A buoyancy question!

[SSerenity]

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If we have a ball that has some density (p) greater than water and a very tall column of water (h). If we drop the ball into the water, it should sink.

But is there a certain depth where the ball will just hover before reaching the bottom of the water? How would we represent this mathematically?

 

[FeinMS]

Nope it will sink indefinitely until some kind of normal force supports the ball. Net force on the ball will be (density of fluid)(V displaced)(g)-mg < 0 giving net downward acceleration. To stop this ball from sinking, the bottom of the floor should provide a normal force to make (density of fluid)(V displaced)(g)+Normal force-mg=0

 

[texan2414]

Yep the normal force on the bottom of the floor keeps it from sinking into the fiery molten depths of magma down to the Earth's inner core where the center of mass for our planet resides,