Respuesta :
Answer: The rank of the items is E,B,F,A,D,C..
Explanation:
In the given problem, The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The centripetal force is acting to keep up the continuous circular motion.
The expression for the centripetal force is as follows;
[tex]F=\frac{m\times v^{2}}{r}[/tex]
Here, m is the mass of the object, v is the velocity and r is the radius.
In the given problem, the orbital period is constant.
[tex]r\propto v[/tex]
Thus,
[tex]F\propto m\times r[/tex]
In the given problem, each satellite has mass m and radius of orbit L.
[tex]r=L+R[/tex]
Calculate the net force acting on each satellite from their rockets for the part A.
[tex]mr=m(L+R)[/tex]
Put m= 200 kg, R=6378 km and L=5000 m.
[tex]mr=200(5000+6378)[/tex]
[tex]mr=1.28\times 10^{9}kg\times m[/tex]
Calculate the net force acting on each satellite from their rockets for the part B.
[tex]mr=m(L+R)[/tex]
Put m= 400 kg, R=6378 km and L=2500 m.
[tex]mr=400(2500+6378)[/tex]
[tex]mr=2.55\times 10^{9}kg\times m[/tex]
Calculate the net force acting on each satellite from their rockets for the part C.
[tex]mr=m(L+R)[/tex]
Put m= 100 kg, R=6378 km and L=2500 m.
[tex]mr=100(2500+6378)[/tex]
[tex]mr=6.38\times 10^{8}kg\times m[/tex]
Calculate the net force acting on each satellite from their rockets for the part D.
[tex]mr=m(L+R)[/tex]
Put m= 100 kg, R=6378 km and L=10000 m.
[tex]mr=100(10000+6378)[/tex]
[tex]mr=6.39\times 10^{8}kg\times m[/tex]
Calculate the net force acting on each satellite from their rockets for the part E.
[tex]mr=m(L+R)[/tex]
Put m= 800 kg, R=6378 km and L=5000 m.
[tex]mr=800(5000+6378)[/tex]
[tex]mr=5.11\times 10^{9}kg\times m[/tex]
Calculate the net force acting on each satellite from their rockets for the part F.
[tex]mr=m(L+R)[/tex]
Put m= 300 kg, R=6378 km and L=7500 m.
[tex]mr=300(7500+6378)[/tex]
[tex]mr=1.92\times 10^{9}kg\times m[/tex]
Therefore, the rank of the items is E,B,F,A,D,C.
