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# Treebeard's Stumper Answer7 September 2001

We're studying water in my Dunn Middle School Science class, beginning with this classic stumper. Your boat is floating in a small pool with a load of heavy rocks. What will happen to the water level of the pool if you throw the rocks over the side? Will the water level rise, fall, or stay exactly the same? Suppose the boat develops a leak and starts to slowly sink. How will the water level change as your boat takes on water and finally sinks to the bottom? Be careful, these are stumpers! Think first, but with summer still upon us, a wet experiment is called for!
Here are a few bonus stumpers:
• What if I empty a 55 gallon drum of water over the side?
• What if a prohibitionist empties a barrel of whisky over the side?
• What if I drop a cubic meter of ice over the side?
• What if the polar ice caps really do melt because of global warming? How will that effect the sea level?

It seems surprising, but the water level drops when you throw rocks from your boat. A volume of rock is heavier than the same amount of water, so it has more effect displacing its weight in the boat than displacing its volume in the lake. As your sinking boat takes on water, there's less water in the lake, but the heavier boat sinks that much deeper. The water level will stay the same until your boat finally goes down, and then it drops suddenly, like tossing another rock over the side. Mass, volume, density, and buoyancy are the concepts involved, and these are the new topics in my science class.

Notes:

It's easy to do this experiment with a graduated cylinder or measuring cup for a lake, a test tube or plastic cup for a boat, and some real rocks or lead fishing weights. Poke a small hole in a plastic cup with a nail to make a sinking boat. It's fun and surprising, and a great way to start a science class. There's a rumor that several fine physicists, including Einstein, George Gamov, Felix Bloch, and Robert Oppenheimer, answered this question wrong. That must be an urban legend. I doubt they all missed that same Physics lecture on Archimedes' Principle.

Graybear had the privilege of sending his answer with a clear mind on Monday before the September 11 attack. He's safe. I'll let it stand.

• Your boat is floating in a small pool with a load of heavy rocks. What will happen to the water level of the pool if you throw the rocks over the side? Will the water level rise, fall, or stay exactly the same?

Assuming that these rocks sink (aren't some rocks able to float?), the water level will go down because at first the rocks were displacing their weight in water, now they are only displacing their volume.

• Suppose the boat develops a leak and starts to slowly sink. How will the water level change as your boat takes on water and finally sinks to the bottom?

Likewise, if the boat actually sinks, the water level goes down.

• What if I dump a 55 gallon drum of water over the side?

Assuming you don't dump the drum, but only the water in it, and assuming the water in the drum has the same specific gravity as the water in the pond, then the level remains the same.

• What if a prohibitionist dumps a barrel of whisky over the side?

Whiskey has a specific gravity less than water so the level will go up instead.

• What if I have drop a cubic meter of ice over the side?

Same as with the drum of water, since the ice will not sink.

• What if the polar ice caps really do melt because of global warming? How will that effect the sea level?

The sea level will rise from all the extra water that is released. Some scientists say that if the ice caps melted entirely, the shape of the earth would change from the shift of mass from the poles to the rest of the globe.

I figure it's always proper to answer a question with another question, and Graybear has a good one:

What if you had an empty barrel (which normally would float high) but had enough weight attached to it so that it would be held underwater. It you threw the contraption overboard, would the water level rise, fall, or remain the same?

• This stumper is a classic. You can find it in print in Jearl Walker's Flying Circus of Physics, or on the Web at Newton Ask A Scientist and Oak Harbor Middle School.

• The story of Archimedes' discovery of the principle of bouyancy is told at The Golden Crown. They share this story and illustration from a 1940's magazine advertisement for NBC:
 ARCHIMEDES was asked to check the suspected presence of silver alloy in the king's gold crown. The solution which occurred when he stepped into his bath and caused it to overflow was to put a weight of gold equal to the crown, and known to be pure, into a bowl which was filled with water to the brim. Then the gold would be removed and the king's crown put in, in its place. An alloy of lighter silver would increase the bulk of the crown and cause the bowl to overflow. So delighted was Archimedes with his solution that he leaped from his bath and ran through the streets of Syracuse crying "Eureka!"
I like this story because my DMS school kids are still working to understand my stumper, so I don't want to give it all away here. And this story is really just another stumper. Archimedes' Principle is usually stated as "An object is buoyed up by a force equal to the weight of the fluid it displaces." How does that explain the story and my stumper? Eureka!

• The global effect of melting polar ice caps is complicated. The oceans are more-dense salt water, but polar ice is less-dense fresh water. Much polar ice is anchored to Greenland and Antarctica and not floating at all. Floating ice would not raise sea levels much if it melted, although it would have other effects on the world's climate. Here are a few starting links at How Stuff Works, USA Today, EPA, and Global Warming: Early Warning Signs. There are many more.

• My Cup Runneth Over? (11 Sep 98) is another Treebeard stumper about water level and bouyancy.

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