As we\'ve seen, astronauts measure their mass by measuring the period of oscilla

Question

As we've seen, astronauts measure their mass by measuring the period of oscillation when sitting in a chair connected to a spring. The Body Mass Measurement Device on Skylab, a 1970s space station, had a spring constant of 606 N/m. The empty chair oscillated with a period of 0.853 s .

Part A

What is the mass of an astronaut who oscillates with a period of 2.14 s when sitting in the chair?

As we've seen, astronauts measure their mass by measuring the period of oscillation when sitting in a chair connected to a spring. The Body Mass Measurement Device on Skylab, a 1970s space station, had a spring constant of 606 N/m. The empty chair oscillated with a period of 0.853 s .

Part A

What is the mass of an astronaut who oscillates with a period of 2.14 s when sitting in the chair?

Explanation / Answer

Using T = 2(m/k) for loaded spring in the form .. T² = 4²(m/k)

For chair unoccupied (m) .. .. .. . 0.853² = 4²(m/606)

For chair + astronaut (m+M) .. .. 2.14² = 4²([m+M]/606)

Subtracting .. (2.14² - 0.853²) = (4²/606)([m+M] - m)

3.852 = 0.065 x M .. .. .. M = 3.852/0.065 .. .. .. M = 59.13 kg

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