Forces and Friction | 力与摩擦

📚 Forces and Friction | 力与摩擦

In Edexcel A Level Physics, forces and friction appear in mechanics problems ranging from free-body diagrams to inclined planes and connected systems. Understanding how to resolve forces, apply Newton’s laws, and model friction with F = μR is essential for both short calculations and extended multi-step questions. This revision guide covers the key definitions, equations, techniques, and common exam pitfalls.

在 Edexcel A Level 物理中，力与摩擦广泛出现在从受力图、斜面到连接体等力学问题中。掌握力的分解、牛顿定律的应用以及用 F = μR 建立摩擦模型，对于简答题和多步骤综合题都至关重要。本复习指南覆盖关键定义、公式、解题方法和常见考试误区。

1. Newton’s Laws and Resultant Force | 牛顿定律与合力

Newton’s first law states that an object remains at rest or moves with constant velocity unless a resultant force acts on it. This is the principle of inertia and explains why a moving object does not require a forward force to continue moving at constant speed.

牛顿第一定律指出，除非受到合力作用，物体将保持静止或匀速直线运动。这是惯性的原理，也解释了为什么匀速运动的物体不需要向前的力来维持运动。

Newton’s second law relates resultant force, mass and acceleration. When several forces act on a particle, you must first find the vector sum of all forces along each axis. The resultant force then produces acceleration in the same direction.

牛顿第二定律将合力、质量和加速度联系起来。当多个力作用在质点上时，必须首先求出各坐标轴上所有力的矢量和，然后合力在同一方向产生加速度。

ΣF = ma

Here ΣF is the resultant force in newtons, m is mass in kilograms, and a is acceleration in m s⁻².

这里 ΣF 是合力，单位为牛顿；m 是质量，单位为千克；a 是加速度，单位为 m s⁻²。

Newton’s third law says forces always occur in equal and opposite action-reaction pairs. The two forces act on different objects, so they do not cancel in a free-body diagram of one object.

牛顿第三定律指出力总是成对出现，作用力与反作用力大小相等、方向相反。这两个力作用在不同物体上，因此在单个物体的受力图中不会相互抵消。

2. Free-Body Diagrams and Resolving Forces | 受力图与力的分解

Start every mechanics problem by drawing a free-body diagram showing all forces. Common forces include weight W = mg acting vertically downward, normal reaction R perpendicular to the contact surface, friction F along the surface opposing relative motion, tension T along a string, and any applied force.

解答力学问题时，首先要画出标明所有力的受力图。常见的力有：竖直向下的重力 W = mg、垂直于接触面的法向反力 R、沿接触面且阻碍相对运动的摩擦力 F、沿绳方向的张力 T，以及任何外力。

W = mg

Resolving forces means splitting a vector into perpendicular components. Choose axes that simplify the problem: for slopes, use one axis parallel to the slope and one perpendicular. Then apply equilibrium or ΣF = ma separately in each direction.

力的分解是将矢量分解成相互垂直的分量。选择能简化问题的坐标轴：对于斜面，通常沿斜面方向取一个轴，垂直斜面方向取另一个轴。然后分别对每个方向应用平衡条件或 ΣF = ma。

3. Static and Kinetic Friction | 静摩擦与动摩擦

Friction is a contact force that opposes the relative motion or tendency of motion between two surfaces. Static friction acts when there is no sliding; its magnitude can vary from zero up to a maximum value. Kinetic friction acts during sliding and is usually taken as constant for a given normal reaction.

摩擦力是一种接触力，阻碍两个表面之间的相对运动或相对运动趋势。静摩擦在尚未滑动时起作用，其大小可以从零变化到最大值。动摩擦在滑动过程中起作用，对于给定的法向反力通常视为恒定。

static: F ≤ μR
sliding/limiting: F = μR

The symbol μ is the coefficient of friction. It has no units and depends on the two materials in contact. A-level problems usually give μ or ask you to calculate it from limiting equilibrium data.

μ 是摩擦系数。它没有单位，取决于接触的两种材料。A-Level 题目通常给出 μ，或要求你根据极限平衡数据计算 μ。

4. Coefficient of Friction F = μR | 摩擦系数 F = μR

The normal reaction R is the force a surface exerts perpendicular to itself. It is not automatically equal to weight. On a horizontal plane with no vertical applied force, R = mg; on a slope, R = mg cos θ.

法向反力 R 是表面对物体施加的垂直力。它并不总是等于重力。在没有竖直外力作用的水平面上，R = mg；在斜面上，R = mg cos θ。

A 5 kg box rests on a horizontal table where μ = 0.4. Taking g = 9.8 N kg⁻¹, the maximum static friction is F = μR = 0.4 × 5 × 9.8 = 19.6 N. Any horizontal force below 19.6 N will not move the box; at 19.6 N the box is in limiting equilibrium.

一个 5 kg 的箱子静止在水平桌面上，μ = 0.4。取 g = 9.8 N kg⁻¹，最大静摩擦力为 F = μR = 0.4 × 5 × 9.8 = 19.6 N。任何小于 19.6 N 的水平力都不能推动箱子；力等于 19.6 N 时箱子处于极限平衡。

5. Motion on a Horizontal Plane | 水平面上的运动

For a horizontal plane, always split forces into vertical and horizontal components. The

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