# Floatation

#### ByReeko

Mar 29, 2014

There’s an old saying that if you are standing in a boat in the middle of a lake and dropped a cannonball into the water, the water level of the lake would actually drop? This seems contradictory to common sense because as we all know, when you drop an object into a body of water the water level rises because of the volume of water that the object displaces. But guess what?  This old saying is really true.  Read on…

For example, if you fill your bathtub with water all the way to the brim and then climb into the tub, the water will spill over the edge of the tub. This happens because of the large amount of water that your body displaces when you jump in the tub.

But the cannonball trick is indeed true. If you drop a cannonball in the lake, the water level will drop. Here’s why…

Wile the cannonball is in your boat, the great weight of the cannonball causes the boat to displace quite a bit of water. Remember, Archimedes’ principle states that an object must displace its own weight in water. Since the cannonball is very dense, the boat would displace around 10 cannonball volumes of water in order to maintain the buoyancy needed to support the weight of the cannonball. Thus at this point, the water level has risen.

Now we toss the cannonball over the edge of the boat. The boat will now float higher than before because it does not need to displace the 10 cannonball volumes of water. But, the cannonball is now displacing 1 cannonballs volume of water as it sinks to the bottom of the lake. Now we are displacing 1 cannonball volume of water versus the 10 cannonball volumes of water before (when the cannonball was in the boat). That means we are actually displacing less water with the cannonball out of the boat than we were with the cannonball in the boat. Thus the water level of the lake actually rises.

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