Ice Cubes (a) Consider an ice cube floating in your favorite non-alcoholic bever

Question

Ice Cubes
(a) Consider an ice cube floating in your favorite non-alcoholic beverage (physical properties the same as pure water). For simplicity, assume that the ice cube is, indeed, a cube with edge length of 1 inch. What fraction of the volume of the ice cube is submerged in the beverage? You will need to find the density or specific weight of ice from another source if it is not in your text.

For part a my professor wants us to use a force balance to solve the problem

(b) At a party, you notice that a 1 inch ice cube in your beverage does not float, but sinks instead (just barely – apparently the cube is nearly neutrally buoyant in your drink). You suspect that someone has served you a beverage containing ethyl alcohol, which is a problem since you may not be of legal drinking age. What is the specific weight of the liquid beverage? What is the estimated volume percent of ethyl alcohol in the beverage? Assume that the beverage’s specific weight is the volume-fraction-weighted average of the specific weights of water and ethyl alcohol:
beverage =EtOHEtOH +H2OH2O =EtOHEtOH +(1-EtOH)H2O where EtOH is the volume fraction of ethyl alcohol in the beverage.

Explanation / Answer

Here the weight of the ice ( sp. gravity = 0.91) is balanced by the buoyant force on the submerged part,

let f be the volume fraction submerged,

a3 * 0.91 (wt of the ice cube) = f*a3 * (1) (buoyant force = vol submerged x density of fluid,here water)

f = 0.91 is the volume fraction of ice submerged under water

For the next part the specific gravity of the beverage is an unknown, say s and the entire ice is just submerged,meaning f=1,

a3 * 0.91 = 1*a3 * (s)

s=0.91 is the specific gravity of the beverage

specific density of the fluid = sp.gravity of eth.alcohol x vol fraction of Eth.alcohol + 1 x vol fraction of water

let vol fraction of Eth.alcohol= k

then vol fraction of water = 1-k

0.91 = 0.789* k + (1-k) * 1

k=0.427 is the fraction of ethyl alcohol

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