Kinetic Energy in CIE A-Level Physics | CIE A-Level 物理中的动能

📚 Kinetic Energy in CIE A-Level Physics | CIE A-Level 物理中的动能

Kinetic energy is the energy possessed by an object due to its motion. In CIE A-Level Physics, it is one of the core mechanical energy concepts alongside gravitational potential energy and elastic potential energy. A solid understanding of KE = ½mv² and the work–energy theorem is essential for solving problems involving motion, collisions, and energy conservation.

动能是物体由于运动而具有的能量。在 CIE A-Level 物理中，它与重力势能、弹性势能并列为机械能的核心概念。扎实掌握 KE = ½mv² 以及功–能定理，是解决运动、碰撞与能量守恒问题的关键。

1. Definition of Kinetic Energy | 动能的定义

Kinetic energy (KE) is the energy a body possesses because it is moving. Any object with non-zero speed relative to an observer has kinetic energy; an object at rest has zero kinetic energy in that frame of reference.

动能（KE）是物体因运动而具有的能量。任何相对于观察者速度不为零的物体都具有动能；在所选参考系中静止的物体动能为零。

The kinetic energy of a particle of mass m moving with speed v is defined by KE = ½mv². This is a scalar quantity and is always non-negative in classical mechanics.

质量为 m、速度为 v 的质点，其动能定义为 KE = ½mv²。动能是标量，在经典力学中始终为非负值。

2. The Formula KE = ½mv² | 动能公式 KE = ½mv²

The formula shows that KE depends linearly on mass and quadratically on speed. If the mass is doubled, kinetic energy doubles; if the speed is doubled, kinetic energy increases by a factor of 2² = 4.

该公式表明，动能与质量成正比，与速度的平方成正比。质量变为原来的两倍，动能也变为两倍；速度变为原来的两倍，动能则增大到原来的 2² = 4 倍。

KE = ½ m v²

Because v is squared, a negative velocity gives the same KE as a positive velocity of the same magnitude, since only speed matters.

由于 v 被平方，速度大小相同、方向相反时动能相同，因为只有速度大小影响动能。

3. Deriving KE from Work and Newton’s Second Law | 从功和牛顿第二定律推导动能

Consider a constant net force F acting on a particle of mass m over a displacement s along a straight line. The work done by the force is W = F s.

考虑恒定的合外力 F 沿直线作用在质量为 m 的质点上，位移为 s。该力所做的功为 W = F s。

By Newton’s second law, F = m a. Using the equation of motion v² = u² + 2 a s, we can write a s = (v² – u²) / 2.

根据牛顿第二定律，F = m a。利用运动学公式 v² = u² + 2 a s，可得 a s = (v² – u²) / 2。

The work done becomes W = m a s = m × (v² – u²) / 2 = ½ m v² – ½ m u². The terms on the right are the final and initial kinetic energies, so W = ΔKE.

因此功为 W = m a s = m × (v² – u²) / 2 = ½ m v² – ½ m u²。右端两项分别是末动能与初动能，所以 W = ΔKE。

This derivation is valid for a constant resultant force. A more general proof using integration shows that the work done by the resultant force always equals the change in kinetic energy.

该推导适用于恒定合力。使用积分进行的更一般证明表明，合力所做的功总是等于动能的变化量。

4. Units and Dimensions of Kinetic Energy | 动能的单位与量纲

Kinetic energy is a form of energy, so its SI unit is the joule (J). One joule is defined as 1 J = 1 kg m² s⁻².

动能是能量的一种形式，因此其国际单位是焦耳（J）。1 焦耳被定义为 1 J = 1 kg m² s⁻²。

The dimensional formula for kinetic energy is [M][L]²[T]⁻². This follows from ½ m v²: mass has dimension M, speed has dimension L T⁻¹, so v² gives L² T⁻².

动能的量纲式为 [M][L]²[T]⁻²。这可以从 ½ m v² 得出：质量的量纲是 M，速度的量纲是 L T⁻¹，因此 v² 对应 L² T⁻²。

In calculations, always convert mass to kg and speed to m s⁻¹ before applying KE = ½ m v², otherwise the energy will not be in joules.

在计算中，务必先将质量换算为 kg、速度换算为 m s⁻¹，再代入 KE = ½ m v²，否则得到的能量单位将

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）