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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.
Contributed by:
Vincent Shatlock
and
Autar Kaw
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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
.
RELATED LINKS
Equilibrium of a Floating Vessel
(
Wolfram Demonstrations Project
)
Learning Newton’s Method
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
"
Floating Ball
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/FloatingBall/
Contributed by:
Vincent Shatlock
and
Autar Kaw
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