Final answer:
To find the astronaut's mass, given a force of 50.0 N and an acceleration of 0.893 m/s², use Newton's Second Law (F=ma). The mass is approximately 56 kg. Recoil from the astronaut's chair should be neutralized to avoid affecting the acceleration measurement.
Step-by-step explanation:
The question asks about measuring an astronaut's mass in orbit. Newton's Second Law of Motion, which states that force equals mass times acceleration (F=ma), is used to solve for the astronaut's mass given a known force and measured acceleration. If a net external force of 50.0 N produces an acceleration of 0.893 m/s², the mass (m) can be calculated like this:
m = F/a
m = 50.0 N / 0.893 m/s²
m ≈ 56 kg
Thus, the astronaut's mass is approximately 56 kilograms. Considering Newton's Third Law, the force exerted by the astronaut on their chair would cause an equal and opposite reaction force; this recoil must be accounted for to prevent affecting the measurement. To avoid recoil of the vehicle, the measurement should be done in a way that compensates or neutralizes this opposite force, possibly using internal mechanisms within the space station that can absorb the force without altering the station's momentum. An example could be a stabilizing system that pushes against the station's structure to counteract the applied force.