动量与能量Momentum & energy

动量与能量是 Section 1 反复出现的基础题型。本页选五题，共 19 分，每题 2–6 分；常见失分点是混淆守恒条件、忽略质量比，以及把能量与功率当成同一个量。Momentum and energy recur throughout Section 1. These five questions total 19 marks, with 2–6 marks each. Common losses come from confusing conservation conditions, overlooking mass ratios, and mixing energy with power.

1动量、冲量与碰撞Momentum, impulse and collisions

先选系统与正方向。外冲量可忽略时系统动量守恒；弹性碰撞还守恒动能，粘连碰撞则不守恒动能。Choose a system and positive direction. Negligible external impulse gives momentum conservation; elastic collisions also conserve KE, while coupling collisions do not.

一维碰撞：e = 1 为弹性，e = 0 为粘连。In one dimension: e = 1 for elastic impact, e = 0 for coupling.

2功与能量账目Work and energy accounting

合力做功等于动能变化。若有摩擦，机械能的减少转化为内能；可把耗散项写入总能量账目。Net work equals the change in kinetic energy. With friction, lost mechanical energy becomes internal energy; include dissipation in the energy balance.

恒定摩擦力且运动路径长 s 时，耗散为 fs；自由落体中该项为零。For constant friction over path length s, dissipation is fs; it is zero in ideal free fall.

3功率与质量流率Power and mass flow

功率描述能量传递快慢。连续落链则要计算单位时间到达的质量，再乘每单位质量的动量变化。Power measures energy transfer rate. For a continuously falling chain, find the arriving mass per second and multiply by momentum change per unit mass.

区分储能、能量流率和动量流率，单位是最直接的检查。Distinguish stored energy, energy flow rate and momentum flow rate; check their units.