普通物理

注意：

1. 本条目为个人之重点笔记，非完整讲义。
2. 请在偏好设定中关闭章节编号。
3. 本教材以 General Physics for Sciences and Engineering Faculties e.10 (Serway, Jewett)

12

• Equilibrium ($\Sigma F=0,\Sigma \tau =0$)

14 流体力学 Fluid Mechanics

例题: 10 16 21 29 34 38 44 46 48 49
流体力学是研究流体运动及受力的物理分支。流体分为气液两种。

气体 Gases	液体 Liquid
均匀分布整个空间 Fill their containers	占据空间中最低的地方，具有固定体积 Occupies the lowest possible regions
relatively incompressible 相对不可压缩	compressible (whose $\rho$ is strongly dependent on T, P)
molecules with short-ranged bond 具有分子间引力	molecules hardly interact with one another 分子间几乎不互相作用

Pressure in fluid

• Pressure $P=r{\frac {F}{A}}$ 压力为力面之商。
  • Pascal (SI, $1Pa={\frac {1N}{m^{2}}}$, 中文称帕斯卡
  • Torr (=mmHg, 中文称托)
  • Bar (=100kPa, 中文称巴，气象学常用)。
• Density 密度 $\rho ={\frac {m}{\text{V}}}$
  

$${\begin{aligned}{\text{in Equilibrium,}}\\P_{1}\cdot A-(P+dP)A-\rho (Ady)g&=0\\-dP-\rho gdy&=0\\\int _{P_{1}}^{P_{2}}dP&=\int _{y_{1}}^{y_{2}}\rho gdy\\{\text{for Liquid, the density is const.}}\\\Delta P=-\rho g\int dy=-\rho g\Delta y\\P=P_{0}+\rho gh\\{\text{for Gases, the density is variable.}}\\{\frac {\rho }{\rho _{0}}}={\frac {P}{P_{0}}}\Rightarrow \rho =P\cdot {\frac {\rho _{0}}{P_{0}}}\\dP=-\rho gdy=-P{\frac {\rho _{0}}{P_{0}}}gdy\\\Rightarrow {\frac {dP}{P}}&=-{\frac {\rho _{0}}{P_{0}}}gdy\\&=-a\cdot dy{\text{, where a is 0.116 }}km^{-1}\\\int _{P_{0}}^{P}{\frac {dP}{P}}=-a\int _{y_{0}}^{y}dy\\lnP-lnP_{0}=-ay\\P=P_{0}\cdot \exp(-{\frac {\rho _{0}}{P_{0}}}gy)\end{aligned}}$$

• Pascal's law:${\text{P is const, }}{\frac {F_{1}}{A_{1}}}={\frac {F_{2}}{A_{2}}}$

Fluid Dynamics流体动力学

• Ideal Fluid理想液体:
  • luminar flow:
    • 不旋转、不可压缩、稳定流动、
  • streamline流线, 类似磁力线的东西
    • smooth path 物体在流体中时沿平滑路径，即流线运动
    • no crossing 两条流线不相交
    • 与流速的关系：速度方向即流线切向，大小即流线密度。

• Continuity equation for an incompressible fluid: 任一处密度相等，且任一截面单位时间流过质量相等。

$\rho \cdot A\cdot v{\text{ is const., so }}A\cdot v{\text{ is const.}}$

16 Wave Functio

8,14,18,22,30,37,42,51,57,60

16.1 type of waves

• Transverse Wave 横波
• Longitudinal Wave 纵波
• Surface wave 表面波:Particles move along a circular trace, i.e. it has both perpendicular wave and parallel wave components.

16.2 Wave Funtio du Travelling Wave

• 匴法：平移回t=0时位置

$y_{t=0}=f(x)$，给出t=0时原本波形。 $y(x,t)=f(x_{t=0})=f(x-vt)$, where the velocity is const. (注意 v, t的正负)

• 周期波：以Sinusoidal Wave弦波为举例：

$y(x,t=0)=f(x)=A\sin(ax)$ $y({\frac {\lambda }{2}},0)=0\Rightarrow a={\frac {2\pi }{\lambda }}$ $y(x,t\neq 0)=f(x-vt)=A\sin[{\frac {2\pi }{\lambda }}\cdot (x-vt)]$，又 $v={\frac {\lambda }{T}}$，则
$y(x,t)=A\sin[2\pi ({\frac {x}{\lambda }}-{\frac {t}{T}})]=A\sin(2\pi \lambda ^{-1}-\omega t+\phi )$ (因为 $\omega ={\frac {2\pi }{T}}$

18 Temperature

• from Macroscopic view:
  • Thermodynamics - eto empirical laws
  • Uses scalars (P, V, T, m)
• from Microscopic view:
  • Kinetic theory of gas - Newton's law is applied to describe the motion of molecule of system.
  • Uses vectors (r, v, a)

18.1 Temperature

• Thermal contact (热交换):Energy can exchange between the 2 system
• Thermal equilibrium (热平衡): the 2 system dont exchange energy by heat or electromagnetic radiation.
• Zeroth Law of Thermodynamics: A and C are in ThEq, B and C are in ThEq then A and B are in ThEq.

18.2 Thermometres

气相液相固相的温度计。

19 the First Law of Thermodynamics

圈题目：6 14 15 22 23 34 35 40 44 45

19.2 Heat and Internal Energy

• Heat 热 - ecce energia.