Question

A space habitat for a long space voyage consists of two cabins each connected by a cable to a central hub as shown in the figure below.The cabins are set spinning around the hub axis, which is connected to the rest of the spacecraft to generate artificial gravity.
http://www.webassign.net/sercp8/p7-26.gif
(a) What forces are acting on an astronaut in one of the cabins?

(b) Write Newton's second law for an astronaut lying on the "floor"of one of the habitats, relating the astronaut's mass m,his velocity v, his radial distance from the hubr, and the normal force n.

Answer 1

(c) What would n have to equal if the 60-kg astronaut is to experience half his normal Earth weight?

(d) Calculate the necessary tangential speed of the habitat fromNewton's second law.

(e) Calculate the angular speed from the tangential speed.

(f) Calculate the period of rotation from the angular speed.

(g) If the astronaut stands up, will his head be moving faster,slower, or at the same speed as his feet? Why?

(i) Calculate the tangential speed at the top of his head if he is 1.80 m tall.

Answer 2

The astronaut experiences a normal force from the wall of the cabin, since he is 'stuck' to it. This normal force provides the necessary centripetal force to make him revolve around the central hub.
\[N=mv ^{2}/r\]
Also he must experience friction from the wall, in the direction opposite to the artificial gravity created, to prevent him from falling down.

Answer 3

(a) Think about the centripetal force acting on the cabin
(b) F= ma = (mv^2)/r
(c) F = 60*9.8 = 588n, so half would be 294n? This would be achieved by halving a
(d) F = 588 = (60*v^2)/10, so v = 9.899 m/s
(e) F = 588 = m*r*w^2 (w = omega = angular velocity), so w = 0.98 rads

and @ Mani Jha
the astronaut is not stuck to the wall, the centripetal force is acting towards the center, so the force acting on the astronaut will pull him downwards. He will not be stuck to the sides. (remember he is in space and the only force acting on him will be the centripetal force)