It was developed through Democritus who was a greek philosopher.
Hope this helps
Answer:
The time rate of change in air density during expiration is 0.01003kg/m³-s
Explanation:
Given that,
Lung total capacity V = 6000mL = 6 × 10⁻³m³
Air density p = 1.225kg/m³
diameter of the trachea is 18mm = 0.018m
Velocity v = 20cm/s = 0.20m/s
dv /dt = -100mL/s (volume rate decrease)
= 10⁻⁴m³/s
Area for trachea =
![\frac{\pi }{4} d^2\\= 0.785\times 0.018^2\\= 2.5434 \times10^-^4m^2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20d%5E2%5C%5C%3D%200.785%5Ctimes%200.018%5E2%5C%5C%3D%202.5434%20%5Ctimes10%5E-%5E4m%5E2)
0 - p × Area for trachea =
![\frac{d}{dt} (pv)=v\frac{ds}{dt} + p\frac{dv}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%28pv%29%3Dv%5Cfrac%7Bds%7D%7Bdt%7D%20%2B%20p%5Cfrac%7Bdv%7D%7Bdt%7D)
![-1.225\times2.5434\times10^-^4\times0.20=6\times10^-^3\frac{ds}{dt} +1.225(-1\times10^-^4)](https://tex.z-dn.net/?f=-1.225%5Ctimes2.5434%5Ctimes10%5E-%5E4%5Ctimes0.20%3D6%5Ctimes10%5E-%5E3%5Cfrac%7Bds%7D%7Bdt%7D%20%2B1.225%28-1%5Ctimes10%5E-%5E4%29)
![-1.225\times2.5434\times10^-^4\times0.20=6\times10^-^3\frac{ds}{dt} +1.225(-1\times10^-^4)](https://tex.z-dn.net/?f=-1.225%5Ctimes2.5434%5Ctimes10%5E-%5E4%5Ctimes0.20%3D6%5Ctimes10%5E-%5E3%5Cfrac%7Bds%7D%7Bdt%7D%20%2B1.225%28-1%5Ctimes10%5E-%5E4%29)
⇒![-0.623133\times10^-^4+1.225\times10^-^4=6\times10^-^3\frac{ds}{dt}](https://tex.z-dn.net/?f=-0.623133%5Ctimes10%5E-%5E4%2B1.225%5Ctimes10%5E-%5E4%3D6%5Ctimes10%5E-%5E3%5Cfrac%7Bds%7D%7Bdt%7D)
![\frac{ds}{dt} = \frac{0.6018\times10^-^4}{6\times10^-^3} \\\\= 0.01003kg/m^3-s](https://tex.z-dn.net/?f=%5Cfrac%7Bds%7D%7Bdt%7D%20%3D%20%5Cfrac%7B0.6018%5Ctimes10%5E-%5E4%7D%7B6%5Ctimes10%5E-%5E3%7D%20%5C%5C%5C%5C%3D%200.01003kg%2Fm%5E3-s)
ds/dt = 0.01003kg/m³-s
Thus, the time rate of change in air density during expiration is 0.01003kg/m³-s
Answer:
![\mathbf{F_1=4.41*10^4\ N}](https://tex.z-dn.net/?f=%5Cmathbf%7BF_1%3D4.41%2A10%5E4%5C%20N%7D)
![\mathbf{F_2 = 1.176*10^5 \ N}](https://tex.z-dn.net/?f=%5Cmathbf%7BF_2%20%3D%201.176%2A10%5E5%20%5C%20N%7D)
Explanation:
The missing image of the figure slide is attached in below.
However, from the model, it is obvious that it is in equilibrium.
As a result, the relation of the force and the torque is said to be zero.
i.e.
and ![\sum \tau = 0](https://tex.z-dn.net/?f=%5Csum%20%5Ctau%20%3D%200)
From the image, expressing the forces through the y-axis, we have:
![F_1+F_2 = W_B + W_P \\ \\ \implies 9.8(1500+15000) \\ \\ \implies \mathtt{1.617\times 10^5 \ N}](https://tex.z-dn.net/?f=F_1%2BF_2%20%3D%20W_B%20%2B%20W_P%20%5C%5C%20%5C%5C%20%5Cimplies%209.8%281500%2B15000%29%20%5C%5C%20%5C%5C%20%5Cimplies%20%20%5Cmathtt%7B1.617%5Ctimes%2010%5E5%20%5C%20N%7D)
Also, let the force
be the pivot and computing the torque to determine
:
Then:
![F_1(0)+F_2(20.0) = 10.0W_B + 15.0W_P](https://tex.z-dn.net/?f=F_1%280%29%2BF_2%2820.0%29%20%3D%2010.0W_B%20%2B%2015.0W_P)
![F_2 = \dfrac{((10*1500)+(15*15000))*9.8}{20.0}](https://tex.z-dn.net/?f=F_2%20%3D%20%5Cdfrac%7B%28%2810%2A1500%29%2B%2815%2A15000%29%29%2A9.8%7D%7B20.0%7D)
![F_2 = 117600 \ N](https://tex.z-dn.net/?f=F_2%20%3D%20117600%20%5C%20N)
![\mathbf{F_2 = 1.176*10^5 \ N}](https://tex.z-dn.net/?f=%5Cmathbf%7BF_2%20%3D%201.176%2A10%5E5%20%5C%20N%7D)
For the force equation:
![F_1+F_2=1.617*10^5 \ N;](https://tex.z-dn.net/?f=F_1%2BF_2%3D1.617%2A10%5E5%20%5C%20N%3B)
where:
![F_2 = 1.176*10^5 \ N](https://tex.z-dn.net/?f=F_2%20%3D%201.176%2A10%5E5%20%5C%20N)
Then:
![F_1+1.176*10^5 \ N=1.617*10^5 \ N](https://tex.z-dn.net/?f=F_1%2B1.176%2A10%5E5%20%5C%20N%3D1.617%2A10%5E5%20%5C%20N)
![F_1=1.617*10^5 \ N-1.176*10^5 \ N](https://tex.z-dn.net/?f=F_1%3D1.617%2A10%5E5%20%5C%20N-1.176%2A10%5E5%20%5C%20N)
![F_1=44100\ N](https://tex.z-dn.net/?f=F_1%3D44100%5C%20N)
![\mathbf{F_1=4.41*10^4\ N}](https://tex.z-dn.net/?f=%5Cmathbf%7BF_1%3D4.41%2A10%5E4%5C%20N%7D)
1.022 km/s
Hope this helps~~~~~~~~