A space habitat for a long space voyage consists of two cabins each connected by
ID: 1698779 • Letter: A
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.(a) What forces are acting on an astronaut in one of the cabins?
1
(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 hub r, and the normal force n. (Use any variable or symbol stated above as necessary.)
F =
n =
(c) What would n have to equal if the 52.9-kg astronaut is to experience half his normal Earth weight?
n = 4 N
(d) Calculate the necessary tangential speed of the habitat from Newton's second law.
tangential speed = 5 m/s
(e) Calculate the angular speed from the tangential speed.
angular speed = 6 rad/s
(f) Calculate the period of rotation from the angular speed.
period = 7 s
(g) If the astronaut stands up, will his head be moving faster, slower, or at the same speed as his feet? Why?
Explanation / Answer
a ) since there is no gravity the normal force is acting on the astronaut in the one of the cabin
b ) F = mv^2 / r
normal force n = mv^2 / r
c ) Normal force F = ma
= 52.9 kg * 9.8
= 518.4 N
if half the force is 518.4 N / 2
= 259.2 N
d ) F = mv^2 / r
259.2 N = 52.9 kg * v^2 / 10 m
v = 7.0 m/s
e ) angular speed v = r
7.0 m/s = 10 m *
= 0.7 rad /s
f ) period of rotation T = 2/
= 2/ 0.7
= 8.97 s
g ) The astronaut 's head willbe move faster than his feet because the radius from his head to the center of the hub is shorter than that from his feet to the hub.
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