A novel space station design has been proposed to allow for experiments that leverage rotational motion...

Transcribed Image Text:

A novel space station design has been proposed to allow for experiments that leverage rotational motion to simulate low-gravity environments. This could, for instance, let astronauts conduct experiments on how plants grow under different gravitational acceleration (yes, I am talking about Space Potatoes), or to help astronauts themselves not lose muscle mass due to less resistance as they conduct day-to-day activities. A simplified design is included above; we can treat this like a hoop, radius 1.5 m, with six radial spokes. Assume the structure is made of hollow metal tunnels of consistent wall thickness and mass per meter. a) What fraction of the space station's mass is in the outer hoop? Mtotal b) If the total mass of the space station is 1550 kg, calculate its moment of inertia. kg m c) In order to simulate Earth's gravity, how fast (in terms of angular speed) would the station need to rotate? rad/s d) Engineers calculating what will get the space station rotating have determined NASA will need six motors, evenly spaced, each applying forces of 24 N along the space station's outer rim. Calculate the net torque on the space station provided by these motors. Nm e) Once the space station is launched, astronauts turn on the motors, beginning rotation from rest. How long does it take for them to attain the speed you determined in part c? If you googled this question, which you should not have done, your search results would have included links to International Space Station microgravity experiments, upon which this question was based. R Constants & other possibly-useful information: sin(30) cos(60) 1/2 (for any 6) sin(45) = cos(45) = 1/2 = 2/2 sin(60) cos(30)=3/2 Mass of Earth: ME = 6.0x1024 kg 1 mile = 1609.34 m; 1 mile per hour = 1.61 km/hr = 0.447 m/s = 2688 furlongs per fortnight 1 atm 1.01x105 Pa Rotational inertia formulas for common shapes: hoop or hollow cylinder: I MR2 thin rod about center: I (1/12) ML disk or solid cylinder: I = (1/2) MR thin rod about end: I = (1/3) ML uniform solid sphere: I = (2/5) MR2 point mass a distance r from axis: I = mr A novel space station design has been proposed to allow for experiments that leverage rotational motion to simulate low-gravity environments. This could, for instance, let astronauts conduct experiments on how plants grow under different gravitational acceleration (yes, I am talking about Space Potatoes), or to help astronauts themselves not lose muscle mass due to less resistance as they conduct day-to-day activities. A simplified design is included above; we can treat this like a hoop, radius 1.5 m, with six radial spokes. Assume the structure is made of hollow metal tunnels of consistent wall thickness and mass per meter. a) What fraction of the space station's mass is in the outer hoop? Mtotal b) If the total mass of the space station is 1550 kg, calculate its moment of inertia. kg m c) In order to simulate Earth's gravity, how fast (in terms of angular speed) would the station need to rotate? rad/s d) Engineers calculating what will get the space station rotating have determined NASA will need six motors, evenly spaced, each applying forces of 24 N along the space station's outer rim. Calculate the net torque on the space station provided by these motors. Nm e) Once the space station is launched, astronauts turn on the motors, beginning rotation from rest. How long does it take for them to attain the speed you determined in part c? If you googled this question, which you should not have done, your search results would have included links to International Space Station microgravity experiments, upon which this question was based. R Constants & other possibly-useful information: sin(30) cos(60) 1/2 (for any 6) sin(45) = cos(45) = 1/2 = 2/2 sin(60) cos(30)=3/2 Mass of Earth: ME = 6.0x1024 kg 1 mile = 1609.34 m; 1 mile per hour = 1.61 km/hr = 0.447 m/s = 2688 furlongs per fortnight 1 atm 1.01x105 Pa Rotational inertia formulas for common shapes: hoop or hollow cylinder: I MR2 thin rod about center: I (1/12) ML disk or solid cylinder: I = (1/2) MR thin rod about end: I = (1/3) ML uniform solid sphere: I = (2/5) MR2 point mass a distance r from axis: I = mr