How could you determine mass using Archimedes' principle?

Answer 1

The overall force Fan object submerged in liquid experiences is,

F = ∮S(-)ρgzds, S is the submerged boundary of the object.

∵ ds = i(i⋅ds) + j(j⋅ds) + k(k⋅ds), i, j and k are unit vector in +x, +y and +z direction respectively.

∴ F = -ρg∮Sz(i(i⋅ds) + j(j⋅ds) + k(k⋅ds)) = (-ρg∮S(zi)⋅ds)i + (-ρg∮S(zj)⋅ds)j + (-ρg∮S(zk)⋅ds)k = (-ρg∮V∇⋅ (zi)⋅dv)i + (-ρg∮V∇⋅ (zj)⋅dv)j + (-ρg∮V∇⋅ (zk)⋅dv)k

∵ ∇⋅ (zi) = 0, ∇⋅ (zj) = 0, ∇⋅ (zk) = 1

∴ F = (-ρg∮Vdv)k =-ρgVk

The magnitude of the overall force (buoyant force) is ρgV, and the direction is -k.

--JF Hu

Answer 2

If the solid is less dense than water, it can be pushed until it is just submerged and the volume of water it displaces measured. Determine the mass by weighing it, divide the mass by the volume and you have the density.

If the solid is more dense than water, the difference in weight when it is suspended in air vs. suspended in water equals the volume times the density of water. You can determine the volume by the amount of water displaced, so the density is the mass over the volume, or the weight (in water) over g, plus the mass of water displaced, over the volume.

Answer 3

When the upward force of displacedfluid; causing flotation