Skylab Body Mass Device
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Exercise:
Normal bathroom scales do not work on the International Space Station ISS. Still it is relevant for astronauts staying there for up to several months to regularly measure their mass. This can be done with a chair susped from several springs forming a simple mass chair and astronaut on a spring system. The figure below shows the system that was used in the Skylab module. It is now on display in the Smithsonian National Air and Space Museum. center includegraphicswidthcm#image_path:skylab-body-mass-device# center For astronaut Tamara Jernigan an oscillation period of TCAO was measured. The empty chair mCO oscillates with a period of TCO. abcliste abc Determine Tamara’s mass at the time this measurement was taken. abc Why do normal bathroom scales not work on the ISS? Why is regularly measuring the body mass relevant for astronauts? abcliste
Solution:
abcliste abc The period for a mass on a spring system is given by T fracpiomega pisqrtfracmk The ratio of the period for the chair and the astronaut to the period of the empty chair is fracsscTC+AsscTC sqrtfracsscmA+sscmCsscmC where sscmC is the mass of the empty chair and sscmA the mass of the astronaut. Solving for the mass of the astronaut leads to sscmA mAF mCtimesleftleftfracTCATCright^-right mA approx resultmAP abc Normal bathroom scales measure the normal force acting on the platform of the scale. On the ISS the astronauts are in a constant free fall i.e. the gravitational force keeps them on their orbit around the Earth. The astronauts are floating in the space station no normal force would act on a normal scale. Measuring the body mass is important because in a weightless state there is barely any work done by the mussles so astronauts t to lose mussle mass during their time in the space station. abcliste
Normal bathroom scales do not work on the International Space Station ISS. Still it is relevant for astronauts staying there for up to several months to regularly measure their mass. This can be done with a chair susped from several springs forming a simple mass chair and astronaut on a spring system. The figure below shows the system that was used in the Skylab module. It is now on display in the Smithsonian National Air and Space Museum. center includegraphicswidthcm#image_path:skylab-body-mass-device# center For astronaut Tamara Jernigan an oscillation period of TCAO was measured. The empty chair mCO oscillates with a period of TCO. abcliste abc Determine Tamara’s mass at the time this measurement was taken. abc Why do normal bathroom scales not work on the ISS? Why is regularly measuring the body mass relevant for astronauts? abcliste
Solution:
abcliste abc The period for a mass on a spring system is given by T fracpiomega pisqrtfracmk The ratio of the period for the chair and the astronaut to the period of the empty chair is fracsscTC+AsscTC sqrtfracsscmA+sscmCsscmC where sscmC is the mass of the empty chair and sscmA the mass of the astronaut. Solving for the mass of the astronaut leads to sscmA mAF mCtimesleftleftfracTCATCright^-right mA approx resultmAP abc Normal bathroom scales measure the normal force acting on the platform of the scale. On the ISS the astronauts are in a constant free fall i.e. the gravitational force keeps them on their orbit around the Earth. The astronauts are floating in the space station no normal force would act on a normal scale. Measuring the body mass is important because in a weightless state there is barely any work done by the mussles so astronauts t to lose mussle mass during their time in the space station. abcliste