9716

Floating Ball

This Demonstration shows how far a floating spherical ball sinks into water by applying Archimedes's principle, calculus, and the solution of nonlinear equations.

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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
.
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