In a cylindrical space station, radius 1 km, the architect, an arts major, tries
ID: 2186871 • Letter: I
Question
In a cylindrical space station, radius 1 km, the architect, an arts major, tries to simulate the earth's gravity by rotating the station with angular speed w radians/s, and having people walk on the curved inside surface. What must he choose for w? A physicist points out one snag with this: if you drop something it will not fall to your feet. If you are facing the direction you are moving in due to the spin of the lab, a dropped object will either fall in front of you or behind you? Which is it? If a ball is dropped from a height of 1m, how far is it from your feet? For w if got 0.1 the ball will fall behind a person I need help with last part of questions "if a ball is dropped...."Explanation / Answer
To simulate gravity, centripetal acceleration = w^2*r = 9.8 so 9.8=w^2 * 1000m, w=0.099 rad/s. If you drop a ball, both you and the ball have a velocity of v = w*r = 0.099*1000= 99 m/s The ball will continue to move in this straight line while you continue on the circular path. Draw a picture and then calculate how long it would take for the ball to hit the floor (use trigonometry to find the point along the circle it would hit at - you would have to find the angle where r * cos (theta) = 1000 meters - 1 meter (the X position where it would hit the circle)...let me know if this is enough of a hint