📚 Combined Science Unit 3: Energy, Forces and Motion | 综合科学第三单元：能量、力与运动
This article provides a comprehensive revision guide for Edexcel International A-Level Combined Science (YCH11) Unit 3: Physics – Energy, Forces and Motion. We break down the key concepts you need to master, from mechanical work and conservation of energy to Newton’s laws and momentum. Each section pairs an English explanation with a Chinese translation, helping you build a solid bilingual understanding for your examinations.
本文为 Edexcel 国际 A-Level 综合科学 (YCH11) 第三单元——物理：能量、力与运动提供全面的复习指南。我们将逐一拆解你需要掌握的核心概念，从机械功和能量守恒到牛顿定律与动量。每一小节都提供了中英对照的讲解，帮你建立扎实的双语理解，从容应对考试。
1. Work and Energy | 功与能
In physics, work is done when a force causes an object to move in the direction of the force. Work (W) is the product of the force (F) and the displacement (s) in the direction of the force: W = F × s. If the force is applied at an angle θ to the displacement, only the component F cos θ does work. The SI unit of work is the joule (J), where 1 J = 1 N m.
在物理学中，当一个力使物体沿力的方向移动时，就做了功。功（W）是力（F）与沿力方向位移（s）的乘积：W = F × s。如果力与位移成角度 θ，则只有分量 F cos θ 做功。功的国际单位是焦耳（J），1 J = 1 N m。
Energy is defined as the capacity to do work. When work is done on an object, energy is transferred to it, often causing an increase in its kinetic or potential energy. Conversely, an object that possesses energy can do work on its surroundings. Understanding the work–energy relationship is fundamental to solving mechanics problems at A-Level.
能量被定义为做功的能力。对一个物体做功时，能量会转移到该物体上，经常使其动能或势能增加。反之，具有能量的物体可以对其周围环境做功。理解功与能的关系是解决 A-Level 力学问题的基础。
| Work Done (Constant Force) | W = F s cos θ |
| Work done by a varying force | Area under force–displacement graph |
2. Conservation of Energy | 能量守恒
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred between different forms. In a closed system, the total energy remains constant. For example, when an object falls under gravity, gravitational potential energy (GPE) is converted into kinetic energy (KE), and the sum remains constant if we ignore air resistance.
能量守恒原理指出，能量既不能被创造也不能被消灭，只能在不同形式之间转移。在一个封闭系统中，总能量保持不变。例如，物体在重力作用下下落时，重力势能（GPE）转化为动能（KE），若忽略空气阻力，总和保持不变。
Common energy transfers you must be able to describe include: chemical energy to kinetic and thermal energy in a car engine; electrical energy to light and heat in a filament lamp; and kinetic energy to electrical energy in a wind turbine. Always consider work done against friction as a pathway for energy to dissipate as thermal energy, leading to a rise in temperature.
你必须能够描述的常见能量转换包括：汽车发动机中化学能转化为动能和热能；白炽灯中电能转化为光和热；风力涡轮机中动能转化为电能。始终要考虑克服摩擦做功是能量以热能形式耗散的途径，从而导致温度升高。
Total initial energy = Total final energy
3. Kinetic and Potential Energy | 动能与势能
Kinetic energy (KE) is the energy an object possesses due to its motion. For an object of mass m moving at speed v, KE = ½ m v². Notice that kinetic energy depends on the square of the speed – doubling the speed quadruples the KE. This has important implications for stopping distances of vehicles.
动能（KE）是物体因运动而具有的能量。对于质量为 m、速度为 v 的物体，KE = ½ m v²。注意动能与速度的平方成正比——速度加倍，动能变为原来的四倍。这对车辆的制动距离有重要意义。
Gravitational potential energy (GPE) is stored energy due to an object’s position in a gravitational field. Near the Earth’s surface, GPE = m g h, where g is the gravitational field strength (9.81 N/kg on Earth) and h is the height above a chosen reference level. The change in GPE depends only on the vertical height gained or lost, not on the path taken.
重力势能（GPE）是因物体在引力场中的位置而储存的能量。在地球表面附近，GPE = m g h，其中 g 是重力场强度（地球上为 9.81 N/kg），h 是相对于选定参考水平面的高度。重力势能的变化只取决于获得或失去的垂直高度，与路径无关。
KE = ½ m v² GPE = m g h
4. Power | 功率
Power is defined as the rate of doing work or the rate of energy transfer. The average power P = W / t or E / t, where W is the work done and t is the time taken. The SI unit of power is the watt (W), equivalent to one joule per second (J/s). A higher power rating means the device transfers energy more quickly.
功率定义为做功的速率或能量转移的速率。平均功率 P = W / t 或 E / t，其中 W 为做功，t 为所用时间。功率的国际单位是瓦特（W），相当于焦耳每秒（J/s）。功率额定值越高，说明设备转移能量的速度越快。
An alternative expression is P = F v for an object moving at constant velocity v under a constant driving force F. This formula is especially useful when analysing the maximum speed of a vehicle given the engine power and resistive forces. In questions involving inclined planes, you may need to resolve forces to find the net driving force before using P = F v.
另一个表达式为 P = F v，适用于在恒定驱动力 F 作用下以恒定速度 v 运动的物体。该公式在分析给定发动机功率和阻力时车辆的最大速度时特别有用。在涉及斜面的问题中，你可能需要先分解力求出净驱动力，再使用 P = F v。
| Power (average) | P = W / t |
| Power (constant force and velocity) | P = F v |
5. Forces and Free-body Diagrams | 力与受力图
A force is a push or pull that can change an object’s motion. Forces are vector quantities: they have both magnitude and direction. Contact forces include tension, friction, normal reaction and air resistance, while non-contact forces include weight (gravitational force), electrostatic and magnetic forces.
力是能够改变物体运动状态的推或拉。力是矢量：它们既有大小又有方向。接触力包括张力、摩擦力、法向反作用力和空气阻力，而非接触力包括重力（引力）、静电力和磁力。
Free-body diagrams are a crucial tool for visualising all forces acting on a single object. Draw arrows to represent each force, labelling them clearly. Always start with weight acting downwards from the centre of mass, then add the normal reaction perpendicular to a surface, and finally frictional or tension forces. Never include forces exerted by the object on other bodies.
受力图是可视化作用在单个物体上所有力的重要工具。用箭头表示每个力，并清楚标注。始终从重心向下的重力开始，然后添加垂直于表面的法向反作用力，最后添加摩擦力或张力。切勿包含该物体施加给其他物体的力。
- Weight: W = m g, always vertically downwards.
- Normal reaction: perpendicular to the contact surface.
- Friction: parallel to the surface, opposing motion or tendency of motion.
- 重力：W = m g，总是竖直向下。
- 法向反作用力：垂直于接触表面。
- 摩擦力：平行于表面，阻碍运动或运动趋势。
6. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law states that an object will remain at rest or move with constant velocity unless acted upon by a resultant external force. This property is known as inertia. In everyday situations, friction often complicates matters, but on an ice rink or in deep space the law is more clearly observed.
牛顿第一定律指出，除非受到合外力的作用，否则物体将保持静止或匀速直线运动状态。这一性质称为惯性。在日常情景中，摩擦力常常使问题复杂化，但在冰场或太空中该定律更容易观察到。
Newton’s Second Law relates the resultant force to the rate of change of momentum. For constant mass systems, it simplifies to F = m a, where a is the acceleration. This is one of the most frequently used equations in mechanics. Always remember that F is the vector sum of all forces acting on the body.
牛顿第二定律将合外力与动量变化率联系起来。对于质量不变的系统，它简化为 F = m a，其中 a 为加速度。这是力学中最常用的方程之一。始终记住 F 是作用在物体上所有力的矢量和。
Newton’s Third Law tells us that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These two forces act on different bodies and are of the same type. Distinguishing between third-law pairs and equilibrium forces is a key skill tested in multiple-choice questions.
牛顿第三定律告诉我们，若物体 A 对物体 B 施加一个力，则物体 B 会对 A 施加一个大小相等、方向相反的力。这两个力作用在不同的物体上，且属于同一类型。区分第三定律中的作用力与反作用力对与平衡力是选择题中考查的关键技能。
F = m a (for constant mass)
7. Momentum and Impulse | 动量与冲量
Linear momentum p is the product of an object’s mass and its velocity: p = m v. Momentum is a vector quantity with direction identical to velocity. The SI unit is kg m/s. Objects with larger mass or higher speed have greater momentum, making it harder to change their state of motion.
线动量 p 是物体质量与速度的乘积：p = m v。动量是矢量，方向与速度相同。国际单位是 kg m/s。质量更大或速度更高的物体具有更大的动量，因此更难改变其运动状态。
Impulse is defined as the change in momentum caused by a resultant force acting over a time interval. From Newton’s second law: Impulse = F Δt = Δp = m v – m u. The impulse–momentum theorem is especially useful when forces vary with time; the impulse equals the area under a force–time graph.
冲量定义为合外力在一段时间间隔内导致的动量变化。由牛顿第二定律：冲量 = F Δt = Δp = m v – m u。冲量-动量定理在力随时间变化时特别有用；冲量等于力-时间图线下方的面积。
Safety features such as airbags and crumple zones are designed to increase the collision time Δt, thereby reducing the average impact force for a given change in momentum. This is a classic application examined regularly at A-Level.
安全气囊和溃缩区等安全设计旨在增加碰撞时间 Δt，从而在动量变化一定时降低平均冲击力。这是 A-Level 考试中经常考查的经典应用。
Impulse = F Δt = Δp
8. Collisions and Conservation of Momentum | 碰撞与动量守恒
In any collision or explosion where no external forces act, the total momentum of the system is conserved. This means total momentum before the event equals total momentum after the event. For two colliding objects of masses m₁ and m₂ with initial velocities u₁ and u₂:
在任何没有外力作用的碰撞或爆炸中，系统的总动量守恒。这意味着事件发生前的总动量等于事件发生后的总动量。对于两个碰撞物体，质量分别为 m₁ 和 m₂，初速度为 u₁ 和 u₂：
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
Collisions are classified as elastic or inelastic. In an elastic collision, both momentum and kinetic energy are conserved – idealised but useful for understanding microscopic interactions. In an inelastic collision, momentum is conserved but kinetic energy is not; some KE is transformed into thermal energy, sound or permanent deformation. If the bodies stick together, the collision is perfectly inelastic and the loss of KE is maximum.
碰撞可分为弹性碰撞和非弹性碰撞。在弹性碰撞中，动量和动能都守恒——这是一种理想化情形，但有助于理解微观相互作用。在非弹性碰撞中，动量守恒，但动能不守恒；部分动能转化为热能、声音或永久形变。若物体粘在一起运动，则为完全非弹性碰撞，动能损失最大。
Explosions are the reverse of collisions: a single object splits into fragments. The total momentum before the explosion is zero (if initially at rest), so the fragments must fly apart in such a way that their vector momenta sum to zero.
爆炸是碰撞的逆过程：一个物体分裂成若干碎片。爆炸前总动量为零（若初始静止），因此碎片必须以矢量动量和为零的方式飞散。
9. Practical Skills and Data Analysis | 实验技能与数据分析
Unit 3 also assesses your understanding of experimental techniques. You must be able to plan investigations, identify independent, dependent and control variables, and evaluate sources of error. Common practicals include measuring acceleration due to gravity using a pendulum or a light gate, and verifying conservation of momentum using an air track and ticker timers.
第三单元还考查你对实验技术的理解。你必须能够规划探究方案，识别自变量、因变量和控制变量，并评估误差来源。常见的实验包括利用单摆或光门测量重力加速度，以及使用气垫导轨和打点计时器验证动量守恒。
When analysing data, plot graphs with appropriate scales and line of best fit. Learn to interpret the gradient and intercept of linear graphs. For example, when plotting distance against time squared for a freely falling object, the gradient equals ½ g. Also be able to describe how to use a light gate and data logger to record velocity and acceleration precisely.
在分析数据时，要选择合适的标度绘制图像并画出最佳拟合线。要学会解读线性图像的斜率和截距。例如，对于自由下落物体绘制距离-时间平方图，斜率等于 ½ g。同样要能够描述如何使用光门和数据记录器精确记录速度和加速度。
Always quote results with the correct number of significant figures and absolute uncertainties. Percentage difference between experimental and accepted values helps evaluate systematic errors. Safety considerations – such as keeping the runway clear and wearing eye protection during spring experiments – should also be included in your write-up.
实验结果的记录应使用正确的有效数字位数和绝对不确定度。通过实验值与公认值之间的百分比差异来评估系统误差。安全注意事项——比如在弹簧实验中保持跑道畅通并佩戴护目镜——也应包括在你的实验报告中。
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