Answer:
![\alpha = 0.305 rad/s^2](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.305%20rad%2Fs%5E2)
Explanation:
initial frequency of revolution is given as
![f_1 = 100/3 rpm](https://tex.z-dn.net/?f=f_1%20%3D%20100%2F3%20rpm)
now initial angular speed is
![\omega_i = 2\pi f](https://tex.z-dn.net/?f=%5Comega_i%20%3D%202%5Cpi%20f)
![\omega_i = 2\pi(\frac{100}{3\times 60})](https://tex.z-dn.net/?f=%5Comega_i%20%3D%202%5Cpi%28%5Cfrac%7B100%7D%7B3%5Ctimes%2060%7D%29)
![\omega_i = 3.49 rad/s](https://tex.z-dn.net/?f=%5Comega_i%20%3D%203.49%20rad%2Fs)
Similarly final angular speed is given as
![\omega_f = 2\pi f_2](https://tex.z-dn.net/?f=%5Comega_f%20%3D%202%5Cpi%20f_2)
![\omega_f = 2\pi(\frac{45}{60})](https://tex.z-dn.net/?f=%5Comega_f%20%3D%202%5Cpi%28%5Cfrac%7B45%7D%7B60%7D%29)
![\omega_f = 4.71 rad/s](https://tex.z-dn.net/?f=%5Comega_f%20%3D%204.71%20rad%2Fs)
Now angular acceleration is given as
![\alpha = \frac{\omega_f - \omega_i}{\Delta t}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B%5Comega_f%20-%20%5Comega_i%7D%7B%5CDelta%20t%7D)
![\alpha = \frac{4.71 - 3.49}{4}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B4.71%20-%203.49%7D%7B4%7D)
![\alpha = 0.305 rad/s^2](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.305%20rad%2Fs%5E2)
Use the formula. Plug in known values, so you get f = 3000*2 and get 6000N as a result.
Answer:
rise the air temperature is 0.179241 K
Explanation:
Given data
mass = 20000 kg
velocity = 18.5 m/s
long = 65 m
wide = 20 m
height = 12 m
density of the air = 1.20 kg/ m³
specific heat = 1020 J/(kg*K)
to find out
how much does the air temperature in the station rise
solution
we know here Energy lost by the train that is calculated by
loss in the kinetic energy that is = 1/2 m v²
loss in the kinetic energy = 0.5 × 20000 ×18.5²
loss in the kinetic energy is 3422500 J
and
this energy is used here to rise the air temperature that is KE / ( specific hat × mass )
so here
air volume = 65 ×20×12
air volume = 15600 m³
air mass = ρ × V = 1.2 × 15600
air mass = 18720 kg
so
rise the air temperature = 3422500 / ( 1020 × 18720)
rise the air temperature is 0.179241 K
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