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. The period of oscillation of the 11.5 kg chair when empty is 0.760 s. What is the effective force constant of the springs? What is the mass of an astronaut who has an oscillation period of 2.00 s when in the chair? 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

here,

mass of chair , m = 11.5 kg

let the spring constant be k

a)

time period , T = 0.76 s

2 * pi * sqrt(m/k) = 0.76

2 * pi*sqrt( 11.5 /k) = 0.76

k = 750.6 N/m

the spring constant is 750.6 N/m

b)

let the mass of the asternaut be M

time period , T = 2 s

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

2 * pi * sqrt( ( 11.5 + M) / 750.6) = 2

M = 64.63 kg

the mass of the asternaut is 64.63 kg

c)

mass of the space station , M1 = 100000 kg

amplitude of oscillation , A2 = 0.1 m

let the maximum displacement be A1

M1 * A1 - ( M + m) * A2 = 0

100000 * A1 - ( 64.63 + 11.5) * 0.1 = 0

A1 = 7.61 * 10^-5 m

the maximum displacement to the spacestation is 7.61 * 10^-5 m

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