Potential Energy · 势能
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| potential energy/pəˈtenʃl ˈenədʒi/ | 势能 | shì néng |
A raised hammer holds energy, waiting
- Lift a hammer above a nail and it just... waits. Yet it now holds energy, ready to strike.
- Energy can be stored by position or shape, not only by motion.
- We call this stored energy potential energy 势能.
- Release it and the store pours back out as motion.
举起的锤子握着能量,在等待
- 把锤子举到钉子上方,它只是……等着。可它此刻握着能量,随时准备击下。
- 能量可以由位置或形状储存,而不只是由运动。
- 我们把这种储存的能量叫作势能。
- 释放它,储存就重新化为运动倾泻而出。
Gravitational potential energy
- Lifting a mass $m$ to a height $h$ stores gravitational PE: $E_p = mgh$.
- It equals the work done against gravity to raise it.
- The higher you lift, or the heavier the mass, the more energy is stored.
- Let it fall and this $mgh$ converts into kinetic energy.
重力势能
- 把质量 $m$ 举到高度 $h$ 会储存重力势能:$E_p = mgh$。
- 它等于克服重力把它举起所做的功。
- 举得越高、质量越大,储存的能量越多。
- 让它落下,这个 $mgh$ 就转化为动能。
Store energy by lifting · 通过提升储存能量
Raise the starting height and see how much potential energy is stored, ready to become kinetic energy. · 提高起始高度，观察储存了多少势能，准备转化为动能。
Lift a $2\ \text{kg}$ book to a $1.5\ \text{m}$ shelf ($g = 9.8\ \tfrac{\text{N}}{\text{kg}}$). How much gravitational PE is stored, in joules? · 将一本$2\ \text{kg}$的书举到$1.5\ \text{m}$的架子上（$g = 9.8\ \tfrac{\text{N}}{\text{kg}}$）。储存了多少重力势能，单位为焦耳？
$E_p = mgh = 2 \times 9.8 \times 1.5 = 29.4\ \text{J}$.
Gravitational potential energy · 重力势能 $mgh$ increases when you increase which of these? · 增加以下哪项会使重力势能$mgh$增大？
$E_p = mgh$ grows with mass, height and $g$. Colour is irrelevant. · $E_p = mgh$随质量、高度和$g$增大。颜色无关紧要。
When a raised object falls, its gravitational potential energy converts into kinetic energy. · 当被举高的物体下落时，其重力势能转化为动能。
As height drops, $mgh$ falls and the lost PE reappears as kinetic energy $\tfrac12 mv^2$. · 随着高度下降，$mgh$减小，损失的势能重新出现为动能$\tfrac12 mv^2$。
Elastic potential energy
- A stretched or compressed spring also stores energy: elastic PE $E_p = \tfrac12 k x^2$.
- Here $k$ is the spring constant and $x$ the extension.
- A drawn bow, a wound spring, a squeezed trampoline — all hold elastic PE.
- Release the deformation and the store becomes motion.
弹性势能
- 被拉伸或压缩的弹簧也储存能量:弹性势能 $E_p = \tfrac12 k x^2$。
- 这里 $k$ 是弹簧常数,$x$ 是伸长量。
- 拉开的弓、上紧的发条、压下的蹦床——都握着弹性势能。
- 释放这种变形,储存就化为运动。
The elastic potential energy of a spring is $\tfrac12 k \_\_$ (fill in the missing part). · 弹簧的弹性势能为$\tfrac12 k \_\_$（填入缺失部分）。
$E_p = \tfrac12 k x^2$ — it grows with the square of the extension. · $E_p = \tfrac12 k x^2$ — 它随伸长量的平方增大。
Potential energy is relative
- Gravitational PE depends on the reference level you choose for $h = 0$.
- Only changes in PE ($\Delta E_p$) matter physically, so you may pick any zero.
- PE goes with conservative forces — gravity and springs — whose stored energy is fully recoverable.
- Friction is not conservative: its energy turns to heat and cannot be recovered as PE.
势能是相对的
- 重力势能取决于你为 $h = 0$ 选择的参考水平面。
- 只有 PE 的变化($\Delta E_p$)才有物理意义,所以你可以任选一个零点。
- 势能对应保守力——重力和弹簧——它们储存的能量可以完全收回。
- 摩擦力不是保守的:它的能量变成热,无法作为势能收回。
Gravitational potential energy has one absolute value, the same for every observer. · 重力势能有一个绝对值，对所有观察者都相同。
It is measured relative to a chosen zero height; only the change · 变化 in PE is physically meaningful. · 它是相对于选定的零高度测量的；只有势能的变化具有物理意义。
Which force's stored energy can be fully recovered as potential energy? · 哪种力的储存能量可以完全恢复为势能？
Gravity is a conservative force — its energy is fully recoverable. Friction turns energy into heat. · 重力是保守力 — 其能量可完全恢复。摩擦力将能量转化为热。
Gravitational PE is measured relative to a chosen zero height — there is no absolute value. Always state where $h = 0$ is (the floor, the ground, the table). Only the change in PE affects the physics.
重力势能是相对于选定的零高度测量的——没有绝对值。总要说明 $h = 0$ 在哪里(地板、地面、桌面)。只有 PE 的变化才影响物理。
Lift a $2\ \text{kg}$ book to a shelf $1.5\ \text{m}$ high ($g = 9.8\ \tfrac{\text{N}}{\text{kg}}$).
- $E_p = mgh = 2 \times 9.8 \times 1.5 = 29.4\ \text{J}$.
That $29.4\ \text{J}$ is stored, ready to become kinetic energy if the book falls.
把一本 $2\ \text{kg}$ 的书举到 $1.5\ \text{m}$ 高的架上($g = 9.8\ \tfrac{\text{N}}{\text{kg}}$)。
- $E_p = mgh = 2 \times 9.8 \times 1.5 = 29.4\ \text{J}$。
这 $29.4\ \text{J}$ 被储存起来,若书落下就随时化为动能。
Potential energy is stored energy of position or shape. Gravitational PE is $E_p = mgh$; elastic PE is $E_p = \tfrac12 kx^2$. Gravitational PE is measured relative to a chosen zero, and only its change matters. It comes from conservative forces.
势能是位置或形状储存的能量。重力势能是 $E_p = mgh$;弹性势能是 $E_p = \tfrac12 kx^2$。重力势能是相对于选定的零点测量的,只有它的变化才重要。它来自保守力。