Summary

Fluid particles obey Newton laws.
Buoyant force is a net upwards force on an object in a fluid, caused by pressure and increases with depth.
Buoyant force equals weight of fluid displaced: F_b=pVg where p is fluid density and V is displaced volume.
For a floating object, buoyant force equals the object's weight: V_{submerged}/V=p_{object}/P_{fluid}
Object floats when density is less than fluids and sinks when it's greater.