Question

NASA scientists suggest using rotating cylindrical spacecraft to replicate gravity while in a weightless environment. Consider such a spacecraft that has a diameter of d = 148 m. What is the speed v, in meters per second, the spacecraft must rotate at its outer edge to replicate the force of gravity on earth?

Answer 1

Answer:

Explanation:

Given

diameter of spacecraft $d=148\ m$

radius $r=74\ m$

Force of gravity $F_g$=mg

where m =mass of object

g=acceleration due to  gravity on earth

Suppose v is the speed at which spacecraft is rotating so a net centripetal  acceleration is acting on spacecraft which is given by

$F_c=\frac{mv^2}{r}$

$F_c=F_g$

$\frac{mv^2}{r}=mg$

$\frac{v^2}{r}=g$

$v=\sqrt{gr}$

$v=\sqrt{1450.4}$

$v=38.08\ m/s$