May 16, 2020
Author - manisar
Saturn, the mighty Saturn, will float in water!
If one claims to have a scientific bent of mind and have never wondered about these two at any time in his/her life, I'll doubt 🙂:
Just gonna talk about a bit on the first one here - how objects float in water (or any liquid).
The main explanation that is taught in schools is based on the Archimedes' principle. But in order to understand this phenomenon more intuitively I found out that there are at least two other very legitimate explanations. Let me explain them here starting with the Archimedes principle.
It's a simple explanation (though not very intuitive) - the weight of an object immersed in a liquid is reduced by the weight of the amount of the liquid displaced by it. In order to apply this to the idea of flotation, let's imagine we have a cube with cross-sectional surface area equal to S. If it is immersed in water up to a depth d, the upward force on it will be given by the pressure at the bottom times the area of its bottom-facing surface (since the sideways forces cancel out). Remember that pressure at any depth d of any liquid is given by p=ρdg where ρ is the density of the liquid.
So, the moment this force becomes equal to mg - the weight of the cube, the object will start floating. Note that this may not happen at all in which case the object will sink.
This is a simple explanation based on a simple law. But let's see if there is something more intuitive.
This interpretation always made more sense to me. When the cube is immersed in water, it displaces some water. That water has to go somewhere.
Every vessel, howsoever big it is, has its boundaries.This means that in effect the water level has risen in the vessel.
So, if d denotes the submerged height of the cube, it means the volume of water displaced is S x d. This in turn means that this much volume of water is now floating above the original level of water.
Guess what, this amount of water also has some weight - just like our cube - this volume of water pushes the (rest of the) water in the same way as our cube does. The result - the downward force of this displaced water starts cancelling out the weight of the cube.
And finally, if and when the weight of this displaced water becomes equal to that of the cube, there is equilibrium (or the cube starts floating)!
We get the same equation as we got from Archimedes' principle!
So, to repeat, if the weight of this displaced water becomes equal to that of our cube, there has to be equilibrium - the two pieces of mass - our cube and the displaced water - both equal in weight - are now pushing the water downward at different places, and in a way, cancelling out each other!
(if you think about it, Pasca's law is fitting here in support of this interpretation)
Between two objects of differing densities, if possible, the one with the greater density will assume the lower position. And, if the densities are same, there is no competition.
If the cube is already having a density lower than that of water, it's going to float. But what about a ship made of iron? Let's take that case.