Answer :
The work done in propelling a four-ton satellite to various heights neglecting air resistance and the weight of the propellant can be calculated using the equation:
Work = mgh
where m is the mass of the satellite, g is the acceleration due to gravity, and h is the height of the satellite above Earth. The acceleration due to gravity can be calculated using the equation:
g = G * M/R^2
where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth. For this problem, M = [tex]5.97 x 10^24[/tex] kg and R =[tex]6.37 x 10^6 m.[/tex]
For (a) 100 miles above Earth:
h = 100 miles = 160934 m
g = 9.82 m/s^2
m = 4 tons = 4000 kg
Work = mgh = [tex]4000 x 9.82 x 160934 = 6.22 x 10^9 J[/tex](1 decimal place)
For (b) 700 miles above Earth:
h = 700 miles = 1126542 m
g = 9.82 m/s^2
m = 4 tons = 4000 kg
Work = mgh = [tex]4000 x 9.82 x 1126542 = 4.54 x 10^10 J[/tex] (1 decimal place)
for such more questions on radius
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