The masses of astronauts are monitored during long stays in orbit, such as when

Question

The masses of astronauts are monitored during long stays in orbit, such as when visiting a space station. The astronaut is strapped into a chair that is attached to the space station by springs and the period of oscillation of the chair in a frictionless track is measured.

(a) The period of oscillation of the 10.0 kg chair when empty is 0.720 s. What is the effective force constant of the springs? I got 769.2 N/m which is correct but I can't get (b) and (c)

b)What is the mass of an astronaut who has an oscillation period of 2.00 s when in the chair (kg)?

c)The movement of the space station should be negligible. Find the maximum displacement to the 100000 kg space station if the astronaut's motion has an amplitude of 0.100 m. In (m)

Explanation / Answer

b)
from part a,
K = 769.2 N/m
Now,
total mass= m+10
where m is mass of Astrenaut in Kg
use:
T =2pi* sqrt (total mass/K)
2 = 2*pi*sqrt((m+10)/769.2)
(m+10)/769.2 = 0.1
m= 67.9 Kg
Answer: 67.9 Kg

c)
centre of mass should not move
so,
(m1*x1 + m2*x2) / (m1+m2) = 0
(m1*x1 + m2*x2) =0
100000*x1 + (10+67.9)*0.1 = 0
x1= -7.79*10^-5 m
Maximum displacement is 7.79*10^-5 m

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