其弹性限度，将发生永久形变，胡克定律不再适用。工程师在设计依赖弹簧的悬架系统或测量装置时，必须保持在安全工作范围内。
12. Energy Forms and Conservation | 能量形式与守恒
Energy is the ability to do work. It exists in many forms that engineers encounter daily: kinetic energy, gravitational potential energy, elastic potential energy, thermal energy, chemical energy and electrical energy.
能量是做功的能力。工程师每天都接触到多种形式的能量：动能、重力势能、弹性势能、热能、化学能和电能。
The principle of conservation of energy is a fundamental law of physics: energy cannot be created or destroyed; it can only be transferred from one form to another. The total energy of an isolated system remains constant.
能量守恒原理是一条基本物理定律：能量既不会创生也不会消失，只能从一种形式转化为另一种形式。孤立系统的总能量保持不变。
Kinetic energy is calculated as KE = ½ m v² and gravitational potential energy as GPE = m g h, where g is the gravitational field strength (approximately 9.8 N/kg on Earth, often rounded to 10 N/kg) and h is the height above a reference level.
动能的计算公式为 KE = ½ m v²，重力势能为 GPE = m g h，其中 g 是重力场强度（地球表面约为9.8 N/kg，常取10 N/kg），h 是相对于参考平面的高度。
These energy equations allow engineers to predict how fast a roller coaster will travel, how high a rocket can rise or how much a spring will compress, all by following the simple rule that energy in must equal energy out, minus losses.
利用这些能量方程，工程师可以预测过山车的行驶速度、火箭的上升高度或弹簧的压缩量，只需遵循一条简单规则：输入能量等于输出能量加上损耗。
Published by TutorHao | Engineering Revision Series | aleveler.com
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