The masses of astronauts are monitored during long stays in orbit, such as when
ID: 1396063 • Letter: T
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 10.5 kg chair when empty is 0.700 s. What is the effective force constant of the springs?
1 N/m
(b) What is the mass of an astronaut who has an oscillation period of 2.00 s when in the chair?
2 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.
3 m
Explanation / Answer
A)
T = 2*pi*sqrt(m/k)
T is time period = 0.7 S
m = 10.5 kg
0.7 = 2*3.142*sqrt(10.5/k)
10.5/k = (0.7/6.284)^2
k = 846.2 N/m
B) Now T = 2 S
m = 10.5+M
then 2 = 2*3.142*sqrt((10.5+M)/(846.2))
10.5+M = 85.7
M = 75.2 Kg
3) From law of conservation of energy
enrgy of the astronaut = energy of the space station
0.5*k*A^2 = m*g*h
0.5*846.2*0.1^2 = 100000*9.81*h
h = 4.31*10^-6 m
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