📚 Combined 210: Edexcel A-Level Mechanics – Forces, Motion and Energy | 综合 210：爱德思 A-Level 力学——力、运动与能量
Welcome to this Combined 210 revision guide for Edexcel A-Level Mechanics. Whether you are preparing for A-Level Physics or the Mechanics components of A-Level Mathematics, a clear grasp of forces, motion and energy is essential. In this article, we break down the core concepts, equations and common exam pitfalls so you can revise efficiently.
欢迎阅读本份爱德思 A-Level 力学综合 210 复习指南。无论你是在准备 A-Level 物理还是 A-Level 数学中的力学模块，清楚地掌握力、运动和能量都是关键。本文将拆解核心概念、公式和常见考试陷阱，帮助你高效复习。
1. Scalar and Vector Quantities | 标量与矢量
A scalar quantity has magnitude only, while a vector quantity has both magnitude and direction. In mechanics, direction is essential when adding forces, velocities or momenta.
标量只有大小，而矢量既有大小又有方向。在力学中，叠加力、速度或动量时，方向非常重要。
| Scalars | 标量 | Vectors | 矢量 |
|---|---|
| distance 距离 | displacement 位移 |
| speed 速率 | velocity 速度 |
| mass 质量 | weight 重力 |
| energy 能量 | force 力 |
| time 时间 | momentum 动量 |
You can resolve any vector into perpendicular components, usually horizontal and vertical, using trigonometry. For a force F at angle θ to the horizontal, the components are F cos θ and F sin θ.
你可以用三角函数把任何矢量分解为互相垂直的分量，通常是水平和竖直方向。对于与水平方向夹角为 θ 的力 F，其分量为 F cos θ 和 F sin θ。
2. Kinematics: The SUVAT Equations | 运动学：SUVAT 方程
The SUVAT equations describe motion with constant acceleration in a straight line. The five variables are displacement s, initial velocity u, final velocity v, acceleration a and time t.
SUVAT 方程描述匀加速直线运动。五个变量分别是位移 s、初速度 u、末速度 v、加速度 a 和时间 t。
You must choose the equation that contains only the three known quantities and the one unknown you want to find. The four standard equations are shown below.
你必须选择只包含三个已知量和待求量的那个方程。四个标准方程如下所示。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u + v)/2 × t
Remember that s, u, v and a are vectors. If a projectile moves upwards but gravity acts downwards, take one direction as positive and assign signs consistently.
请记住 s、u、v 和 a 都是矢量。如果物体向上运动而重力向下，要先规定正方向，并始终按该方向赋予符号。
A typical exam question gives three values and asks for a fourth. Always list u, v, a, s and t before substituting, and include units.
典型考题会给出三个量，要求第四个量。代入前务必先列出 u、v、a、s 和 t，并带上单位。
3. Forces and Free-Body Diagrams | 力与受力分析图
A free-body diagram shows all the forces acting on a single object. The main forces in A-Level mechanics are weight, normal reaction, tension, friction, driving force and air resistance.
受力分析图显示作用在单个物体上的所有力。A-Level 力学中主要的力有重力、法向反力、张力、摩擦力、驱动力和空气阻力。
To find the resultant force, resolve all forces into two perpendicular directions and then use Pythagoras and trigonometry. If the resultant force is zero, the object is in equilibrium and has zero acceleration.
求合力时，先把所有力分解到两个垂直方向，再用勾股定理和三角函数合成。若合力为零，物体处于平衡状态，加速度为零。
For an object on a smooth inclined plane, the weight mg is resolved into mg sin θ parallel to the slope and mg cos θ perpendicular to the slope. The normal reaction always acts perpendicular to the surface.
对于放在光滑斜面上的物体，重力 mg 分解为沿斜面向下的 mg sin θ 和垂直于斜面的 mg cos θ。法向反力始终垂直于接触面。
4. Newton’s Laws of Motion | 牛顿运动定律
Newton’s first law states that an object remains at rest or moves with constant velocity unless acted on by a resultant force. Newton’s second law states that the resultant force equals the rate of change of momentum, which for constant mass gives F = ma. Newton’s third law states that if object A exerts a force on object B, then B exerts an equal and opposite force on A.
牛顿第一定律指出，除非受到合力作用，物体将保持静止或匀速直线运动。牛顿第二定律指出，合力等于动量的变化率，在质量不变时给出 F = ma。牛顿第三定律指出，若 A 对 B 施加力，则 B 对 A 施加大小相等、方向相反的力。
F = m × a
When analysing connected bodies, such as a car towing a trailer, apply F = ma to the whole system first to find the acceleration, and then apply F = ma to one body alone to find the tension in the coupling.
分析连接体时，例如汽车牵引拖车，先对整体应用 F = ma 求加速度，再对单个物体应用 F = ma 求连接处的张力。
Always remember that F is the resultant force, not the applied force. Subtract opposing forces before using F = ma.
务必记住 F 是合力，不是某个施加的力。使用 F = ma 前要先减去相反的力。
5. Friction and Drag Forces | 摩擦力与阻力
Friction arises between two surfaces in contact and acts parallel to the surface, opposing motion or attempted motion. The maximum static friction is usually larger than kinetic friction.
摩擦力产生于两个接触面之间，方向平行于接触面，阻碍运动或相对运动趋势。最大静摩擦力通常大于动摩擦力。
Drag forces, such as air resistance, increase with speed. An object falling through a fluid reaches terminal velocity when the upward drag force balances its weight, so the resultant force becomes zero.
阻力（如空气阻力）随速度增大而增大。物体在流体中下落时，当向上的阻力与重力平衡，合力为零，物体达到终极速度。
In most Edexcel A-Level questions, you will use a simple model where friction is constant and air resistance is ignored unless stated. Always read the wording ‘smooth’, ‘rough’ or ‘negligible air resistance’ carefully.
在大多数爱德思 A-Level 考题中，你会使用简单模型：摩擦力恒定，空气阻力除非说明否则忽略。务必仔细阅读“光滑”“粗糙”或“空气阻力可忽略”等条件。
6. Work, Energy and Kinetic Energy | 功、能量与动能
Work is done when a force moves its point of application in the direction of the force. Work is a scalar and is measured in joules.
当力的作用点沿力的方向移动时，力做功。功是标量，单位为焦耳。
W = F d cos θ
Kinetic energy is the energy possessed by a moving object. It is given by the equation below.
动能是运动物体具有的能量，公式如下。
KE = ½mv²
When a resultant force does work on an object, the work done is equal to the change in kinetic energy. This is the work–energy principle.
当合力对物体做功时，所做的功等于动能的变化量。这就是功–能原理。
Wₙₑₜ = ΔKE = ½mv² − ½mu²
This principle is especially useful for solving problems where the force is not constant, or where acceleration is not needed directly.
功–能原理在力不恒定或不需要直接求加速度的问题中特别有用。
7. Gravitational Potential Energy and Conservation | 重力势能与能量守恒
Gravitational potential energy is the energy stored by an object because of its height above a reference level. It is calculated using the equation below.
重力势能是物体因高于参考水平面而储存的能量，计算公式如下。
GPE = m g h
If there is no work done against friction or air resistance, the total mechanical energy is conserved. Kinetic energy and gravitational potential energy can be exchanged freely.
如果没有克服摩擦或空气阻力做功，总机械能守恒。动能和重力势能可以相互转化。
KE₁ + GPE₁ = KE₂ + GPE₂
When friction is present, some mechanical energy is transferred to internal energy, usually as heat or sound. In these cases, use the work–energy principle rather than conservation of mechanical energy.
当存在摩擦时，部分机械能转化为内能，通常表现为热或声。在这种情况下应使用功–能原理，而不是机械能守恒。
Always define the reference level for GPE before starting a calculation, because GPE depends on the chosen zero point.
计算前一定要规定重力势能的参考水平面，因为重力势能取决于所选的零点。
8. Power and Efficiency | 功率与效率
Power is the rate of doing work or the rate of transferring energy. It is measured in watts, where 1 W = 1 J s⁻¹.
功率是做功或能量转移的速率，单位为瓦特，1 W = 1 J s⁻¹。
P = W / t
For a constant force acting on an object moving at constant speed v, power can also be written as the product of force and velocity.
对于恒力作用在匀速运动物体上的情况，功率还可以写成力与速度的乘积。
P = F v
Efficiency compares useful output energy or power with total input energy or power. It is usually expressed as a percentage.
效率将有用的输出能量或功率与总输入能量或功率进行比较，通常用百分比表示。
Efficiency = (useful output energy / total input energy) × 100%
Efficiency can never be greater than 100% because energy cannot be created. Most real machines lose some energy to friction, sound or heat.
效率不可能超过 100%，因为能量不能被创造。大多数真实机器都会因摩擦、声音或热损失部分能量。
9. Momentum and Impulse | 动量与冲量
Momentum is a vector quantity defined as the product of mass and velocity. It is measured in kg m s⁻¹ or N s.
动量是矢量，定义为质量与速度的乘积，单位为 kg m s⁻¹ 或 N s。
p = m v
Impulse is the change in momentum of an object, and it is also equal to the force applied multiplied by the time for which it acts.
冲量是物体动量的变化量，也等于施加的力乘以作用时间。
Impulse = F Δt = Δ(mv)
The area under a force–time graph gives the impulse. This is useful when the force changes over time, such as in a kick or collision.
力–时间图下方的面积表示冲量。当力随时间变化时，例如踢球或碰撞，这个方法非常有用。
Remember that momentum is a vector, so you must assign positive and negative directions in any problem involving opposite velocities.
请记住动量是矢量，因此在涉及相反速度的问题中必须规定正方向和负方向。
10. Conservation of Momentum and Collisions | 动量守恒与碰撞
In a closed system with no external resultant force, the total momentum before an event is equal to the total momentum after the event. This applies to collisions and explosions.
在没有外力合力的封闭系统中，事件前后的总动量相等。这适用于碰撞和爆炸。
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In perfectly elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not.
在完全弹性碰撞中，动量和动能都守恒。在非弹性碰撞中，动量守恒但动能不守恒。
When two objects stick together after a collision, the collision is completely inelastic. You can still use conservation of momentum because kinetic energy is lost to heat, sound or deformation.
当两个物体碰撞后粘在一起时，碰撞是完全非弹性的。你仍然可以使用动量守恒，因为动能已经转化为热、声或形变能。
In explosion problems, the total momentum before the explosion is often zero, so the fragments must fly apart with equal and opposite momenta.
在爆炸问题中，爆炸前的总动量通常为零，因此碎片必须以大小相等、方向相反的动量飞散。
11. Moments and Equilibrium | 力矩与平衡
The moment of a force about a point is the force multiplied by the perpendicular distance from the point to the line of action of the force.
力对某点的力矩等于力与该点到力的作用线的垂直距离的乘积。
Moment = F × d
For an object in static equilibrium, two conditions must be satisfied: the resultant force is zero and the resultant moment about any point is zero.
物体处于静力平衡时，必须满足两个条件：合力为零，以及对任意点的合力矩为零。
When choosing a point to take moments about, pick the point where an unknown force acts. This removes that unknown force from the moment equation and simplifies the algebra.
选择取矩点时，应选未知力作用点。这样该未知力就在力矩方程中消失，简化计算。
Common exam questions involve beams, ladders, bridges or signposts with one or two supports. Always draw the forces clearly and mark distances from the pivot.
常见考题涉及梁、梯子、桥梁或指示牌，带有一个或两个支撑点。一定要清楚画出各力，并标出到支点的距离。
12. Exam Technique and Common Errors | 考试技巧与常见错误
Before any calculation, write down the given quantities with units and choose a positive direction. This reduces sign errors in forces, velocities and momenta.
在任何计算之前，先写下已知量及单位，并规定正方向。这样可以减少力、速度和动量中的符号错误。
Common errors include using the vertical component instead of the horizontal, forgetting to square velocity in kinetic energy, and mixing up mass and weight. A weight force is always mg, not mass.
常见错误包括：用了竖直分量而不是水平分量、动能公式中忘记对速度平方、混淆质量和重力。重力始终是 mg，不是质量。
Check that your final answer has the correct unit and a sensible magnitude. For example, a car acceleration of 500 m s⁻² is almost certainly wrong in a road-traffic question.
检查最终答案的单位是否合理、数量级是否正常。例如，道路交通问题中汽车加速度为 500 m s⁻² 几乎肯定是错误的。
Finally, show all steps clearly in structured answers. Even if the final answer is wrong, you can gain method marks for writing the correct equation and substituting correctly.
最后，结构化作答时要展示所有步骤。即使最终答案错误，写出正确方程并正确代入也能获得方法分。
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