Identification and Analysis of Common Forces | 常见力的识别与分析

📚 Identification and Analysis of Common Forces | 常见力的识别与分析

In A-Level Physics, one of the most fundamental skills is to correctly identify the forces acting on an object and to analyse their effects. Forces are vector quantities, meaning both magnitude and direction matter. This article provides a systematic guide to recognising and analysing the common forces you will meet in CIE A-Level Physics, including weight, normal contact forces, friction, tension, elasticity, drag, and buoyancy.

在 A-Level 物理中，最基本的技能之一就是正确识别作用在物体上的力并分析它们的效果。力是矢量，大小和方向都很重要。本文系统介绍 CIE A-Level 物理中常见的力，包括重力、法向接触力、摩擦力、张力、弹力、阻力和浮力，教你如何识别和分析它们。

1. What is a Force? | 什么是力？

A force is a push or pull that can change an object’s state of motion or shape. In SI units, force is measured in newtons (N). According to Newton’s second law, the net force on an object is equal to the rate of change of its momentum; for constant mass, this simplifies to \( F = ma \). However, you should never rely on the formula alone — physical identification of the force is the first step.

力是能够改变物体运动状态或形状的推或拉。在国际单位制中，力的单位是牛顿（N）。根据牛顿第二定律，物体所受合力等于其动量的变化率；当质量恒定时，简化为 F = ma。但是，不要只依赖公式——首先要在物理上识别出力。

2. Weight (Gravitational Force) | 重力（重量）

Weight is the gravitational force exerted by a planet on an object. It always acts towards the centre of the planet, i.e. vertically downward. The magnitude is \( W = mg \), where \( m \) is mass in kilograms and \( g \) is the gravitational field strength (approximately 9.81 N kg⁻¹ near the Earth’s surface).

重力是行星对物体施加的万有引力。它总是朝向行星中心，即竖直向下。大小为 W = mg，其中 m 是以千克为单位的质量，g 是重力场强度（地球表面附近约为 9.81 N kg⁻¹）。

Identify weight whenever an object has mass and is within a gravitational field.

只要物体有质量并且处于重力场中，就存在重力。
Weight is measured with a balance or a spring scale, but the scale reading is the normal force or tension required to support the object.

重力可用天平或弹簧秤测量，但秤的读数实际上是支撑物体所需的法向力或张力。
Weight is not the same as mass; mass is a scalar quantity, weight is a vector.

重量不等于质量；质量是标量，重量是矢量。

3. Normal Contact Force | 法向接触力

The normal force (often denoted \( N \) or \( R \)) is the perpendicular component of the contact force exerted by a surface on an object. It prevents the object from penetrating the surface. The normal force is always perpendicular to the surface, not necessarily vertical.

法向力（通常用 N 或 R 表示）是表面对物体施加的接触力中垂直于表面的分量。它阻止物体穿透表面。法向力总是垂直于表面，不一定是竖直的。

On a horizontal plane with no vertical acceleration, \( N = mg \).

在水平面上且无竖直加速度时，N = mg。
On an inclined plane of angle \( \theta \), \( N = mg\cos\theta \).

在倾角为 θ 的斜面上，N = mg cosθ。
If an additional force pushes the object into the surface, the normal force increases accordingly.

如果另有额外的力将物体压向表面，法向力会相应增大。
The normal force is not a “reaction” to weight in a strict Newton-third-law sense; it is a separate contact force.

严格来说，法向力并不是重力在牛顿第三定律意义上的“反作用力”；它是一种独立的接触力。

4. Friction | 摩擦力

Friction is the component of the contact force that acts parallel to the surface, opposing relative motion (or attempted motion) between two surfaces. There are two main types: static friction and kinetic (sliding) friction.

摩擦力是接触力中平行于表面的分量，它阻碍两个表面之间的相对运动（或企图发生的运动）。主要有两种类型：静摩擦力和动摩擦力（滑动摩擦力）。

Type \| 类型	Magnitude \| 大小	Direction \| 方向
Static friction \| 静摩擦力	0 ≤ f ≤ μₛN	Opposes attempted motion \| 阻碍运动的企图
Kinetic friction \| 动摩擦力	fₖ = μₖN	Opposes actual relative motion \| 阻碍实际相对运动

Here μₛ and μₖ are the coefficients of static and kinetic friction, and \( N \) is the normal force. Generally, μₖ is less than μₛ.

其中 μₛ 和 μₖ 分别是静摩擦系数和动摩擦系数，N 是法向力。通常 μₖ 小于 μₛ。

5. Tension | 张力

Tension is the pulling force transmitted through a string, rope, cable, or wire when it is stretched. It acts along the direction of the string, away from the object to which the string is attached. An ideal string is massless and inextensible, so the tension is constant throughout the string.

张力是绳子、绳索、缆线或金属丝被拉伸时沿其方向传递的拉力。它沿着绳子的方向，指向远离所连接物体的方向。理想绳子的质量可忽略且不可伸长，因此张力在整个绳子上处处相等。

Tension always pulls, never pushes.

张力只能拉，不能推。
For a suspended object at rest, the tension equals the weight of the object if the rope is vertical and only two forces act.

对于静止悬挂的物体，如果绳子竖直且只受两个力，则张力等于物体的重量。
In a pulley system, the tension may be the same on both sides of a smooth, massless pulley.

在滑轮系统中，如果是光滑且无质量的滑轮，两侧的张力相同。
When drawing free-body diagrams, show the tension force pointing along the rope and away from the object.

画受力分析图时，张力应沿绳子方向指向远离物体。

6. Elastic Force and Hooke’s Law | 弹力与胡克定律

An elastic material exerts a restoring force when deformed. For a spring or wire that obeys Hooke’s law, the force is proportional to the extension: \( F = kx \), where \( k \) is the spring constant (N m⁻¹) and \( x \) is the extension from the natural length.

弹性材料在形变时会产生恢复力。对于遵守胡克定律的弹簧或金属丝，力与伸长量成正比：F = kx，其中 k 是劲度系数（N m⁻¹），x 是从自然长度算起的伸长量。

The direction of the elastic force is always towards the equilibrium position (restoring force).

弹力的方向总是指向平衡位置（它是恢复力）。
Hooke’s law only applies up to the limit of proportionality.

胡克定律只在比例限度内适用。
For a spring in series, the effective spring constant is smaller; for parallel springs, it is larger.

串联弹簧的等效劲度系数更小；并联弹簧的等效劲度系数更大。

F = kx

7. Air Resistance and Drag | 空气阻力与阻力

Air resistance (also called drag) is the resistive force exerted by a fluid on a moving object. It always opposes the object’s motion relative to the fluid. The magnitude depends on the relative speed, the shape of the object, and the density of the fluid.

空气阻力（也称阻力）是流体对运动物体施加的阻力。它总是阻碍物体相对于流体的运动。其大小取决于相对速度、物体的形状以及流体的密度。

For small objects moving slowly, the drag force is often modelled as proportional to speed: \( F \propto v \).

对于缓慢运动的小物体，阻力通常建模为与速度成正比：F ∝ v。
For larger objects at higher speeds, drag is proportional to the square of the speed: \( F \propto v^2 \).

对于高速运动的大物体，阻力与速度的平方成正比：F ∝ v²。
When an object falls and drag equals weight, the net force is zero and the object reaches terminal velocity.

当下落物体的阻力等于重力时，合力为零，物体达到终端速度。

8. Buoyancy (Upthrust) | 浮力

Buoyancy, or upthrust, is the upward force exerted by a fluid on a submerged or floating object. According to Archimedes’ principle, the magnitude of the upthrust equals the weight of the fluid displaced by the object: \( U = \rho_{\text{fluid}} V_{\text{displaced}} g \).

浮力是流体对浸没或漂浮物体施加的向上的力。根据阿基米德原理，浮力的大小等于物体排开流体的重量：U = ρ_流体 V_排开 g。

The upthrust acts through the centre of buoyancy, not necessarily through the centre of mass.

浮力作用点位于浮心，不一定是重心。
If \( U > W \), the object rises; if \( U < W \), it sinks; if \( U = W \), it floats in equilibrium.

如果 U > W，物体上升；如果 U < W，物体下沉；如果 U = W，物体悬浮平衡。
In A-Level problems, remember to include upthrust when drawing free-body diagrams for objects in water or air.

在 A-Level 题目中，画水面或空气中物体的受力分析图时，别忘了加入浮力。

9. Resultant Force and Free-Body Diagrams | 合力与受力分析图

To analyse a physical situation, you must first draw a free-body diagram showing every force acting on the chosen object. Only forces on the object are included; forces exerted by the object on other bodies are not.

要分析一个物理情景，首先必须画出受力分析图，标出作用在所选物体上的每一个力。只包括作用在该物体上的力，不包括该物体对其他物体施加的力。

F_net = ma

Resolve forces into perpendicular components (usually horizontal and vertical).

将力分解为互相垂直的分量（通常是水平和竖直方向）。
Use F_net = ma for translational motion.

使用 F_net = ma 来分析平动。
If the object is in equilibrium, the vector sum of all forces is zero.

如果物体处于平衡状态，所有力的矢量和为零。
Check your diagram: the arrows should clearly show direction and relative magnitude.

检查你的图示：箭头应清楚显示方向和相关大小。

10. Newton’s Three Laws and Force Identification | 牛顿三定律与力的识别

Newton’s laws are the backbone of force analysis. The first law tells us that if an object is at rest or moving with constant velocity, the net force on it is zero. The second law relates net force to acceleration. The third law states that every action has an equal and opposite reaction.

牛顿定律是受力分析的支柱。第一定律告诉我们，如果物体静止或匀速直线运动，则它所受合力为零。第二定律将合力与加速度联系起来。第三定律指出，每个作用力都有一个大小相等、方向相反的反作用力。

Law \| 定律	Key idea \| 核心思想	Force identification hint \| 识别力的提示
First \| 第一定律	Net force = 0 for equilibrium or constant velocity	Equal forces must balance
Second \| 第二定律	F = ma	Unbalanced force causes acceleration
Third \| 第三定律	Action and reaction are equal and opposite	Identify pairs on different objects

Common mistake: action-reaction pairs do not act on the same object, so they cannot cancel each other out in a free-body diagram.

常见错误：作用力与反作用力作用在不同的物体上，因此在同一个受力分析图中不能相互抵消。

11. Common Errors in Recognising Forces | 识别力时的常见错误

Forgetting to include the normal force on an inclined plane, or drawing it vertically instead of perpendicular to the surface.

在斜面上忘记画法向力，或将其画成竖直方向而不是垂直于斜面。
Thinking that a moving object always has a force in the direction of motion. In fact, if it moves at constant velocity, the net force is zero.

认为运动的物体在运动方向上一定受力。实际上，如果物体匀速运动，合力为零。
Confusing weight and mass: weight is a force, measured in newtons; mass is a property, measured in kilograms.

混淆重量与质量：重量是力，单位是牛顿；质量是属性，单位是千克。
Assuming the normal force always equals \( mg \). This is only true on a horizontal surface with no vertical acceleration and no other vertical forces.

假定法向力总是等于 mg。只有在水平面上、没有竖直加速度且没有其他竖直力时才成立。
Forgetting that tension in a massless, inextensible string is the same throughout the string, but the string pulls with different magnitudes on different objects if pulleys are not light and smooth.

忘记在无质量且不可伸长的绳子中张力处处相等；但如果滑轮不是轻质光滑的，绳子拉不同物体的力可能不同。

12. Strategy for Analysing Forces in Exam Problems | 考试中分析力的策略

Follow this structured approach to avoid missing forces or double-counting them.

按照以下结构化的方法，可以避免漏力或重复计算力。

Identify the object of interest. Draw a closed boundary around it.

明确研究对象。围绕它画一个封闭的边界。
List all external forces: gravitational (weight), contact forces (normal, friction), tension, applied forces, and fluid forces (drag, upthrust).

列出所有外力：重力、接触力（法向力、摩擦力）、张力、施加的外力以及流体作用力（阻力、浮力）。
Draw a free-body diagram with the forces as arrows from the center of the object.

画出受力分析图，所有力箭头从物体中心画出。
Choose a coordinate system, usually along the direction of acceleration and perpendicular to it.

选择坐标系，通常一个轴沿加速度方向，另一个垂直于它。
Resolve forces into components and apply Newton’s second law in each direction.

将力分解为分量，并在每个方向应用牛顿第二定律。
Check whether the object is in equilibrium or accelerating, and use the appropriate equation.

判断物体是平衡还是加速，并选择合适的方程。

By mastering these steps, you can identify forces confidently and solve problems accurately in CIE A-Level Physics.

掌握了这些步骤，你就能自信地识别力，并在 CIE A-Level 物理中准确解题。

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Type \| 类型	Magnitude \| 大小	Direction \| 方向
Static friction \| 静摩擦力	0 ≤ f ≤ μₛN	Opposes attempted motion \| 阻碍运动的企图
Kinetic friction \| 动摩擦力	fₖ = μₖN	Opposes actual relative motion \| 阻碍实际相对运动

Identification and Analysis of Common Forces | 常见力的识别与分析