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 effective force constant of the springs is 888.54 N/m

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

For a oscillating body we have the equation ,

T = 2 (m/k)1/2

Substituting the values of T and k , we can get the value of k

2 = 2 * 3.14 * (m/888.54) ½            

4 = 4 * 9.85 * (m/888.54)

m = 888.54 / 9.85

m = 90 kg

From the conservation of momentum law

mass of astronaut * astronaut amplitude = mass of spaceship * spaceship amplitude

m * 0.100 = 100000*X
X = 90 * 0.100/ 100000

X = 9 * 10-5 m

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