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.

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Suppose that humans have created a colony outside of our solar system on a planet called Wfirst21. Wfirst21 has a mass of 2.65×1025 kg2.65×1025 kg and a day that lasts 23.7 h23.7 h (which defines the rotational period of the planet). The colony is located on the planet's equator. The colonists set up a communications satellite which orbits Wfirst21. The satellite has a circular orbit that keeps it positioned directly above the colony. Calculate the radius ?r of the satellite's orbit in kilometers.
Now we have a rod-shaped space station of length 1296 m and mass 1.43 x 10^6 kg, which can change its length (kind of like an old-fashioned telescope), without changing its overall mass. Suppose that the station is initially rotating at a constant rate of 1.83 rpm. If the length of the rod is reduced to 1.83 m, what will be the new rotation rate of the space station? 1. 3.01 rpm 6.27 rpm 3 3.76 rpm 4 9.41 rpm
In 2015, in Warsaw, Poland, Olivia Oliver of Nova Scotia broke the world record for being the fastest spinner on ice skates. She achieved a record 342 rev/min, beating the existing Guinness World Record by 34 rotations. If an ice skater extends her arms at that rotation rate, what would be her new rotation rate? Assume she can be approximated by a 45-kg rod that is 1.7 m tall with a radius of 15 cm in the record spin.With her arms stretched take the approximation of a rod of length 130 cm with 10% of her body mass aligned perpendicular to the spin axis. Neglect frictional forces.
Suppose that humans have created a colony outside of our solar system on a planet called Wfirst21. Wfirst21 has a mass of 1.45×1025 kg and a day that lasts 24.1 h (which defines the rotational period of the planet). The colony is located on the planet's equator. The colonists set up a communications satellite which orbits Wfirst21. The satellite has a circular orbit that keeps it positioned directly above the colony. Calculate the radius ?r of the satellite's orbit in kilometers.
A 50.0 kg child stands at the rim of a merry-go-round of radius 1.70 m, rotating with an angular speed of 2.95 rad/s. (a) What is the child's centripetal acceleration? m/s2(b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? N(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?
Artificial gravity is a must for any space station if humans are to live there for extended length of time. An effective way to create artificial gravity is using a rotating enclosed cylinder. Humans walk on the inside of the outer edge of the cylinder, which has a diameter of D=3450m that is large enough such that its curvature is not readily noticeable to the inhabitants. Once the space station is rotating at the necessary angular speed w to create an artificial gravity of 1g, how many minutes would it take the space station to make one revolution?
After a nuclear apocalypse on Earth, humans have built a space station known as the Ark. It has multiple sections controlled by different political factions, but one thing they all have in common is the need for artificial gravity. This is done in each section by setting a piece of the Ark spinning around the central axis of the station. The largest section of the station is a complete ring with a radius of 1000 m.a) What is the rotational velocity required to simulate gravity?b) One day on Earth is the defined by the amount of time it takes the Earth to rotate once around its axis and is 86,400 s. How many seconds is one “day” on this section of the station?c) When an inhabitant standing as they would on Earth, In which direction do their heads points? (which piece of the station)
A space station is constructed in the shape of a wheel 20 m in diameter, with essentially all of its 5.2×105 kg mass at the rim. Once the station is completed, it is set rotating at a rate that requires an object at the rim to have radial acceleration g , thereby simulating Earth's surface gravity. This is accomplished using two small rockets, each with 130 N thrust, that are mounted on the rim of the station. How long will it take to reach the desired spin rate, and how many revolutions will the station make in this time?
Now we have a rod-shaped space station of length 1402 m and mass 8.50 x 10^6 kg, which can change its length (kind of like an old-fashioned telescope), without changing its overall mass. Suppose that the station is initially rotating at a constant rate of 1.51 rpm. If the length of the rod is reduced to 1.51 m, what will be the new rotation rate of the space station? 5.08 rpm 2.54 rpm 3 8.13 rpm 4 1.52 rpm
The Wheatstone bridge in the circuit is balanced when R3 equals 3000 ohm. If the galvanometer has a resistance of 32 ohm, how much current in microampere will the galvanometer detect, when the bridge is unbalanced by setting R3 to 3003 ohm? Take v = 19 V. (Hint: Find the Thevenin equivalent with respect to the galvanometer terminals when R3 = 3003 ohm. Note that once we have found this Thevenin equivalent, it is easy to find the amount of unbalanced current in the galvanometer branch for different galvanometer movements.)
There is a rod-shaped space station of length 687 m and mass 5.35 x 10^6 kg, which can change its length (kind of like an old-fashioned telescope), without changing its overall mass. Suppose that the station is initially rotating at a constant rate of 2.26 rpm. If the length of the rod is reduced to 2.26 m, what will be the new rotation rate of the space station? 4.38 rpm 7.50 rpm 3.50 rpm 6.25 rpm