Recall the artificial space habitat we saw in an earlier homework (3A), where a

Question

Recall the artificial space habitat we saw in an earlier homework (3A), where a rotating cylindrial pod was spun so as to produce a centripetal acceleration matching the acceleration due to gravity near the surface of the Earth. When the pod is first launched into space, it is of course not rotating, but a series of thrusters around the circumference act to accelerate the pod up to its final angular speed. Assume the thrusters act at a radius of 10.5 m from the axis of rotation, and can provide a constant tangential acceleration of 1.01 m/s2. If the usable part of the pod (i.e. where the people are, and where they experience an acceleration of 1g) is located at a radius of 7.9 m from the axis of rotation, how long should the thrusters fire for in order to achieve the necessary rate of rotation?

Explanation / Answer

Here ,

radius ,r = 10.5 m

at = 1.01 m/s^2

R = 7.9 m

let the time taken is t

angular speed for reaching the necessary centripetal acceleration

9.8 = w^2 * R

9.8 = w^2 * 7.9

w = 1.113 rad/s

Now , for the tangential speed needed at the thrusters

v = r * w

v = 1.113 * 10.5

v = 11.7 m/s

Now , Using first equation of motion

v = u + at * t

11.7 = 1.01 * t

t= 11.58 s

the time taken to reach the desired acceleration is 11.58 s

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