Understanding and Applying Newton's Third Law | 牛顿第三定律的理解与应用

📚 Understanding and Applying Newton’s Third Law | 牛顿第三定律的理解与应用

Newton’s third law of motion is one of the most fundamental principles in physics, yet it is often misunderstood. This article will clarify its true meaning, distinguish it from balanced forces, and demonstrate its practical applications in everyday life and advanced mechanics.

牛顿第三定律是物理学中最基本的原则之一，但它常常被误解。本文将澄清其真正含义，区分它与平衡力的不同，并展示它在日常生活和高等力学中的实际应用。

1. Statement of Newton’s Third Law | 牛顿第三定律的表述

Newton’s third law states: ‘If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.’ Mathematically, this is written as:

牛顿第三定律表述为：’如果物体 A 对物体 B 施加一个力，那么物体 B 必然对物体 A 施加一个大小相等、方向相反的力。’ 用数学式表示为：

F₁₂ = −F₂₁

Here, F₁₂ is the force exerted by A on B, and F₂₁ is the force exerted by B on A. The minus sign indicates opposite direction. These two forces always come in pairs and act on different objects.

其中 F₁₂ 是 A 对 B 的力，F₂₁ 是 B 对 A 的力。负号表示方向相反。这两个力总是成对出现，并且作用在不同的物体上。

2. Characteristics of Action and Reaction Forces | 作用力与反作用力的特点

Action and reaction forces have three key characteristics:

作用力与反作用力具有三个关键特点：

They are equal in magnitude and opposite in direction. | 它们大小相等、方向相反。
They act on two different objects. | 它们作用在两个不同的物体上。
They are of the same type (both contact forces or both field forces) and occur simultaneously. | 它们是同种性质的力（同为接触力或同为场力），并且同时产生、同时消失。

Because the forces act on different objects, they never cancel each other out when considering a single object’s motion.

由于这两个力作用在不同物体上，因此在分析单个物体的运动时，它们绝不会相互抵消。

3. Common Misconceptions | 常见误解

A frequent error is to think that action and reaction forces cancel each other. In fact, cancellation requires forces to act on the same object. Since action and reaction forces act on different bodies, they cannot directly cancel.

一个常见错误是认为作用力与反作用力会相互抵消。实际上，抵消要求两个力作用在同一物体上。由于作用力和反作用力作用在不同物体上，它们不能直接抵消。

Another misconception is that the ‘larger’ or ‘more active’ object exerts a bigger force. For example, when a car hits a wall, many people think the car exerts a greater force on the wall. In reality, the wall exerts exactly the same force on the car, but the car’s greater acceleration change makes the effect more visible.

另一个误解是认为’更大’或’更主动’的物体施加的力更大。例如，当汽车撞墙时，许多人认为汽车对墙施加的力更大。实际上，墙对汽车施加的力完全相同，只是汽车的速度变化更明显，因此效果更显著。

4. Action-Reaction Pairs vs. Balanced Forces | 作用力反作用力对与平衡力的区别

It is essential to distinguish between action-reaction pairs and balanced forces. The table below summarises the differences:

区分作用力反作用力对与平衡力至关重要。下表总结了它们的区别：

Aspect	Action-Reaction Pair	Balanced Forces
Objects	Act on two different objects	Act on the same object
Nature	Same type of force	Can be different types
Effect	Cannot cancel; they cause acceleration of different bodies	Net force is zero; the body remains in equilibrium
Example	Book pulls Earth down; Earth pulls book up	Gravity pulls book down; table pushes book up

In the balanced force example, the book is stationary because the gravitational force and the normal force from the table are equal and opposite on the same object. In the action-reaction example, the book and Earth attract each other, but they act on different objects.

在平衡力的例子中，书静止是因为重力和桌面对书的支持力大小相等、方向相反且作用在同一物体上。在作用力反作用力的例子中，书和地球相互吸引，但这两个力作用在不同物体上。

5. Walking and Standing | 行走与站立中的应用

When you walk, you push backward against the ground with your foot. According to Newton’s third law, the ground pushes forward on your foot with an equal force. This forward push is what propels you ahead. Without friction, walking would be impossible.

当你行走时，你的脚向后蹬地面。根据牛顿第三定律，地面对你的脚施加一个大小相等、方向向前的力。正是这个向前的推力推动你前进。如果没有摩擦力，行走就不可能实现。

Similarly, when you stand still, gravity pulls you downward, and the floor pushes you upward. The pair of forces between you and the floor is an action-reaction pair, while the balance between gravity and the floor’s push on you is a balanced-force situation.

同样地，当你静止站立时，重力向下拉你，地板向上推你。你与地板之间的力是作用力反作用力对，而重力与地板对你的支撑力之间则是平衡力关系。

6. Rockets and Propulsion | 火箭与推进中的应用

Rocket propulsion is a direct application of Newton’s third law. The rocket engine expels hot gas downward at high speed. The gas exerts an upward reaction force on the rocket, causing it to accelerate upward. Even in the vacuum of space, the rocket works because it does not rely on pushing against the ground or air.

火箭推进是牛顿第三定律的直接应用。火箭发动机向下高速喷出高温气体，气体对火箭产生一个向上的反作用力，使火箭向上加速。即使在太空真空中，火箭也能工作，因为它并不依赖推地面或空气。

F_rocket on gas = −F_gas on rocket

This principle is also used in jet engines and even in the swimming of squid and jellyfish, which eject water to move forward.

这一原理也用于喷气发动机，甚至用于鱿鱼和水母的游动，它们通过喷水来前进。

7. Collisions and Impacts | 碰撞与冲击中的应用

During a collision, two objects exert equal and opposite forces on each other for the same amount of time. This is why a cricket ball hitting a bat deforms, and the bat exerts the same force back on the ball. The effects differ because the masses and structural properties of the objects differ.

在碰撞过程中，两个物体在相同时间内相互施加大小相等、方向相反的力。这就是为什么板球撞击球拍时球会发生形变，而球拍也对球施加同样的力。效果不同是因为两个物体的质量和结构特性不同。

When you catch a ball, you pull your hands backward. This increases the time of impact, reducing the average force on your hands. The impulse-momentum relationship can be expressed as:

当你接球时，手向后收，这增加了撞击时间，从而减小了手受到的平均力。冲量-动量关系可以表示为：

F × Δt = Δ(mv)

A longer impact time Δt reduces the force F for the same change in momentum. This is also why airbags save lives in car accidents.

更长的撞击时间 Δt 在动量变化相同的情况下会减小力 F。这也是安全气囊在车祸中能救人的原因。

8. Connection with Momentum Conservation | 与动量守恒的联系

Newton’s third law is the foundation of the law of conservation of momentum. When two objects interact, the forces between them are equal and opposite and act for the same time. Therefore, the impulses are equal and opposite, so the total momentum of the system remains constant.

牛顿第三定律是动量守恒定律的基础。当两个物体相互作用时，它们之间的力大小相等、方向相反，且作用时间相同。因此，冲量大小相等、方向相反，所以系统的总动量保持不变。

For a two-body system, the conservation law is written as:

对于两体系统，守恒定律可写为：

m₁v₁ + m₂v₂ = m₁v₁’ + m₂v₂’

This applies to explosions, recoil of guns, and all types of collisions, provided no external force acts on the system.

这适用于爆炸、枪支后坐力和所有类型的碰撞，前提是系统不受外力作用。

9. Analysing Systems and Free-Body Diagrams | 系统分析与受力图

To correctly apply Newton’s third law, always draw free-body diagrams for each object separately. First identify the action-reaction pairs between objects. Then determine the net force on the object of interest.

要正确应用牛顿第三定律，务必分别对每个物体画出受力图。首先找出物体之间的作用力反作用力对，然后确定所研究物体上的合力。

Consider a person pushing a trolley. The person exerts a force on the trolley, and the trolley exerts an equal and opposite force on the person. However, when analysing the trolley’s motion, only the force on the trolley matters. The force on the person affects the person’s motion, not the trolley’s.

考虑一个人推手推车。人对车施加一个力，车对人施加一个大小相等、方向相反的力。然而，在分析车的运动时，只有作用在车上的力才重要。作用在人身上的力影响人的运动，而不影响车的运动。

10. Common Exam Pitfalls | 常见考试陷阱

Examiners often design questions to test your understanding of the third law. Here are typical pitfalls:

出题者经常设计问题来考查你对第三定律的理解。以下是常见的陷阱：

Forgetting that action-reaction forces act on different objects. | 忘记作用力反作用力作用在不同物体上。
Confusing the normal force and weight as an action-reaction pair when an object rests on a surface. | 混淆物体静止在平面上时的支持力与重力，误以为它们是作用力反作用力对。
Assuming that a ‘stronger’ object exerts a greater force than a ‘weaker’ object. | 假设’更强的’物体比’更弱的’物体施加更大的力。

Remember that the third law applies to all forces, including friction, tension, normal contact forces, and gravitational forces.

记住，第三定律适用于所有力，包括摩擦力、张力、法向接触力和万有引力。

11. Problem-Solving Strategy | 解题策略

Follow these steps to solve problems involving Newton’s third law:

按照以下步骤来解决涉及牛顿第三定律的问题：

Identify the two interacting objects. | 确定两个相互作用的物体。
Name the force exerted by object A on object B. Then state that the reaction force is exerted by B on A, equal in magnitude and opposite in direction. | 指出物体 A 对物体 B 施加的力，然后说明反作用力由 B 对 A 施加，大小相等、方向相反。
Draw a free-body diagram for each object separately, showing only the forces acting on that object. | 分别对每个物体画受力图，只画作用在该物体上的力。
Apply Newton’s second law (F = ma) to each object to find its acceleration or the unknown forces. | 对每个物体应用牛顿第二定律（F = ma）来求加速度或未知力。
Check that the action-reaction pair has the same sign when written as opposite vectors. | 检查作用力反作用力对在写成相反矢量时是否符号相反。

12. Conclusion | 总结

Newton’s third law is a cornerstone of classical mechanics. Understanding it correctly prevents common errors and enables the analysis of complex systems, from everyday walking to space flight. Keep in mind the key points: forces always occur in pairs, act on different bodies, are equal in magnitude, and opposite in direction.

牛顿第三定律是经典力学的基石。正确理解它能够避免常见错误，并帮助我们分析从日常行走到太空飞行的复杂系统。牢记关键点：力总是成对出现，作用在不同物体上，大小相等、方向相反。

Master this concept, and you will find it easier to solve mechanics problems and to see the physics at work all around you.

掌握这个概念，你会发现解决力学问题更加容易，并能看到周围处处体现的物理原理。

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Understanding and Applying Newton’s Third Law | 牛顿第三定律的理解与应用