Question

Astronauts measure their mass by measuring the period of oscillation when sitting in a chair connected to a spring. The Body Mass Measurement Device on Skylab, 1970s space station, had a spring constant of 600 N/m. The empty chair has a mass of 12 kg. What is the mass of an astronaut who oscillates with a period of 2.1 sec when sitting in the chair?

Answer 1

55 kg

Step-by-step explanation:

spring constant (k) = 600 N/m

mass of chair (Mc) = 12 kg

period of oscillation of chair and man (T) = 2.1 s

what is the mass of the astronaut (Ma) ?

mass of the astronaut (Ma) = total mass (Mt) - mass of chair (Mc)

where

• total mass (Mt) =
  `(T^(2))/(4π^(2))k`

taking π as 3.142

total mass (Mt) =
`(2.1^(2))/(4 x 3.142^(2))600`

total mass (Mt) = 67 kg

therefore

mass of astronaut = 67 - 12 = 55 kg