FLUIDS: Understanding Buoyancy Question

[FatherTime-PhD]

Hi,

So, I know that if an object if floating, then
density object x Volume of the object x gravity = density of the fluid x volume submerged x gravity

g cancels out, we're left with:

density of the object x volume of the object = density of the fluid x volume submerged

by re-arranging, we get a ratio:
density of the object/density of the fluid = volume submerged/volume of the object

This makes sense to me. Now, if two balls of equal volume are completely submerged in water, BUT one is at the bottom while the other is just not moving midway through the water, I know it makes sense to say that the ball at the bottom is more dense because it is deeper in the water.

BUT looking @ the equation I just talked about, if the volume is completely submerged, that means volume submerged = volume of the object, therefore that ratio = 1? Thus, density of the object = density of the fluid? In which case, the densities of the balls should be equal because in the end, they're both completely submerged?

I KNOW THIS IS WRONG TO THINK LIKE THIS ... but why? please help, it's been bugging me.

Thank you thank you thank you.

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[FatherTime-PhD]

please

 

[AdaptPrep]

Hi, Doctors' Docta--

Remember, when the object is sitting on the bottom of the container, it is no longer floating. So you cannot compare the two with that formula. When an object is floating, there are two forces acting on it: weight force downward and buoyant force upward. When you are on the bottom, you now introduce a third force upward called the normal force. Hence, the weight force of the ball on the bottom must be greater than the weight force of the floating one (and greater mass over same volume means more dense).

I hope that helps.