Find the velocity such that the normal force between the track and the roller co

Question

Find the velocity such that the normal force between the track and the roller coaster (weight of 500 lb) is zero at point B. On May 15th, Space X launched a satellite to a geostationary orbit (altitude of approximately 36000 km). Find the magnitude of the velocity of the satellite to reach this orbit. Note that the radius of the Earth is approximately 6400 km which is much smaller than the altitude of a geostationary orbit. Therefore, the strength of Earth's gravitational field will be greatly reduced at this distance compared to at Earth's surface. The mass of the earth is approximately 5.972 times 10^24 kg. Check that the velocity you find would result in an approximately geostationary orbit.

Explanation / Answer

Here ,

let the velocity at the point B is v

Now , for the normal force

weight force = centripetal force

m * g = m * v^2/r

9.8 = v^2/(12/2)

v = 7.7 m/s

the velocity of roller coaster at B is 7.7 m/s

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