Find the force constant of the spring.k=? Find the mass of the astronaut.m=? In

Question

Find the force constant of the spring.k=? Find the mass of the astronaut.m=? In order to study the long-term effects of weightlessness,astronauts in space must be weighed (or atleast ''massed''). One way in which this is done is toseat them in a chair of known mass attached to a spring of knownforce constant and measure the period of the oscillations of thissystem. The 35.4 kg chair alone oscillateswith a period of 1.25 s, and the period with theastronaut sitting in the chair is2.23 s. Find the force constant of the spring.k=? Find the mass of the astronaut.m=?

Explanation / Answer

given mass of the chair m = 35.4kg time period of chair alone T = 1.25s time period of chair & astronaut T' = 2.23s mass of the astronaut = m' a) the force constant of the spring can be obtained from thetime period of chair alone       T = 2*(m/k)      T2 =42(m/k)      k =42*(m/T2)   calculate  for k b) the time period when the astronaut is in the chair      T' = 2*[(m+m')/k]       T'2 =42*[(m+m')/k]     or (m+m') =kT'2/42 simplify & calculate for m'

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