So dVdisplacedg = dVduckg

vdisplaced = vduck

Can someone please go over this and check if it is correct? I thought the density on the left was the density of the fluid, while that on the right was the density of the duck (from his/her derivation) Why did both cancel out?

Can someone please confirm the following for me so I can determine if my understanding of fluids is correct. I may have over analyzed/complicated it and gotten myself confused so please bear with me.

1) Buoyant force is always equal to m(fluid displaced) * g, if the object is floating or submerged/suspending in the fluid.

i'll use fd for fluid displaced

2)In the 2 scenarios above; partially or fully submerged (but not sinking) m(fd) * g is always equal to mg (object)

3) When the object sinks, mg (object) > m(fd) * g Therefore the object sinks, since the buoyant force cannot overcome the downward gravitational force.

4)When an object is fully submerged but suspended in the fluid, mg (fd) = mg (object), If g is canceled from both sides, both masses are equal. Because the volume of fluid displaced is equal to the volume of the object in this case, and both masses are the same, both object must have the same density...?

5) Is it right to say the density of the fluid is equal to m (fd)/ V(fd)? Since the density of the fluid is uniform, this derivation will be correct, right?

6) So I tried to apply the following logic to a partially submerged object; I equated the two known equations for buoyant force

mg (fd) = Rho (fluid) * V (obj) * g ...g cancels out

Instead of mass, substitute Rho (fluid) * V (fd) for m

Rho will cancel out on both sides

Yet I am left with V(fd) = V(obj)

But this would be wrong for a partially submerged object. Did I make a wrong assumption somewhere?

I have wracked my brain but I'm still missing something, and I have missed all the buoyancy questions on my practice exams.

Please help! thanks in advance.