This Demonstration shows how far a floating spherical ball sinks into water by applying Archimedes's principle, calculus, and the solution of nonlinear equations.
The solution runs as follows. Let
be the weight of the ball and
be the buoyancy force. Then
Let the volume of the ball be
is the radius),
be its density
be the acceleration due to gravity
The weight of the ball is given by the product of the volume, density, and
The buoyancy force is given by the weight of water displaced, which is the product of the volume under water and the density of water
is the depth to which ball is submerged.
Therefore, with the specific gravity of the ball
, we have