Answer:
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 :
[tex]t=2\pi \sqrt{\dfrac{m}{K}}[/tex]
m is the mass of the empty chair
[tex]m=\dfrac{t^2K}{4\pi^2}[/tex]
[tex]m=\dfrac{(0.901)^2\times 606}{4\pi^2}[/tex]
m = 12.46 kg
Let m' is the mass of the spring and empty chair. It can be calculated as :
[tex]m'=\dfrac{t'^2K}{4\pi^2}[/tex]
[tex]m'=\dfrac{(2.28)^2\times 606}{4\pi^2}[/tex]
m' = 79.79 kg
Let M is the mass of the astronaut. It is equal to:
M= m' - m
[tex]M=79.79-12.46[/tex]
M = 67.33 kg
So, the mass of the astronaut is 67.33 kg
