A fisherman and his young daughter are in a boat on a small pond. Both are wearing life jackets. The daughter is holding a large helium filled balloon by a string. Consider each action below independently and indicate whether the level of the water in the pond, Rises, Falls, is Unchanged or Cannot tell.
The daughter gets in the water and pops the helium ballon
The daughter pops the helium balloon.
The fisherman knocks the tackle box overboard and it sinks to the bottom.
The fisherman fills a glass with water from the pond and drinks it.
The fisherman lowers the anchor and it hangs one foot above the bottom of the pond.
The fisherman lowers himself in the water and floats on his back.
The daughter gets in the water and pops the helium ballon
The daughter pops the helium balloon.
The fisherman knocks the tackle box overboard and it sinks to the bottom.
The fisherman fills a glass with water from the pond and drinks it.
The fisherman lowers the anchor and it hangs one foot above the bottom of the pond.
The fisherman lowers himself in the water and floats on his back.
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a) The child floats, and displaces as much water as her mass did when in the boat.The balloon hardly matters, but the level rises.
b) The level rises the same distance as in (a).
c) The tackle box volume presumably will not displace as much mass of water as its weight did when in the boat. The level falls.
d) No change, the water mass now in the man is equal to the mass removed from the pond.
e) The anchor mass was in the boat, displacing water equal to its mass. When hanging in the water, it only displaces its own volume of water. The level falls.
f) No change, the fisherman is still displacing his own mass of water when in the boat, or out of the boat and floating.
b) The level rises the same distance as in (a).
c) The tackle box volume presumably will not displace as much mass of water as its weight did when in the boat. The level falls.
d) No change, the water mass now in the man is equal to the mass removed from the pond.
e) The anchor mass was in the boat, displacing water equal to its mass. When hanging in the water, it only displaces its own volume of water. The level falls.
f) No change, the fisherman is still displacing his own mass of water when in the boat, or out of the boat and floating.
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The daughter gets in the water and pops the helium balloon
Lowers
The daughter pops the helium balloon.
Lowers
The fisherman knocks the tackle box overboard and it sinks to the bottom.
Unchanged
The fisherman fills a glass with water from the pond and drinks it.
Unchanged
The fisherman lowers the anchor and it hangs one foot above the bottom of the pond.
Unchanged
The fisherman lowers himself in the water and floats on his back.
Unchanged
I base my answers upon the fact that the only changes that occur above the water are in the first two scenarios. The remaining scenarios are merely the repositioning of masses that have already impacted the level of the water. However, I do have to wonder about the trade-off between being in a boat ON the water as opposed to being IN the water. Plus the fact that the question leaves out what sort of medium the pond, boat and people exist in. That's important because in a vacuum, the gas inside of the balloon may as well be outside of the balloon.
Lowers
The daughter pops the helium balloon.
Lowers
The fisherman knocks the tackle box overboard and it sinks to the bottom.
Unchanged
The fisherman fills a glass with water from the pond and drinks it.
Unchanged
The fisherman lowers the anchor and it hangs one foot above the bottom of the pond.
Unchanged
The fisherman lowers himself in the water and floats on his back.
Unchanged
I base my answers upon the fact that the only changes that occur above the water are in the first two scenarios. The remaining scenarios are merely the repositioning of masses that have already impacted the level of the water. However, I do have to wonder about the trade-off between being in a boat ON the water as opposed to being IN the water. Plus the fact that the question leaves out what sort of medium the pond, boat and people exist in. That's important because in a vacuum, the gas inside of the balloon may as well be outside of the balloon.