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A Boat, Rock and Lake
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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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Update: June 2012
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