Weight of cup of Water With a Floating Piece of Wood?

What weighs more: a cup of water filled to the brim or that same cup of water, also filled to the brim, with a piece of wood floating in it? Why?
- Ellie (age 15)
Austin, Texas

Nice question: it makes you think.   The answer is they weigh the same because the floating wood displaces an amount of water equivalent to its own weight. That's what Archimedes figured out a long time ago. This displaced water dribbles down the side of the glass.  The remaining water plus the weight of the wood add up to the amount of the water only case.

LeeH

(published on 10/09/2011)

Are you sure about that? Archimedes law states that the weight of water displaced is equal to the upward thrust and not its own weight right? Assume a cuboid wood of some area (area = A) and height h is in water. Let it be immersed till height x (x < h). So the volume of wood immersed in water is A*x. The Volume of water displaced is also A*x. The Density of water > density of wood. So the weight of water displaced is more than the weight of wood immersed. So the weight of the cup with water till brim must weigh more than the one with wood, right?
- Dee (age 29)

Don't forget to include the weight of the part of the wood out of the water. Including that makes them equal.

Mike W.

(published on 12/20/2016)