# 功率

## 平均功率

$P_{avg} = \frac{\Delta W}{\Delta t}$

$P = \lim _{\Delta t\to 0} \frac{\Delta W}{\Delta t} = \frac{{\rm d}W}{{\rm d}t}$

## 力学

$W = \mathbf{F} \cdot \mathbf{d}$

$P(t) = \mathbf{F}(t) \cdot \mathbf{v}(t)$

$P_{avg} = \frac{1}{\Delta t}\int\mathbf{F} \cdot \mathbf{v}\;\mathrm{d}t$

$P(t) = \boldsymbol{\tau}\cdot \boldsymbol{\omega}$

$P_{avg}=\frac{1}{\Delta t}\int\boldsymbol{\tau} \cdot \boldsymbol{\omega}\mathrm{d}t$.

$P = p \cdot Q$

### 機械功率

$P = F_A v_A = F_B v_B, \!$

$\mathrm{MA} = \frac{F_B}{F_A} = \frac{v_A}{v_B}.$

$P = T_A \omega_A = T_B \omega_B, \!$
$\mathrm{MA} = \frac{T_B}{T_A} = \frac{\omega_A}{\omega_B}.$

## 电功率

$P =IV$

$P=I^2 R = \frac{V^2}{R}$

## 峰值功率及占空比

$P_0 = \max [p(t)]$.

$\epsilon_\mathrm{pulse} = \int_{0}^{T}p(t) \mathrm{d}t \,$

$P_\mathrm{avg} = \frac{1}{T} \int_{0}^{T}p(t) \mathrm{d}t = \frac{\epsilon_\mathrm{pulse}}{T} \,$

$\frac{P_\mathrm{avg}}{P_0} = \frac{\tau}{T} \,$

## 参考

1. ^ Halliday and Resnick. 6. Power. Fundamentals of Physics. 1974.
2. ^ Chapter 13, § 3, pp 13-2,3 The Feynman Lectures on Physics Volume I, 1963
3. ^ Chapter 6 § 7 Power Halliday and Resnick, Fundamentals of Physics 1974.
4. ^ Chapter 13, § 3, pp 13-2,3 The Feynman Lectures on Physics Volume I, 1963
5. ^ 燒一公斤的煤會放出每公斤15-30百萬焦耳的能量，而引爆一公斤的三硝基甲苯會產生4.7百萬焦耳的能量，有關煤的熱值，可以參考Fisher, Juliya. Energy Density of Coal. The Physics Factbook. 2003 [30 May 2011].，。有關三硝基甲苯的熱值，可以參考爆炸当量條目
6. ^ 6.0 6.1 Electric Power and Energy. [2010-05-18].