Newton's second law: 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

The magnitude of the acceleration of the space station can be found using the principle of conservation of momentum. Since the total momentum of the system (astronaut + space station) must remain constant, the momentum gained by the astronaut is equal in magnitude and opposite in direction to the momentum gained by the space station. The formula for momentum is $p = mv$, and the change in momentum ($\Delta p$) leads to acceleration ($a$) when a force is applied, as described by Newton's second law ($F = ma$). Given the mass of the astronaut and her acceleration, we can calculate the force she exerts and thus the acceleration of the space station by rearranging the formula to $a = F/m$, where $F$ is the force exerted by the astronaut (equal and opposite to the force the space station exerts on her) and $m$ is the mass of the space station. The small acceleration of the space station reflects its much larger mass compared to the astronaut.

Newton's Second Law: the International Space Station Has a Mass