Bucket with water

A bucket filled to the brim filled with water is placed on one cup of the scale, the other - exactly the same bucket, also full to the brim, but there is a piece of wood floating in it. Which bucket with water pulls?

A bucket filled to the brim filled with water is placed on one cup of the scale, the other - exactly the same bucket, also full to the brim, but there is a piece of wood floating in it. Which bucket with water pulls?

If you assign this task to different people, you get contradictory answers. Some answered that they had to draw a bucket of water in which the tree was swimming, because "besides water, there is also a tree in the bucket". Others - that, on the contrary, will pull the first bucket, "because the water is heavier than the tree." Neither of these is true: both buckets have the same weight. In the second bucket, however, there is less water than in the first, because a floating piece of wood displaces some of its volume.

But, according to the law of swimming, every floating body displaces with its submerged part exactly as much liquid (by weight) as the whole body weighs. That's why the balance must remain in balance.

Decide now another task. I put a bucket of water on the scales and put a weight next to it. When the balance is balanced with weights on a cup, I drop the weigher into a bucket of water. What will become of the weights?

According to Archimedes' law, the weight in the water becomes easier than it was outside the water. One might, it would seem, expect that a cup of scales with a bucket will rise. Meanwhile, in reality, the balance will remain in balance. How can I explain this?

The weights in the bucket drove out part of the water, which was higher than the original level; As a result, the pressure on the bottom of the bucket with water increases, so that the bottom experiences an additional force equal to the weight loss of the weigher.

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