What happens to the water level when boat drops rock?
If you have a large boat carrying a large rock floating in a lake, what happens if you drop the rock off the boat (and it sinks into the lake)? Does the water level stay the same, go up, or go down?
Um, water level doesn’t stay the same…guess again.
Here is a hint… compare the rock volume to the displaced water volume.
Archimedes Principle:
F = weight of water displaced
When the rock is in the boat, it causes the boat to sink, raising the water.
For a boat with sharp edges:
Force of Rock = Area of Boat Bottom*Depth Displaced*Density of Water
When you toss a rock in the water (and it sinks), the volume displaced is equal to the volume of the rock.
In general, the volume displaced by the boat with a large rock is larger then that the rock itself.
Say a piece of granite ~3 g/cc and 1000 cc, so 3000 grams. The volume displaced by the boat is going to be 3000g/1 g/cc (the density of water), or 3000 cc. Compare this with the 1000 cc if the rock is thrown in – less water is displaced, and lake falls in level.
This will be true for any substance more dense then water.
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