Potential Energy · 势能
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| potential energy/pəˈtenʃl ˈenədʒi/ | 势能 | shì néng |
| gravitational potential energy/ˌɡrævɪˈteɪʃənl pəˈtenʃl ˈenədʒi/ | 引力势能 | yǐn lì shì néng |
| elastic potential energy/ɪˈlæstɪk pəˈtenʃl ˈenədʒi/ | 弹性势能 | tán xìng shì néng |
| conservative force/kənˈsɜːvətɪv fɔːs/ | 保守力 | bǎo shǒu lì |
| stable equilibrium/ˈsteɪbl ˌiːkwɪˈlɪbrɪəm/ | 稳定平衡 | wěn dìng píng héng |
| unstable equilibrium/ʌnˈsteɪbl ˌiːkwɪˈlɪbrɪəm/ | 不稳定平衡 | bù wěn dìng píng héng |
Energy waiting to happen
- Lift a book onto a shelf and it just sits there -- but it now holds hidden energy.
- Nudge it off and that stored energy becomes motion as it falls.
- Energy tied up in position is called potential energy.
- It is nature's rechargeable battery.
蓄势待发的能量
- 把书举到书架上,它只是待在那儿——但它现在储存着隐藏的能量。
- 把它推下来,那储存的能量在下落时变成运动。
- 与位置相关的能量叫做势能。
- 它是大自然的充电电池。
Potential energy
- Potential energy 势能 is energy stored in the arrangement of a system, not its motion.
- It depends only on where things are.
- Two common kinds power most of mechanics.
势能
- 势能是储存在系统排布中的能量,而不是它的运动中。
- 它只取决于东西在哪里。
- 两种常见的势能驱动着大部分力学。
Gravitational and elastic
- Gravitational potential energy 引力势能 near the ground: $U_g = mgy$ -- lift higher, store more.
- Elastic potential energy 弹性势能 in a spring: $U_s = \tfrac{1}{2}kx^2$ -- stretch more, store more.
- Release either and it converts into kinetic energy.
引力势能与弹性势能
- 地面附近的引力势能:$U_g = mgy$——举得越高,储存越多。
- 弹簧中的弹性势能:$U_s = \tfrac{1}{2}kx^2$——拉得越多,储存越多。
- 释放任一种,它都转化为动能。
Lift a $2\ \text{kg}$ book $1.5\ \text{m}$ ($g = 9.8$). How much gravitational potential energy is stored (in J)? · 举起一本重 $2\ \text{kg}$ 的书至高度 $1.5\ \text{m}$（$g = 9.8$）。储存的重力势能是多少（单位：J）？
$U_g = mgy = 2 \times 9.8 \times 1.5 = 29.4\ \text{J}$.
A spring ($k = 200\ \tfrac{\text{N}}{\text{m}}$) is compressed $0.10\ \text{m}$. Elastic potential energy stored (in J)? · 一根弹簧（$k = 200\ \tfrac{\text{N}}{\text{m}}$）被压缩了 $0.10\ \text{m}$。储存的弹性势能是多少（单位：J）？
$U_s = \tfrac{1}{2}kx^2 = \tfrac{1}{2}(200)(0.10)^2 = 1\ \text{J}$.
Select all · 所有 forms of potential energy covered here. · 选择所有本节涵盖的势能形式。
Gravitational and elastic are conservative-force energies. There is no frictional potential energy. · 重力和弹性是保守力的能量。不存在摩擦势能。
Force is the slope of energy
- A conservative force 保守力 (gravity, springs) is the negative slope of its potential energy:
- Steep energy hill → strong force. Flat → no force.
- This turns an energy graph into a force map.
力是能量的斜率
- 保守力(重力、弹簧)是其势能的负斜率:
- 陡峭的能量山坡 → 强力。平坦 → 无力。
- 这把能量图变成了一张力的地图。
Gravitational potential energy · 重力势能
Near the surface, gravitational potential energy is proportional to height. · 在地表附近，重力势能与高度成正比。
Friction has an associated potential energy, just like gravity. · 摩擦力具有 associated 势能，就像重力一样。
Only conservative forces have potential energy. Friction dissipates energy as heat -- it cannot be stored. · 只有保守力才有势能。摩擦力将能量耗散为热量——无法储存。
A conservative force equals the ____ slope of its potential energy, $F_x = -dU/dx$. · 保守力等于其势能 $F_x = -dU/dx$ 的 ____ 斜率。
$F_x = -dU/dx$ -- the force points "downhill" on the energy graph. · $F_x = -dU/dx$ —— 力指向能量图的“下坡”方向。
Reading a potential-energy graph
- On a $U$-versus-position graph, valleys are points of stable equilibrium 稳定平衡 (a nudge brings it back).
- Hilltops are unstable equilibrium 不稳定平衡 (a nudge sends it away).
- An object speeds up rolling downhill on the graph and slows going up.
读势能图
- 在 $U$-位置图上,谷底是稳定平衡点(轻推一下会回来)。
- 山顶是不稳定平衡(轻推一下就跑掉)。
- 在图上物体下坡时加速,上坡时减速。
On a potential-energy graph, a valley (local minimum) is a point of... · 在势能图上，山谷（局部最小值）是...的点。
At a valley a small nudge brings the object back -- stable equilibrium. A hilltop is unstable. · 在山谷处，轻微扰动会使物体回到原位——这是稳定平衡。山顶是不稳定的。
For a spring, $U_s = \tfrac{1}{2}kx^2$.
- The force is $F_x = -\dfrac{dU}{dx} = -kx$ -- Hooke's law falls right out of the derivative.
- The graph of $U_s$ is a parabola with its minimum at $x = 0$ -- a stable equilibrium.
对于弹簧,$U_s = \tfrac{1}{2}kx^2$。
- 力是 $F_x = -\dfrac{dU}{dx} = -kx$——胡克定律直接从导数里出来。
- $U_s$ 的图是一条最小值在 $x = 0$ 处的抛物线——一个稳定平衡。
Only conservative forces have a potential energy. Friction does not -- the energy it removes turns to heat and cannot be "stored" or recovered. So there is no "friction potential energy."
只有保守力才有势能。摩擦力没有——它移走的能量变成热,无法被"储存"或收回。所以不存在"摩擦势能"。
Potential energy is stored by position: gravitational $U_g = mgy$ and elastic $U_s = \tfrac{1}{2}kx^2$. A conservative force is the negative slope of its energy, $F_x = -dU/dx$. On a $U$-graph, valleys are stable equilibrium, hilltops unstable.
势能由位置储存:引力势能 $U_g = mgy$ 和弹性势能 $U_s = \tfrac{1}{2}kx^2$。保守力是其势能的负斜率,$F_x = -dU/dx$。在 $U$ 图上,谷底是稳定平衡,山顶是不稳定平衡。