Long-term space missions require some form of artificial gravity to prevent astronauts losing bone mass. One method would be to use a tether to connect a spent booster to the astronauts’ capsule and set the system rotating to provide artificial gravity in the noninertial frame of the capsule. Tests suggest that rotation rates less than 2 rpm are needed to avoid the astronauts experiencing inner-ear problems as they move about. About how long must the tether be, if you need an apparent gravitational field in the capsule of at least half of the earth’s field? (Assume that the capsule and booster have roughly the same mass.)

The tether must be about  ________m long.

Long-term space missions require some form of artificial gravity to prevent astronauts losing bone mass. One method would be to use a tether to connect a spent booster to the astronauts’ capsule and set the system rotating to provide artificial gravity in the noninertial frame of the capsule. Tests suggest that rotation rates less than 2 rpm are needed to avoid the astronauts experiencing inner-ear problems as they move about. About how long must the tether be, if you need an apparent gravitational field in the capsule of at least half of the earth’s field? (Assume that the capsule and booster have roughly the same mass.)

The tether must be about  ______m long.

Long-term space missions require reclamation of the oxygen in the carbon dioxide exhaled by the crew. In one method of reclamation, 1.00 mol of carbon dioxide produces 1.00 mol of oxygen, with 1.00 mol of methane as a by-product. The methane is stored in a tank under pressure and is available to control the attitude of the spacecraft by controlled venting. A single astronaut exhales 1.21 kg of carbon dioxide each day. If the methane generated in the recycling of three astronauts’ respiration during one week of flight is stored in an originally empty 155-L tank at