📚 Mechanics and Materials (Unit 1) Revision | 力学与材料 (单元1) 复习
Welcome to your complete revision guide for Edexcel A-Level Physics Unit 1: Mechanics and Materials. This article covers the core concepts, definitions, equations, and typical problem-solving strategies you need to master for the exam. Work through each section carefully, and you will build a solid understanding of motion, forces, energy, materials, and fluids.
欢迎来到 Edexcel A-Level 物理单元 1：力学与材料的完整复习指南。本文涵盖了考试中需要掌握的核心概念、定义、公式以及典型的解题策略。认真研读每一节，你将系统地建立起对运动、力、能量、材料和流体的坚实理解。
1. Scalars and Vectors | 标量与矢量
A scalar quantity has only magnitude, while a vector quantity has both magnitude and direction. Common scalars include distance, speed, mass, energy, and time. Vectors include displacement, velocity, acceleration, force, and momentum. It is essential to treat vectors carefully by resolving them into perpendicular components or by using vector addition.
标量只有大小，而矢量既有大小又有方向。常见的标量有路程、速率、质量、能量和时间。矢量包括位移、速度、加速度、力和动量。处理矢量时必须谨慎，通常需要将其分解为相互垂直的分量，或者采用矢量加法。
p of the last. For perpendicular vectors, the magnitude of the resultant R is given by R = √A² + B² an θ = B/A. Always remember to specify the direction relative to a reference line, such as '30° above the horizontal'.
要将两个矢量相加，可将它们首尾相接放置，从第一个矢量的起点到最后一个矢量的末端画出合矢量。对于相互垂直的矢量，合矢量的大小 R 由 R = √A² + B² 给出，方向 θ 可由 tan θ = B/A 求得。请始终记住相对于参考线指明方向，例如 "与水平线成 30° 向上"。
2. Motion Graphs | 运动图像
Understanding displacement–time, velocity–time, and acceleration–time graphs is fundamental. The gradient of a displacement–time graph gives the velocity. A curved line indicates changing velocity, meaning the object is accelerating. The gradient of a velocity–time graph gives the acceleration, and the area under a velocity–time graph gives the displacement.
理解位移—时间图像、速度—时间图像和加速度—时间图像是基础。位移—时间图像的斜率表示速度。曲线则表明速度在变化，即物体在加速。速度—时间图像的斜率表示加速度，而速度—时间图像下的面积则表示位移。
For uniformly accelerated motion, the velocity–time graph is a straight line with a constant gradient. In such cases, you can use the suvat equations. Be careful when the motion involves multiple stages, such as a car accelerating, then moving at constant speed, and finally braking. Split the graph into sections, analyse each separately, and then combine the results.
对于匀加速运动，速度—时间图像是一条斜率恒定的直线。这时可以使用 suvat 方程组。当运动分为多个阶段时，例如汽车先加速，再匀速行驶，最后制动，需要格外小心。应将图像分段处理，分别分析每个阶段，再综合结果。
3. Equations of Motion (SUVAT) | 运动方程 (SUVAT)
The five equations of motion for constant acceleration in a straight line link the variables s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). The most commonly used forms are:
描述匀加速直线运动的五个方程联系了变量 s（位移）、u（初速度）、v（末速度）、a（加速度）和 t（时间）。最常用的形式如下：
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Always list the known quantities and the one you need to find, then choose the equation that does not include the unknown variable you are not interested in. Remember that these equations only apply when acceleration is constant. If acceleration varies, you must use graphical methods or calculus.
先列出已知量和待求量，然后选择一个不包含你不需要的那个未知变量的方程。请记住，这些方程仅在加速度恒定时适用。若加速度变化，必须使用图像法或微积分求解。
4. Forces and Newton’s Laws | 力与牛顿定律
es the concept of inertia. Newton’s second law relates resultant force F, mass m and acceleration a: F = ma. The third law states that if body A exerts a force on body B, then B exerts an equal and opposite force on A; these paired forces act on different bodies and are of the same type.
牛顿第一定律指出，除非受到净力作用，否则物体将保持静止或匀速直线运动状态。这引入了惯性的概念。牛顿第二定律将净力 F、质量 m 和加速度 a 联系起来：F = ma。第三定律指出，若物体 A 对物体 B 施加一个力，那么 B 同时会对 A 施加一个大小相等、方向相反的力；这对力作用在不同物体上且属于同种性质的力。
n, friction, and applied forces. Resolve forces into components parallel and perpendicular to the plane of motion. If the object is in equilibrium, the net force in any direction is zero. When applying F = ma, use the net force in the direction of acceleration.
受力图对于求解力的问题至关重要。画出作用在单个物体上的所有力，包括重力、法向反作用力、张力、摩擦力以及施加的外力。将力沿运动平面的平行和垂直方向分解。若物体处于平衡状态，则任意方向上的净力均为零。在应用 F = ma 时，应使用加速度方向上的净力。
5. Momentum and Impulse | 动量与冲量
or quantity measured in kg m s⁻¹. The principle of conservation of momentum states that in a closed system with no external forces, total momentum before a collision or explosion equals total momentum after the event. This applies to all interactions and is especially useful for solving problems involving collisions and recoil.
动量 p 定义为质量与速度的乘积：p = mv。它是一个矢量，单位为 kg m s⁻¹。动量守恒定律指出，在没有外力的封闭系统中，碰撞或爆炸前的总动量与事件后的总动量相等。这适用于所有相互作用，对于解决涉及碰撞和反冲的问题尤为有用。
Impulse is the change in momentum, given by Impulse = FΔt = Δp. The area under a force– he contact time and change in momentum are known. Always assign a positive direction when dealing with momentum to keep signs consistent.
冲量是动量的变化量，由 冲量 = FΔt = Δp 给出。力—时间图像下的面积代表冲量。在碰撞中，作用在物体上的力可能非常大但持续时间极短；如果知道接触时间和动量的变化，就可以计算出平均力。处理动量问题时，始终要规定一个正方向，以保持符号一致。
6. Work, Energy and Power | 功、能量与功率
joules (J). The principle of conservation of energy tells us that energy cannot be created or destroyed, only transferred from one form to another. Kinetic energy Eₖ = ½mv²; gravitational potential energy Eₚ = mgΔh.
恒力所做的功 W = Fs cos θ，其中 θ 是力与位移之间的夹角。能量是做功的能力，单位为焦耳 (J)。能量守恒定律告诉我们，能量既不能凭空产生，也不能凭空消失，只能从一种形式转化为另一种形式。动能 Eₖ = ½mv²；重力势能 Eₚ = mgΔh。
f the force. Efficiency is calculated as (useful energy output / total energy input) × 100% ces are present; if they are, the work done against them dissipates energy, often as heat.
功率 P 是做功或能量转化的速率：对于以恒定速率 v 沿力的方向运动的物体，P = W/t = Fv。效率的计算公式为 (有用能量输出 / 总能量输入) × 100%。解题时，要考虑是否存在阻力；如果有，克服阻力所做的功会耗散能量，通常以热能形式散失。
7. Materials: Stress, Strain and Young Modulus | 材料：应力、应变与杨氏模量
ls (Pa). Tensile strain ε is the extension per unit original length: ε = ΔL/L₀, a dimensionless ratio. A stress– shows distinct regions: elastic deformation, plastic deformation, and eventually fracture.
当材料受到力的作用时，会发生形变。拉伸应力 σ 定义为单位横截面积上的力：σ = F/A，单位为帕斯卡 (Pa)。拉伸应变 ε 是单位原始长度的伸长量：ε = ΔL/L₀，是一个无量纲的比值。像铜这样的延性材料的应力—应变图呈现出清晰的区域：弹性形变、塑性形变，最终断裂。
elastic region: E = σ/ε = (F L₀)/(A ΔL). The gradient of the linear portion of the stress– applies up to the limit of proportionality; beyond this, Hooke’s law is no longer obeyed.
杨氏模量 E 是衡量材料在弹性区域刚度的物理量：E = σ/ε = (F L₀)/(A ΔL)。应力—应变图线性部分的斜率就是杨氏模量。斜率越大，表明材料越刚硬。切记杨氏模量仅在比例极限以下适用；超过此极限后，胡克定律不再成立。
8. Hooke’s Law and Elasticity | 胡克定律与弹性
Mathematically, F = kΔL, where k is the spring constant. The elastic limit is the point beyond which the material does not return to its original shape when the load is removed; plastic deformation has occurred.
胡克定律指出，只要不超过弹性极限，弹簧或金属丝的伸长量与所施加的力成正比。数学表达式为 F = kΔL，其中 k 为弹簧常数。弹性极限是这样一个临界点：超过它之后，卸去载荷时材料不再恢复原状，即发生了塑性形变。
potential energy stored in a stretched spring or wire is equal to the area under the force– ring constant depends on whether they are arranged in series or in parallel. For springs in series, 1/kₑ = 1/k₁ + 1/k₂; for parallel, kₑ = k₁ + k₂.
储存在拉伸弹簧或金属丝中的弹性势能等于力—伸长图像下的面积。对于遵守胡克定律的材料，该面积是一个三角形，因此 Eₑₗ = ½FΔL = ½k(ΔL)²。当两个弹簧组合使用时，等效弹簧常数取决于它们是串联还是并联。串联时，1/kₑ = 1/k₁ + 1/k₂；并联时，kₑ = k₁ + k₂。
9. Fluids: Density and Upthrust | 流体：密度与浮力
to the weight of the fluid displaced. This is Archimedes’ principle. The upthrust U = ρ_fluid V_submerged g. An object floats if its average density is less than or equal to the fluid density; it sinks if its density is greater.
密度 ρ 是单位体积的质量：ρ = m/V，单位为 kg m⁻³。当物体浸没在流体中时，会受到一个向上的浮力，其大小等于被排开流体的重量。这就是阿基米德原理。浮力 U = ρ_fluid V_submerged g。当物体的平均密度小于或等于流体的密度时，物体漂浮；若密度更大，则下沉。
g a pipe: A₁v₁ = A₂v₂, where A is the cross-sectional area and v is the velocity. This is the continuity equation. It explains why the speed of a river increases when it narrows.
在流体流动中，单位时间内通过某一点的流体质量称为质量流量。对于不可压缩流体，沿管道的体积流量保持不变：A₁v₁ = A₂v₂，其中 A 为横截面积，v 为流速。这就是连续性方程。它解释了为什么河道变窄时流速会增加。
10. Projectile Motion | 抛体运动
rizontal and vertical components. Horizontally, velocity remains constant because there is no acceleration. Vertically, the motion is uniformly accelerated with acceleration g = 9.81 m s⁻² downwards. Use suvat equations separately for each direction.
假设空气阻力可以忽略，抛体仅在重力作用下运动。其运动可通过将水平和竖直分量分开来分析。水平方向上，由于没有加速度，速度保持不变。竖直方向上，运动是加速度 g = 9.81 m s⁻² (向下) 的匀加速运动。分别在每个方向上运用 suvat 方程。
The time of flight depends only on the vertical motion. The maximum height is reached when the vertical component of velocity becomes zero. The horizontal range is the constant horizontal velocity multiplied by the time of flight. Remember that the trajectory of a projectile is parabolic. Typical problems involve finding the range, maximum height, or impact velocity given the launch speed and angle.
飞行时间只取决于竖直运动。当竖直分速度变为零时，达到最大高度。水平射程等于恒定的水平速度乘以飞行时间。记住，抛体的轨迹是抛物线。典型的问题包括给定发射速度和角度，求射程、最大高度或落地速度。
11. Moments and Equilibrium | 力矩与平衡
F × d. The principle of moments states that for a body in rotational equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments. This is used extensively in problems with beams, levers, and bridges.
力对某点的力矩等于力乘以该点到力作用线的垂直距离：力矩 = F × d。力矩原理指出，对于处于转动平衡的物体，绕任意支点的顺时针力矩之和等于逆时针力矩之和。这一原理广泛应用于横梁、杠杆和桥梁相关问题。
, including the weight of the beam acting at its centre of mass. Choose a convenient pivot—often a support or hinge— forces, and its torque is given by Torque = F × perpendicular distance between the forces.
求解力矩问题时，务必画出清晰的示意图，并标出所有力，包括作用在质心处的梁的重力。选择一个方便的支点——通常是一个支座或铰链——以从方程中消去该点未知的反作用力。力偶是一对大小相等、方向相反的平行力，其力偶矩为 力偶矩 = 力 × 两力之间的垂直距离。
12. General Problem-Solving Tips | 普遍解题技巧
Examination questions in Unit 1 often combine several concepts. Start by reading the question carefully and underlining key quantities. Convert all units to SI: metres, kilograms, seconds, newtons. Decide on a sign convention and apply it consistently. Always check whether a quantity is a scalar or a vector before using it in calculations. Show your working step by step, and include formulas before substituting numbers.
单元 1 的考题常常综合多个概念。解题时应先仔细读题，在关键量下面画线。将所有单位转换为国际单位制：米、千克、秒、牛顿。确定正负号规则并始终如一地运用。在用于计算之前，始终要先判断一个量是标量还是矢量。逐步展示解题过程，代入数值之前先写出公式。
When you finish, verify that your answer is reasonable. Does the magnitude match the physical situation? Are the units correct? A common error is omitting to square a velocity or forgetting to resolve a force. Practice with past papers is the best way to identify your weak areas and build confidence. Remember, the principles of mechanics are logical – understanding them deeply will help you tackle even the most unfamiliar problems.
完成解题后，检查答案是否合理。数值是否符合实际物理情景？单位是否正确？最常见的错误包括遗漏对速度的平方或者忘记分解力。通过练习历年真题来发现薄弱环节并树立信心，是最佳方法。请记住，力学原理是合乎逻辑的——深入理解它们将帮助你解决哪怕是最陌生的问题。
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