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This is related to other questions that are similar, but it's somewhat different. I was discussing the following situation with my father, and we don't quite agree on the result.
The situation is this: you have a jar, closed, falling due to gravity with no air resistance. Inside the jar, full of air, there's a fly, falling with the jar, located at the bottom. While the jar is falling, the fly lifts and goes to the top of the jar. The question is: does the jar reach the ground after, before or at the same time as if the fly hadn't moved?
My father thinks that the answer is this: you take the jar+air+fly as your system. The only external force acting on the system is gravity, so the trajectory of the center of mass follows the trajectory imposed by a=-g; the fly moves "up" respect to the center of mass, so it gets higher. In order to have that the trajectory is not altered, that lifting of the center of mass must result on the system "accelerating" and hitting the ground EARLIER than if the fly hadn't moved.
Me, I think there's something fishy about that "acceleration" in order to keep the trajectory invariant, because it's caused, somehow, by internal forces.
What do you think?
PS: editing to add the "homework and exercises" tag. It's not homework I have, but the question can be thought as belonging there. Thanks.