📚 Forces and Acceleration | 力与加速度
Understanding how forces cause acceleration is central to Edexcel A Level Physics mechanics. This topic links Newton’s laws, free-body diagrams, friction, connected particles, momentum and impulse. Exam questions often ask you to calculate acceleration, tension, friction or a scale reading from a given force diagram.
理解力如何产生加速度是 Edexcel A Level 物理力学的核心。本专题将牛顿定律、受力分析图、摩擦力、连接体、动量和冲量等知识串联起来。考试题常要求根据给定的受力图计算加速度、张力、摩擦力或秤的读数。
1. Newton’s Laws of Motion Overview | 牛顿运动定律概览
Newton’s first law states that an object remains at rest or in uniform motion unless a resultant force acts on it. The second law states that the resultant force on a body equals the rate of change of its momentum; for constant mass this gives F = ma. The third law states that forces between two bodies are equal in magnitude and opposite in direction, but act on different bodies.
牛顿第一定律指出，物体在不受合力作用时保持静止或匀速直线运动。第二定律指出，物体所受合力等于其动量变化率；质量不变时即 F = ma。第三定律指出，两个物体之间的作用力和反作用力大小相等、方向相反，但作用在不同物体上。
ΣF = m × a
In Edexcel mechanics, you must be able to apply all three laws to explain motion, identify force pairs and set up equations of motion.
在 Edexcel 力学中，你必须会应用三大定律解释运动、识别作用力与反作用力对，并建立运动方程。
2. Mass, Weight and Gravitational Field Strength | 质量、重量与重力场强度
Mass is a scalar quantity measured in kilograms that measures inertia, the resistance of a body to acceleration. Weight is a force measured in newtons and equals mass multiplied by the gravitational field strength g.
质量是标量，单位为千克，用于度量惯性，即物体抵抗加速的能力。重量是一种力，单位为牛顿，等于质量乘以重力场强度 g。
W = m × g
Near the surface of the Earth, g is approximately 9.81 N kg⁻¹. Do not confuse mass with weight: mass is unchanged everywhere, while weight changes if the gravitational field changes.
在地球表面附近，g 约为 9.81 N kg⁻¹。不要混淆质量与重量：质量在任何地方都不变，而重量会随重力场的改变而改变。
3. Free-Body Diagrams and Resultant Force | 受力分析图与合力
A free-body diagram shows all the forces acting on one body using arrows. The resultant force is the vector sum of these forces. If forces act along perpendicular directions, use Pythagoras’ theorem or resolve components to find the resultant.
受力分析图用箭头标出一个物体受到的所有力。合力是这些力的矢量和。如果力沿相互垂直的方向作用，可以使用勾股定理或分解分量来求合力。
In Edexcel questions, isolate the body first. Label weight, normal reaction, tension, friction and applied forces clearly. Then choose the direction of acceleration as positive and apply F = ma.
在 Edexcel 考试题中，首先要隔离物体。清楚标出重力、法向反力、张力、摩擦力和外加力。然后选择加速度方向为正，应用 F = ma。
4. Using F = ma in a Straight Line | 直线运动中 F = ma 的应用
For motion in a straight line, choose a positive direction and apply the resultant force equation along that direction. A resultant force causes acceleration; no resultant force means no acceleration.
对于直线运动，选定正方向，沿该方向应用合力方程。有合力就产生加速度；合力为零则加速度为零。
F = m × a
A car of mass 1200 kg accelerates at 2.0 m s⁻² when the driving force is 3200 N. The resistive force is found from 3200 − R = 1200 × 2.0, so R = 800 N.
一辆质量 1200 kg 的汽车以 2.0 m s⁻² 加速，驱动力为 3200 N。由 3200 − R = 1200 × 2.0 得阻力 R = 800 N。
5. Tension, Normal Reaction and Friction | 张力、法向反力和摩擦力
Tension is the pulling force transmitted through a string or cable. For a light inextensible string, the tension is the same throughout the string. Normal reaction acts perpendicular to the contact surface. Friction opposes relative motion or attempted relative motion.
张力是通过绳子或缆绳传递的拉力。对于轻质不可伸长的绳子，绳中各点张力相同。法向反力垂直于接触面。摩擦力阻碍相对运动或相对运动趋势。
Friction does not always equal μR; μR is the maximum possible static friction or the kinetic friction during sliding. The coefficient of friction μ has no units.
摩擦力并不总等于 μR；μR 只是最大静摩擦或滑动时的动摩擦。摩擦系数 μ 没有单位。
maximum friction = μ × R
6. Friction and Limiting Equilibrium | 摩擦力与极限平衡
A body is in limiting equilibrium when the applied force is just large enough to make it slide but the body is still at rest. At that point static friction reaches its maximum value μR.
当外力刚好大到使物体即将滑动但仍静止时，物体处于极限平衡。此时静摩擦达到最大值 μR。
A block on a horizontal surface has a normal reaction of 50 N and μ = 0.4. The maximum static friction is 0.4 × 50 = 20 N. A pulling force of 15 N produces 15 N of friction and no acceleration; a pulling force of 25 N exceeds the maximum static friction and the block accelerates with kinetic friction acting.
水平面上的物块法向反力为 50 N，μ=0.4。最大静摩擦为 0.4 × 50 = 20 N。拉力 15 N 时摩擦力为 15 N，不产生加速度；拉力 25 N 时超过最大静摩擦，物块加速并受到动摩擦作用。
7. Forces on an Inclined Plane | 斜面上的力
On a smooth inclined plane at angle θ to the horizontal, the weight component parallel to the slope is mg sin θ and the component perpendicular to the slope is mg cos θ. The normal reaction equals mg cos θ.
在与水平面成 θ 角的光滑斜面上，重力沿斜面的分量为 mg sin θ，垂直斜面的分量为 mg cos θ。法向反力等于 mg cos θ。
a = g × sin θ
The acceleration down a smooth slope is g sin θ. If friction is present, the resultant force down the slope is mg sin θ − F_friction, and the acceleration is found using F = ma.
光滑斜面上的下滑加速度为 g sin θ。如果存在摩擦，沿斜面向下的合力为 mg sin θ − 摩擦力，再用 F = ma 求加速度。
8. Connected Particles: Pulley and Tow Systems | 连接体：滑轮与拖拽系统
For two particles connected by a light inextensible string over a pulley, both particles have the same magnitude of acceleration and the same tension in the string. Treat each mass separately, or use the equation for the whole system.
对于由轻质不可伸长的绳子跨过滑轮连接的两个物体，两者加速度大小相同、绳子中的张力大小相同。可以分别对每个物体列方程，也可以对整体列方程。
a = (m₂ − m₁) × g ÷ (m₂ + m₁)
For masses m₁ and m₂ with m₂ greater than m₁, this equation gives the acceleration of the system. The tension is found by substituting a back into one equation: T = m₁(g + a) or T = m₂(g − a).
对于质量 m₁ 和 m₂ 且 m₂ 大于 m₁，该方程给出系统的加速度。张力可通过将 a 代回任一方程求出：T = m₁(g + a) 或 T = m₂(g − a)。
9. Lift and Scale Problems | 电梯与秤问题
In a lift accelerating upward, the reading on a weighing scale or the tension in the cable increases because the resultant force must provide the acceleration. The equation is R − mg = ma upward, so R = mg + ma.
电梯向上加速时，秤的读数或缆绳张力增大，因为合力必须提供加速度。方程 R − mg = ma 向上，得 R = mg + ma。
R = m × (g + a) upward; R = m × (g − a) downward
If the lift moves at constant velocity, acceleration is zero and the scale reads the normal weight mg. If the lift decelerates while moving upward, the scale reads less than mg.
如果电梯匀速运动，加速度为零，秤读数为正常重量 mg。如果电梯向上运动时减速，秤读数小于 mg。
10. Momentum, Impulse and Newton’s Second Law | 动量、冲量与牛顿第二定律
Newton’s second law was originally expressed as F =
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