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 1970 s space station, had a spring constant of 606 n/m. the empty chair oscillated with a period of 0.901 s . part a what is the mass of an astronaut who oscillates with a period of 2.28 s when sitting in the chair?

The mass of the astronaut is 67.33 kg

Explanation:

Given that,

Astronauts measure their mass by measuring the period of oscillation when sitting in a chair connected to a spring.

Spring constant of the spring, K = 606 N/m

The empty chair oscillated with a period of 0.901 s, t = 0.901 s

When an astronaut when sitting in the chair, the time period of oscillation is, t' = 2.28 s

To find,

The mass of an astronaut

Solution,

The time period of spring is given by :

m is the mass of the empty chair

m = 12.46 kg

Let m' is the mass of the spring and empty chair. It can be calculated as :

m' = 79.79 kg

Let M is the mass of the astronaut. It is equal to:

M= m' - m

M = 67.33 kg

So, the mass of the astronaut is 67.33 kg