Identifying Forces | 力的识别

📚 Identifying Forces | 力的识别

In A-level Physics, many problems begin with a simple instruction: identify the forces acting on a body. This skill is not just about naming pushes and pulls; it is the foundation of free-body diagrams, Newton’s laws, equilibrium, and dynamics. If you misidentify a force or include a force that does not act on the chosen body, every calculation that follows can go wrong.

在 A-level 物理中,许多题目都从同一个简单要求开始:识别作用在物体上的力。这个技能不只是说出推力和拉力的名称;它是受力图、牛顿定律、平衡和动力学问题的基础。如果你误判一个力,或画上了一个并不作用在所研究物体上的力,后续所有计算都可能出错。


1. The purpose of force identification | 力识别的目的

In mechanics, a force is any interaction that can change the motion or shape of an object. It is a vector quantity, so it has both magnitude and direction, and its SI unit is the newton, N. Identifying forces correctly allows you to construct free-body diagrams, apply Newton’s second law F = ma, and decide whether a system is in equilibrium. The key question is always: what is touching the body, and what non-contact fields act on it?

在力学中,力是能够改变物体运动状态或形状的任何相互作用。力是矢量,既有大小又有方向,其国际单位是牛顿,符号为 N。正确识别力可以让你画出受力图,应用牛顿第二定律 F = ma,并判断系统是否处于平衡状态。关键问题始终是:什么物体与被研究的物体接触?什么非接触场作用在它上面?


2. Contact and non-contact forces | 接触力与非接触力

A useful first step is to divide forces into contact forces and non-contact forces. Contact forces arise when two bodies touch: normal contact force, friction, tension, air resistance, and upthrust. Non-contact forces act at a distance through fields: gravitational force, electrostatic force, and magnetic force. In most CIE mechanics problems, the non-contact force you include is weight; electric and magnetic forces appear only when fields are explicitly given.

一个有用的第一步是把力分为接触力和非接触力。接触力在两个物体接触时产生:法向接触力、摩擦力、张力、空气阻力和浮力。非接触力通过场在远处起作用:万有引力、静电力和磁力。在大多数 CIE 力学问题中,你需要包含的非接触力是重量;电场力和磁力只在题目明确给出场时出现。


3. Weight as a gravitational force | 重量作为万有引力

Weight is the gravitational force exerted by a planet on a body. It acts from the centre of mass and points vertically downwards towards the centre of the Earth. Its magnitude is given by W = mg, where m is mass in kg and g is the gravitational field strength, about 9.81 N kg⁻¹ near the Earth’s surface. Remember that mass is a scalar and does not change with location, whereas weight is a force and can change if g changes.

重量是行星对物体施加的万有引力。它作用在质心上,方向竖直向下,指向地球中心。其大小由 W = mg 给出,其中 m 是物体的质量,单位为 kg,g 是引力场强度,在地球表面附近约为 9.81 N kg⁻¹。要记住质量是标量,不随位置变化;而重量是力,如果 g 改变,重量也会改变。

W = mg


4. Normal contact force | 法向接触力

The normal contact force is the push exerted by a surface on a body in contact with it. It acts perpendicular to the surface, not necessarily vertically upwards. A common error is to assume that the normal force always equals weight. On a horizontal surface at rest, R = mg; on an inclined plane, R = mg cos θ; in a lift accelerating upwards, R is greater than mg.

法向接触力是接触面对物体施加的推力。它垂直于接触面,不一定是竖直向上的。一个常见错误是认为法向力总是等于重量。在水平面上静止时,R = mg;在斜面上,R = mg cos θ;在向上加速的电梯中,R 大于 mg。

R = mg cos θ


5. Tension and thrust in strings and rods | 绳和杆中的张力与推力

Tension is the pulling force transmitted through a string, rope, or cable. It always acts along the length of the string and points away from the object on each end. A string can only pull, never push. In contrast, a rigid rod can exert either tension, a pull, or thrust, a push, along its length. When identifying forces, label tension as T and draw arrows away from the body.

张力是通过绳子、绳索或缆绳传递的拉力。它总是沿着绳子的长度方向,并在两端指向远离物体的方向。绳子只能拉,不能推。相反,刚性杆可以沿其长度方向施加张力(拉力)或推力(压力)。在识别力时,将张力标记为 T,并画出箭头指向远离物体的方向。


6. Friction and air resistance | 摩擦力与空气阻力

Friction is a contact force that opposes relative motion, or attempted motion, between two surfaces. Static friction prevents motion from starting, while dynamic friction opposes motion already occurring. The magnitude of limiting friction is often modelled by f ≤ μR, where μ is the coefficient of friction and R is the normal contact force. Air resistance is a type of fluid resistance that increases with speed; it always opposes the velocity of the object through the air.

摩擦力是一种接触力,它阻碍两个表面之间的相对运动或运动趋势。静摩擦力阻止物体开始运动,动摩擦力阻碍已经发生的运动。极限摩擦力的大小通常用 f ≤ μR 表示,其中 μ 是摩擦系数,R 是法向接触力。空气阻力是流体阻力的一种,它随速度增大而增大;空气阻力的方向总是与物体在空气中的速度方向相反。

f ≤ μR


7. Upthrust and fluid forces | 浮力与流体力

An object submerged or floating in a fluid experiences an upward force called upthrust. It arises because pressure in a fluid increases with depth, so the pressure on the bottom of the object is greater than on the top. By Archimedes’ principle, upthrust equals the weight of the fluid displaced. In force identification, upthrust should be included for objects in water or air when buoyancy is significant, such as balloons, ships, and bubbles.

浸没或漂浮在流体中的物体会受到一个向上的力,称为浮力。浮力产生的原因是流体中的压强随深度增加,因此物体底部的压强大于顶部。根据阿基米德原理,浮力等于物体排开流体的重量。在识别力时,当浮力显著时,例如气球、船舶和气泡,应该把浮力纳入水中或空气中的物体受力分析。


8. Electric and magnetic forces | 电场力与磁力

Electric and magnetic forces are field forces you may need to identify in charged particle problems. In a uniform electric field, a charge q experiences F = qE, with direction parallel to the field for positive charges and opposite for negative charges. In a magnetic field, a charge moving with velocity v perpendicular to field B experiences F = Bqv sin θ, and its direction is given by Fleming’s left-hand rule. These forces are not contact forces and can act in a vacuum.

电场力和磁力是你在带电粒子问题中可能需要识别的场力。在匀强电场中,电荷 q 受到的力为 F = qE,正电荷受力方向与电场方向平行,负电荷则相反。在磁场中,以速度 v 垂直于磁场 B 运动的电荷受到的力为 F = Bqv sin θ,其方向由左手定则确定。这些力不是接触力,可以在真空中作用。

F = qE F = Bqv sin θ


9. Free-body diagram rules | 受力图绘制规则

A free-body diagram shows only the forces acting on the chosen body. Do not include forces exerted by the body on other objects. Represent each force by an arrow starting from the body, with length indicating relative magnitude, and label it clearly. If the body is in equilibrium, the vector sum of all forces is zero; if it accelerates, the resultant force equals ma in the direction of acceleration.

受力图只显示作用在所研究物体上的力。不要包括该物体对其他物体施加的力。每个力用从物体出发的箭头表示,箭头的长度表示相对大小,并清楚标注。如果物体处于平衡状态,所有力的矢量和为零;如果物体加速,合力等于 ma,方向与加速度方向相同。


10. Common misidentifications | 常见误判

Students often include forces that are not real separate forces. For example, centripetal force is not an additional force; it is the name given to the resultant force towards the centre of circular motion. There is no forward ‘motion force’ on a ball after it leaves the hand; only weight and air resistance act if we ignore the hand. Also, Newton’s third law pairs act on different bodies, so action and reaction never cancel on the same free-body diagram.

学生常常画出一些并非真实独立力的“力”。例如,向心力不是额外的力;它是对指向圆周运动中心的合力的命名。球离开手后并没有向前的“运动力”;如果忽略手的作用,球只受重力和空气阻力。此外,牛顿第三定律中的作用力和反作用力

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