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More Fish in a Bucket

Last time I left you with a question. We were imagining fish swimming in a container of water. When I was a child, I was told that you could put the container on a scale, and as long as the fish did not touch the sides or bottom; you would only be weighing the water.

We substituted a brick for the fish, and found that if we lowered it into the water, the scale went up enough to equal the weight of the water it displaced. Then we placed it on the bottom, and found that the scale went up to equal the full weight of the brick.

Now, for the question I left you with. What if you put the brick on a scale, and then submerged both of them in the bucket of water? How much weight would the scale show for the brick?

Hopefully, you spent some time thinking about it. We know that the brick felt lighter when we held it under water, because the water was pushing up on it with a force equal to the weight of the water it displaced. That gives us our clue. If the scale was in the water, with the brick on it, it would show the weight of the brick, minus the weight of the water it displaces.

We can find that, without even putting the scale in the water. If we take the weight of the brick and subtract the reading on the scale when we held the brick under water, we get the weight minus the weight of the displaced water.

But that still leaves one more thing to check, as a couple of clever readers pointed out to me. What if the brick (or fish) were suspended in the water without your hand or anything else holding it up?

Well that would be easy to test if we had a fish, but the closest thing I have is a can of tuna, and somehow I don't think that would work the same way. Instead, lets use a water balloon. After all, a fish, like most living things, is mostly water. If we fill a balloon with water, and put in a tiny bit of air, it should float just at the surface and make a very suitable fish replica.

OK, so what do you think will happen? Think about it another way. What if we left out the balloon, and just added the water? Would the scale show an increase of weight then? Yes, of course it would. Do you think that putting the water inside a balloon would change that? No. What about putting that water inside a fish? No, it would still show up as an increase in weight, and since the water is supporting the full weight of the fish, the scale would show an increase of the full weight of the fish, or in this case, the water balloon.

When I was younger, this experiment would have ended with me throwing the water balloon at my brother or my sister. Now that I am older, I wouldn't do that. They live too far away.