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 12.5 kg chair when empty is 0.760 s. What is the effective force constant of the springs?

B.) What is the mass of an astronaut who has an oscillation period of 2.00 s when in the chair?

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.

Explanation / Answer

1)
The period is defined as follows:

T = 2*pi*sqrt(m/k)

0.76 = 2*pi* sqrt [12.5 / k]

Therefore, the spring constant is,

k = 854.36 N/m

2)

If the oscillation period is T = 2 s, the mass is,

m = 12.5 + M

Use the above period equation to find the mass M.

2 = 2*pi*sqrt((12.5+M)/(854.36))

M = 74 Kg

3)

Apply the law of conservation of energy, we get

0.5*kA^2 = mgh

0.5*854.36*0.1^2 = 100000*9.81*h

Hence, the maximum displacement: h = 4.35*10^-6 m

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