📚 Year 8 Cambridge Engineering: Formula & Theorem Quick Reference Handbook | Year 8 剑桥工程：公式定理速查手册
This handy reference collects all the essential formulas, principles and theorems you will encounter in the Year 8 Cambridge Engineering course. Work through each section to build your confidence in applying these concepts to problems involving structures, mechanisms, energy and electrical systems.
这本便捷的手册汇集了你在 Year 8 剑桥工程课程中将遇到的所有核心公式、原理和定理。逐节掌握这些内容，你将能自信地运用它们解决关于结构、机构、能量和电学系统的各种问题。
1. Work and Energy | 功与能量
Work is done when a force moves an object in the direction of the force. The amount of work done depends on the size of the force and the distance the object moves in that direction.
当一个力使物体沿力的方向移动时，我们就说力做了功。做功的大小取决于力的大小以及物体在该方向上移动的距离。
W = F × d
W is work done 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 of work is done when a force of one newton moves an object one metre.
W 为功，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)。1 牛顿的力使物体移动 1 米，做功为 1 焦耳。
Energy is the capacity to do work, and it can be stored in different forms. When an object is lifted against gravity, it gains gravitational potential energy (GPE).
能量是做功的本领，能以不同形式储存。当物体被抬高克服重力时，它获得了重力势能 (GPE)。
ΔEₚ = m × g × Δh
he gravitational field strength (on Earth ≈ 9.8 N/kg), and Δh is the change in height (m).
ΔEₚ 为重力势能变化量 (J)，m 为质量 (kg)，g 为重力场强度 (地球表面约 9.8 N/kg)，Δh 为高度差 (m)。
2. Power | 功率
Power measures how quickly work is done or energy is transferred. A machine with a high power rating performs work in a shorter time.
功率衡量做功或能量转化的快慢。高功率的机器能在更短的时间内完成同样的功。
P = W ÷ t
P is power in watts (W), W is work done in joules (J), and t is the time taken in seconds (s). One watt equals one joule of work done per second.
P 为功率，单位瓦特 (W)；W 为功，单位焦耳 (J)；t 为时间，单位秒 (s)。1 瓦特等于每秒做 1 焦耳的功。
a constant force moves an object at constant speed: P = F × v, where v is velocity (m/s).
当恒力使物体匀速运动时，功率也可表示为力与速度的乘积：P = F × v，其中 v 为速度 (m/s)。
3. Simple Machines: Mechanical Advantage | 简单机械：机械效益
Simple machines such as levers, pulleys, gears and inclined planes allow a small effort to overcome a larger load. Mechanical advantage (MA) tells us how much the machine multiplies the effort force.
杠杆、滑轮、齿轮和斜面等简单机械能让我们用较小的作用力克服较大的负载。机械效益 (MA) 表示机械将作用力放大了多少倍。
MA = L ÷ E
L is the load (the force we need to overcome) in newtons (N), and E is the effort (the force we apply) in newtons (N). MA has no units—it is a pure ratio.
L 为负载，即我们需要克服的力 (N)；E 为作用力，即我们施加的力 (N)。MA 无单位，是一个纯比值。
If MA > 1, the machine multiplies the effort; if MA < 1, the machine actually reduces the effort force but is still useful for increasing speed or distance moved.
如果 MA > 1，机械放大了作用力；如果 MA < 1，机械实际上减小了作用力，但仍可用来提高速度或增大移动距离。
4. Velocity Ratio and Efficiency | 速比与效率
Velocity ratio (VR) compares the distance moved by the effort to the distance moved by the load in the same time. It depends only on the geometry of the machine.
速比 (VR) 是指在相同时间内作用力端移动的距离与负载端移动的距离之比。它仅取决于机械的几何构造。
VR = dₑ ÷ dₗ
dₑ is the distance the effort moves (m), and dₗ is the distance the load moves (m). Like MA, VR has no units.
dₑ 为作用力端移动的距离 (m)，dₗ 为负载端移动的距离 (m)。与 MA 一样，VR 也没有单位。
Efficiency (η) measures how much of the input work is converted into useful output work. Friction always causes some energy to be lost as heat, so efficiency is always less than 100%.
效率 (η) 衡量输入功中有多少转化为有用的输出功。摩擦总会导致部分能量以热的形式散失，所以效率总是低于 100%。
η = (MA ÷ VR) × 100%
Alternatively, efficiency can also be found from work done: η = (Wout ÷ Win) × 100%, where Wout is the useful work output and Win is the work input.
效率也可由做功量求得：η = (Wout ÷ Win) × 100%，其中 Wout 为有用输出功，Win 为输入功。
5. Hooke's Law and Springs | 胡克定律与弹簧
When a spring or an elastic material is stretched, the extension is directly proportional to the force applied—as long as the elastic limit is not exceeded. This relationship is known as Hooke's Law.
当弹簧或弹性材料被拉伸时，只要不超过弹性极限，伸长量与所施加的力成正比。这一关系称为胡克定律。
