Respuesta :
Answer:
The force induced on the aircraft is 2.60 N
Solution:
As per the question:
Power transmitted, [tex]P_{t} = 8 kW = 8000 W[/tex]
Now, the force, F is given by:
[tex]P_{t} = Force(F)\times velocity(v) = Fv[/tex] (1)
where
v = velocity
Now,
For a geo-stationary satellite, the centripetal force, [tex]F_{c}[/tex] is provided by the gravitational force, [tex]F_{G}[/tex]:
[tex]F_{c} = F_{G}[/tex]
[tex]\frac{mv^{2}}{R} = \frac{GM_{e}m{R^{2}}[/tex]
Thus from the above, velocity comes out to be:
[tex]v = \sqrt{\frac{GM_{e}}{R}}[/tex]
[tex]v = \sqrt{\frac{6.67\times 10^{- 11}\times 5.979\times 10^{24}}{42166\times 10^{3}}} = 3075.36 m/ s[/tex]
where
R = [tex]R_{e} + H[/tex]
R = [tex]\sqrt{GM_{e}(\frac{T}{2\pi})^{2}}[/tex]
where
G = Gravitational constant
T = Time period of rotation of Earth
R is calculated as 42166 km
Now, from eqn (1):
[tex]8000 = F\times 3075.36[/tex]
F = 2.60 N
