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 25 kg. With and astronaut strapped into the chair, the period of the oacillation increases by 123 %. What is the mass of the astronaut?

Explanation / Answer

According to the article "Theory predicted that T would be proportional to the square root of the oscillating mass"

So , T=k * sqrt(m) where k is a constant of proportionality

When there's empty chair

T=k*5 (since mass is 25) -----eqn 1

With and astronaut strapped into the chair, the period of the oacillation increases by 123%

So, 2.23T= k*sqrt(m) ----eqn 2

Dividing eqn 2 by eqn 1 we get

2.23=sqrt(m)/5

sqrt(m)= 11.15

So total mass=124.32 kg

Mass of chair =25kg

So mass of astronaut =(124.32-25)= 99.32Kg

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