Apparent Weight in a Spinning Space Station

HarleyM

1. The problem statement, all variables and given/known data
To simulate gravity, a circular space station with a radius of 150 m is rotated so that astronauts standing on the inner surface move at 30 m/s. If the 75 kg astronaut stands on a bathroom scale what reading will it give? (assume the scale is calibrated in newtons)


2. Relevant equations

F_c=mv²/r
3. The attempt at a solution

Fnet=F_c
=(75)(30)²/150
=450 N

So does this look correct? Im not really sure whether to include F_N and F_G or if they just cancel out.
Thanks!

technician

You should draw a diagram showing the forces acting on the astronaut.... you will find that there is only one (of any consequence !!!!) It is the force between the floor (wall !!!) of the space station and the astronaut.
This is the centripetal force and you have calculated it correctly.
You do not need to take gravity into account since the astronaut and the space station are in orbit i.e 'free fall'