Circular Motion Ranking Task Six artificial satellites circle a space station at
ID: 1625444 • Letter: C
Question
Circular Motion Ranking Task
Six artificial satellites circle a space station at 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. To rank items as equivalent, overlap them.
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m=200kg
L=5000m
v=160m/s
m=100kg
L=2500m
v=160m/s
m=400kg
L=2500m
v=80m/s
m=800kg
L=10000m
v=40m/s
m=200kg
L=5000m
v=120m/s
m=300kg
L=10000m
v=80m/s
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m=200kg
L=5000m
v=160m/s
m=100kg
L=2500m
v=160m/s
m=400kg
L=2500m
v=80m/s
m=800kg
L=10000m
v=40m/s
m=200kg
L=5000m
v=120m/s
m=300kg
L=10000m
v=80m/s
Explanation / Answer
For mass m1 = 200 kg, we have
a1 = v12 / L = (160 m/s)2 / (5000 m)
a1 = 5.12 m/s2
For mass m2 = 100 kg, we have
a2 = v22 / L = (160 m/s)2 / (2500 m)
a2 = 10.2 m/s2
For mass m3 = 400 kg, we have
a3 = v32 / L = (80 m/s)2 / (2500 m)
a3 = 2.56 m/s2
For mass m4 = 800 kg, we have
a4 = v42 / L = (40 m/s)2 / (10000 m)
a4 = 0.16 m/s2
For mass m5 = 200 kg, we have
a5 = v52 / L = (120 m/s)2 / (5000 m)
a5 = 2.88 m/s2
For mass m = 300 kg, we have
a6 = v62 / L = (80 m/s)2 / (10000 m)
a6 = 0.64 m/s2
To rank for each satellite based on its acceleration from largest to smallest which will be given as :
a2 > a1 > a5 > a3 > a6 > a4