10.0 m Figure P7.26 000 000

A space habitat for a long space voyage consists of two
cabins each connected by a cable to a central hub as shown
in Figure P7.26. 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? (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. (c) What would n have to
equal if the 60.0 - kg astronaut is to experience half his normal
Earth weight? (d) Calculate the necessary tangential speed of
the habitat from Newton’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? Calculate the tangential speed at the top of
his head if he is 1.80 m tall.