Re: A TRUE/FALSE question for your kids

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Wed, 28 Jan 1998, LUDWIK KOWALSKI wrote:

> A boat is floating in a small swimming pool and the occupant drops a large
> rock into the water. Will the level of water in the pool rise, fall or
> remain the same?

I've not been paying close attention to this thread, and assume that
someone has already given a correct answer, perhaps with explanation,
perhaps with some nice equations. (For an answer without supporting
argument is worthless.)

Some of the quibbles I've seen can be eliminated by a more careful
statement of the problem:

	You are in a boat floating in a small swimming pool. You have a
	large rock in the boat, which you drop overboard. The rock sinks
	to the bottom of the pool. Will the level of water in the pool
	rise, fall or remain the same?

The analysis then goes something like this:

We know the rock has density greater than water, because it sinks.

Therefore the rock weighs more than an equivalent volume of water.

When in the boat, the rock displaces its own weight of water. (Archimedes'
principle and Newton's laws.)

When at the bottom of the pool, the rock displaces its own volume of
water. (Displacement principle.)

Therefore, since the rock's weight is greater than the weight of an
equivalent volume of water, it displaces more water when it is in the boat
than when it is at the bottom of the pool.

Therefore the water level of the pool drops when the rock is dumped
overboard.

The boat and passenger need not concern us, for in both cases they are
displacing their own weight of water, which doesn't change.

One could ask about the level of the boat with respect to the water
surface (a different question) and of course, the boat rises with respect
to the water surface after the rock is dumped. 


Then there's some related questions:

You are in a boat floating in a small swimming pool. You have a large log
in the boat, which you drop overboard. The log floats. Will the level of
water in the pool rise, fall or remain the same?

You are in a boat floating in a small swimming pool. You have a large log
and a rock in the boat. You tie the rock to the log and throw both
overboard. They both sink together. Will the level of water in the pool
rise, fall, or remain the same? 

You are in a boat floating in a small swimming pool. A large log is
floating nearby, which you grab and take onto the boat. Will the level of
water in the pool rise, fall, or remain the same?

You are fishing in a small pond, and your hook snags a submerged old tire. 
You haul it aboard to dispose of properly later (doing your bit to improve
the environment). Does the level of water in the lake rise, fall, or
remain the same? 

Always milk a good problem idea for all it's worth.

	-- Donald Simanek