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 0.837 s . What is the mass of an astronaut who oscillates with a period of 2.25 s when sitting in the chair?

Answer 1

k = spring constant = 606 N/m

m = mass of chair

T_s = time period with chair alone

M = mass of astronaut

T = time period with astronaut on chair

using the formula

T_s = 2 sqrt(m/k)              

0.837 = (2 x 3.14) sqrt(m/606)

m = 10.76 kg

also

T = 2 sqrt((m + M)/k)                  

2.25 = (2 x 3.14) sqrt((10.76 + M)/606)

M = 67.03 kg