Question

In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least "massed"). One way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. The 35.2 kg chair alone oscillates with a period of 1.50 s , and the period with the astronaut sitting in the chair is 2.22 s . Part A Find the force constant of the spring. Part B Find the mass of the astronaut.

Answer 1

(A) T = 2 pi squareroot m/k => 1.5 = 2 pi squareroot 35.2/k => k = 617.6 N/m (B) T' = 2 pi squareroot m + m'/k => 2.22 = 2 pi squareroot 35.2 + m'/k From equation of T & T' dividing both 1.5/2.22 = squareroot 35.2/35.2 + m' => m' = 41.9 kg