Final answer:
The astronaut's mass is calculated using Newton's second law of motion, with a given force of 50.0 N and measured acceleration of 0.893 m/s²; the mass is approximately 56.0 kg, hence the correct option is (a) 55.9 kg. To avoid the spacecraft's recoil affecting the astronaut's acceleration measurement, a counteracting system like a reaction wheel can be used.
Step-by-step explanation:
To calculate the mass of the astronaut when a net external force of 50.0 N is exerted and the astronaut's acceleration is measured to be 0.893 m/s², we use Newton's second law of motion, which states that the force applied on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Therefore, to find the mass (m), we rearrange the equation to m = F/a.
Given:
- Net external force (F) = 50.0 N
- Astronaut's acceleration (a) = 0.893 m/s²
Using these values:
m = 50.0 N / 0.893 m/s²
m ≈ 55.9945 kg
When we round to the nearest tenth, the mass of the astronaut is approximately 56.0 kg, which makes the correct option (a) 55.9 kg.
For part (b), the exertion of a force on the astronaut would also apply an equal and opposite force on the spacecraft due to Newton's third law of motion. This would cause the spacecraft to experience recoil, which could affect the measurement of the astronaut's acceleration. To avoid this, a system that counteracts the applied force, such as a reaction wheel or a thruster firing in the opposite direction, could be used to maintain the spacecraft's position.