Forces and Motion | 力与运动

📚 Forces and Motion | 力与运动

Forces and motion form the core of Edexcel A-Level Mechanics. This topic connects the language of vectors, kinematic equations, Newton’s laws, friction and momentum. A clear modelling process, careful free-body diagrams and consistent sign conventions are the keys to full marks.

力与运动是爱德思 A-Level 力学的核心。该主题将矢量语言、运动学方程、牛顿定律、摩擦和动量联系起来。清晰的建模过程、规范的受力分析图和一致的符号约定是获得满分的关键。

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1. Modelling Assumptions and SI Units | 建模假设与 SI 单位

In Edexcel mechanics, real objects are simplified using models such as a particle, a light inextensible string, a smooth pulley, or a uniform rod.

在爱德思力学中，真实物体会被简化为模型，如质点、轻质不可伸长的绳、光滑滑轮或均匀杆。

The SI base units used in motion problems are metre (m), kilogram (kg) and second (s); force is measured in newtons (N), where 1 N = 1 kg m s⁻².

运动问题中使用的 SI 基本单位是米 (m)、千克 (kg) 和秒 (s)；力的单位是牛顿 (N)，其中 1 N = 1 kg m s⁻²。

Quantity | 物理量	Symbol | 符号	SI unit | 单位
Displacement | 位移	s	m
Velocity | 速度	u, v	m s⁻¹
Acceleration | 加速度	a	m s⁻²
Time | 时间	t	s
Mass | 质量	m	kg
Force | 力	F	N

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2. Scalars and Vectors | 标量与矢量

Scalars have magnitude only: examples are distance, speed, mass, time and energy.

标量只有大小：例如路程、速率、质量、时间和能量。

Vectors have both magnitude and direction: examples are displacement, velocity, acceleration, force and momentum.

矢量既有大小又有方向：例如位移、速度、加速度、力和动量。

In two dimensions, a vector can be written in unit-vector form, e.g. r = xi + yj, where i and j are perpendicular unit vectors.

在二维问题中，矢量可用单位矢量表示，例如 r = xi + yj，其中 i 和 j 是相互垂直的单位矢量。

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3. Constant Acceleration Equations (SUVAT) | 恒定加速度方程 (SUVAT)

The SUVAT equations apply only when acceleration is constant and motion is in a straight line.

SUVAT 方程只适用于加速度恒定且沿直线运动的情况。

The symbols are: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time.

符号含义为：s = 位移，u = 初速度，v = 末速度，a = 加速度，t = 时间。

v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t

If three quantities are known, the remaining quantities can be found; choose the equation that avoids the unknown you are not asked for.

若已知三个量，即可求出其余量；选择不含题目未要求未知量的方程。

Example: a car starts from rest, u = 0, accelerates at a = 2 m s⁻² for t = 5 s; then v = 0 + 2 × 5 = 10 m s⁻¹ and s = 0 × 5 + ½ × 2 × 5² = 25 m.

示例：汽车从静止启动，u = 0，以 a = 2 m s⁻² 加速 t = 5 s；则 v = 0 + 2 × 5 = 10 m s⁻¹，s = 0 × 5 + ½ × 2 × 5² = 25 m。

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4. Motion Graphs | 运动图像

Displacement-time graphs: the gradient equals velocity; a straight line means constant velocity.

位移-时间图像：斜率等于速度；直线表示速度恒定。

Velocity-time graphs: the gradient equals acceleration; the area under the graph equals displacement.

速度-时间图像：斜率等于加速度；图像下方的面积等于位移。

Acceleration-time graphs: the area under the graph equals the change in velocity.

加速度-时间图像：图像下方的面积等于速度的变化量。

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5. Newton’s Three Laws | 牛顿三定律

Newton’s first law states that a body remains at rest or moves with constant velocity unless a resultant external force acts on it.

牛顿第一定律指出，若无合外力作用，物体将保持静止或匀速直线运动。

Newton’s second law is usually written as F = ma: the resultant force equals mass times acceleration.

牛顿第二定律通常写作 F = ma：合外力等于质量乘以加速度。

Newton’s third law states that if A exerts a force on B, B exerts an equal and opposite force on A; these two forces act on different bodies, so they do not cancel in one free-body diagram.

牛顿第三定律指出，若 A 对 B 施加一个力，B 对 A 施加一个大小相等、方向相反的力；这两个力作用在不同物体上，因此不能在同一个受力分析图中抵消。

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6. Common Forces: Weight, Tension and Normal Reaction | 常见力：重力、张力和法向反作用力

Weight W = mg acts vertically downwards; tension T acts along a string away from the object; the normal reaction R acts perpendicular to a contact surface.

重力 W = mg 竖直向下；张力 T 沿绳方向远离物体；法向反作用力 R 垂直于接触面。

A free-body diagram should show all forces acting on one object only, never forces exerted by that object on other bodies.

受力分析图应只画出作用在一个物体上的所有力，不应画出该物体对其他物体施加的力。

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7. Equilibrium and Resolution of Forces | 平衡与力的分解

An object is in equilibrium if the resultant force is zero: all horizontal and vertical components must balance separately.

若合外力为零，则物体处于平衡状态：水平方向和竖直方向的分量必须分别平衡。

To resolve a force F at angle θ to the horizontal: the horizontal component is F cos θ and the vertical component is F sin θ.

将一个与水平方向成 θ 角的力

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