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20050220 Sunday February 20, 2005

The Boat & The Bowling Ball Puzzles

My dad sent me this logic puzzle... It isn't that hard, but takes some thought. Don't answer too quickly!

Say you're in a small row boat on a lake. Inside the row boat is a bowling ball. You take the bowling ball and throw it over board. It sinks down to and settles on the sandy bottom of the lake.

Question: If we had measured the level of the lake before the ball was thrown over board, and again after the ball settled on the bottom of the lake, would we have found that the level of the lake increased, decreased, or remained the same?

In case you give up, here is the solution:
http://blogs.sun.com/roller/resources/dcb/SOLUTION_Boat_and_Ball.html


February 20, 2005 07:44 AM EST Permalink

Comments:

How do you expect me to figure this bowling ball problem out when it took me 20 minutes to figure out the math problem that I have to do to send this email?

Posted by Kevin Davis on February 20, 2005 at 09:51 AM EST #

I'm going to say no change - the bowling ball is displacing its weight in water both before and after the movement from the boat to the bottom. Chris Morgan

Posted by Chris Morgan on February 20, 2005 at 10:19 AM EST #

Hi Chris... That is not correct, but is a common answer. Key hint... the bowling ball does not weigh the same as an equal volume of water.

Posted by Dave Brillhart on February 20, 2005 at 02:35 PM EST #

Well, it would depend on the weight of the bowling ball. A 6 lb kid's bowling ball is actually less dense than water, so it would float, displacing the same amount of water it had when in the boat. No change in water level of the lake.

Any bowling ball over about 7 lbs would sink, and since it is more dense than water, it would be displacing less volume than the boat was displacing because of the weight of the ball. The level of the lake would lower.

Of course, this doesn't take into account the evaporation or the run-off flowing into the lake between the measurements, or the fact that *most* lakes have a outgoing river or stream that keeps the lake level constant anyway.

Maybe if we were floating that boat in a swimming pool...

:D
bill.

(and yes, I did play with bowling balls as a profession before becoming a geek)

Posted by Bill Walker on February 20, 2005 at 06:55 PM EST #

Very good Bill! When the ball is in the boat, it pushes down with "N"lbs of displacement, raising the level of the lake. But when it is thrown in the lake, the ball's *volume* (no longer its weight) causes the displacement. Since the ball sinks, we know its volume displaces LESS than its weight. Therefore, the overall level of the lake will lower, since the displacement is less, as you said.
Just for fun I added an additional aspect to the problem. It doesn't change the answer, but does make the effect more pronounced. I mentioned that the ball settles on the sandy bottom. If the ball compresses the sandy bottom and M% of the ball sinks beneath the surface of the bottom of the lake (without otherwise deforming the bottom), then less of the ball's volume will contribute to the displacement and the level of the lake will lower even more than expected.
Again, good thinking Bill!

Posted by Dave Brillhart on February 20, 2005 at 10:44 PM EST #

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