Figure 17-28 shows an astronaut on a Body Mass Measurement Device (BMMD). Designed for use on orbiting space vehicles, its purpose is to allow astronauts to measure their mass in the weightless conditions in Earth orbit. The BMMD is a spring-mounted chair; an astronaut measures his or her period of oscillation in the chair; the mass follows from the formula for the period of an oscillating block–spring system. (a) If M is the mass of the astronaut and m the effective mass of that part of the BMMD that also oscillates, show that where T is the period of oscillation and k is the force constant. (b) The force constant is k = 605.6 N/m for the BMMD, and the period of oscillation of the empty chair is 0.90149 s. Calculate the effective mass of the chair. (c) With an astronaut in the chair, the period of oscillation becomes 2.08832 s. Calculate the mass of the astronaut.

Figure 17-28 shows an astronaut on a Body Mass Measurement Device (BMMD). Designed for use on orbiting space vehicles, its purpose is to allow astronauts to measure their mass in the weightless conditions in Earth orbit. The BMMD is a spring-mounted chair; an astronaut measures his or her period of oscillation in the chair; the mass follows from the formula for the period of an oscillating block–spring system. (a) If M is the mass of the astronaut and m the effective mass of that part of the BMMD that also oscillates, show that

where T is the period of oscillation and k is the force constant. (b) The force constant is k =   605.6 N/m for the BMMD, and the period of oscillation of the empty chair is 0.90149 s. Calculate the effective mass of the chair. (c) With an astronaut in the chair, the period of oscillation becomes 2.08832 s. Calculate the mass of the astronaut.