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 |
| perfectly inelastic collision/ˈpɜːfektlɪ ɪnɪˈlæstɪk kəˈlɪʒn/ | 完全非弹性碰撞 | wán quán fēi tán xìng pèng zhuàng |
| energy lost/ˈenədʒi lɒst/ | 损失的能量 | sǔn shī de néng liàng |
Pool balls versus clay
- Two pool balls click off each other and both keep rolling briskly.
- Two lumps of clay smack together and stop dead, stuck as one.
- Both obey the same momentum law -- yet feel completely different.
- The difference is what happens to the energy.
台球与黏土
- 两个台球相互一碰,都继续轻快地滚动。
- 两块黏土啪地撞在一起,当场停下,黏成一体。
- 两者都遵守同一条动量定律——感觉却完全不同。
- 区别在于能量发生了什么。
Momentum yes, energy maybe
- Momentum is conserved in every collision -- always.
- Kinetic energy is not always conserved -- some can turn to heat, sound, or dents.
- That single difference sorts collisions into two families.
动量一定守恒,能量不一定
- 动量在每一次碰撞中都守恒——总是如此。
- 动能并不总是守恒——有些会变成热、声或凹痕。
- 就这一个区别,把碰撞分成两大类。
Momentum is conserved in every collision, elastic or not. · 动量在每一次碰撞中都守恒，无论是弹性的还是非弹性的。
Yes -- momentum is always conserved (no net external force). Only kinetic energy may or may not be. · 是的——动量总是守恒的（没有净外力）。只有动能可能守恒也可能不守恒。
Elastic versus inelastic
- An elastic collision 弹性碰撞 conserves kinetic energy too (ideal, like hard spheres).
- An inelastic collision 非弹性碰撞 loses some kinetic energy to other forms.
- Most real collisions are at least a little inelastic.
弹性碰撞与非弹性碰撞
- 弹性碰撞也守恒动能(理想情形,如硬球)。
- 非弹性碰撞把一些动能损失为其他形式。
- 大多数真实碰撞至少有点非弹性。
In which collision is kinetic energy conserved? · 在哪次碰撞中动能守恒？
Only an elastic collision conserves kinetic energy. Momentum, though, is conserved in all of them. · 只有弹性碰撞才守恒动能。不过，动量在所有碰撞中都守恒。
Select all · 所有 true statements about collisions. · 选择关于碰撞的所有正确陈述。
Momentum always holds; kinetic energy holds only when the collision is elastic. · 动量始终成立；动能仅在碰撞是弹性时才成立。
Perfectly inelastic
- A perfectly inelastic collision 完全非弹性碰撞 is the extreme case: the objects stick together and move off with one common velocity.
- Momentum conservation alone gives that final velocity.
- The clay lumps are the classic example.
完全非弹性
- 完全非弹性碰撞是极端情形:物体黏在一起,以一个共同速度一起运动。
- 仅凭动量守恒就能给出这个末速度。
- 黏土块就是经典例子。
Elastic or inelastic? · 弹性或非弹性？
Momentum is always conserved, but kinetic energy is not. Sort each collision. · 动量总是守恒的，但动能不是。对每次碰撞进行分类。
A $3\ \text{kg}$ cart at $4\ \tfrac{\text{m}}{\text{s}}$ sticks to a stationary $1\ \text{kg}$ cart. Their common speed afterward (in m/s)? · A $3\ \text{kg}$ 购物车在 $4\ \tfrac{\text{m}}{\text{s}}$ 粘在一个静止的 $1\ \text{kg}$ 购物车上。它们之后的共同速度（以米/秒为单位）？
$3(4) = (3 + 1)v_f$, so $v_f = 12/4 = 3\ \tfrac{\text{m}}{\text{s}}$. · $3(4) = (3 + 1)v_f$，所以 $v_f = 12/4 = 3\ \tfrac{\text{m}}{\text{s}}$。
A collision where the objects stick together is called perfectly . · 物体粘在一起的碰撞称为完全。
In a perfectly inelastic collision the objects move off with one common velocity. · 在完全非弹性碰撞中，物体以一个共同速度飞出。
Finding the energy lost
- Compare total kinetic energy before and after the collision.
- Any drop is the energy lost 损失的能量 -- gone to heat, sound, or deformation.
- In a perfectly inelastic collision this loss is the largest.
求损失的能量
- 比较碰撞前后的总动能。
- 任何减少就是损失的能量——变成了热、声或形变。
- 在完全非弹性碰撞中,这种损失最大。
Before a collision the total KE is $20\ \text{J}$; after it is $14\ \text{J}$. How much energy was lost (in J)? · 碰撞前总动能是 $20\ \text{J}$；碰撞后是 $14\ \text{J}$。损失了多少能量（单位：J）？
Energy lost · 损失的能量 $= 20 - 14 = 6\ \text{J}$, gone to heat, sound, or deformation. · 损失的能量 $= 20 - 14 = 6\ \text{J}$，转化为热、声或变形。
A $2\ \text{kg}$ cart at $3\ \tfrac{\text{m}}{\text{s}}$ hits and sticks to a stationary $4\ \text{kg}$ cart.
- Momentum: $2(3) = (2 + 4)v_f$, so $v_f = 1\ \tfrac{\text{m}}{\text{s}}$.
- KE before $= \tfrac{1}{2}(2)(9) = 9\ \text{J}$; after $= \tfrac{1}{2}(6)(1) = 3\ \text{J}$ -- so $6\ \text{J}$ was lost to heat.
一个 $2\ \text{kg}$ 的小车以 $3\ \tfrac{\text{m}}{\text{s}}$ 撞上并黏住一个静止的 $4\ \text{kg}$ 小车。
- 动量:$2(3) = (2 + 4)v_f$,所以 $v_f = 1\ \tfrac{\text{m}}{\text{s}}$。
- 碰前动能 $= \tfrac{1}{2}(2)(9) = 9\ \text{J}$;碰后 $= \tfrac{1}{2}(6)(1) = 3\ \text{J}$——所以 $6\ \text{J}$ 损失为热。
Never assume kinetic energy is conserved unless a collision is stated to be elastic. Using energy conservation on an inelastic collision gives a wrong answer -- momentum is the law that always holds.
除非碰撞被明确说明为弹性,否则绝不要假设动能守恒。对非弹性碰撞用能量守恒会得到错误答案——动量才是永远成立的定律。
Momentum is conserved in every collision; kinetic energy only in an elastic collision. An inelastic collision loses some energy; a perfectly inelastic collision (objects stick together) loses the most. Compare KE before and after to find the energy lost to heat and sound.
动量在每一次碰撞中都守恒;动能只在弹性碰撞中守恒。非弹性碰撞损失一些能量;完全非弹性碰撞(物体黏在一起)损失最多。比较碰前碰后的动能,就能求出损失为热和声的损失的能量。