Elastic and Inelastic Collisions · 弹性与非弹性碰撞
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| elastic collision/ɪˈlæstɪk kəˈlɪʒn/ | 弹性碰撞 | tán xìng pèng zhuàng |
| inelastic collision/ɪnɪˈlæstɪk kəˈlɪʒn/ | 非弹性碰撞 | fēi tán xìng pèng zhuàng |
Click-clack balls vs a lump of clay
- Drop a steel ball onto a Newton's cradle and it clicks crisply — energy bounces along, barely lost.
- Throw a lump of clay at a wall and it just... splats, going nowhere.
- Both obey momentum conservation, but they treat kinetic energy very differently.
- Sorting collisions by what happens to KE is the last big idea of momentum.
咔哒作响的球 vs 一团黏土
- 把钢球放到牛顿摆上,它清脆地咔哒响——能量沿着弹过去,几乎没有损失。
- 把一团黏土扔向墙,它只是……啪地一声,哪也没去。
- 两者都遵守动量守恒,但它们对待动能的方式截然不同。
- 按动能发生的变化给碰撞分类,是动量的最后一个大概念。
Elastic collisions keep kinetic energy
- In an elastic collision 弹性碰撞, total kinetic energy is conserved as well as momentum.
- The objects bounce apart with no energy lost to heat or sound.
- Perfectly elastic collisions are an idealisation — gas molecules come close.
- Both $\sum p$ and $\sum E_k$ are the same before and after.
弹性碰撞保持动能
- 在弹性碰撞中,总动能和动量一样都守恒。
- 物体弹开,没有能量损失为热或声音。
- 完全弹性碰撞是一种理想化——气体分子接近这种情形。
- $\sum p$ 和 $\sum E_k$ 在碰撞前后都相同。
In an · 在 elastic · 弹性 collision, which quantity is conserved besides momentum? · 在弹性碰撞中，除了动量外，哪个量守恒？
An elastic collision conserves kinetic energy · 动能 as well as momentum. · 弹性碰撞既守恒动能也守恒动量。
Inelastic collisions lose kinetic energy
- In an inelastic collision 非弹性碰撞, momentum is conserved but kinetic energy is not.
- The "lost" KE turns into heat, sound and deformation.
- A perfectly inelastic collision is the extreme case: the objects stick together.
- Most real, everyday collisions (cars, clay, tackles) are inelastic.
非弹性碰撞损失动能
- 在非弹性碰撞中,动量守恒,但动能不守恒。
- "损失"的动能变成热、声音和形变。
- 完全非弹性碰撞是极端情形:物体粘在一起。
- 大多数真实的日常碰撞(汽车、黏土、擒抱)都是非弹性的。
Run a collision · 运行碰撞
Change the masses and speeds, run the collision, and compare the kinetic energy before and after. · 改变质量和速度，运行碰撞，比较碰撞前后的动能。
In a perfectly inelastic collision the objects ____ together. · 在完全非弹性碰撞中，物体____在一起。
A perfectly inelastic collision has the objects stick together and move as one. · 完全非弹性碰撞是指物体粘合在一起作为一个整体运动。
Select all · 所有 true statements about collisions. · 选择关于碰撞的所有正确陈述。
Elastic keeps KE; all isolated collisions keep momentum; perfectly inelastic means sticking. Inelastic collisions do not · 不 keep KE. · 弹性保持动能；所有孤立碰撞都保持动量；完全非弹性意味着粘连。非弹性碰撞不保持动能。
Momentum is always conserved — energy is the test
- Momentum is conserved in every collision, elastic or not (given an isolated system).
- Kinetic energy is the dividing line: kept ⇒ elastic, lost ⇒ inelastic.
- To classify a collision, compare the total KE before and after.
- Never assume KE is conserved unless the collision is stated to be elastic.
动量总是守恒——能量才是判据
- 动量在每一次碰撞中都守恒,无论弹性与否(在孤立系统中)。
- 动能才是分界线:保持 ⇒ 弹性,损失 ⇒ 非弹性。
- 要给碰撞分类,就比较碰撞前后的总动能。
- 除非声明碰撞是弹性的,否则绝不要假设动能守恒。
Momentum is conserved in both elastic and inelastic collisions (for an isolated system). · 对于孤立系统，动量在弹性和非弹性碰撞中都守恒。
Momentum is always conserved in an isolated collision. Kinetic energy is the quantity that distinguishes the two types. · 动量在孤立碰撞中始终守恒。动能是区分两种类型的量。
A collision keeps total momentum the same but the total kinetic energy drops. It is: · 一次碰撞保持总动量不变但总动能下降。这是：
Momentum conserved but KE lost ⇒ inelastic collision (the missing KE became heat). · 动量守恒但动能损失 ⇒ 非弹性碰撞（损失的动能转化为热能）。
Do not assume kinetic energy is conserved in a collision. Momentum is always conserved (isolated system), but KE is conserved only in an elastic collision. In an inelastic one, some KE becomes heat — even though momentum is unchanged.
不要假设碰撞中动能守恒。动量总是守恒(孤立系统),但动能只在弹性碰撞中守恒。在非弹性碰撞中,部分动能变成热——尽管动量不变。
A $2\ \text{kg}$ trolley at $3\ \tfrac{\text{m}}{\text{s}}$ sticks to a $1\ \text{kg}$ trolley at rest; together they move at $2\ \tfrac{\text{m}}{\text{s}}$. How much kinetic energy is lost, in joules? · A $2\ \text{kg}$ 静止在 $3\ \tfrac{\text{m}}{\text{s}}$ 的推车粘在一起，它们以 $1\ \text{kg}$ 的速度一起运动；总共损失了多少动能，单位为焦耳？ $2\ \tfrac{\text{m}}{\text{s}}$。损失了多少动能，以焦耳为单位？
KE before $= \tfrac12(2)(9) = 9\ \text{J}$; after $= \tfrac12(3)(4) = 6\ \text{J}$. Lost $= 9 - 6 = 3\ \text{J}$. · 碰撞前 KE $= \tfrac12(2)(9) = 9\ \text{J}$；碰撞后 $= \tfrac12(3)(4) = 6\ \text{J}$。损失 $= 9 - 6 = 3\ \text{J}$。
The stick-together trolleys from the last lesson: $2\ \text{kg}$ at $3\ \tfrac{\text{m}}{\text{s}}$ into a $1\ \text{kg}$ at rest, ending at $2\ \tfrac{\text{m}}{\text{s}}$ together.
- KE before $= \tfrac12(2)(3^2) = 9\ \text{J}$.
- KE after $= \tfrac12(3)(2^2) = 6\ \text{J}$.
$3\ \text{J}$ was lost to heat — so this is an inelastic collision, as expected for sticking.
上一节粘在一起的小车:$2\ \text{kg}$ 以 $3\ \tfrac{\text{m}}{\text{s}}$ 撞上静止的 $1\ \text{kg}$,最后一起以 $2\ \tfrac{\text{m}}{\text{s}}$ 运动。
- 碰撞前动能 $= \tfrac12(2)(3^2) = 9\ \text{J}$。
- 碰撞后动能 $= \tfrac12(3)(2^2) = 6\ \text{J}$。
$3\ \text{J}$ 损失为热——所以这是一次非弹性碰撞,正如粘在一起所预期的。
Momentum is conserved in all collisions. In an elastic collision, kinetic energy is also conserved (objects bounce). In an inelastic collision, some kinetic energy becomes heat; a perfectly inelastic collision has the objects stick together. Compare total KE to classify.
动量在所有碰撞中都守恒。在弹性碰撞中,动能也守恒(物体弹开)。在非弹性碰撞中,部分动能变成热;完全非弹性碰撞中物体粘在一起。比较总动能来分类。