📚 2 Forces | 力
Forces are the fundamental interactions that govern motion, shape and equilibrium in the physical world. This article explores the core concepts of forces as required by the IB Physics syllabus, covering their types, vector nature, Newton’s laws, equilibrium, friction, drag and problem-solving strategies. Understanding these ideas is essential for mastering mechanics and performing well in examinations.
力是支配物理世界中物体运动、形状和平衡状态的基本相互作用。本文根据IB物理课程大纲，深入探讨力的核心概念，涵盖力的类型、矢量本质、牛顿定律、平衡、摩擦力、阻力以及解题策略。理解这些概念是掌握力学并在考试中取得好成绩的关键。
1. What is a Force? | 什么是力？
A force is a vector quantity that can cause an object to accelerate, decelerate, change direction or deform. The SI unit of force is the newton (N), where 1 N = 1 kg m s⁻². Forces are vector quantities, meaning they have both magnitude and direction, and they must be added using vector addition principles.
力是一种矢量，能够使物体加速、减速、改变运动方向或发生形变。国际单位制中力的单位是牛顿（N），1 N = 1 kg m s⁻²。力是矢量，具有大小和方向，必须依据矢量加法原则进行合成。
When several forces act on a single object, we are interested in the net (resultant) force, which is the vector sum of all individual forces. A net force produces acceleration according to Newton’s second law, while zero net force corresponds to translational equilibrium.
当多个力作用于同一物体时，我们关注的是净力（合力），即所有力的矢量和。净力会依据牛顿第二定律产生加速度，而净力为零则对应平动平衡状态。
2. Types of Forces | 力的类型
In mechanics, forces are usually categorised as contact forces (which arise from physical contact) or non-contact forces (which act over a distance). Recognising different force types is crucial for drawing free-body diagrams and applying Newton’s laws correctly.
在力学中，力通常分为接触力（因物体接触而产生）和非接触力（超距作用）。识别不同的力类型对于正确绘制自由体图和应用牛顿定律至关重要。
| Force Type | Description | 常见示例 |
| Weight (W or Fg) | Gravitational pull on an object, W = mg, directed towards the centre of the Earth. | 重力 |
| Normal reaction (N or R) | Force perpendicular to a surface that supports an object. | 法向力 |
| Tension (T) | Pulling force transmitted through a string, rope or cable. | 张力 |
| Friction (f) | Force that opposes relative motion between surfaces; static (fs) and kinetic (fk). | 摩擦力 |
| Drag (FD) | Resistive force experienced by an object moving through a fluid. | 阻力 |
| Spring force (Fs) | Restoring force exerted by a compressed or stretched spring; Hooke’s law: Fs = −kx. | 弹力 |
In problem-solving, always identify all forces acting on the chosen system. Remember that weight acts from the object’s centre of mass, normal force is perpendicular to the contact surface, and tension pulls along the direction of the string.
在解题时，务必找出作用在所选系统上的所有力。记住，重力作用在物体质心，法向力垂直于接触面，而张力沿着绳子方向拉动。
3. Representing Forces: Free-Body Diagrams | 力的表示：自由体图
A free-body diagram (FBD) is a simplified sketch showing a single object isolated from its surroundings, with all external forces acting on it represented by vectors. The length of each vector is proportional to the magnitude of the force, and the direction must be accurate.
自由体图是一种简化示意图，它将一个物体从周围环境中孤立出来，并用矢量表示所有作用在该物体上的外力。每个矢量的长度与力的大小成正比，方向必须准确。
To draw an FBD: represent the object as a point or a simple shape; draw force arrows starting from the object; label each force clearly (e.g., W, N, T, f); and include a coordinate system if needed. Never include forces exerted by the object on its surroundings.
绘制自由体图的步骤：将物体表示为一个点或简单形状；从物体出发画出力的箭头；清楚地标出每个力（例如 W、N、T、f）；必要时加上坐标系。千万不要包含物体对周围环境施加的力。
Well-constructed FBDs help to resolve forces into components and apply Newton’s second law along perpendicular axes. In IB exams, accurately drawn diagrams are often part of the mark scheme.
构建良好的自由体图有助于将力分解为分量，并沿垂直轴应用牛顿第二定律。在IB考试中，准确绘制的图示通常是评分标准的一部分。
4. Newton’s First Law & Inertia | 牛顿第一定律与惯性
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 property of resisting changes in motion is called inertia, and mass is a measure of inertia.
牛顿第一定律指出，除非受到净外力的作用，否则物体将保持静止或匀速直线运动状态。这种抵抗运动状态改变的性质称为惯性，质量是惯性的量度。
When the net force on an object is zero, the object is in translational equilibrium. This can mean the object is stationary or moving with constant velocity. The law highlights that force is not required to maintain motion—only to change it.
当作用在物体上的净力为零时，物体处于平动平衡。这意味着物体可能静止，也可能以恒定速度运动。该定律强调，维持运动并不需要力——力只是用来改变运动状态的。
Common misconception: a moving object needs a forward force to keep going. In reality, in the absence of friction and air resistance, an object would continue moving indefinitely at constant velocity.
常见误区：运动的物体需要持续的向前力才能继续运动。实际上，若没有摩擦力和空气阻力，物体将无限期地以恒定速度运动下去。
5. Newton’s Second Law & Net Force | 牛顿第二定律与净力
Newton’s second law of motion links net force, mass and acceleration. The law is expressed as:
牛顿第二定律将净力、质量和加速度联系起来。该定律表达为：
Fnet = m a
where Fnet is the vector sum of all forces acting on the object, m is the inertial mass, and a is the acceleration vector. The direction of acceleration is always the same as the direction of the net force.
其中 Fnet 是作用在物体上所有力的矢量和，m 是惯性质量，a 是加速度矢量。加速度的方向始终与净力的方向相同。
When solving problems, resolve all forces into perpendicular components (usually horizontal and vertical) and apply the equation independently to each axis. For example, on an inclined plane, one axis is parallel to the slope and the other perpendicular to it.
在解题时，将所有力分解为相互垂直的分量（通常沿水平和竖直方向），并对每个坐标轴独立地应用该方程。例如，在斜面上，一个轴平行于斜面，另一个垂直于斜面。
The proportionality constant between net force and acceleration is mass. A larger mass experiences smaller acceleration for the same net force, illustrating inertia.
净力与加速度之间的比例常数是质量。对于相同的净力，质量越大，加速度越小，这体现了惯性。
6. Newton’s Third Law & Action-Reaction Pairs | 牛顿第三定律与作用力-反作用力对
Newton’s third law states: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These forces are often called action–reaction pairs.
牛顿第三定律指出：如果物体A对物体B施加一个力，那么物体B会对物体A施加一个大小相等、方向相反的力。这两个力常被称为作用力与反作用力对。
Key points: the two forces act on different objects, are of the same type (e.g., both gravitational, both contact), and occur simultaneously. They never cancel each other because they are applied to different bodies.
关键点：这两个力作用在不同的物体上，属于同种类型（例如都是引力，或都是接触力），并且同时产生。它们永远不会相互抵消，因为作用在不同物体上。
Common exam question: ‘Identify the reaction force to the weight of a book on a table.’ The reaction force is the gravitational pull exerted by the book on the Earth, not the normal force from the table. The normal force is the reaction to the book pushing down on the table.
常见考试问题：’找出放在桌上的书本所受重力的反作用力。’反作用力是书本对地球的引力，而不是桌面的法向力。法向力是书本向下压桌面的反作用力。
7. Translational Equilibrium | 平动平衡
An object is in translational equilibrium when the vector sum of all forces acting on it is zero. This condition means the net force is zero, so the object’s velocity remains constant—either zero (static equilibrium) or non-zero constant velocity (dynamic equilibrium).
当作用在物体上的所有力的矢量和为零时，物体处于平动平衡。这一条件意味着净力为零，因此物体的速度保持不变——要么为零（静态平衡），要么为非零恒定速度（动态平衡）。
∑Fx = 0 and ∑Fy = 0
These two scalar equations are used to analyse equilibrium situations. For instance, a lamp hanging from two strings requires the vertical components of tension to balance the weight, and horizontal components to cancel each other.
这两个标量方程用于分析平衡情况。例如，悬挂在两根绳子上的灯需要张力的竖直分量与重力平衡，而水平分量相互抵消。
Equilibrium problems often involve solving simultaneous equations after resolving forces. Mastery of this topic is fundamental for later topics such as moments and static structures.
平衡问题通常涉及分解力之后联立解方程。掌握这一主题对学习力矩和静定结构等后续内容至关重要。
8. Friction: Static and Kinetic | 摩擦力：静摩擦与动摩擦
Friction is a force that opposes relative motion between two surfaces in contact. Static friction (fs) acts when there is no relative motion, while kinetic (or dynamic) friction (fk) acts when surfaces slide past each other.
摩擦力是阻碍两个接触表面相对运动的力。当没有相对运动时产生静摩擦力（fs），当表面相互滑动时产生动摩擦力（或滑动摩擦力，fk）。
The magnitude of static friction can vary from zero up to a maximum value: fs,max = μs N, where μs is the coefficient of static friction and N is the normal reaction. Kinetic friction has a nearly constant magnitude: fk = μk N.
静摩擦力的大小可以从零变化到最大值：fs,max = μs N，其中 μs 是静摩擦系数，N 是法向力。动摩擦力的大小几乎恒定：fk = μk N。
Generally, μs > μk, meaning it is harder to initiate sliding than to maintain it. Friction does not depend significantly on the apparent contact area, only on the normal force and the nature of the surfaces.
通常 μs > μk，意味着开始滑动比维持滑动更难。摩擦力与表观接触面积关系不大，主要取决于法向力和表面性质。
9. Drag Forces & Terminal Velocity | 阻力与终极速度
When an object moves through a fluid (liquid or gas), it experiences a resistive drag force. At low speeds, drag is approximately proportional to velocity; at higher speeds, it is often proportional to the square of velocity.
当物体在流体（液体或气体）中运动时，会受到一个阻碍运动的阻力。在低速下，阻力大约与速度成正比；在较高速度下，阻力通常与速度的平方成正比。
Consider a skydiver falling from rest. Initially, weight is the only significant force, so acceleration is g. As speed increases, air resistance grows until it balances weight. At this point, net force is zero, and the skydiver reaches terminal velocity, falling at constant speed.
考虑从静止下落的跳伞者。最初，重力是唯一显著的力，加速度为 g。随着速度增加，空气阻力增大，直到与重力平衡。此时净力为零，跳伞者达到终极速度，以恒定速度下落。
Terminal velocity depends on mass, cross-sectional area and shape of the object. The concept is important in explaining motion through fluids and in designing vehicles and sports equipment.
终极速度取决于物体的质量、横截面积和形状。这一概念对于解释流体中物体的运动以及交通工具和运动器材的设计都很重要。
10. Tension, Normal Force & Springs | 张力、法向力与弹簧
Tension is the force transmitted through a string, rope or cable when it is pulled tight by forces acting from opposite ends. In ideal strings (light, inextensible), tension is the same throughout the string and acts parallel to the string away from the object.
张力是通过绳子、绳索或缆绳在两端受到拉力时传递的力。对于理想绳（轻质、不可伸长），绳上各点的张力大小相等，且方向沿着绳子背离物体。
The normal reaction force arises when two surfaces are pressed together. It is always perpendicular to the surface and adjusts its magnitude to prevent interpenetration. On an inclined plane, the normal force equals the component of weight perpendicular to the surface: N = mg cos θ.
法向反作用力是当两个表面压在一起时产生的。它始终垂直于该表面，并调整其大小以防止物体相互穿透。在斜面上，法向力等于重力垂直于表面的分量：N = mg cos θ。
Springs exert a restoring force according to Hooke’s law: Fs = –k x, where k is the spring constant and x is the extension or compression from natural length. The negative sign indicates that the force opposes the displacement. This model is used extensively in simple harmonic motion.
弹簧依据胡克定律施加恢复力：Fs = –k x，其中 k 是劲度系数，x 是相对于原长的伸长量或压缩量。负号表示力与位移方向相反。这一模型广泛应用于简谐运动。
11. Solving Force Problems | 解决力的问题
A systematic approach to force problems is essential for success. Follow these steps: 1) Identify the object(s) of interest. 2) Draw a clear free-body diagram for each object. 3) Choose a convenient coordinate system and resolve forces into components. 4) Apply Newton’s second law (∑F = m a) along each axis. 5) Use any additional constraint equations (e.g., kinematics, friction laws). 6) Solve the equations algebraically before substituting numbers.
系统地处理力的问题是成功的关键。遵循以下步骤：1) 确定研究对象。2) 为每个物体绘制清晰的自由体图。3) 选择合适的坐标系，并将力分解为分量。4) 沿各个轴应用牛顿第二定律 (∑F = m a)。5) 使用任何附加的约束方程（例如运动学方程、摩擦定律）。6) 先进行代数解算，再代入数字。
Common pitfalls include forgetting to include all forces, using the wrong sign for components, confusing mass and weight, and misidentifying Newton’s third law pairs. Practising a variety of questions—inclined planes, pulleys, elevators, connected bodies—builds confidence.
常见误区包括遗漏某些力、分量符号错误、混淆质量和重量、以及错误识别牛顿第三定律中的力对。通过练习斜面、滑轮、电梯、连接体等各种题目，可以建立信心。
When tackling multiple-object systems, you may need to treat each object separately and then link their motions through common acceleration or tension. Selecting the system cleverly can simplify the equations.
解决多物体系统问题时，可能需要分别处理每个物体，然后通过共同的加速度或张力将它们联系起来。巧妙地选择系统可以简化方程。
12. Summary & Exam Tips | 总结与考试技巧
This article has covered the nature of forces, their vector addition, Newton’s three laws, equilibrium, friction, drag and common force types. A deep understanding of these concepts forms the backbone of mechanics and is frequently assessed through calculation, explanation and diagram questions.
本文涵盖了力的本质、矢量合成、牛顿三大定律、平衡、摩擦力、阻力以及常见力类型。深刻理解这些概念构成了力学的支柱，考试中常通过计算、解释和作图题目来评估这些知识。
In the exam: always draw a free-body diagram even if it is not asked for; clearly state Newton’s laws by name when using them; watch for ‘constant velocity’ meaning a = 0; and distinguish between static and kinetic friction. Use appropriate significant figures and show units throughout your working.
考试中：即使题目未要求，也要画出自由体图；运用牛顿定律时明确写出定律名称；留意’恒定速度’意味着 a = 0；区分静摩擦与动摩擦。使用恰当的有效数字，并在解题过程中一直标注单位。
Above all, practice linking theoretical understanding to real-world situations—a hallmark of IB assessment. Recognising forces in everyday contexts, from a car turning a corner to a parachutist reaching terminal velocity, will help you master this topic.
最重要的是，要练习将理论理解与实际情境联系起来——这是IB评价的显著特点。在日常情境中识别力，从汽车转弯到跳伞者达到终极速度，将有助于你精通这一专题。
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