Conservation of Energy · 能量守恒
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| conservation of energy/ˌkɒnsəˈveɪʃn ɒv ˈenədʒi/ | 能量守恒 | néng liàng shǒu héng |
| thermal energy/ˈθɜːml ˈenədʒi/ | 热能 | rè néng |
A roller coaster with no engine — yet it races on
- After the first climb, a roller coaster's motor switches off. Still it races through loops and hills.
- Its energy is never created or destroyed — only passed between forms.
- At the top it is mostly potential energy; at the bottom, mostly kinetic.
- This is the conservation of energy 能量守恒, one of physics' deepest laws.
没有引擎的过山车——却依然飞驰
- 爬完第一个坡后,过山车的马达就关掉了。它仍然穿过环圈和山坡飞驰。
- 它的能量既不会被创造也不会被毁灭——只是在不同形式之间传递。
- 在顶端它主要是势能;在底端,主要是动能。
- 这就是能量守恒,物理学最深刻的定律之一。
Mechanical energy transforms
- Mechanical energy is the sum of kinetic and potential energy: $E_k + E_p$.
- With no friction, this total stays constant as motion unfolds.
- Going down, $E_p$ falls and $E_k$ rises by the same amount; going up, the reverse.
- Energy is simply shifted from one account to the other.
机械能相互转化
- 机械能是动能与势能之和:$E_k + E_p$。
- 没有摩擦时,这个总量在运动展开时保持恒定。
- 下降时,$E_p$ 减小而 $E_k$ 等量增大;上升时则相反。
- 能量只是从一个账户转到另一个账户。
Watch PE turn into KE · 观察势能转化为动能
Drop from a height and watch potential energy convert to kinetic energy; add friction to send some to heat. · 从高度落下并观察势能转化为动能；加入摩擦使部分能量变为热。
Mechanical energy is the sum of kinetic energy and ____ energy. · 机械能是动能和____能之和。
Mechanical energy $= E_k + E_p$ — kinetic plus potential · 势. · 机械能$= E_k + E_p$ — 动能加势能。
On a frictionless track, where is the kinetic energy greatest? · 在无摩擦轨道上，动能最大的位置在哪里？
At the lowest point the PE is smallest, so the most energy is kinetic — the fastest point. · 在最低点势能最小，因此最多能量是动能 — 即最快点。
Where friction sends the energy
- Real tracks have friction, so mechanical energy seems to "disappear".
- It hasn't — it becomes thermal energy 热能 (heat) in the surfaces.
- Counting heat too, the total energy is still perfectly conserved.
- The universe keeps an exact ledger: energy only changes form.
摩擦把能量送去哪里
- 真实轨道有摩擦,所以机械能似乎"消失"了。
- 它没有消失——它变成了表面里的热能(热)。
- 把热也算进去,总能量仍然被完美地守恒。
- 宇宙记着一本精确的账:能量只是改变形式。
When friction slows a sliding block, that energy is destroyed. · 当摩擦力减缓滑动的滑块时，该能量被销毁了。
It is not destroyed — it becomes thermal energy (heat). The total energy is conserved. · 它没有被销毁 — 变成了热能（热量）。总能量是守恒的。
On a real (rough) slide, where does the "missing" mechanical energy go? · 在真实的（粗糙）滑梯上，“丢失”的机械能去哪了？
Friction converts mechanical energy into thermal energy. Counting heat, the total is conserved. · 摩擦力将机械能转化为热能。计算热量后，总量是守恒的。
Using conservation to solve problems
- Set the energy at the start equal to the energy at the end: $E_{k,i} + E_{p,i} = E_{k,f} + E_{p,f}$.
- For a drop from rest through height $h$: $mgh = \tfrac12 m v^2$, so $v = \sqrt{2gh}$.
- No need to track the messy forces along the way — just compare start and end.
- This shortcut is one of the most powerful tools in mechanics.
用守恒解题
- 把开始时的能量等于结束时的能量:$E_{k,i} + E_{p,i} = E_{k,f} + E_{p,f}$。
- 从静止经高度 $h$ 下落:$mgh = \tfrac12 m v^2$,所以 $v = \sqrt{2gh}$。
- 不必追踪途中杂乱的力——只要比较开始和结束。
- 这个捷径是力学中最有力的工具之一。
A ball is dropped from rest at $5\ \text{m}$ ($g = 10\ \tfrac{\text{m}}{\text{s}^2}$, no air resistance). What is its speed at the bottom, in $\tfrac{\text{m}}{\text{s}}$? · 一个球从静止状态在$5\ \text{m}$（$g = 10\ \tfrac{\text{m}}{\text{s}^2}$，无空气阻力）处落下。它在底部的速度是多少，单位为$\tfrac{\text{m}}{\text{s}}$？
$mgh = \tfrac12 mv^2 \Rightarrow v = \sqrt{2gh} = \sqrt{2\times10\times5} = 10\ \tfrac{\text{m}}{\text{s}}$.
Select all · 所有 correct statements about a frictionless pendulum swing. · 选择关于无摩擦单摆摆动的所有正确陈述。
Energy is conserved, not created: PE peaks at the top of the swing and becomes KE at the bottom. · 能量守恒而非产生：顶部势能峰值，底部转化为动能。
Energy is never destroyed — when it seems to vanish, it has usually turned into heat through friction or air resistance. "Energy lost" really means "energy transferred to a form we are no longer counting".
能量绝不会被毁灭——当它似乎消失时,通常是通过摩擦或空气阻力变成了热。"能量损失"其实是指"能量转移到了我们不再计入的形式"。
A ball is dropped from rest at a height of $5\ \text{m}$ ($g = 10\ \tfrac{\text{m}}{\text{s}^2}$, no air resistance).
- All the PE becomes KE: $mgh = \tfrac12 m v^2$, so $gh = \tfrac12 v^2$.
- $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 5} = \sqrt{100} = 10\ \tfrac{\text{m}}{\text{s}}$.
一个球从 $5\ \text{m}$ 高处静止下落($g = 10\ \tfrac{\text{m}}{\text{s}^2}$,无空气阻力)。
- 所有 PE 变成 KE:$mgh = \tfrac12 m v^2$,所以 $gh = \tfrac12 v^2$。
- $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 5} = \sqrt{100} = 10\ \tfrac{\text{m}}{\text{s}}$。
Conservation of energy: energy is never created or destroyed, only transformed. Without friction, mechanical energy $E_k + E_p$ stays constant, so $E_{k,i} + E_{p,i} = E_{k,f} + E_{p,f}$. Friction turns mechanical energy into heat, but the total is always conserved.
能量守恒:能量既不被创造也不被毁灭,只被转化。没有摩擦时,机械能 $E_k + E_p$ 保持恒定,所以 $E_{k,i} + E_{p,i} = E_{k,f} + E_{p,f}$。摩擦把机械能变成热,但总量始终守恒。