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Question:
You are standing in a boat with a rock in the middle of a lake. You throw the rock into the lake. with respect to the land, does the water level rise/fall or stay the same?



Replies:
How much water does the brick displace when it is in the boat? How much water does the brick displace when it is in the water? The lake level will be highest when the brick is displacing the most water. The boat and everything that stays in it is a constant and can be ignored.


An interesting question. Here are my thoughts. When the rock is supported by the buoyant force holding the boat afloat, it displaces its mass in water. When you throw it into the lake, it will displace its own volume (which is smaller than the volume of a like mass of water). My conclusion would be that the level of the lake would go down when you threw the rock in. It would be interesting to try to prove this experimentally. If you do, use the smallest quantity of water you can and the heaviest object you can. Doing this, you will get the greatest possible difference in water level.

Larry Krengel


Boat will rise. The amount of water displaced is the same, but consider the difference in volumes of the lake and the boat. Lake volume is much greater than that of the boat.


With the rock in the boat, the entire weight of the rock pushes the boat into the water. But when the rock is submerged, only its volume and not its weight is displaced. Since the rock is denser that water (presumably), then less water is displaced when the rock is submerged. The boat rises, and the water level falls.



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