# Floating Ball

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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