Answer:
a) 19.4 m/s
b) 19 m/s
Explanation:
a) In the given question,
the potential energy at the initial point = Ui = 0
the potential energy at the final point = Uf = mgh
the kinetic energy at the initial point = Ki = 1/2 mv₀².
the kinetic energy at the final point = Kf = 0
work done by air= Ea= fh = 0.262 N
Now, using the law of conservation of energy
initial energy= final energy
Ki +Ui = Kf + Uf +Ea
1/2 mv₀² + 0 = 0 + mgh + fh
1/2 mv₀² = mgh + fh
h = v₀²/ 2g (1 +f/w)
calculate m
m= w/g = 5.29 /9.8
= 0.54 kg
h = 20 ²/ (2 x9.80) x (1 0.265/5.29)
h = 19.4 m.
b) 1/2 mv² + 2fh = 1/2 mv₀²
Vg = 19 m/s
Wavelength of any wave = (speed) / (frequency)
Speed of light = 300,000,000 m/sec
Wavelength = 3 x 10 to the 8 / 750 x 10 to the 12 = 4 x 10 to the -7 or 400 nanometers.
Answer:
![V_2 = 0.125 m^3](https://tex.z-dn.net/?f=V_2%20%3D%200.125%20m%5E3)
Work done = = 5 kJ
Explanation:
Given data:
volume of nitrogen ![v_1 = 0.08 m^3](https://tex.z-dn.net/?f=%20v_1%20%3D%200.08%20m%5E3)
![P_1 = 150 kPa](https://tex.z-dn.net/?f=P_1%20%3D%20150%20kPa)
![T_1 = 200 degree celcius = 473 Kelvin](https://tex.z-dn.net/?f=T_1%20%3D%20200%20degree%20celcius%20%3D%20473%20Kelvin)
![P_2 = 80 kPa](https://tex.z-dn.net/?f=P_2%20%3D%2080%20kPa)
Polytropic exponent n = 1.4
![\frac{T_2}{T_1} = [\frac{P_2}{P_1}]^{\frac{n-1}{n}](https://tex.z-dn.net/?f=%5Cfrac%7BT_2%7D%7BT_1%7D%20%3D%20%5B%5Cfrac%7BP_2%7D%7BP_1%7D%5D%5E%7B%5Cfrac%7Bn-1%7D%7Bn%7D)
putting all value
![\frac{T_2}{473} = [\frac{80}{150}]^{\frac{1.4-1}{1.4}](https://tex.z-dn.net/?f=%5Cfrac%7BT_2%7D%7B473%7D%20%3D%20%5B%5Cfrac%7B80%7D%7B150%7D%5D%5E%7B%5Cfrac%7B1.4-1%7D%7B1.4%7D)
![\frac{T_2} = 395.23 K = 122.08 DEGREE \ CELCIUS](https://tex.z-dn.net/?f=%5Cfrac%7BT_2%7D%20%3D%20395.23%20K%20%3D%20122.08%20DEGREE%20%5C%20CELCIUS)
polytropic process is given as
![P_1 V_1^n = P_2 V_2^n](https://tex.z-dn.net/?f=P_1%20V_1%5En%20%3D%20P_2%20V_2%5En)
![150\times 0.08^{1.4} = 80 \times V_2^{1.4}](https://tex.z-dn.net/?f=150%5Ctimes%200.08%5E%7B1.4%7D%20%3D%2080%20%5Ctimes%20V_2%5E%7B1.4%7D)
![V_2 = 0.125 m^3](https://tex.z-dn.net/?f=V_2%20%3D%200.125%20m%5E3)
work done ![= \frac{P_1 V_1 -P_2 V_2}{n-1}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7BP_1%20V_1%20-P_2%20V_2%7D%7Bn-1%7D)
![= \frac{150 \times 0.8 - 80 \times 0.125}{1.4-1}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B150%20%5Ctimes%200.8%20-%2080%20%5Ctimes%200.125%7D%7B1.4-1%7D)
= 5 kJ
Answer:
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