Maddenation
Bowling with Archimedes
This one appeared in “Ask Marilyn” today.
I go out in a boat to the center of Lake Michigan (or Hopatcong, or McQuain pond) carrying a bowling ball. Out in the lake, I drop the bowling ball overboard. Does the level of the lake rise or fall?
Answer:
First of all, we have to acknowledge that the effect we’re talking about is extremely small, essentially theoretical. Second, we should be careful about the lake we pick. McQuain pond, for example, is maintained at a constant level by the dam on one end (where the big, scary rocks can be seen). Likewise (lakewise?) Michigan and Hopatcong have many inlets and outlets that may or may not be dammed or otherwise level-controlled. Better to use a small lake/pond that is isolated and whose level will actually go up slightly when a boat is launched. (Bee Meadow Pond?) On that basis, the level of the lake falls when the ball is thrown overboard. The reason? The ball is denser than water. By the Archimedes principle, the ball in the boat displaces a volume of water equal to the weight of the ball (which is bigger than the volume of the ball). After the ball is dropped, it sinks to the bottom of the lake and occupies a volume of water equal only equal to the volume of the ball. So the ball displaces less water at the bottom of the lake than it did in the boat. Hence, the level of the lake must go down.
Comments
Patrick • 08/03/03 • 4:25 PM:But initially, assuming you “drop” the ball, the water goes up, in a big ker-schloop splash.
David • 08/03/03 • 8:52 PM:i don’t like that explanation. i’m calling you now to talk about it. so there!
Dad • 08/03/03 • 9:29 PM:Hey, the comments count says one comment, but there are obviously two!? Maybe the previous comments were two short and movable type combined them into one.
David • 08/03/03 • 10:43 PM:Okay, Dad was right. I was wrong.
Nancy • 02/02/04 • 7:19 AM:I don’t think this would apply to a body of water, like the Ohio River. Which is controlled by locks & dams etc. What do you think??? Thanks, Nancy
Dad • 02/02/04 • 10:38 AM:No, Nancy, it would not apply to a body of water controlled by locks, dams, and etc. I think this was made clear in the answer section above.
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