1. A rectangular block of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. a. Derive a formula for the block density, b, in terms of the fluid densities 1 and 2, the heights h0,h1, and h2, and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.) b. Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) 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. 1. A rectangular block of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. a. Derive a formula for the block density, b, in terms of the fluid densities 1 and 2, the heights h0,h1, and h2, and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.) b. Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) 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