Fundamental Concepts of Force and Common Forces | 力的基本概念与常见力

📚 Fundamental Concepts of Force and Common Forces | 力的基本概念与常见力

Force is one of the most fundamental ideas in physics. It governs everything from the fall of an apple to the orbit of planets, and it lies at the very heart of Newtonian mechanics. In this article, we explore the definition, nature, and classification of forces, along with the most common forces encountered in IB Physics.

力是物理学中最基本的概念之一。它支配着从苹果落地到行星轨道的一切运动，是牛顿力学的核心。在本文中，我们将探讨力的定义、本质与分类，并系统介绍IB物理中最常见的几种力。

1. What is a Force? | 什么是力

A force is a push or a pull acting on an object, resulting from its interaction with another object. Forces can cause an object to accelerate, deform, or change direction. In the SI system, force is measured in newtons (N), where 1 N = 1 kg·m/s². The concept of force is closely linked to mass and acceleration through Newton’s second law.

力是一个物体对另一个物体的推或拉，源于物体之间的相互作用。力可以使物体加速、形变或改变运动方向。在国际单位制中，力的单位是牛顿（N），且 1 N = 1 kg·m/s²。力的概念通过牛顿第二定律与质量和加速度紧密相连。

F = ma

This equation tells us that the net force acting on an object equals the product of its mass and its acceleration. If the net force is zero, the object remains at rest or continues moving at constant velocity — a statement that forms the basis of Newton’s first law.

该公式表明，作用在物体上的合力等于其质量与加速度的乘积。若合力为零，物体将保持静止或匀速直线运动——这正是牛顿第一定律的核心内容。

2. Fundamental Properties of Forces | 力的基本性质

Forces are vector quantities, meaning they possess both magnitude and direction. This has several important consequences:

力是矢量，具有大小和方向。这带来几个重要的推论：

Forces obey vector addition rules; the resultant force is found by vector addition, not simple arithmetic.

力遵循矢量加法法则，合力需通过矢量合成而非简单算术相加求得。
Forces always come in pairs according to Newton’s third law: if object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

根据牛顿第三定律，力总是成对出现：若物体A对物体B施力，则物体B必然对物体A施以大小相等、方向相反的力。
To describe a force fully, one must specify its magnitude, direction, and point of application.

完整描述一个力，需要指明其大小、方向和作用点。

3. Contact Forces vs. Non-Contact Forces | 接触力与非接触力

Forces can be broadly divided into two categories based on whether physical contact is required.

根据是否需要直接接触，力可分为两大类。

Contact forces arise from direct physical interaction between objects. Examples include friction, tension, normal force, and air resistance. These forces are ultimately electromagnetic in origin, arising from the interactions between atoms at the surfaces of objects.

接触力源于物体间的直接物理接触，例如摩擦力、张力、法向力和空气阻力。这类力本质上是电磁力的宏观表现，源于物体表面原子间的相互作用。

Non-contact forces act at a distance without any physical contact. The most important examples are gravitational force, electrostatic force, and magnetic force. In IB Physics, gravitational force is particularly significant because it governs the motion of objects near Earth’s surface and throughout the universe.

非接触力无需接触即可作用于远处物体，最重要的例子是万有引力、静电力和磁力。在IB物理中，引力尤为重要，因为它主宰着地球表面附近物体乃至整个宇宙中天体的运动。

4. Gravitational Force | 重力与万有引力

Every object with mass attracts every other object with mass. For objects near the Earth’s surface, this gravitational attraction produces a force we call weight. The weight of an object is calculated as:

任何有质量的物体都会相互吸引。对于地球表面附近的物体，这种引力作用产生了我们称之为重力的力。物体的重量（重力）计算如下：

F_g = mg

Here, m is the mass of the object in kilograms, and g is the gravitational field strength, approximately 9.8 N/kg (or 9.8 m/s²) on Earth. Importantly, mass is a scalar quantity representing the amount of matter in an object, while weight is a force vector pointing toward the centre of the Earth.

其中 m 是物体的质量（单位：千克），g 是重力场强度，在地球表面约为 9.8 N/kg（即 9.8 m/s²）。需要特别注意的是，质量是标量，表示物体所含物质的多少；而重力是矢量，方向指向地心。

For larger distances, the universal law of gravitation applies:

对于更远的距离，则需应用万有引力定律：

F = G·m₁m₂ / r²

where G = 6.674 × 10⁻¹¹ N·m²/kg², and r is the distance between the centres of the two masses.

其中 G = 6.674 × 10⁻¹¹ N·m²/kg²，r 为两物体质心之间的距离。

5. Normal Force | 法向力（支持力）

The normal force is the perpendicular force exerted by a surface on an object in contact with it. It is called “normal” because in mathematics and physics, “normal” means perpendicular to a surface. The normal force prevents objects from falling through surfaces.

法向力是表面对与之接触的物体施加的垂直于接触面的力。在数学和物理学中，“法向”即“垂直”之意。法向力防止物体穿透表面下落。

The magnitude of the normal force is not always equal to the weight of the object. On an inclined plane, for instance, the normal force equals mg·cos θ, where θ is the angle of inclination. If additional vertical forces are applied, the normal force adjusts accordingly. In IB Physics problems, always draw a free-body diagram to determine the correct value of the normal force.

法向力的大小并不总等于物体的重力。例如在斜面上，法向力等于 mg·cos θ，其中 θ 为斜面倾角。若物体还受到其他竖直方向的外力，法向力会相应调整。在IB物理解题中，务必先画受力分析图，以正确确定法向力的值。

6. Friction | 摩擦力

Friction is a resistive force that opposes relative motion between two surfaces in contact. It arises from the microscopic irregularities of surfaces interlocking with each other.

摩擦力是阻碍两个接触表面之间相对运动的阻力，源于表面微观粗糙结构的相互咬合。

There are two main types of friction: static friction and kinetic (dynamic) friction. Static friction acts on objects at rest and prevents them from starting to move. Kinetic friction acts on objects already in motion and opposes their motion. Their maximum values are given by:

摩擦分为两类：静摩擦力和动摩擦力（滑动摩擦力）。静摩擦作用在静止物体上，阻止其开始运动；动摩擦作用在已运动物体上，阻碍其继续运动。两者的最大值分别为：

f_s(max) = μₛN | f_k = μₖN

Here, μₛ is the coefficient of static friction, μₖ is the coefficient of kinetic friction, and N is the normal force. Generally, μₛ > μₖ, meaning it takes more force to start moving an object than to keep it moving. Note that friction depends on the nature of the surfaces and the normal force, but not on the contact area.

其中 μₛ 是静摩擦系数，μₖ 是动摩擦系数，N 为法向力。通常 μₛ > μₖ，即让物体开始运动比维持其运动需要更大的力。值得注意的是，摩擦力与接触面积无关，仅取决于接触面的性质和法向力大小。

7. Tension Force | 张力

Tension is the pulling force transmitted through a rope, string, cable, or any flexible connector when it is pulled taut by forces acting from opposite ends. Tension always acts along the direction of the string and pulls away from the object to which it is attached.

张力是绳子、细线、缆绳等柔性连接物两端受拉时内部传递的拉力。张力始终沿绳子的方向作用，并且对连接物体施加背离物体的拉力。

For a massless, inextensible string, the tension is the same throughout the entire length of the string. This simplification is commonly assumed in IB Physics problems. When a string passes over a frictionless pulley, the tension remains unchanged, allowing us to analyse connected systems easily.

对于无质量、不可伸长的轻绳，绳中各处的张力处处相等。这一简化假设在IB物理解题中被广泛使用。当绳子绕过光滑定滑轮时，张力不发生改变，这使得连接体系统的分析变得简单明了。

8. Resultant Force and Vector Addition | 合力与力的矢量合成

When multiple forces act on a single object, they can be replaced by a single force that produces the same effect. This single force is called the resultant force (or net force). To find the resultant, we use vector addition.

当多个力同时作用于同一物体时，可以用一个具有相同效果的力来替代，这个力称为合力（净力）。求合力需要运用矢量加法。

For forces acting along the same line, simple addition or subtraction suffices. For forces at angles, we use the parallelogram law or break each force into perpendicular components. In two dimensions, a force F at angle θ to the horizontal has components:

对于同一直线上的力，直接相加或相减即可；对于成角度的力，则需使用平行四边形法则或将力分解为相互垂直的分量。在二维平面中，与水平方向成 θ 角的作用力 F 的分量为：

Fₓ = F·cos θ | Fᵧ = F·sin θ

The resultant force is then found using the Pythagorean theorem: R = √(Fₓ² + Fᵧ²), and its direction is tan θ = Fᵧ / Fₓ. This technique is indispensable in solving IB Physics problems involving inclined planes, projectiles, and equilibrium.

合力大小用勾股定理求得：R = √(Fₓ² + Fᵧ²)，方向满足 tan θ = Fᵧ / Fₓ。这一方法在IB物理中处理斜面、抛体运动及平衡问题时不可或缺。

9. Free-Body Diagrams | 受力分析图

A free-body diagram is a simplified sketch showing all the forces acting on a single object. It is the single most powerful tool for solving force problems in IB Physics. In a proper free-body diagram:

受力分析图是仅展示作用于某一物体上所有力的简化示意图，是解决IB物理力学问题最强大的工具。绘制规范受力分析图时：

Represent the object as a dot or a simple box.

将物体表示为一个点或一个简化的方框。
Draw arrows for every force acting on the object, with the arrow direction indicating the force direction and the arrow length proportional to the force magnitude.

用箭头画出作用在物体上的每一个力，箭头方向表示力的方向，长度与力的大小成比例。
Label each force with its name or standard symbol (e.g., F_g, N, T, f).

用名称或标准符号标注每个力（如 F_g、N、T、f）。
Do not include forces the object exerts on other objects, and do not include components unless asked.

不要画出物体施加给其他物体的力，除非题目要求，通常也不在图中画出力的分量。

Once the free-body diagram is drawn, apply Newton’s second law separately along perpendicular axes to solve for unknown quantities.

画好受力分析图后，分别在相互垂直的轴上应用牛顿第二定律，即可解出未知量。

10. Equilibrium: When Forces Balance | 力的平衡

An object is in translational equilibrium when the resultant force acting on it is zero. Mathematically, this means:

当作用于物体上的合力为零时，物体处于平动平衡状态。数学上表示为：

ΣF = 0

Equilibrium can be static (the object is at rest) or dynamic (the object moves at constant velocity). In both cases, the forces balance perfectly. The conditions for equilibrium in two dimensions are:

平衡分为静态平衡（物体静止）和动态平衡（物体匀速运动）。两种情况下力都达到完全平衡。二维平衡条件为：

ΣFₓ = 0 and ΣFᵧ = 0

This principle is crucial for analysing objects on inclined planes, hanging masses, and systems of connected objects. If three forces act on an object in equilibrium, they must form a closed triangle when drawn head-to-tail.

这一原则对分析斜面上的物体、悬挂物以及连接体系统至关重要。若三力使物体平衡，则三力首尾相连必构成闭合三角形。

11. Apparent Weight: Elevator Problems | 表观重力：电梯问题

The sensation of weight arises from the normal force acting on our bodies, not from gravity alone. In an accelerating elevator, the normal force changes, creating an “apparent weight” that differs from actual weight. This is a classic IB Physics application of Newton’s laws.

人对重量的感觉来源于身体受到的法向力，而不仅仅来自重力本身。在加速运动的电梯中，法向力发生变化，产生与真实重力不同的“表观重力”。这是IB物理中应用牛顿定律的经典问题。

Elevator motion 电梯运动状态	Apparent weight 表观重力
At rest or constant velocity 静止或匀速	N = mg
Accelerating upward 加速上升	N = m(g + a)
Accelerating downward 加速下降	N = m(g − a)
Free fall (a = g) 自由落体	N = 0 (weightlessness)

In free fall, the apparent weight becomes zero — this is the state of weightlessness experienced by astronauts, even though gravity still acts on them.

在自由落体中，表观重力变为零——这正是宇航员所体验到的“失重”状态，尽管重力实际上仍然作用在他们身上。

12. Summary and Exam Tips | 总结与备考建议

Force is a vector quantity measured in newtons; it comes in pairs and obeys vector addition. The main forces in IB Physics are gravitational force (weight), normal force, friction, and tension. Mastering free-body diagrams and vector resolution is essential for solving force problems accurately.

力是矢量，单位是牛顿；力总是成对出现，遵循矢量合成法则。IB物理中的主要力包括重力（重量）、法向力、摩擦力和张力。熟练绘制受力分析图并掌握矢量分解是准确解决力学问题的关键。

Always identify all forces acting on the object before writing equations. Missing a force is the most common error.

写方程前务必先找出物体所受的全部力，漏力是最常见的错误。
Choose convenient coordinate axes — often aligning one axis parallel to the direction of motion or the inclined surface.

选择方便的坐标轴——通常让一个轴平行于运动方向或斜面方向。
Remember that the normal force is not always equal to mg; it adjusts to balance perpendicular forces.

切记法向力并不总等于 mg，它会根据垂直方向的力平衡情况进行调整。
Distinguish between mass (scalar, in kg) and weight (vector, in N).

严格区分质量（标量，单位 kg）和重力（矢量，单位 N）。

By mastering these fundamentals, you will build a solid foundation for tackling more advanced topics such as momentum, circular motion, and simple harmonic motion in your IB Physics course.

掌握这些基本概念，你将为进一步学习动量、圆周运动和简谐运动等更高级的IB物理专题打下坚实基础。

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Fundamental Concepts of Force and Common Forces | 力的基本概念与常见力