A 60 kg astronaut stands on a bathroom scale in a 2 km diameter rotating space station that spins every 62.8 sec. What does the scale read?

Question

A astronaut stands on a bathroom scale in a 2 km diameter
rotating space station that spins every 62.8 sec

Answer 1

The scale will read the magnitude of the centripetal force acting on the astronaut.

 

F_c = mv²/r

 

m = 60 kg

 

r = (2 km)/2 = 1000 m

 

T = 62.8 s

 

v = 2πr/T

 

F_c = m(2πr/T)² / r = (4π²r/T²)m

 

F_c = (4π²r/T²)m

 

Now just plug in the values of r, T, and m, and get a force in newtons.  You should be able to finish from here.

Answer 2

In continuation to Arturo Sir

 

m^' g = (4π²r/T²)m

 

       = 4x10x1000x60/(62.8x62.8) approx

 

       =608 N approx

m^' = 60.8 Kg approx 

Is it correct?

But this works out to be more than his mass on earth