# 力

## 描述

### 平衡

#### 狹義相對論

$\mathbf{F} = \mathrm{d}\mathbf{p}/\mathrm{d}t$

$\mathbf{p} = \cfrac{m\mathbf{v}}{\sqrt{1 - \cfrac{v^2}{c^2}}}$

$v$是速度，
$c$是光速。

$F_x = \gamma^3 m a_x \,$
$F_y = \gamma m a_y \,$
$F_z = \gamma m a_z \,$

$\gamma = \cfrac{1}{\sqrt{1 - \cfrac{v^2}{c^2}}}.$

## 基礎模型

### 重力

$\mathbf{F} = m\mathbf{g}$

$\mathbf{g}=-\frac{GM_\oplus}{{R_\oplus}^2} \hat\mathbf{r}$

$\mathbf{F}=-\frac{Gm_{1}m_{2}}{r^2} \hat\mathbf{r}$

## 位能

$\mathbf{F}=-\boldsymbol{\nabla} U.$

### 守恆力

$\mathbf{F} = - \frac{G m_1 m_2 \mathbf{r}}{r^3}$

$\mathbf{F} = \frac{q_{1} q_{2} \mathbf{r}}{4 \pi \epsilon_{0} r^3}$

$\mathbf{F} = - k \mathbf{r}$

## 測量單位

N (國際單位制導出單位)

dyne

kgf

lbf

pdl
1 N ≡ 1 kg·m/s² = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbfF ≈ 7.2330 pdl
1 dyn = 10−5 N ≡ 1 g·cm/s² ≈ 1.0197×10−6 kp ≈ 2.2481×10−6 lbfF ≈ 7.2330×10−5 pdl
1 kp = 9.80665 N = 980665 dyn gn·(1 kg) ≈ 2.2046 lbfF ≈ 70.932 pdl
1 lbfF ≈ 4.448222 N ≈ 444822 dyn ≈ 0.45359 kp gn·(1 lb) ≈ 32.174 pdl
1 pdl ≈ 0.138255 N ≈ 13825 dyn ≈ 0.014098 kp ≈ 0.031081 lbfF ≡ 1 lb·ft/s²

## 參考

• Corbell, H.C.; Philip Stehle. Classical Mechanics p 28,. New York: Dover publications. 1994. ISBN 0-486-68063-0.
• Cutnell, John d.; Johnson, Kenneth W. Physics, Sixth Edition. Hoboken, NJ: John Wiley & Sons Inc. 2004.
• Feynman, R. P., Leighton, R. B., Sands, M. Lectures on Physics, Vol 1. Addison-Wesley. 1963. ISBN 0-201-02116-1.
• Halliday, David; Robert Resnick; Kenneth S. Krane. Physics v. 1. New York: John Wiley & Sons. 2001. ISBN 0-471-32057-9.
• Parker, Sybil. Encyclopedia of Physics, p 443,. Ohio: McGraw-Hill. 1993. ISBN 0-07-051400-3.
• Francis W. Sears, Mark W. Zemansky, Hugh D. Young. University Physics. Reading, MA: Addison-Wesley. 1982. ISBN 0-201-07199-1.
• Serway, Raymond A. Physics for Scientists and Engineers. Philadelphia: Saunders College Publishing. 2003. ISBN 0-534-40842-7.
• Tipler, Paul. Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics 5th. W. H. Freeman. 2004. ISBN 0-7167-0809-4.
• Verma, H.C. Concepts of Physics Vol 1. 2004 Reprint. Bharti Bhavan. 2004. ISBN 81-7709-187-5.