A space station is to provide artificial gravity to support long-term stay of as

Question

A space station is to provide artificial gravity to support long-term stay of astronauts and cosmonauts. It is designed as a large wheel, with all the compartments in the rim, which is to rotate at a speed that will provide an acceleration similar to that of terrestrial gravity for the astronauts. After the space station is assembled in orbit, its rotation will be started by the firing of a rocket motor fixed to the outer rim, which fires tangentially to the rim. The radius of the space station is R=51.7 m, and the mass is 6.23 * 10^5 kg. If the thrust of the rocket motor is F=121 N, how long should the motor fire?

Explanation / Answer

To provide artificial gravity, the centripetal acceleration must be equal to g

Since ac = 2r, we can find the angular velocity

(9.8) = 2(51.7)

= .435 rad/s

Since this force provides a torque on the space station, we have

= FL = I

The moment of inertia for a "wheel" is MR2

so, (121)(51.7) = (6.23 X 105)(51.7)2

= 3.76 X 10-6 rad/s2

Then, using the formula f = 0 + t, we can find the time knowing that the ship starts from rest

.453 = (0) + (3.76 X 10-6)t

t = 1.21 X 105 sec, which is 33.5 hours

(Note: If that is not the correct answer, and they meant that the "Wheel" of the space station should have a moment of inertia of a "Disc" rather than a "Hoop", then I = .5MR2, the angular acceleration becomes 7.52 X 10-6 rad/s2, and the time becomes 6.02 X 104 s, which is 16.7 hrs.)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.