Question

As we've seen, 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, a 1970s space station, had a spring constant of 606 N/m. The empty chair oscillated with a period of 0.848 s.What is the mass of an astronaut who oscillates with a period of 2.26 s when sitting in the chair?

Answer 1

mass of astronaut is M 67.362 kg

Step-by-step explanation:

Given details:

spring constant k = 606 N/m

Time T = 0.848 s

The time period is

`T = (2\pi)\sqrt{(m)/(k)}`

So the mass of the empty chair is

`m = [(T)/(2\pi)]^2 k`

`= [(0.848)/(2\pi)]^2*606`

= 11.038 kg

When astronaut is sitting in the chair then the time period is

`T' = (2\pi)\sqrt{(m')/(k)}`

`m' = [(T')/(2\pi)]^2k`

`=[(2.26)/(2\pi)]^2*606`

m' = 78.40 kg

mass of astronaut is M = m' - m

= (78.40 kg) - ( 11.038 kg)

= 67.362 kg