# When putting a floating object in water, why the displacement of mass of water is not equal to only the part of the object inside the water?

In this question Will a bathtub full of water weigh more if I add something that floats in the water? the marked answers mentioned a special case where the bathtub is full to a brim and the boat is put into it, floats and it weighs the same, justifying that the extra mass is the spilled water.

I can't wrap my head around the "The boat will displace a mass of water equal to the mass of the boat", If I imagine the boat as a rectangle where the mass is distributed uniformly and half of the rectangle is inside the water and half of it outside the water. Shouldn't the mass of water displaced be equal to half the mass of the rectangle, the part inside the water? Why is also the amount of mass outside of the water being displaced?

• The volume of the water displaced is equal to the volume of the part of the boat inside the water. However, since the water has different density, its mass is greater, and is equal to the mass of the boat, as per Archimedes law. Apr 20, 2021 at 19:54
• I do not vote to close, I find the question appropriate and interesting. Apr 20, 2021 at 20:13
• It sinks until it displaces its weight with an equal weight of water then it stops sinking Apr 20, 2021 at 20:36
• Think of it like putting the water displaced and the boat on opposite sides of a balance scale. There is only one situation where the scale will be balanced (floating). Apr 21, 2021 at 5:17

It is called Archimedes principle

Principles in physics are a part of the extra axioms needed in order to be able to model with mathematics physical observations, in this case the way the water (or fluid) is being displaced by the addition of an object in a bath of water.

A principle is the result of observing a physical phenomenon and finding out that a specific statement applies for all similar cases. At the time it was established as true, that it always worked , it helped in the progress we have made to the physics model we use now, where why this happens can be explained with more elaborate theories and different axiomatic assumptions.that make up the theory of thermodynamics, the concept of buoyancy.

We now describe matter in terms of temperature, volume pressure, density ... and the axioms of thermodynamics are far removed from Archimedes principle, but it still holds because it depends on the observations of matter. Buoyancy arises from the fact that fluid pressure increases with depth and from the fact that the increased pressure is exerted in all directions (Pascal's principle) so that there is an unbalanced upward force on the bottom of a submerged object.