A space station consists of two donut-shaped living chambers, A andB, that have the radii shown in the drawing. As the stationrotates, an astronaut in chamber A is moved 2.82 102 m along acircular arc. How far along a circular arc is an astronaut inchamber B moved during the same time?
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Beverley SmithLv2

23 Nov 2019

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1)The National Aeronautics and Space Administration (NASA) studiesthe physiological effects of large accelerations on astronauts.Some of these studies use a machine known as a centrifuge. Thismachine consists of a long arm, to one end of which is attached achamber in which the astronaut sits. The other end of the arm isconnected to an axis about which the arm and chamber can berotated. The astronaut moves on a circular path, much like a modelairplane flying in a circle on a guideline. The chamber is located15 m from the center of the circle. At what speed must the chambermove so that an astronaut is subjected to 6.9 times theacceleration due to gravity? (in m/s)

2)At an amusement park there is a ride in which cylindricallyshaped chambers spin around a central axis. People sit in seatsfacing the axis, their backs against the outer wall. At one instantthe outer wall moves at a speed of 4.0 m/s, and an 83 kg personfeels a 460 N force pressing against his back. What is the radiusof the chamber?
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3)A "swing" ride at a carnival consists of chairs that are swung ina circle by 12.0 m cables attached to a vertical rotating pole, asthe drawing shows. (? = 55.5Â°) Suppose the total mass of a chairand its occupant is 230 kg.
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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.