Six artificial satellites circle a space station at constant speed. The mass m of each satellite, distance L from the space stat
ion, 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. 1. m=200kg,L= 5000 m, v=120 m/s 2. m=800kg,l= 10,000 m, v=40m/s 3. m=400kg,L= 2500 m, v=80m/s 4. m=100kg, L=2500 m, V=160m/s 5. m=300kg, L=10,000m, V=80 m/s 6. m=200kg, L=5000 m, V=160 m/s Part A Rank each satellite from largest to smallest based on its period. Part B Rank each satellite from largest to smallest based on its acceleration.
a) Since we are told the satellites circle the space station at constant speed, we can assume they follow a uniform circular motion and their tangential speeds are given by:
(1)
Where:
is the angular frequency
is the radius of the orbit of each satellite
is the period of the orbit of each satellite
Isolating :
(2)
Applying this equation to each satellite:
(3)
(4)
(5)
(6)
(7)
(8)
Ordering this periods from largest to smallest:
b) Acceleration is defined as the variation of velocity in time:
(9)
Applying this equation to each satellite:
(10)
(11)
(12)
(13)
(14)
(15)
Ordering this acceerations from largest to smallest:
The word to fill in the blank is "equal". Because the time taken to rotate (spin on its axis) is equal to the time of revolution (going around the earth), this means that both have the same rate of angular rotation. So for every bit that the moon goes around its orbit around earth, the moon itself rotates accordingly to present the exact same side to earth.
Crime scenes contain physical evidence that is pertinent to a criminal investigation. This evidence is collected by crime scene investigators (CSIs) and law enforcement. The location of a crime scene can be the place where the crime took place or can be any area that contains evidence from the crime itself.