BATHTUB PHYSICS, 2 (18 march 2004)
Yesterday I described a problem that involved a closed empty shampoo bottle. I was wondering how it would behave if it was released under water from the bottom of the bath - with its top up, and with the bottom up:
The question was: will the bottle jump higher in case A or in case B? Or is the speed the same in in either case?
You might expect that the bottle would behave like cigar-shaped submarine:
It is clear that if both submarines are propelled to the right by the same amount of power, the speed of A would be greater than the speed of B.
But engineers have found ways to hold submarines in a horizontal position. Shampoo bottles, however, don't have ways to be stabilized.
In case A, the bottle has most of its volume at the bottom. So if we follow Archimedes, the bottom will be pushed up with greater force than the top. And the bottle will "try to" turn around. It is clear that this will cause a lot of resistance in the water.
In case B, the shampoo bottle has most of its volume at its highest point. So the upward force there will be greater than at the lowest point, where the bottle has less volume. B will stay in the same position and float to the surface without a hitch.
So the bottle that is turned upside down at the start (B) will jump considerably higher above the water than the bottle in case A, where the upward force will try to turn it upside down.
Which also goes to show that appearances can be deceptive.
