Question

It is important for astronauts in space to monitor their body weight. In Earth orbit, a simple scale only reads an apparent weight of zero, so another method is needed. NASA developed the body mass measuring device (BMMD) for Skylab astronauts. The BMMD is a spring-mounted chair that oscillates in simple harmonic motion (see figure below). From the period of the motion, the mass of the astronaut can be calculated. In a typical system, the chair has a period of oscillation of 0.851 s when empty. The spring constant is 546 N/m. When a certain astronaut sits in the chair, the period of oscillation increases to 2.32 s. Determine the mass of the astronaut.
kg?

Answer 1

the expression for the time period of oscillating body is

T = 2π√(m/k)

where m is the mass of chair and k is the spring constant

for period 0.851 s with no astronaut sitting on that chair,so we can calculate the mass of the chair,

0.851 = 2π√(m/546)

m = (0.851/2π)² * 546

solving for m,

m = 10 Kg

Now when the astronaut sits on that chair having spring constant 546 N/m.

T= 2π√((M+m)/k)

where M is the mass of astronaut

2.32 = 2π√((M+10)/546)

M + 10 = (2.32/2π)² * 546

M = 64.4 Kg

The mass of the astronaut is 64.4 Kg.