Floating Ball

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration shows how far a floating spherical ball sinks into water by applying Archimedes's principle, calculus, and the solution of nonlinear equations.
Contributed by: Vincent Shatlock and Autar Kaw (June 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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 (where
is the radius),
be its density
), and
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 :
,
where
is the depth to which ball is submerged.
Therefore, with the specific gravity of the ball , we have
, or
.
Permanent Citation