Power · 功率
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| power/ˈpaʊə/ | 功率 | gōng lǜ |
| watt/wɒt/ | 瓦特 | wǎ tè |
Two cranes, same load — which one wins the race?
- Two cranes lift an identical crate to the same rooftop. Both do exactly the same work.
- But one finishes in ten seconds and the other in a full minute.
- The fast crane is more powerful — it does the work at a higher rate.
- Power 功率 is not how much work, but how fast it is done.
两台起重机,同样的载荷——哪台更强?
- 两台起重机把一个相同的箱子吊到同一屋顶。两者做的功完全相同。
- 但一台十秒完成,另一台用了整整一分钟。
- 那台快的起重机功率更大——它以更高的速率做功。
- 功率不是做了多少功,而是做得多快。
Power is a rate
- Power is the rate of doing work, or of transferring energy: $P = \dfrac{W}{t}$.
- It is measured in watts 瓦特 ($1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$).
- Same work in less time means more power; same time with more work means more power too.
- A $100\ \text{W}$ bulb turns $100$ joules of electrical energy into light and heat each second.
功率是一个速率
- 功率是做功或传递能量的速率:$P = \dfrac{W}{t}$。
- 它以瓦特为单位($1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$)。
- 同样的功用更少的时间意味着更大功率;同样的时间做更多功也意味着更大功率。
- 一只 $100\ \text{W}$ 的灯泡每秒把 $100$ 焦耳的电能变成光和热。
Faster work, more power · 更快的做功，更大的功率
Relate how quickly motion builds up to the rate at which energy is delivered. · 关联运动建立的速度与能量输送的速率。
A motor does $600\ \text{J}$ of work in $3\ \text{s}$. What is its power, in watts? · 一台电动机在 $600\ \text{J}$ 时间内做功 $3\ \text{s}$。其功率是多少瓦？
$P = W/t = 600/3 = 200\ \text{W}$.
What is the SI unit of power? · 功率的SI单位是什么？
Power is measured in watts, where $1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$. · 功率以瓦特为单位测量，其中$1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$。
Power equals work divided by . · 功率等于功除以。
$P = W/t$ — work per unit time · 时间. · $P = W/t$ — 单位时间内的功。
One watt is equal to: · 一瓦特等于：
$1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$ — one joule of energy transferred each second. · $1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$ — 每秒转移一焦耳的能量。
Power, force and speed
- For a steady force pushing at constant speed, power is also $P = Fv$.
- A car engine pushing harder or driving faster delivers more power.
- This links the "energy" view ($W/t$) to the "force" view ($Fv$) of power.
- Both give watts, and both describe the same rate of energy transfer.
功率、力与速度
- 对以恒定速度施加的稳定力,功率也是 $P = Fv$。
- 汽车引擎推得更用力或开得更快,就输出更大功率。
- 这把功率的"能量"观点($W/t$)与"力"观点($Fv$)联系起来。
- 两者都给出瓦特,都描述同一个能量传递速率。
A motor pushes with $50\ \text{N}$ at a steady $4\ \tfrac{\text{m}}{\text{s}}$. What power does it deliver, in watts? · 一台电动机以$50\ \text{N}$的力在恒定的$4\ \tfrac{\text{m}}{\text{s}}$下运行。它输出的功率是多少瓦特？
$P = Fv = 50 \times 4 = 200\ \text{W}$.
Power in everyday life
- A sprinter, a kettle, a phone charger — each is rated by its power in watts.
- Bigger power means faster energy delivery, not more total energy.
- Over time, energy used $= P \times t$ (this is what electricity bills charge for).
- A low-power device left on for hours can use more energy than a high-power one used briefly.
日常生活中的功率
- 短跑运动员、水壶、手机充电器——每一个都用它的功率(瓦特)来标定。
- 功率越大意味着能量传递越快,而不是总能量越多。
- 随着时间,所用能量 $= P \times t$(这正是电费所收取的)。
- 一个低功率设备开几个小时,可能比一个高功率设备用一会儿耗更多能量。
Two machines that transfer the same total energy always have the same power. · 两台转移相同总能量的机器总是具有相同的功率。
Power is energy per second. The machine that does it faster has more power, even for the same total energy. · 功率是每秒的能量。即使总能量相同，做得更快的机器功率更大。
Power is not the same as energy. Two devices can transfer the same total energy, yet the one that does it faster has the higher power. Power is energy per second, not the energy itself.
功率不等同于能量。两个设备可以传递相同的总能量,但做得更快的那个功率更高。功率是每秒的能量,而不是能量本身。
A motor does $600\ \text{J}$ of work in $3\ \text{s}$.
- $P = \dfrac{W}{t} = \dfrac{600}{3} = 200\ \text{W}$.
If it instead pushes with $50\ \text{N}$ at $4\ \tfrac{\text{m}}{\text{s}}$: $P = Fv = 50 \times 4 = 200\ \text{W}$ — the same power.
一台马达在 $3\ \text{s}$ 内做 $600\ \text{J}$ 的功。
- $P = \dfrac{W}{t} = \dfrac{600}{3} = 200\ \text{W}$。
如果它改为以 $50\ \text{N}$、$4\ \tfrac{\text{m}}{\text{s}}$ 推动:$P = Fv = 50 \times 4 = 200\ \text{W}$——同样的功率。
Power is the rate of doing work or transferring energy: $P = \dfrac{W}{t} = Fv$, measured in watts ($1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$). It measures how fast energy moves, not how much — energy used is $P \times t$.
功率是做功或传递能量的速率:$P = \dfrac{W}{t} = Fv$,以瓦特为单位($1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$)。它量度能量移动得多快,而非多少——所用能量是 $P \times t$。