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

Step-by-step explanation:

Below is an attachment containing the solution.

Answer 2

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.

Step-by-step explanation:

Acceleration is given by
`(v^2)/(r)`

Therefore the acceleration for each of the satellite is given by

Satellite A)
`(160^2)/(5000)` = 5.12 m/s²

Satellite B)
`(160^2)/(2500)` = 10.24 m/s²

Satellite C)
`(80^2)/(2500)` = 2.56 m/s²

Satellite D)
`(40^2)/(10000)` = 0.16 m/s²

Satellite E)
`(120^2)/(5000)` = 2.88 m/s²

Satellite F)
`(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).