Combining Forces: Resultant, Equilibrium and Resolution | 力的合成：合力、平衡与分解

📚 Combining Forces: Resultant, Equilibrium and Resolution | 力的合成：合力、平衡与分解

Combining forces is one of the most fundamental skills in CIE A-Level Physics. Whether you analyse a suspended mass, an object on a slope, or a bridge in equilibrium, you must be able to replace several forces with a single resultant force, break forces into perpendicular components, and apply the condition that the vector sum of forces is zero when acceleration is zero. This article develops those ideas from basic vector language to worked numerical examples.

力的合成是 CIE A-Level 物理中最基本的技能之一。无论是分析悬挂的物体、斜面上的物体，还是处于平衡状态的桥梁，你都必须能够用一个合力替代多个力，将力分解为垂直分量，并在加速度为零时应用合力矢量和为零的条件。本文将从基本矢量语言出发，逐步发展到数值例题。

1. Scalar vs Vector and Force as a Vector | 标量与矢量及力作为矢量

A scalar quantity has magnitude only: examples include mass, time, temperature and energy. A vector quantity has both magnitude and direction: examples include displacement, velocity, acceleration, momentum and force. Force is a vector because its effect depends on direction as well as size.

标量只有大小，例如质量、时间、温度和能量。矢量既有大小又有方向，例如位移、速度、加速度、动量和力。力是矢量，因为它的作用效果既取决于大小，也取决于方向。

In SI units, force is measured in newtons (N). One newton is the force needed to give a 1 kg mass an acceleration of 1 m s⁻², so 1 N = 1 kg m s⁻². When forces act on a body, their directions must be included before any addition is carried out.

在国际单位制中，力的单位是牛顿（N）。一牛顿是使 1 kg 质量产生 1 m s⁻² 加速度所需的力，因此 1 N = 1 kg m s⁻²。当多个力作用在物体上时，在进行任何加法之前都必须考虑它们的方向。

2. Representing Forces and Free-Body Diagrams | 力的表示与受力分析图

A force is drawn as an arrow. The length of the arrow represents the magnitude to scale, the arrowhead shows the direction, and the starting point shows the point of application. Clear diagrams reduce mistakes in multi-force problems.

力用箭头表示。箭头的长度按比例表示大小，箭头指向表示方向，起点表示作用点。清晰的示意图可以减少多力问题中的错误。

A free-body diagram isolates a single object and shows all external forces acting on it. Typical forces include weight W = mg acting vertically downwards, the normal contact force N perpendicular to a surface, tension T along a string or cable, friction f opposing sliding, and applied forces such as pushes or pulls. Always check that no force is counted twice, especially when a force has been resolved into components.

受力分析图将单个物体隔离出来，并画出作用在它上面的所有外力。常见的力包括：竖直向下的重力 W = mg、垂直于表面的法向接触力 N、沿

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