3. for a boat to float on water, it must have a density lower than the density of water. compare the densities of your unknown liquid and solid. if a boat was made of the unknown solid, would it float on the unknown liquid? explain your answer.

Archimedes' principle  find that the density of the body must be less than the density of the liquid for the body to float.

                         ρ_{body} < ρ _{liquid}

Archimeds' principle states that the thrust of a body in a fluid is equal to the weight of the desalted liquid. If we apply the equilibrium equation to a body in a liquid

              B- W = 0

              B = ρ g V_{liquid}

Where B is the thrust and w the weight of the body, ρ  the density of the liquid, g the acceleration of gravity and V the volume liquid

if we use the concept of density of the body

             ρ  = m / V

            W = ρ  g V

we substitute in the equilibrium equation

          ρ_{liquid}  V_{liquid} = ρ_{body} V_{body}

this is the relationship for the body to float in the water

When analyzing this expression, if the density of the body is less than the density of the liquid, the body must float

One way to artificially create the density of the body to be less than that of the liquid is to increase the volume of the body by having a hollow part using the ratio

               ρ  = m / V

Consequently if increasing the volume of the body the density should decrease, this method is used by the ships.

In conclusion, using Archimedes' principle we find that the density of the body must be less than the density of the liquid for the body to float.

                         ρ_{body} < ρ _{liquid}

Learn more about the Archimedes principle here:

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