Question

An ice cube floats in a beaker of ice cold water. Since the water is ice cold, the ice cube is not melting and hence its volume is not changing. The density of water and ice are, respectively,

ρ_w = 1,000 kg/m³

and

ρ_i = 917 kg/m³.

(Assume one of the ice cube's faces is parallel to the water's surface.)

(a)

If the ice cube is 17.0 mm on each side, how far below the surface (in mm) is the bottom face?

mm

(b)

Ice-cold ethyl alcohol is gently poured onto the water's surface to form a layer

d = 5.50 mm

thick above the water. The alcohol does not mix with the water. When the ice cube again attains hydrostatic equilibrium, what will be the distance (in mm) from the top of the water to the bottom face of the block? The density of ethyl alcohol is

ρ_a = 806 kg/m³.

mm

(c)

Additional cold ethyl alcohol is poured onto the water's surface until the top surface of the alcohol coincides with the top surface of the ice cube (in hydrostatic equilibrium). How thick is the required layer of ethyl alcohol? (Give your answer in mm between its top and bottom surfaces.)

Answer 1