Archimedes

[CardiacArrest]

Quick concept question:

Two objects have the same size, but objA is twice as heavy as objB.
If submerged in water, the buoyant force upon both objects will be the same since they are the same size and the same amount of water has been displaced.
Assuming ObjA has a density greater than water due to more mass, and ObjB has less density, ObjA will sink all the way down, despite the same buoyancy force.

Is my thought process correct?

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[lorenzomicron]

nope.
bouyant force depends on mass not "size".
so the bouyant force Fb on object A is Fba=g*massa
on object two Fbb=g*massb

Fba=2*Fbb because mass a= 2*massb

but bouyant force comes for water volume displaced: Fb= V*densitywater*g

Fbb= Vb*density water*g
Fba=2*Fbb= 2*Vb*densitywater*g

Fba/Fbb= 2

Va=2*Vb

if there are the same size, then this volume has the same area
V=A*h

ha=2*hb

object A sinks twice as far compared to object b.

 

[venacontracta]

nope.
bouyant force depends on mass not "size".

Err, sort of. Buoyant force is equal to the weight of fluid displaced by the object, which is dependent on the volume of the object which is displacing the fluid. And volume is sort of along the lines of "size."

And the explanation above isn't correct. I think it makes the assumption that the density of object A is greater than the density of object B but that the densities of both objects is greater than water, and that's not what you asked.

Objects A and B will have the same buoyant force if they are both fully submerged because they both displace the same volume, and thus the same weight, of water.

Your assumption regarding object A sinking is correct. The two vertical forces on object A will be:

buoyant force (upward-acting) = (mass of fluid displaced by obj A)(g)
= (volume of obj A)(density of water)(g)

gravitational force (downward acting) = (weight of object B) = (mass of object A)(g)

The gravitational force will have greater magnitude and thus the net force will be directed downward.

Object B will float to the top of the water, since in the case of an object less dense than the fluid it is in, buoyant force will have greater magnitude than gravitational force.

If you really want to see the dependence on the relative densities of the fluid and object for whether an object will rise to the top or sink to the bottom, look at the equations this way:

buoyant force = = (volume of object)(density of water)(g)
gravitational force = (volume of object)(density of object)(g)

 

[lorenzomicron]

oh yeah, david 06, i was thinking too much about point masses. thanks for the correction.