Archimedes' principle buoyancy explained
Ease an object into water and water is pushed aside by as much as the object enters, the surface rises, and at the same time the hand feels a force holding it up. The deeper you push, the harder this force pushes up. That force is buoyancy. The surprise is that the size of this buoyancy equals exactly the weight of the water the object pushed aside, the very fact Archimedes saw in a bath 2200 years ago. What sets buoyancy is not whether the object is heavy or light, but how much water it pushed aside, so a lump of iron sinks while a ship made of the same iron floats. The weight of the water pushed aside presses the palm upward.
First drag how far the object sinks in the water, and water that was there is pushed aside by the volume of the object that is under water. That is the displaced volume. The larger the submerged volume, the more water is pushed aside and the larger the upward buoyancy. Half submerged means half the buoyancy, and fully submerged means the maximum. What makes buoyancy is not the object itself but the water the object shouldered aside, and you can see it as the water that used to fill that place trying to take the place back. The larger the submerged place, the more water tries to take it back.
Why does it push up, of all directions? Pressure grows with depth, so the bottom face of a submerged object is deeper than the top face and holds it up with a stronger pressure. The pressure holding from below is larger than the pressure pushing from above, so a purely upward force remains, equal to that difference. Drag the depth to send the object deeper and both pressures grow, while their difference stays, because the height of the object sets it. So buoyancy is constant regardless of depth, and its size is exactly the weight of the displaced water. The difference between above and below is the force that holds it up.
Now drag the density of the object. An object lighter than water rises and stops at the depth where it displaces water equal to its own weight, and the submerged fraction is the object density divided by the water density. If the density is 0.6 times water it floats with only 60% submerged, and an iceberg sits mostly under water because the density of ice is about 0.9 times water, so 90% is submerged. An object heavier than water sinks even when fully submerged, because buoyancy cannot beat the weight. Floating or sinking is split by a comparison of density with water, not by weight. The density ratio sets the submerged share and leaves the rest above the water.
Tie this into one formula and the buoyancy is F = ρ g V. ρ is the density of the surrounding fluid, not of the object, g is the gravitational acceleration, and V is the submerged volume, the displaced volume, and the product of the three is exactly the weight of the displaced fluid. Drag the fluid density ρ and for the same volume a heavier fluid gives a larger buoyancy. The point is that ρ is the density of the fluid. In seawater the buoyancy is a little larger than in fresh water, and in mercury even iron floats. What the object is made of never appears in the buoyancy formula. Only the fluid and the displaced volume are needed. A heavier fluid pushes the same place up harder.
Last, look at a ship made of iron. Switch the same amount of iron, with a button, between a solid lump and a hollow hull. As a lump it displaces little water, so buoyancy cannot beat the weight and it sinks. Spread wide and hollowed into a hull, the same weight displaces far more water, and the moment the weight of the displaced water equals the weight of the whole ship, the ship floats. The point is the average density. Hollow it out and the average density, including the space inside the ship, falls below water. The secret of a huge cargo ship is this empty space, and the great amount of water it displaces. Empty space pulls the average down below the water.