Question Gravity - LessWrong
Earlier today, I was in the shower. I had just finished a bottle of shampoo, and I tried balancing it on the thin railing of the shower door. I expected it to fall down, but instead it stayed there. From the side, it certainly looked like it was sticking out more than halfway over the edge. (Picture) Yet it stubbornly stayed put.
Wait, what? Filling it up shouldn't change the location of its center of gravity, so why would that make it fall over? I started performing more experiments. I rotated the bottle to see if there was some asymmetry in its construction. I thought maybe the water sloshing around could cause its center of gravity to move over the edge, so I I tried holding it there for several seconds before letting go, in order to let the water settle. I noticed the door had some wiggle room, and the weight of the bottle could be causing the door to shift to a different angle, so I tried holding it at different angles. Nothing caused any different behavior. I put it on the ledge empty and slowly filled it with water. When it got to around 1/20 full, it fell over. I found a second bottle and performed all the same tests on it; same results.
At this point I was thoroughly confused. I figured some assumption of mine must have been wrong, so I tried inspecting them. Does the center of gravity of an object really have to be over the edge in order for it to fall? I couldn't think of any situation where that wasn't true. (Generalizing from a non-exhaustive list of arbitrary examples is obviously not a great approach, but I couldn't do much better while in the shower.) Does filling it with water really not change its center of gravity? Oh wait; it does! The center of gravity doesn't move it laterally, but it does move it vertically. That assumption was wrong. (I probably wouldn't have made this mistake if I had been thinking of it as the center of mass rather than the center of gravity. Framing is important.) Unfortunately, that epiphany didn't lead to anything useful; I couldn't see how moving the center of mass vertically could affect whether it was balanced or not.
