Volume Displaced

Stability of Floating Bodies

Any floating body is subjected by two opposing vertical forces. One is the body's weight W which is downward, and the other is the buoyant force BF which is upward. The weight is acting at the center of gravity G and the buoyant force is acting at the center of buoyancy BO. W and BF are always equal and if these forces are collinear, the body will be in upright position as shown below.




Archimedes Principle

Archimedes (287-212 B.C.)

Any body immersed in a fluid is subjected to an upward force called buoyant force equal to the weight of the displaced fluid.

$BF = \gamma V_D$

$BF$ = buoyant force
$\gamma$ = unit weight of fluid
$V_D$ = volume of fluid displaced by the body

034 Review Problem - Sphere dropped into a cone

034-cone-sphere.gifThe inside of a vase is an inverted cone 2.983 in. across the top and 5.016 in. deep. If a heavy sphere 2.498 in. in diameter is dropped into it when the vase is full of water, how much water will overflow?

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