In the third century B.C., King Hieron of Syracuse asked the famous mathematician Archimedes to determine if his crown was made of pure gold. This was a puzzling problem for Archimedes-he knew how to measure the weight of the crown, but how could he measure the volume? Archimedes solved the problem when he got into his bath and noticed the water spilling over the sides of the tub. He realized that the volume of the displaced water must be equal to the volume of the object placed into the water. Archimedes was so excited by. his discovery that he jumped out of the bath and ran through the streets shouting "Eureka!" a. How can you tell if a crown is made of solid gold? b. Gold is one of the densest substances known, with a density of 19.3 g/mL. If the gold in the crown was mixed with a less-valuable metal like bronze or copper, how would that affect its density? c. What is the relationship between the object density, the liquid density, and the tendency of the object to float? d. From the experimental results obtained by you in the lab of the density of the liquid and the object, could the object float in that liquid? Explain.

a. I can conclusively tell if the crown was made of gold by measuring its density. First the mass of the crown is measured on a weighing balance. The crown is now put into a given volume of water and the volume of water displaced is accurately measured. The density of the crown is computed as mass/volume of fluid displaced. If the density of the crown is 19.3 g/mL, then it is made of solid gold.

b) When less valuable metals such as bronze or copper is mixed with gold in the crown, the density of the crown decreases and the crown becomes more brittle.

c) An object will float in a liquid when the density of the object is less than the density of the liquid. Hence the tendency of an object to float in a liquid depends on the density of the object and the density of the liquid.

d) Even though i do not know the results from your experiment but as regards the decision as to whether the object will float in the given liquid or not, reference must be made to the measured density of the object as well as the given density of the liquid. If the object is less dense (from values of density obtained from the experiment) than the liquid, then the object will float in the liquid and vice versa.