Force Diagrams | 力的图示

📚 Force Diagrams | 力的图示

Force diagrams are the first essential tool in A-level Mechanics. They allow you to turn a written physical situation into a clear, labelled vector picture before you apply Newton’s laws or equilibrium conditions. In Edexcel A-level Physics, free-body diagrams appear in almost every mechanics question, from a block on a slope to connected particles and projectiles with drag.

力的图示是 A-level 力学中最基础也是最重要的工具。它能将一个文字描述的物理情境转化为清晰、带标注的矢量图，然后再应用牛顿定律或平衡条件。在 Edexcel A-level 物理中，从斜面上的物块到连接体，再到受空气阻力作用的抛体，几乎每道力学题都会涉及受力分析图。

1. What Is a Force Diagram? | 什么是力的图示

A force diagram is a simplified drawing of a body with all the external forces acting on it represented by arrows. Each arrow starts from the body, usually from its centre of mass, and points in the direction of the force. The length of the arrow is proportional to the magnitude of the force when the forces are drawn to scale.

力的图示是将一个物体以及作用在其上的所有外力用箭头表示出来的简化图。每个箭头通常从物体的质心画起，指向力的作用方向。当按比例绘制时，箭头的长度正比于力的大小。

There are two common forms: a full force diagram may include the surroundings and joints, while a free-body diagram isolates the object and shows only the forces acting on that object. In Edexcel exams, the term ‘free-body diagram’ usually expects this isolated representation.

常见的图示有两种：完整力示图可能包括周围物体和接触点，而受力分析图（自由体图）则把物体隔离开来，只画出作用在该物体上的力。在 Edexcel 考试中，’free-body diagram’ 通常指的就是这种隔离体的表示法。

2. Representing Forces as Vectors | 用矢量表示力

Force is a vector quantity, which means it has both magnitude and direction. In a force diagram, the direction of the arrow shows the direction of the force, and the relative length or a labelled value shows its magnitude.

力是矢量，既有大小又有方向。在力的图示中，箭头方向表示力的方向，相对长度或所标注的数值表示力的大小。

For calculations, you often resolve a force into perpendicular components. A force F at an angle θ to the horizontal has components F cos θ horizontally and F sin θ vertically. You should choose axes that make the problem simplest, often along and perpendicular to an inclined plane.

在计算中，通常需要将力分解为相互垂直的分量。一个与水平方向成 θ 角的力 F，其水平分量为 F cos θ，竖直分量为 F sin θ。应选择使问题最简化的坐标轴，通常是沿斜面和垂直于斜面。

F_x = F cos θ, F_y = F sin θ

The component notation used in many textbooks is F_x and F_y, meaning the components along the x and y axes. If you prefer, you can write them as horizontal and vertical components without subscripts.

许多教材中使用 F_x 和 F_y 表示沿 x 轴和 y 轴的分量。也可以直接写成水平分量和竖直分量，而不使用下标。

3. Common Forces in A-Level Diagrams | A-level 图示中的常见力

Weight W = mg always acts vertically downwards from the centre of mass. It should be included for any object near the Earth’s surface unless the question says the object is ‘weightless’ or in deep space.

重力 W = mg 总是从质心竖直向下作用。对任何靠近地球表面的物体都应画出重力，除非题目说明物体处于’失重’状态或在远离天体的深空。

The normal reaction force N acts perpendicular to the contact surface. It is a contact force and is often shown pointing upwards from a surface. On an inclined plane, the normal reaction is perpendicular to the slope, not vertically upwards.

法向反作用力 N 垂直于接触面作用。它是一种接触力，通常从表面指向物体。在斜面上，法向反作用力垂直于斜面，而不是竖直向上。

Friction f acts parallel to the contact surface and opposes relative motion or the tendency of motion. Tension T in a string or cable acts along the string and pulls the object toward the string. Drag or air resistance acts opposite to the direction of velocity through a fluid.

摩擦力 f 平行于接触面作用，阻碍相对运动或运动趋势。绳或缆绳中的张力 T 沿绳子方向作用，并将物体拉向绳子的方向。阻力或空气阻力与物体在流体中的速度方向相反。

Other common forces include thrust, lift, and upthrust. In Edexcel mechanics questions, you should label forces with standard symbols such as W, N, f, T, F, and R, then write a key if necessary.

其他常见力还包括推力、升力和浮力。在 Edexcel 力学题中，应使用标准符号给力作标注，如 W、N、f、T、F 和 R，必要时可以添加图例说明。

4. Rules for Drawing Free-Body Diagrams | 绘制受力分析图的规则

Always isolate the object. Draw one arrow for each force caused by an external interaction: gravity, contact with a surface, a string, a spring, or a fluid. Do not include internal forces or forces exerted by the object on other bodies.

始终要把物体隔离开来。每个由外部相互作用引起的力画一个箭头：重力、与表面的接触力、绳子、弹簧或流体的作用力。不要画出内力或物体对其他物体的作用力。

Draw arrows from the point representing the object, usually a dot at the centre of mass. If the force acts through a specific point such as a hinge or contact patch, you may show it from that point, but for free-body diagrams the origin is usually the centre of mass.

箭头应从代表物体的点画起，通常是在质心处的一个圆点。如果力通过某个特定点（如铰链或接触面）作用，可以从该点画起，但在受力分析图中，起点通常统一为

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