| English | 意味 |
|---|---|
| power/ˈpaʊə/ | 仕事率 |
| watt/wɒt/ | ワット |
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.
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.
速い仕事＝より大きな出力
運動が how quickly buildup される rates とエネルギーの delivery rate を関連付ける。
モーターが $600\ \text{J}$ の仕事を $3\ \text{s}$ で行う。ワット単位の出力はいくらか？
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
$P = W/t = 600/3 = 200\ \text{W}$.
出力のSI単位は何か？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
出力は ワット で測定され、$1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$ である。
出力は ____ で割った仕事に等しい。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
$P = W/t$ — 単位 時間 あたりの仕事。
1ワットは以下に等しい：
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
$1\ \text{W} = 1\ \tfrac{\text{J}}{\text{s}}$ — 1ジュールのエネルギーが每秒転送される。
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.
モーターが $50\ \text{N}$ の力で定常な $4\ \tfrac{\text{m}}{\text{s}}$ で押す。ワット単位の出力はいくらか？
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
$P = Fv = 50 \times 4 = 200\ \text{W}$.
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.
同じ総エネルギーを転送する2つの機械は、常に同じ出力を持つ。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
出力は秒あたりのエネルギーである。同じ総エネルギーであっても、より速く行う機械の方が出力が高い。
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.
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.
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 $P \times t$.