At time seconds, the mass has angular speed
and hence linear speed
After 8 s, its linear speed is
and has centripetal acceleration with magnitude
To maintain this linear speed, by Newton's second law the required centripetal force should have magnitude
Answer: 5,640 s (94 minutes)
Explanation:
the tangential speed of the HST is given by
(1)
where
is the length of the orbit
r is the radius of the orbit
T is the orbital period
In our problem, we know the tangential speed: . The radius of the orbit is the sum of the Earth's radius and the distance of the HST above Earth's surface:
So, we can re-arrange equation (1) to find the orbital period:
Dividing by 60, we get that this time corresponds to 94 minutes.