An astronaut who weighs 800 N on the surface of the earth lifts off from planet Zuton in a space ship. The free-fall acceleration on Zuton is 3.0 m/s² (down). At the moment of liftoff the acceleration of the space ship is 0.50 m/s² (up). What is the magnitude of the force of the space ship on the astronaut? A) 41 N B) 0.29 kN C) 0.24 kN D) 0.20 kN E) 0.37 kN

Question

Quizplus · Accepted Answer

The force on the astronaut can be calculated using Newton's second law, $F = ma$, where $m$ is the mass of the astronaut and $a$ is the net acceleration. First, find the astronaut's mass by dividing their weight on Earth by Earth's gravitational acceleration ($9.8 m/s^2$): $m = 800N / 9.8m/s^2 = 81.63 kg$. The net acceleration is the sum of Zuton's gravitational acceleration and the spaceship's acceleration, $3.0 m/s^2 + 0.50 m/s^2 = 3.5 m/s^2$. Then, $F = 81.63 kg * 3.5 m/s^2 = 285.71 N$, which is $0.29 kN$.

An Astronaut Who Weighs 800 N on the Surface of the Earth