Answer:
mass of the fish is 8.11 kg
Explanation:
As we know that the frequency of oscillation of spring block system is given as
![f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D)
here we know that the reading of scale varies from 0 to 155 N from length varies from x = 0 to x = 10 cm
Now we have
![k = \frac{155}{0.10} N/m](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B155%7D%7B0.10%7D%20N%2Fm)
![k = 1550 N/m](https://tex.z-dn.net/?f=k%20%3D%201550%20N%2Fm)
so now we have
![2.20 = \frac{1}{2\pi}\sqrt{\frac{1550}{m}}](https://tex.z-dn.net/?f=2.20%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cfrac%7B1550%7D%7Bm%7D%7D)
![m = 8.11 kg](https://tex.z-dn.net/?f=m%20%3D%208.11%20kg)
so mass of the fish is 8.11 kg
The object will sail away in a straight line ... continuing in the same direction it was going when the centripetal force stopped.
Answer:
c. because A will land first becuase its heavier
Explanation:
Answer:
1) Mass that needs to be converted at 100% efficiency is 0.3504 kg
2) Mass that needs to be converted at 30% efficiency is 1.168 kg
Explanation:
By the principle of mass energy equivalence we have
![E=mc^{2}](https://tex.z-dn.net/?f=E%3Dmc%5E%7B2%7D)
where,
'E' is the energy produced
'm' is the mass consumed
'c' is the velocity of light in free space
Now the energy produced by the reactor in 1 year equals
![Energy=Power\times time\\\\\therefore Energy=1\times 10^{9}\times 365\times 24\times 3600\\\\Energy=31.536\times 10^{15}Joules](https://tex.z-dn.net/?f=Energy%3DPower%5Ctimes%20time%5C%5C%5C%5C%5Ctherefore%20Energy%3D1%5Ctimes%2010%5E%7B9%7D%5Ctimes%20365%5Ctimes%2024%5Ctimes%203600%5C%5C%5C%5CEnergy%3D31.536%5Ctimes%2010%5E%7B15%7DJoules)
Thus the mass that is covertred at 100% efficiency is
![mass=\frac{Energy}{c^{2}}\\\\mass=\frac{31.536\times 10^{15}}{(3\times 10^{8})^{2}}\\\\mass=\frac{31.536\times 10^{15}}{9\times 10^{16}}\\\\\therefore mass=0.3504kg](https://tex.z-dn.net/?f=mass%3D%5Cfrac%7BEnergy%7D%7Bc%5E%7B2%7D%7D%5C%5C%5C%5Cmass%3D%5Cfrac%7B31.536%5Ctimes%2010%5E%7B15%7D%7D%7B%283%5Ctimes%2010%5E%7B8%7D%29%5E%7B2%7D%7D%5C%5C%5C%5Cmass%3D%5Cfrac%7B31.536%5Ctimes%2010%5E%7B15%7D%7D%7B9%5Ctimes%2010%5E%7B16%7D%7D%5C%5C%5C%5C%5Ctherefore%20mass%3D0.3504kg)
Part 2)
At 30% efficiency the mass converted equals
![mass|_{30}=\frac{mass|_{100}}{0.3}\\\\mass|_{30}=\frac{0.3504}{0.3}\\\\mass|_{30}=1.168kg](https://tex.z-dn.net/?f=mass%7C_%7B30%7D%3D%5Cfrac%7Bmass%7C_%7B100%7D%7D%7B0.3%7D%5C%5C%5C%5Cmass%7C_%7B30%7D%3D%5Cfrac%7B0.3504%7D%7B0.3%7D%5C%5C%5C%5Cmass%7C_%7B30%7D%3D1.168kg)
Answer:
The resonant frequency of this circuit is 1190.91 Hz.
Explanation:
Given that,
Inductance, ![L=9.4\ mH=9.4\times 10^{-3}\ H](https://tex.z-dn.net/?f=L%3D9.4%5C%20mH%3D9.4%5Ctimes%2010%5E%7B-3%7D%5C%20H)
Resistance, R = 150 ohms
Capacitance, ![C=1.9\ \mu F=1.9\times 10^{-6}\ C](https://tex.z-dn.net/?f=C%3D1.9%5C%20%5Cmu%20F%3D1.9%5Ctimes%2010%5E%7B-6%7D%5C%20C)
At resonance, the capacitive reactance is equal to the inductive reactance such that,
![2\pi f_o L=\dfrac{1}{2\pi f_oC}](https://tex.z-dn.net/?f=2%5Cpi%20f_o%20L%3D%5Cdfrac%7B1%7D%7B2%5Cpi%20f_oC%7D)
f is the resonant frequency of this circuit
![f_o=\dfrac{1}{2\pi \sqrt{LC}}](https://tex.z-dn.net/?f=f_o%3D%5Cdfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7BLC%7D%7D)
![f_o=\dfrac{1}{2\pi \sqrt{9.4\times 10^{-3}\times 1.9\times 10^{-6}}}](https://tex.z-dn.net/?f=f_o%3D%5Cdfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7B9.4%5Ctimes%2010%5E%7B-3%7D%5Ctimes%201.9%5Ctimes%2010%5E%7B-6%7D%7D%7D)
![f_o=1190.91\ Hz](https://tex.z-dn.net/?f=f_o%3D1190.91%5C%20Hz)
So, the resonant frequency of this circuit is 1190.91 Hz. Hence, this is the required solution.