Power · 功率
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| power/ˈpaʊə/ | 功率 | gōng lǜ |
| watts/wɒts/ | 瓦特 | wǎ tè |
| average power/ˈævrɪdʒ ˈpaʊə/ | 平均功率 | píng jūn gōng lǜ |
| instantaneous power/ˌɪnstənˈteɪnɪəs ˈpaʊə/ | 瞬时功率 | shùn shí gōng lǜ |
Same job, but how fast?
- Two cranes lift the same load to the same roof -- one in ten seconds, one in one.
- They do the same work, but the fast one is far more powerful.
- Power is not about how much energy, but how quickly you deliver it.
- It is the difference between a moped and a sports car.
同样的活,但有多快?
- 两台起重机把同样的负载吊到同样的屋顶——一台用十秒,一台用一秒。
- 它们做了同样的功,但快的那台要强大得多。
- 功率关乎的不是能量有多少,而是你交付得有多快。
- 这就是助力车和跑车的区别。
Power
- Power 功率 is the rate of doing work:
- Measured in watts 瓦特 -- one watt is one joule per second.
- Same work in less time means more power.
功率
- 功率是做功的速率:
- 以瓦特为单位——一瓦特就是每秒一焦耳。
- 用更短的时间做同样的功,就意味着更大的功率。
A machine does $600\ \text{J}$ of work in $3\ \text{s}$. What is its average power (in W)? · 一台机器在 $600\ \text{J}$ 内做了 $3\ \text{s}$的功。其平均功率（单位为瓦特）是多少？
$P = W/t = 600/3 = 200\ \text{W}$.
The SI unit of power is the , equal to one joule per second. · 功率的 SI 单位是，等于每秒一焦耳。
One watt = one joule per second. · 一瓦特 = 每秒一焦耳。
A stronger motor does the same $4900\ \text{J}$ of work in only $2\ \text{s}$. Its average power (in W)? · 更强劲的电机在仅 $4900\ \text{J}$ 的时间内完成相同的 $2\ \text{s}$功。其平均功率（单位：W）为？
$P = 4900/2 = 2450\ \text{W}$ -- same work, less time, so more power. · $P = 4900/2 = 2450\ \text{W}$ ——功相同，时间更短，因此功率更大。
Average versus instantaneous
- Average power 平均功率 is the total work divided by the total time.
- Instantaneous power 瞬时功率 is the rate at one exact moment.
- When force or speed changes, the two can differ a lot.
平均功率与瞬时功率
- 平均功率是总功除以总时间。
- 瞬时功率是某一确切时刻的速率。
- 当力或速度变化时,两者可能相差很大。
A car engine pushes with $500\ \text{N}$ while the car moves at $20\ \tfrac{\text{m}}{\text{s}}$. Instantaneous power (in W)? · 汽车引擎以 $500\ \text{N}$ 推动汽车，汽车以 $20\ \tfrac{\text{m}}{\text{s}}$ 移动。瞬时功率是多少（单位：W）？
$P = Fv = 500 \times 20 = 10{,}000\ \text{W}$ (10 kW). · $P = Fv = 500 \times 20 = 10{,}000\ \text{W}$ (10 kW)。
Select all · 所有 ways to increase the power a force delivers. · 选择所有能增加力所提供功率的方法。
$P = Fv$, so more force or more speed raises power. Spreading work over more time lowers power. · $P = Fv$，所以更大的力或更快的速度会提高功率。将功分摊到更长的时间上会降低功率。
Power from force and velocity
- At any instant, power is force times velocity:
- Push harder or move faster and you deliver more power.
- This is why cars need more engine power at high speed to overcome drag.
由力和速度得到功率
- 在任一瞬间,功率是力乘以速度:
- 推得更用力或动得更快,你就交付更多功率。
- 这就是为什么汽车在高速时需要更大的发动机功率来克服拽力。
Power delivered · 提供的功率
At a steady force, the power delivered is proportional to speed. · 在恒定力的情况下，提供的功率与速度成正比。
A more powerful motor always does more total work than a weaker one. · 功率更大的电机总是比功率较小的电机做更多的总功。
Power is a rate · 率. Two motors can do identical total work; the more powerful one just finishes faster. · 功率是一个速率。两台电机可以做相同的总功；功率较大的那台只是完成得更快。
Units and everyday sense
- One watt = one joule per second; a kilowatt is 1000 of them.
- A light bulb is tens of watts; a car engine is tens of thousands.
- Your electricity bill charges for energy (kilowatt-hours), which is power times time.
单位与日常感觉
- 一瓦特 = 每秒一焦耳;一千瓦是 1000 瓦。
- 一个灯泡是几十瓦;一台汽车发动机是几万瓦。
- 你的电费按能量(千瓦时)收费,即功率乘以时间。
A motor lifts a $50\ \text{kg}$ load $10\ \text{m}$ in $5\ \text{s}$ ($g = 9.8$).
- Work: $W = mgh = 50 \times 9.8 \times 10 = 4900\ \text{J}$.
- Average power: $P = \dfrac{W}{t} = \dfrac{4900}{5} = 980\ \text{W}$.
一台电机在 $5\ \text{s}$ 内把 $50\ \text{kg}$ 的负载吊高 $10\ \text{m}$($g = 9.8$)。
- 功:$W = mgh = 50 \times 9.8 \times 10 = 4900\ \text{J}$。
- 平均功率:$P = \dfrac{W}{t} = \dfrac{4900}{5} = 980\ \text{W}$。
More power does not mean more work or more energy -- it means the same work delivered faster. A powerful and a weak motor can do identical total work; the powerful one just finishes sooner.
更大的功率不意味着更多的功或更多的能量——它意味着同样的功被更快交付。一台强大的电机和一台弱的电机可以做完全相同的总功;强大的那台只是更早完成。
Power $P = dW/dt$ is how fast work is done, in watts (J/s). Average power divides total work by total time; instantaneous power is $\vec{F}\cdot\vec{v}$ at one moment. Same work in less time = more power -- power is a rate, not an amount.
功率 $P = dW/dt$ 是做功有多快,单位是瓦特(J/s)。平均功率是总功除以总时间;瞬时功率是某一时刻的 $\vec{F}\cdot\vec{v}$。用更短时间做同样的功 = 更大功率——功率是速率,不是数量。