Answer:
![6.046N](https://tex.z-dn.net/?f=6.046N)
Explanation:
The net force exerted on the mass is the sum of tension force and the external force of gravity.
![F_n_e_t=F_g+F_t](https://tex.z-dn.net/?f=F_n_e_t%3DF_g%2BF_t)
is the tension force.
is the force of gravity.
![F_n_e_t=ma_c=mv^2/r\\](https://tex.z-dn.net/?f=F_n_e_t%3Dma_c%3Dmv%5E2%2Fr%5C%5C)
where
is the rope's radius from the fixed point.
From the net force equation above:
![F_t=F_n_e_t-F_g\\=mv^2/r-mg\\=0.4\times(8.5^2/2.9)-0.4\times9.8\\=6.046N](https://tex.z-dn.net/?f=F_t%3DF_n_e_t-F_g%5C%5C%3Dmv%5E2%2Fr-mg%5C%5C%3D0.4%5Ctimes%288.5%5E2%2F2.9%29-0.4%5Ctimes9.8%5C%5C%3D6.046N)
Hence the tension force is 6.046N
Answer:
208.33 W
141.26626 seconds
Explanation:
E = Energy = ![6\times 10^6\ J](https://tex.z-dn.net/?f=6%5Ctimes%2010%5E6%5C%20J)
t = Time taken = 8 h
m = Mass = 2000 kg
g = Acceleration due to gravity = 9.81 m/s²
h = Height of platform = 1.5 m
Power is obtained when we divide energy by time
![P=\frac{E}{t}\\\Rightarrow P=\frac{6\times 10^6}{8\times 60\times 60}\\\Rightarrow P=208.33\ W](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BE%7D%7Bt%7D%5C%5C%5CRightarrow%20P%3D%5Cfrac%7B6%5Ctimes%2010%5E6%7D%7B8%5Ctimes%2060%5Ctimes%2060%7D%5C%5C%5CRightarrow%20P%3D208.33%5C%20W)
The average useful power output of the person is 208.33 W
The energy in the next part would be the potential energy
The time taken would be
![t=\frac{E}{P}\\\Rightarrow t=\frac{mgh}{208.33}\\\Rightarrow t=\frac{2000\times 9.81\times 1.5}{208.33}\\\Rightarrow t=141.26626\ s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7BE%7D%7BP%7D%5C%5C%5CRightarrow%20t%3D%5Cfrac%7Bmgh%7D%7B208.33%7D%5C%5C%5CRightarrow%20t%3D%5Cfrac%7B2000%5Ctimes%209.81%5Ctimes%201.5%7D%7B208.33%7D%5C%5C%5CRightarrow%20t%3D141.26626%5C%20s)
The time taken to lift the load is 141.26626 seconds
Answer:
change in mass = 2.41*10^{8}kg
Explanation:
The change in the mass can be computed by using the relation
(1)
That is, the energy liberated comes from the mass of the nuclear fuel. The energy generated in one year is
![E=Pt=2.3*10^{9}\frac{J}{s}*1 year*\frac{365.25 day}{1 year}*\frac{24h}{1 day}*\frac{3600s}{1h}=7.25*10^{16}J](https://tex.z-dn.net/?f=E%3DPt%3D2.3%2A10%5E%7B9%7D%5Cfrac%7BJ%7D%7Bs%7D%2A1%20year%2A%5Cfrac%7B365.25%20day%7D%7B1%20year%7D%2A%5Cfrac%7B24h%7D%7B1%20day%7D%2A%5Cfrac%7B3600s%7D%7B1h%7D%3D7.25%2A10%5E%7B16%7DJ)
Hence, by replacing in the equation (1) you have (c=3*10^{8}m/s)
![\Delta m=\frac{7.25*10^{16}J}{3*10^{8}\frac{m}{s}}=2.41*10^{8}kg](https://tex.z-dn.net/?f=%5CDelta%20m%3D%5Cfrac%7B7.25%2A10%5E%7B16%7DJ%7D%7B3%2A10%5E%7B8%7D%5Cfrac%7Bm%7D%7Bs%7D%7D%3D2.41%2A10%5E%7B8%7Dkg)
HOPE THIS HELPS!!