A rectangle block of height L and horizontal cross-section area A floats at the interface between two immiscible liquids.
(a) Derive a formula for the block density, pb, in terms of the fluid densities p1 and p2, the height h0, h1, and h2, and the cross-sectional area A. (It's not necessary that all of these variables appear in the final result.)
(b) Force balances on the block can be calculated in two ways: (1) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (2) in terms of the weight of the block and the buoyant force on the block as expressed by Archimedes' principle. Prove that these two approaches are equivalent.