A space habitat for a long space voyage consists of two cabins eachconnected by a cable to a central hub as shown in the figure below.The cabins are set spinning around the hub axis, which is connectedto the rest of the spacecraft to generate artificial gravity.
(a) What forces are acting on an astronaut in one of thecabins?
(b) Write Newton's second law for an astronaut lying on the "floor"of one of the habitats, relating the astronaut's mass m, hisvelocity v, his radial distance from the hub r, and the normalforce n. (Use any variable or symbol stated above asnecessary.)
(c) What would n have to equal if the 49.4-kg astronaut is toexperience half his normal Earth weight?
(d) Calculate the necessary tangential speed of the habitat fromNewton's second law.
tangential speed=?
(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 is2.08 m tall.
A space habitat for a long space voyage consists of two cabins eachconnected by a cable to a central hub as shown in the figure below.The cabins are set spinning around the hub axis, which is connectedto the rest of the spacecraft to generate artificial gravity.
(a) What forces are acting on an astronaut in one of thecabins?
(b) Write Newton's second law for an astronaut lying on the "floor"of one of the habitats, relating the astronaut's mass m, hisvelocity v, his radial distance from the hub r, and the normalforce n. (Use any variable or symbol stated above asnecessary.)
(c) What would n have to equal if the 49.4-kg astronaut is toexperience half his normal Earth weight?
(d) Calculate the necessary tangential speed of the habitat fromNewton's second law.
tangential speed=?
(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 is2.08 m tall.
