Suppose a space capsule with an astronaut inside is launched from the top of a tower at some angle above the horizontal.
a)While the capsule is in free fall, what are the acceleration of the astronaut and the capsule?
b)If the astronaut measures his acceleration compared with that of the capsule, what value will he get?
c) In what sense can we say that the astronaut is "weightless" in the capsule? Is he "weightless" because the gravity of the earth has gone away?
This real confuses me so I greatly appreciate the help!
when the system is in free fall, both the astronaut and the capsule are accelerating downward at 1 g.
Therefore the person is not accelerating relative to the capsule.
That means that there is no force acting on the bottom of his shoes from the capsule. His gravitational force down is exactly equal to his mass times his acceleration. No other force is needed and if he were standing on a scale the scale would read zero.
I'd be happy to help clarify your confusion!
a) While the capsule is in free fall, both the astronaut and the capsule experience the same acceleration. This acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s² near the surface of the Earth, and acts vertically downwards. Keep in mind that in free fall, the only force acting on the astronaut and the capsule is gravity, which causes an acceleration.
b) If the astronaut measures his acceleration compared to that of the capsule, he will find that the acceleration is zero. This is due to the fact that both the astronaut and the capsule are falling under the influence of gravity together, so they move in unison. Since the astronaut and the capsule are falling with the same acceleration, the relative acceleration between them is zero.
c) The term "weightless" in the context of the astronaut inside the capsule means that the astronaut doesn't experience a sensation of weight, as if there is no gravitational force acting on them. However, it's important to understand that the force of gravity has not gone away. Even though the astronaut and the capsule are falling, they are still subject to the gravitational pull of the Earth. The reason the astronaut feels weightless is because both the astronaut and the capsule are accelerating due to gravity at the same rate. This gives the sensation of weightlessness, as there is no normal force acting on the astronaut to cause a feeling of weight. In simpler terms, the astronaut is essentially in a state of continuous free fall, creating the impression of being weightless.
I hope this explanation helps! Let me know if there's anything else you'd like to understand.