The International Space Station has a mass of 1.8 × 10⁵kg.A 70.0-kg astronaut inside the station pushes off one wall of the station so she accelerates at 1.50 m/s².What is the magnitude of the acceleration of the space station as the astronaut is pushing off the wall? Give your answer relative to an observer who is space walking and therefore does not accelerate with the space station due to the push. A)5.8 × 10^-4 m/s² B)1.50 m/s² C)4.7 × 10^-4 m/s² D)zero E)3.9 × 10^-3 m/s²

Question

Quizplus · Accepted Answer

This is a conservation of momentum problem. The astronaut's push generates an equal and opposite force on the space station, causing it to accelerate in the opposite direction. Using F = ma, we can find the acceleration of the space station:
F = ma
-70.0 kg * 1.50 m/s^2 = (1.8 * 10^5 kg) a
a = -5.8 * 10^-4 m/s^2
Since the astronaut is inside the space station, she is also accelerating with it and therefore does not observe any acceleration. However, an observer outside the space station (e.g. spacewalking) would see the space station accelerating in the direction opposite to the astronaut's push, with an acceleration of 5.8 * 10^-4 m/s^2. Therefore, the answer is A.

The International Space Station Has a Mass of 1