suppose i am standing on a boat in a finite sized pool of water and i have an american quarter in my pocket. if i then take the quarter out of my pocket and drop it into the pool, how does the steady state level in the pool change? does it go up, down, or stay the same?

Originally posted by davegage here is one puzzle that engineers will recognize:

suppose i am standing on a boat in a finite sized pool of water and i have an american quarter in my pocket. if i then take the quarter out of my pocket and drop it into the pool, how does the steady state level in the pool change? does it go up, down, or stay the same?

Moved water mass = weight of mass in water

So the water drops a bit when you toss in the coin

Originally posted by davegage here is one puzzle that engineers will recognize:

suppose i am standing on a boat in a finite sized pool of water and i have an american quarter in my pocket. if i then take the quarter out of my pocket and drop it into the pool, how does the steady state level in the pool change? does it go up, down, or stay the same?

If your pocket (along with the boat) is below the surface of the pool and completely saturated with water then there would be no change in the pool level.

The mass of the quarter is the same in or out of the water, and in each case, it's mass is moving the water aside the same amount. There would be no change whether you were above or below the water's level before you threw the quarter in. (I believe this to be true but I have not had physics in a while).

Originally posted by econundrum The mass of the quarter is the same in or out of the water, and in each case, it's mass is moving the water aside the same amount. There would be no change whether you were above or below the water's level before you threw the quarter in. (I believe this to be true but I have not had physics in a while).

No. TheMaster is right when he says that the level will drop. the reason is because in the boat, the quarter displaces a volume of water that has weight equal to the coin's weight, while in the pool it displaces a volume of water only equal to its own volume. Since the quarter is more dense than water, these values are not equal and the level will drop slightly.

the other assertion about the boat and the guy being submerged is of course correct (no change in level because in each case the coin displaces only its own volume), but i think in that case the guy has bigger things to worry about.