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.

Question

(a) What forces are acting on an astronaut in one of the cabins?

1The tension in the cable connecting the cabin to the central hub as well as the normal force are acting on the astronauts.

(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 = Your answer is correct.
n = Your answer is incorrect.

(c) What would n have to equal if the 52.6-kg astronaut is to experience half his normal Earth weight?
n = 4Your answer is correct. N

(d) Calculate the necessary tangential speed of the habitat from Newton's second law.
tangential speed = 5Your answer is correct. m/s

(e) Calculate the angular speed from the tangential speed.
angular speed = 6Your answer is correct. rad/s

(f) Calculate the period of rotation from the angular speed.
period = 7Your answer is correct. s

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

8

(i) Calculate the tangential speed at the top of his head if he is 1.92 m tall.
tangential speed = 9Your answer is incorrect. m/s

Answer 1

His head will be moving faster than his feet because it is further away from the central hub and is therefore moving at a higher tangential speed.