A common problem inside orbiting space stations is monitoring astronauts weight,

Question

A common problem inside orbiting space stations is monitoring astronauts weight, or better said mass. The apparent weightlessness does not allow the use of conventional scales (note that due to the close proximity to earth, the astronauts weight did not really change drastically.) A solution to this problem is the use of harmonic oscillators (see http://www-spof.gsfc.nasa.gov/stargaze/Sskylab.htm for a description). You have carefully measured the period for the oscillation of the empty chair, which is attached to an ideal spring. You already determined the mass of the empty chair to be 20 kg. With and astronaut strapped into the chair, the period of the oacillation increases by 136 %. What is the mass of the astronaut?

Explanation / Answer

t for chair = T

t with astro = (1+1.36)T = 2.36T

we know t is inverse of frequency or we cn say t is inversely related to

also, = sqrt(k/m)=> = 2/t             sqrt means square root of

Tnew/Told = sqrt(mnew/mold)

2.36 = sqrt(mnew/22)

2.36^2 = mnew/22

5.5696 = mnew/22

mnew = 122.5312

m of chair = 22

thus mass of astronaut = 122.5312 - 22 = 100.5312 kg

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