Jason picked up a plastic water bottle and filled it to the rim with water. He put a ketchup sachet in it and closed it up.
Jason approached his girlfriend Lola and said, "If you can solve how this works, I will give you a dollar."
Jason said, "down" and the sachet of ketchup suddenly went down. Then he said, "up" and it went up. Then he said, "down", and when it was halfway down, he said, "stay" and it stayed.
How did Jason manage to do this?
I assume the sachet of ketchup is:
- a sealed small plastic packet containing a small air bubble
- the averaged density of the ketchup liquid and plastic wrapper is greater than that of water
- at room temperature, the averaged density of the entire sachet including the air bubble is equal to the density of water.
From these assumptions, a room temperature sachet in room temperature water will have completely neutral buoyancy and thus float in the middle. (sort of - see "wrinkle" below)
Jason puts the ketchup sachet in the refrigerator making it cold, then puts this into warm water. Initially, the air bubble is small, so the less buoyant sachet sinks to the bottom. But soon, some heat transfers from the warm water to the sachet. Now the air bubble is larger than it would be at room temperature, so the sachet floats to the top. Eventually, the entire system loses heat; upon returning to room temperature, the sachet's buoyancy becomes neutral.
One final wrinkle could be if Jason has added something to the water bottle to create a gradient of density such that the density of water at the midpoint was equal to the room temperature density of the sachet, then he could guarantee that the sachet would go to the center of the water bottle.
As for the sachet moving apparently on command, Jason would have to practice this in order to predict how long each transition would take.
Edited on March 21, 2022, 8:55 am
|
|
Posted by Larry
on 2022-03-21 08:54:27 |
Solution with other assumptions
