Momentum · 动量
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| momentum/məʊˈmentəm/ | 动量 | dòng liàng |
| conservation of momentum/ˌkɒnsəˈveɪʃn ɒv məʊˈmentəm/ | 动量守恒 | dòng liàng shǒu héng |
| collision/kəˈlɪʒn/ | 碰撞 | pèng zhuàng |
| explosion/ekˈspləʊʒn/ | 爆炸 | bào zhà |
| conserved/kənˈsɜːvd/ | 守恒 | shǒu héng |
| elastic/ɪˈlæstɪk/ | 弹性 | tán xìng |
| kinetic energy/kɪˈnetɪk ˈenədʒi/ | 动能 | dòng néng |
| inelastic/ɪnɪˈlæstɪk/ | 非弹性 | fēi tán xìng |
The crash that proves physics works
- When two cars collide, the total momentum 动量 before equals the total momentum after — even though the cars are crumpled and stopped.
- Conservation of momentum 动量守恒 is one of the most powerful laws in physics. It works for billiard balls, rockets, and subatomic particles.
证明物理有效的碰撞
- 当两辆车相撞时,碰撞前的总动量等于碰撞后的——即使车被撞瘪、停了下来。
- 动量守恒(conservation of momentum)是物理中最强大的定律之一。它对台球、火箭和亚原子粒子都有效。
What is momentum?
- Momentum = mass × velocity (a vector): $\mathbf{p} = m\mathbf{v}$.
- Units: $\text{kg m s}^{-1}$ (or equivalently, N s).
- Because it's a vector, direction matters: a 2 kg ball going right at 3 m/s has momentum $+6$; going left, $-6$.
Worked example. A 0.5 kg tennis ball hits a wall at $20\text{ m s}^{-1}$ and bounces back at $15\text{ m s}^{-1}$. Change in momentum $= 0.5(15) - 0.5(-20) = 7.5 + 10 = 17.5\text{ kg m s}^{-1}$.
A Newton's cradle demonstrates conservation of momentum
什么是动量?
- 动量(momentum)= 质量 × 速度(一个向量):$\mathbf{p} = m\mathbf{v}$。
- 单位:$\text{kg m s}^{-1}$(或等价地,N s)。
- 因为它是一个向量,方向重要:一个 2 kg 的球以 3 m/s 向右,动量为 $+6$;向左,$-6$。
算例。 一个 0.5 kg 的网球以 $20\text{ m s}^{-1}$ 撞墙并以 $15\text{ m s}^{-1}$ 弹回。动量变化 $= 0.5(15) - 0.5(-20) = 7.5 + 10 = 17.5\text{ kg m s}^{-1}$。
一个牛顿摆演示动量守恒
Conservation of momentum · 动量守恒
m₁u₁ + m₂u₂ = (m₁+m₂)v
Two trolleys collide and stick together — the total momentum before equals the total after. · 两个小车碰撞并粘在一起——碰撞前的总动量等于碰撞后的。
Momentum is defined as: · 动量被定义为:
Momentum = mass × velocity, a vector quantity. · 动量 = 质量 × 速度,一个向量量。
A 0.5 kg ball hits a wall at 20 m/s and bounces back at 15 m/s. Change in momentum (kg m/s)? · 一个 0.5 kg 的球以 20 m/s 撞墙并以 15 m/s 弹回。动量变化(kg m/s)?
Change = 0.5(15) − 0.5(−20) = 7.5 + 10 = 17.5 kg m/s. · 变化 = 0.5(15) − 0.5(−20) = 7.5 + 10 = 17.5 kg m/s。
Conservation of momentum
- In a collision 碰撞 (or explosion 爆炸), total momentum is conserved 守恒:
Watch the signs. Momentum is a vector. If one object moves left and another right, one velocity is positive and the other negative. Getting the signs wrong is the most common error.
Total momentum before equals total momentum after a collision
动量守恒
- 在一次碰撞(或爆炸)中,总动量是守恒的:
注意符号。 动量是一个向量。如果一个物体向左移动、另一个向右,一个速度是正的、另一个是负的。把符号弄错是最常见的错误。
碰撞前的总动量等于碰撞后的
In a collision, the total momentum of the two bodies is conserved. · 在一次碰撞中,两个物体的总动量是守恒的。
Total momentum before equals total momentum after the collision. · 碰撞前的总动量等于碰撞后的总动量。
When two objects move in opposite directions, their momenta have opposite signs. · 当两个物体沿相反方向移动时,它们的动量有相反的符号。
Momentum is a vector — opposite directions mean opposite signs. · 动量是一个向量——相反的方向意味着相反的符号。
Worked example — collision
- A 2 kg body at $3\text{ m s}^{-1}$ hits a stationary 1 kg body and they stick together.
Total momentum before equals total momentum after: 2(3) + 1(0) = (2+1)v.
- Before: $2(3) + 1(0) = 6\text{ kg m s}^{-1}$.
- After: $(2+1)v = 3v$.
- Conservation: $3v = 6 \Rightarrow v = 2\text{ m s}^{-1}$.
算例——碰撞
- 一个 2 kg 的物体以 $3\text{ m s}^{-1}$ 撞上一个静止的 1 kg 物体,它们粘在一起。
碰撞前的总动量等于碰撞后的:2(3) + 1(0) = (2+1)v。
- 之前:$2(3) + 1(0) = 6\text{ kg m s}^{-1}$。
- 之后:$(2+1)v = 3v$。
- 守恒:$3v = 6 \Rightarrow v = 2\text{ m s}^{-1}$。
A 2 kg body moving at 3 m/s hits a stationary 1 kg body and they stick together. What is their common speed (m/s)? · 一个以 3 m/s 移动的 2 kg 物体撞上一个静止的 1 kg 物体,它们粘在一起。它们的共同速率是多少(m/s)?
2(3) + 1(0) = (2+1)v, so 6 = 3v, giving v = 2 m/s. · 2(3) + 1(0) = (2+1)v,所以 6 = 3v,给出 v = 2 m/s。
Types of collision
- Perfectly elastic 弹性: kinetic energy 动能 is conserved (rare in practice).
- Inelastic 非弹性: kinetic energy is lost (most real collisions).
- Perfectly inelastic: the bodies stick together (maximum energy loss).
- Momentum is conserved in all types — only kinetic energy may change.
- In a collision the total linear momentum is unchanged — the conservation of linear momentum.
碰撞的类型
- 完全弹性(perfectly elastic):动能守恒(实践中罕见)。
- 非弹性(inelastic):动能损失(大多数真实的碰撞)。
- 完全非弹性(perfectly inelastic):物体粘在一起(最大的能量损失)。
- 动量在所有类型中都守恒——只有动能可能改变。
- 碰撞中总线动量(linear momentum)不变——线动量守恒(conservation of linear momentum)。
In a perfectly elastic collision, which quantity is conserved (in addition to momentum)? · 在一次完全弹性碰撞中,(除了动量之外)哪个量是守恒的?
In a perfectly elastic collision, both momentum and kinetic energy are conserved. · 在一次完全弹性碰撞中,动量和动能都守恒。
You've got it
- momentum = mass × velocity (a vector)
- conservation: $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
- total momentum is the same before and after a collision
- momentum is conserved in all collisions; kinetic energy only in elastic ones
你掌握了
- 动量 = 质量 × 速度(一个向量)
- 守恒:$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
- 碰撞前后总动量相同
- 动量在所有碰撞中守恒;动能只在弹性碰撞中守恒