How do you measure the mass of an astronaut in orbit? (You can\'t just use a sca

Question

How do you measure the mass of an astronaut in orbit? (You can't just use a scale!) For the Skylab program, NASA engineers designed a Body Mass Measuring Device. This is essentially a chair of mass m mounted on a spring wiwth a carefully measured spring constant k=605.6N/m. The other end of the spring is connected to the Skylab itself, which has a mass much larger than the astronaut or the chair and so reminas essentially fixed as the astronaut oscillates. The period of oscillation of the empty chair is measured to be .90149s. When an astronaut is sitting in the chair, the period is 2.12151s. What is the mass of the astronaut? Please describe the reasoning

Explanation / Answer

Simply use the period formula for the mass and spring system:
T = 2*Pi*sqrt(m/k)

solve for m:
m = k*(T/(2*Pi))^2

Mass of chair = 605.6 *(.90149/(2*pi))^2

m=12.4666 kg

Mass of Astronaut + chair= 605.6*(2.12151/(2*pi))^2

M +m= 69.04kg

M=69.04-12.4666

M=56.57kg

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