A future use of space stations may be to provide hospitals for severely burned persons. it is very painful for a badly burned person on earth to lie in bed. in a space station, the effect of gravity can be reduced or even eliminated. how long should each rotation take (in minutes) for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of earth?

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Physics

Bronson Frye

22 February, 03:35

A future use of space stations may be to provide hospitals for severely burned persons. it is very painful for a badly burned person on earth to lie in bed. in a space station, the effect of gravity can be reduced or even eliminated. how long should each rotation take (in minutes) for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of earth?

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Donaldson · Answer 1

1.5 minutes per rotation. The formula for centripetal force is A = v^2/r where A = acceleration v = velocity r = radius So let's substitute the known values and solve for v. So F = v^2/r 0.98 m/s^2 = v^2/200 m 196 m^2/s^2 = v^2 14 m/s = v So we need a velocity of 14 m/s. Let's calculate how fast the station needs to spin. Its circumference is 2*pi*r, so C = 2 * 3.14159 * 200 m C = 1256.636 m And we need a velocity of 14 m/s, so 1256.636 m / 14 m/s = 89.75971429 s Rounding to 2 significant digits gives us a rotational period of 90 seconds, or 1.5 minutes.