Question

Six artificial satellites circle a space station at a constant speed. The mass m of each satellite, distance L from the space station, and the speed v of each satellite are listed below. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible.
Rank each satellite based on its acceleration. Rank from largest to smallest.

A) m= 200 kg, L= 5000 m, v= 160 m/s

B) m= 100 kg, L= 2500 m, v= 160 m/s

C) m= 400 kg, L= 2500 m, v= 80 m/s

D) m= 800 kg, L= 10000 m, v= 40 m/s

E) m= 200 kg, L= 5000 m, v= 120 m/s

F) m= 300 kg, L= 10000 m, v= 80 m/s

Answer 1

Explanation:

Below is an attachment containing the solution.

Answer 2

Answer:

The answer to the question is;

Based on their acceleration the rank of the satellites from largest to smallest is.

B   >→   A   >→    E   >→    C    >→     F    >→     D.

Explanation:

Acceleration is given by $\frac{v^2}{r}$

Therefore the acceleration for each of the satellite is given by

Satellite A)      $\frac{160^2}{5000}$ =    5.12 m/s²

Satellite B)      $\frac{160^2}{2500}$  =   10.24 m/s²

Satellite C)      $\frac{80^2}{2500}$   =  2.56 m/s²

Satellite D)      $\frac{40^2}{10000}$  =  0.16 m/s²

Satellite E)       $\frac{120^2}{5000}$   =  2.88 m/s²

Satellite F)       $\frac{80^2}{10000}$  = 0.64 m/s²

Therefore in order of decreasing acceleration, from largest to smallest we have

Satellite B) > Satellite A) >Satellite E) >Satellite C)>Satellite F)>Satellite D).