IB Physics: Core Concepts of Force Analysis and Newton’s Laws of Motion | IB物理：受力分析与牛顿运动定律核心要点

📚 IB Physics: Core Concepts of Force Analysis and Newton’s Laws of Motion | IB物理：受力分析与牛顿运动定律核心要点

In IB Physics, understanding force analysis and Newton’s laws of motion is foundational for solving mechanics problems. This article consolidates the essential points, including free-body diagrams, the three laws, common force types, and practical problem-solving strategies, to help you master this core topic.

在IB物理中，理解受力分析与牛顿运动定律是解决力学问题的基石。本文整合了核心要点，包括受力分析图、三大定律、常见力类型以及实用的解题策略，帮助你掌握这一核心主题。

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1. What Is Force Analysis? | 什么是受力分析？

Force analysis is the process of identifying all forces acting on a body and representing them in a vector diagram. It is the first step in applying Newton’s laws to a physical situation.

受力分析是确定作用在物体上的所有力并用矢量图表示的过程。这是将牛顿定律应用于物理情境的第一步。

When performing force analysis, you must consider both contact forces (e.g., normal force, friction, tension) and non-contact forces (e.g., gravitational force, electromagnetic force). The object of interest should be isolated; only forces acting on that object are included, not forces it exerts on others.

进行受力分析时，必须同时考虑接触力（如支持力、摩擦力、张力）和非接触力（如重力、电磁力）。应隔离研究对象；只包括作用在该物体上的力，而不包括它施加给其他物体的力。

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2. Free-Body Diagrams | 受力分析图

A free-body diagram (FBD) is a simplified drawing showing the object as a point particle, with all external forces drawn as arrows originating from the centre. The length of each arrow should be proportional to the magnitude of the force, and the direction must be accurate.

受力分析图（FBD）是一种简化的图示，将物体视为质点，所有外力以箭头形式从中心发出。箭头的长度应与力的大小成比例，方向必须准确。

Steps to draw a good FBD:

绘制受力分析图的步骤：

• Isolate the object and draw it as a dot or a simple shape. | 隔离物体，将其画成一个点或一个简单的形状。
• Identify all forces acting on the object. | 找出所有作用在物体上的力。
• Draw arrows for each force, with labels (e.g., Fg, FN, FT, Ff). | 为每个力画箭头并标注（如 Fg、FN、FT、Ff）。
• Choose a coordinate system (usually x-y or along-incline-perpendicular-to-incline). | 选择坐标系（通常为 x-y 或沿斜面-垂直斜面）。
• Resolve forces into components if they are not aligned with the axes. | 如果力不与坐标轴对齐，将其分解为分量。

Common mistake: Including forces that the object exerts on other objects, or omitting forces like air resistance when it is significant. Always ask: “What is touching the object?” and “What is acting at a distance?”

常见错误：包括物体对其他物体施加的力，或在空气阻力显著时忽略了它。始终问自己：“什么在接触物体？”以及“什么在超距作用？”

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3. Newton’s First Law of Motion | 牛顿第一定律

Newton’s first law states that an object remains at rest or in uniform motion in a straight line unless acted upon by a net external force. This is also known as the law of inertia.

牛顿第一定律指出，除非受到合外力的作用，否则物体保持静止或沿直线做匀速运动。这也被称为惯性定律。

Inertia is the tendency of an object to resist changes in its state of motion. The mass of an object is a measure of its inertia; larger mass means greater resistance to acceleration.

惯性是物体抵抗运动状态变化的趋势。物体的质量是其惯性的量度；质量越大，抵抗加速度的能力越强。

For example, a passenger lurching forward when a bus suddenly stops is due to inertia — the passenger’s body tends to maintain its forward velocity while the bus decelerates.

例如，当公交车突然刹车时，乘客前倾是因为惯性——乘客的身体倾向于保持向前的速度，而公交车在减速。

Mathematically, if the net force is zero, the acceleration is zero:

数学上，若合力为零，则加速度为零：

ΣF = 0 → a = 0

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4. Newton’s Second Law of Motion | 牛顿第二定律

Newton’s second law establishes the relationship between net force, mass, and acceleration. The net force acting on an object is equal to the product of its mass and its acceleration, and the acceleration is in the same direction as the net force.

牛顿第二定律建立了合力、质量与加速度之间的关系。作用在物体上的合力等于其质量与加速度的乘积，且加速度的方向与合力方向相同。

In equation form:

其方程形式为：

F_net = m × a

This vector equation can be resolved into components. In two dimensions:

该矢量方程可以分解为分量形式。在二维情况下：

ΣFx = m × ax , ΣFy = m × ay

It is important to remember that F_net is the vector sum of all forces, not any individual force. The unit of force is the newton (N); 1 N = 1 kg·m·s⁻².

必须记住，F_net 是所有力的矢量和，而非某个单独的力。力的单位是牛顿（N）；1 N = 1 kg·m·s⁻²。

Example: A 2.0 kg box is pulled horizontally with a force of 10 N, and friction opposes it with 4 N. The net force is 6 N, so the acceleration is a = 6 N / 2.0 kg = 3.0 m·s⁻².

例如：一个2.0 kg的木箱在水平方向被10 N的力拉动，摩擦力为4 N。合力为6 N，因此加速度 a = 6 N / 2.0 kg = 3.0 m·s⁻²。

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5. Newton’s Third Law of Motion | 牛顿第三定律

Newton’s third law states that for every action force, there is an equal and opposite reaction force. These two forces act on different objects, so they never cancel each other out.

牛顿第三定律指出，每一个作用力都有一个大小相等、方向相反的反作用力。这两个力作用在不同的物体上，因此它们永远不会相互抵消。

For example, when you push against a wall, the wall pushes back on you with the same magnitude but opposite direction. When a rocket expels gas downward, the gas exerts an upward force on the rocket.

例如，当你推墙时，墙以相同大小但相反的方向推你。当火箭向下喷出气体时，气体对火箭施加向上的力。

Critical distinction: In Newton’s third law, action-reaction pairs involve the same type of force (e.g., gravitational-gravitational, normal-normal). They act on different bodies. This is different from forces on the same object that may be equal and opposite in equilibrium (e.g., weight and normal force acting on a book on a table), which are not action-reaction pairs.

关键区别：在牛顿第三定律中，作用力-反作用力对涉及同种类型的力（如引力-引力、支持力-支持力）。它们作用在不同的物体上。这与作用在同一物体上且大小相等、方向相反的平衡力（如放在桌上的书受到的重力和支持力）不同，后者不是作用力-反作用力对。

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6. Types of Forces You Must Know | 必须掌握的力的类型

In IB mechanics problems, the following forces appear frequently:

在IB力学问题中，以下力经常出现：

Force | 力	Symbol | 符号	Direction | 方向	Key Formula | 关键公式
Weight | 重力	Fg or W	Downward toward Earth’s centre | 竖直向下指向地心	Fg = m × g (g ≈ 9.8 m·s⁻²)
Normal force | 支持力	FN	Perpendicular to the contact surface | 垂直于接触面	Varies; often equals component of weight perpendicular to surface | 可变；通常等于重力垂直于表面的分量
Friction | 摩擦力	Ff	Opposes relative motion or attempted motion | 阻碍相对运动或运动趋势	Ff ≤ μ × FN (kinetic: Ff = μk × FN)
Tension | 张力	FT	Along the rope/string, pulling away from the object | 沿绳/弦方向，远离物体	Same magnitude throughout an ideal (massless, inextensible) rope | 理想（无质量、不可伸长）绳上各处大小相等
Applied force | 施加力	Fapp or F	Whatever direction it is applied | 施加的任意方向	Given or determined from other conditions | 由已知条件或其它条件确定

Remember: The normal force is not always equal to the weight. On an inclined plane, FN = m × g × cos θ. If there is an additional vertical force, the normal force adjusts accordingly.

记住：支持力并不总是等于重力。在斜面上，FN = m × g × cos θ。如果有额外的竖直方向的力，支持力也会相应调整。

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7. Applying Newton’s Laws in 1D and 2D | 牛顿定律在一维和二维中的应用

For one-dimensional problems, choose a positive direction and write ΣF = m × a along that axis. All forces in the opposite direction are taken as negative.

对于一维问题，选择一个正方向，并沿该方向写出 ΣF = m × a。相反方向的所有力取负值。

For two-dimensional problems, resolve forces into perpendicular components, usually horizontal and vertical, or parallel and perpendicular to an inclined surface. Then apply Newton’s second law separately along each axis.

对于二维问题，将力分解为垂直分量，通常是水平和竖直，或平行和垂直于斜面。然后沿每个轴分别应用牛顿第二定律。

Example of a box on an incline:

斜面上木箱的例子：

Consider a mass m on a frictionless incline of angle θ. The weight

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