Asap. ethyl alcohol is to be mixed with water to obtain a mixture with density 900 kg/m3. in what proportion by (a) weight and (b) volume must they be mixed?

First of all, let's write the density of water (W) and the density of alcohol (A):


And the relationship between density d, mass m and volume V:

The density of the mixture water+alcohol is 900 kg/m^3. The mass of this mixture is the sum of the masses of water and alcohol, and the volume of this mixture is the sum of the volumes of water and alcohol. So we can write
(2)
Now let's solve the two parts of the problem.

a) Let's rewrite (2) by replacing the volumes with :

By solving this equation, we find:

This means that there are 0.71 kg of alcohol per each kg of water in the mixture.

b) Similarly, let's rewrite (2) by replacing the masses with :

Re-arranging and solving, we find

This means that there are 0.90 L of alcohol per each liter of water in the mixture.

The objects are acted upon by only one force. gravity. mass times the acceleration of gravity (-9.81meters/second squared).