Understanding Buoyancy: Answering the Question on Stone Immersion

[physics kiddy]

Hello everyone,

Suppose, we have a stone tied to one end of a rubber string. We suspend the stone by holding the balance or the string.Then, note the reading on the spring balance. Now, slowly dip the stone in water in a container. Our teacher told that the stone faces buoyancy as soon as it is dipped. When the stone is fully immersed in water, no further decrease in elongation is observed in the string. Please explain why does that happen.

 

[lurflurf]

What have you tried? What determines the amount of buoyancy on an object?

 

[physics kiddy]

Obviously, weight of an object = weight of water displaced by it = buoyant force.

 

[lurflurf]

Good. So how does the buoyant force change as the object is
000% submerged
001% submerged
037% submerged
084% submerged
099% submerged
100% submerged 1 mm under the surface
100% submerged 10 km under the surface

in particular when is the buoyant force maximal?

 

[physics kiddy]

That's the problem. I don't know when it is maximum and minimum.

 

[lurflurf]

So you said "Obviously, ***weight of an object ***= weight of water displaced by it = buoyant force." Which was mostly right, as in general we do not have weight of an object = weight of water displaced by it. So we start lowering the object into water. For simplicity assume that we only lower it, and do not for example alternate raising with lowering. At each instant the buoyancy depends only upon the fraction of the object submerged. Try to write an equation for this. In particular that buoyancy does not change when the fraction submerged does not, including when the object is raised or lowed without changing the fraction submerged.