Momentum · 动量
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| momentum/məʊˈmentəm/ | 动量 | dòng liàng |
| collision/kəˈlɪʒn/ | 碰撞 | pèng zhuàng |
| conservation of momentum/ˌkɒnsəˈveɪʃn ɒv məʊˈmentəm/ | 动量守恒 | dòng liàng shǒu héng |
Hard to stop
- An empty shopping trolley is easy to stop. A loaded truck at the same speed is not.
- The truck has much more momentum 动量.
- Momentum links mass, velocity, force and collisions 碰撞 — and it is always conserved.
难以停下
- 一个空的购物推车容易停下。一辆以相同速率行驶的满载卡车则不然。
- 卡车有多得多的动量。
- 动量连接质量、速度、力和碰撞——而且它总是守恒的。
Momentum
- Momentum is mass times velocity:
- It is a vector — it has a direction (the direction of motion).
- The unit is the kilogram metre per second ($\text{kg}\,\text{m/s}$).
The water an irregular solid pushes up gives its volume
动量
- 动量(momentum)是质量乘速度:
- 它是一个矢量——它有一个方向(运动的方向)。
- 单位是千克米每秒($\text{kg}\,\text{m/s}$)。
Momentum is a vector. · 动量是一个矢量。
Momentum is mass × velocity, and velocity has a direction, so momentum is a vector. · 动量是质量 × 速度,而速度有一个方向,所以动量是一个矢量。
A $1000\ \text{kg}$ car moves at $20\ \text{m/s}$. What is its momentum, in kg m/s? · 一辆 $1000\ \text{kg}$ 的车以 $20\ \text{m/s}$ 运动。它的动量是多少,以 kg m/s 计?
$p = mv = 1000 \times 20 = 20\,000\ \text{kg}\,\text{m/s}$. · $p = mv = 1000 \times 20 = 20\,000\ \text{kg}\,\text{m/s}$。
Force changes momentum
- A resultant force changes momentum. The force is the change in momentum per second:
- So a given change in momentum over a longer time needs a smaller force.
- This is why crumple zones, airbags and crash mats help: they make the stop take longer, so the force is gentler.
力改变动量
- 一个合力改变动量。力是每秒动量的变化:
- 所以一个给定的动量变化在一个更长的时间内需要一个更小的力。
- 这就是为什么溃缩区、安全气囊和防撞垫有帮助:它们使停止花更长时间,所以力更温和。
Why does a car's crumple zone reduce the force on the passengers in a crash? · 为什么一辆车的溃缩区在一次碰撞中减少乘客身上的力?
Since $F = \dfrac{\Delta p}{\Delta t}$, spreading the same momentum change over a longer time gives a smaller force. · 由于 $F = \dfrac{\Delta p}{\Delta t}$,把同样的动量变化分散到更长的时间给出一个更小的力。
A ball's momentum changes by $20\ \text{kg}\,\text{m/s}$ during a push lasting $2.0\ \text{s}$. What is the average force, in N? · 一个球的动量在一次持续 $2.0\ \text{s}$ 的推中变化 $20\ \text{kg}\,\text{m/s}$。平均力是多少,以 N 计?
$F = \dfrac{\Delta p}{\Delta t} = \dfrac{20}{2.0} = 10\ \text{N}$. · $F = \dfrac{\Delta p}{\Delta t} = \dfrac{20}{2.0} = 10\ \text{N}$。
Conservation of momentum 动量守恒
- In a collision with no outside force, the total momentum before = total momentum after:
- Here $u$ is a velocity before and $v$ a velocity after.
- Momentum lost by one object is gained by the other.
动量守恒
- 在一次没有外力的碰撞中,碰撞前的总动量 = 碰撞后的总动量:
- 这里 $u$ 是一个之前的速度而 $v$ 是一个之后的速度。
- 一个物体失去的动量被另一个获得。
See momentum being conserved · 看动量被守恒
Two trolleys collide and stick together. · 两辆小车碰撞并粘在一起。
A $2.0\ \text{kg}$ trolley moving at $3.0\ \text{m/s}$ hits a stationary $1.0\ \text{kg}$ trolley and they stick together. What is their speed afterwards, in m/s? · 一辆 $2.0\ \text{kg}$ 的小车以 $3.0\ \text{m/s}$ 运动,撞上一辆静止的 $1.0\ \text{kg}$ 小车,它们粘在一起。它们之后的速率是多少,以 m/s 计?
Before: $2.0 \times 3.0 + 1.0 \times 0 = 6.0\ \text{kg}\,\text{m/s}$. After: $(2.0 + 1.0)v = 6.0$, so $v = 2.0\ \text{m/s}$. · 之前:$2.0 \times 3.0 + 1.0 \times 0 = 6.0\ \text{kg}\,\text{m/s}$。之后:$(2.0 + 1.0)v = 6.0$,所以 $v = 2.0\ \text{m/s}$。
You've got it
- momentum $p = mv$ — a vector, unit $\text{kg}\,\text{m/s}$
- force $F = \dfrac{\Delta p}{\Delta t}$: a longer stop means a smaller force
- conservation: total momentum before = total momentum after a collision
你掌握了
- 动量 $p = mv$——一个矢量,单位 $\text{kg}\,\text{m/s}$
- 力 $F = \dfrac{\Delta p}{\Delta t}$:一个更长的停止意味着一个更小的力
- 守恒:碰撞前的总动量 = 碰撞后的总动量