Friday, April 11, 2014

Stone thrown from the boat

Problem

Will there be any change in water level/height of floating part of the boat if stones are dropped into the pond from a floating boat?
Follow up - What if you are given empty 2L bottle and chained under the boat?

Solution

There is maybe a little physics needed here...

When an object is floating be it because it is something less dense than water, say polystyrene, or because it is in a boat, say a brick and the whole boat is less dense than water, then it displaces in the water it's own mass. For example a 10 Kg lump of lead on a boat will force the boat to sink by a volume equivalent to 10Kg of water. Hence displacing 10Kg of water. Or indeed forcing the water level to raise by an amount equivalent to 10Kg of water. (Like when you get in the bath.)

When an object sinks in water it necessarily displaces it's own volume.

So when the brick is in the boat it is displacing it's own mass equivalence in water. When the brick is thrown over the side it is displacing it's own volume in water.

So which of these is greater?

Well we know the brick to be more dense than water because it sinks. So the volume of water equivalent to the mass of the brick is greater than the volume of the brick. And so less water is displaced after than before. Hence... 

Water level will go down

Follow up answer
The opposite would happen if you were chained to the bottom and pulled an empty two-liter bottle under the water.  First, it's only displacing water equal to its weight, because it's floating.  But then when you pull it under water, it's displacing water equal to its volume, which is much more.  Then the water level rises.  

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